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<i>Every man can, if he so desires, become the sculptor of his own brain.</i> --- Santiago Ramón y Cajal
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<h1 id="header-title">Michiel Kleinnijenhuis</h1>
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<li><a href="projects.html#Project14" title="Jump to Project14">cerebellar white matter atlas</a></li>
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<li><a href="phdthesis.html#Cover" title="Jump to Cover">cover and title pages</a></li>
<li><a href="phdthesis.html#Chapter01" title="Jump to Chapter 1">chapter 1: introduction</a></li>
<li><a href="phdthesis.html#Chapter02" title="Jump to Chapter 2">chapter 2: history of connectional neuroanatomy</a></li>
<li><a href="phdthesis.html#Chapter03" title="Jump to Chapter 3">chapter 3: MRI of fibre architecture</a></li>
<li><a href="phdthesis.html#Chapter04" title="Jump to Chapter 4">chapter 4: STIFT</a></li>
<li><a href="phdthesis.html#Chapter05" title="Jump to Chapter 5">chapter 5: layer-specific DWI in human V1</a></li>
<li><a href="phdthesis.html#Chapter06" title="Jump to Chapter 6">chapter 6: fibres in the gyrus</a></li>
<li><a href="phdthesis.html#Chapter07" title="Jump to Chapter 7">chapter 7: DTI of gyrencephaly at 7T</a></li>
<li><a href="phdthesis.html#Chapter08" title="Jump to Chapter 8">chapter 8: dissection, plastination, tractography</a></li>
<li><a href="phdthesis.html#Chapter09" title="Jump to Chapter 9">chapter 9: discussion and conclusions</a></li>
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<h3 class="phdthesis-title"> cover from
<a href="http://www.neurocomic.org/" target="_blank" title="Neurocomic website">neurocomic</a>
by matteo farinella
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<h2 class="phdthesis-title"><a class="linkimg" href="MendeleyLibrary/theses/Kleinnijenhuis_2014_Imaging fibres in the brain.pdf" title="Download my PhD thesis"><img height="30px" src="logos/pdf.png" alt="pdf"/>↧ download</a></h2>
<br><hr>
<br><br><br>
<h1 class="phdthesis-title">Imaging fibres in the brain</h1>
<br>
<div class="box">
<p class="phdthesis-title"><b>Proefschrift</b></p>
<br>
<p class="phdthesis-title">ter verkrijging van de graad van doctor</p>
<p class="phdthesis-title">aan de Radboud Universiteit Nijmegen</p>
<p class="phdthesis-title">op gezag van rector magnificus prof. mr. S.C.J.J. Kortmann,
<p class="phdthesis-title">volgens besluit van het college van decanen</p>
<p class="phdthesis-title">in het openbaar te verdedigen</p>
<p class="phdthesis-title">op maandag 19 mei 2014</p>
<p class="phdthesis-title">om 14:30 uur precies</p>
<p class="phdthesis-title">door</p>
<br>
<p class="phdthesis-title"><b>Michiel Kleinnijenhuis</b></p>
<br>
<p class="phdthesis-title">geboren op 19 augustus 1981</p>
<p class="phdthesis-title">te Den Ham</p>
</div>
<br>
<div class="box">
<p>PROMOTOREN:</p>
<p>Prof. dr. Dirk J. Ruiter</p>
<p>Prof. dr. David G. Norris</p>
<br>
<p>COPROMOTOREN:</p><p>Dr. Anne-Marie van Cappellen van Walsum</p>
<p>Dr. ir. Markus Barth</p>
<br>
<p>MANUSCRIPTCOMMISSIE:</p>
<p>Prof. dr. Arend Heerschap</p>
<p>Prof. dr. Derek K. Jones (Cardiff University, UK)</p>
<p>Prof. dr. Jeroen J.G. Geurts (VU Amsterdam)</p>
</div>
<br>
<div class="box">
<p>The experiments that are reported in this thesis were performed at the Department of Anatomy of the Radboud University Nijmegen Medical Centre; the Centre for Cognitive Neuroimaging of the Donders Institute for Brain, Cognition and Behaviour; the Erwin L. Hahn Institute for Magnetic Resonance Imaging in Essen, Germany and the Max-Planck-Institut für neurologische Forschung in Köln, Germany. Financial support was provided by the Ministerie van Economische Zaken, Provincie Overijssel and provincie Gelderland via the ViP-BrainNetworks project.</p>
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<br>
<div class="box">
<p><i>To say that the white matter is but a uniform substance like wax in which there is no hidden contrivance, would be too low an opinion of nature’s finest masterpiece. We are assured that wherever in the body there are fibres, they everywhere adopt a certain arrangement among themselves, created more or less according to the functions for which they are intended. If the substance is everywhere of fibres, as, in fact, it appears to be in several places, you must admit that these fibres have been arranged with great skill, since all the diversity of our sensations and our movements depends upon this. We admire the skilful construction of the fibres in each muscle; how much more then ought we to admire it in the brain, where each of these fibres, confined in a small space, functions without confusion and without disorder.</i></p>
<br><hr>
<p>--- Nicolas Steno, 1669</p>
</div>
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<div class="boxhdr"><span><a href="phdthesis.html#pagetop">▲back to top</a></span></div>
<br><hr><div id="Chapter01" class="equalcolumn21">
<br>
<h2 class="phdthesis-title">Chapter 1</h2>
<hr>
<h2 class="phdthesis-title">General introduction</h2>
<hr>
<h3 class="phdthesis-title" id="Sec11">1.1 A case for connectivity</h3>
<div class="box">
<p>Counting roughly 100 billion neurons, the number of units in the human central nervous system is vast, but not particularly mind-boggling: you have many more blood cells<a href="phdthesis.html#ref001"><sup>1</sup></a>. Now, why can’t your circulatory system—we might assume—do any of the thinking? It is the widespread, though incredibly specific, connectivity of neurons that allows your brain to be the literal nervous centre of your world. Connections are the physical substrate of the enormous repertoire of brain function. The organiza-tion of neurons in a network allows transmission, integration, storage and—perhaps characteristic for the human brain—generation of information. In some respects, the network of neurons inside your head parallels a society. For social animals, connecting to others is a basic necessity of life. Isolated fire ants have a life expectancy that is 2-3 shorter than their well-connected cousins, and the principle generalizes to human society<a href="phdthesis.html#ref002"><sup>2</sup></a>! Analogously, connecting to other neurons is a basic necessity for neurons. Once disconnected—by the event of a stroke, for instance—neurons degenerate. Their utility, i.e. to participate in information processing, has been incapacitated. The often sad and irreversible consequence of connectional loss is a debilitating reduction in a brain’s functional repertoire. On the other hand, just as specific interactions between individuals in human society can result in inspira-tional achievements, you can rest assured that you can achieve extraordinary things with this remarkable dynamic network of connec-tions 3.5 billion years of evolution has endowed you with.</p>
<p>Connectionist accounts of brain function have extensively contributed to contemporary commonly held beliefs. The buzz-word is connectome: the matrix of structural links and functional associations between the basic units of the central nervous system<a href="phdthesis.html#ref003"><sup>3</sup></a>. Undoubtedly, studying the units—be it neurons or brain areas—in isolation is indispensible for explaining brain processes in health and disease. Nevertheless, people have come to realize that this approach falls short when the difficult questions are raised, in particular how the human brain sustains cognition and consciousness. Even relatively straightforward questions about such topics cannot be answered without considering the interactions between the units. Also, the notion of scale is important here. The network description at the neuronal level—the microscopic connectome—is comprehensive in terms of capturing potential information flow through the network of the brain. However, the neuronal scale might not be the optimal scale to study the brain for all questions raised. Although all mechanisms reduce to the neuronal level, and ultimately the chemical and physical levels, the answers to questions asked on the phenomenological level might lose their explanatory power when given at the neuronal level, invoking the need for the mesoscopic (i.e. population) or even macroscopic (i.e. regional) descriptions.</p>
<p>Connecting these concepts of scale to measurement capabilities that have been developed in the past centuries, we can note that this conceptual reason is not the only consideration when opting for a macroscopic description. For one, the construction of the comprehen-sive microscopic human connectome is far from within reach of neuroscience’s current technical capabilities. Pooling neuronal popula-tions into functional units at the meso- or macroscopic scale, however, can make them accessible to whole-brain measurement and analysis methods—as well as to our imagination. Whether these subdivisions are justified with regard to phenomena to be explained is a matter of extensive debate<a href="phdthesis.html#ref004"><sup>4</sup></a>. Over the past century, brain connections have mostly been studied in experimental animals. The method of tracing axons by injecting a label is highly specific and useful, but can only be used to investigate a small number of neurons per case. Knowledge on interregional connectivity in the human brain has been derived mainly from ex vivo cadaver dissections and clinicoanatomical correlations<a href="phdthesis.html#ref005"><sup>5</sup></a>. These methods are limited in their specificity, reproducibility and/or sensitivity. Thus, it comes as no surprise that the development of a magnetic resonance imaging (MRI) technique to measure anatomical connectivity in the living human brain has been met with great enthusi-asm by the neuroscientific community. The technique, introduced in the 1980’s<a href="phdthesis.html#ref006"><sup>6</sup></a>, is called diffusion weighted imaging (DWI; or diffusion MRI). The name is conveniently derived from its working principle. The brain cells’ microstructural constituents hinder diffusion of water molecules in the brain. The attenuation in the magnitude of diffusion can be measured with DWI. Less diffusion implies more—or more impermea-ble—boundaries. Because the number of boundaries encountered in a particular direction depends on the orientation of axonal bundles<a href="phdthesis.html#ref007"><sup>7</sup></a>, it is possible to trace the major pathways in the white matter of the brain. Connecting the orientations from one voxel to the next is called tractography. The progress that has been made in DWI and tractog-raphy has contributed significantly to the surge in connectionist approaches in cognitive neuroscience. Naturally, like any measurement technique, diffusion MRI has its limitations and some unresolved issues, but the practical utility for anatomical and pathological investigations in the human brain is undisputed.</p>
<p>Confronted with a suspected stroke, one of the primary diagnostic tools available to an emergency room physician is DWI. Diffusion MRI’s ability to measure where cells are swollen (cellular oedema: a patholog-ical state) is critical for treatment decisions. This is the single most widely used and, arguably, the most vital application of DWI. As already stated above, the technique is versatile. Variations in the properties of healthy tissue may also be assessed with diffusion MRI. For instance, tissue microstructure (e.g. the cell’s membrane, cytoskele-ton, or myelin sheet) changes with learning, which is reflected in the diffusion image<a href="phdthesis.html#ref008"><sup>8</sup></a>. Additionally, chronic abnormalities of the white matter can be detected. It is fairly well established, owing mainly to investiga-tions with diffusion MRI, that some psychiatric syndromes such as schizophrenia are associated with aberrant white matter microstruc-ture<a href="phdthesis.html#ref009"><sup>9</sup></a><sup>,</sup><a href="phdthesis.html#ref010"><sup>10</sup></a>. Finally, experiments using tractography have led to important discoveries and new hypotheses in the field of brain connectivity. One popular way of defining what might constitute a functional area in the brain is the connectivity fingerprint. The principle assumes that neurons that share connections with the same regions are likely to serve the same function. With tractography, plausible subdivisions on the basis of structural connectivity fingerprints have been produced for e.g. the thalamus<a href="phdthesis.html#ref011"><sup>11</sup></a>, the medial frontal cortex<a href="phdthesis.html#ref012"><sup>12</sup></a> and the amygdala<a href="phdthesis.html#ref013"><sup>13</sup></a>. A further achievement in tractography is the possibility to construct the macro-scopic whole-brain structural connectomes alluded to previously. It has supported the relevance of the connectivity approach to brain function and spawned new hypotheses on global organizational principles of the brain. To mention one example, the structural core of densely connect-ed areas that was discovered with diffusion MRI methods<a href="phdthesis.html#ref014"><sup>14</sup></a> has been an influential notion in human brain connectivity research in recent years.</p>
<p>Convincing evidence for the cardinal importance of DWI to connectivi-ty, don’t you think? To put matters back into perspective, the field of diffusion MRI for research is somewhat cloaked in a shroud of scepti-cism. Fortunately, this criticism is heard mostly from the DWI investiga-tors themselves, suggesting a healthy, realistic attitude towards the limitations of diffusion MRI, and tractography in particular. The tasks that lie ahead for the field can be summarized as disambiguation and validation. The ambiguity of the diffusion MRI experiment relates to two issues: 1) variations in MR diffusion signal cannot be unequivocally assigned to particular microstructural features, e.g. it cannot be ascertained from the diffusion MRI experiment whether an increase in diffusion is due to degradation of the axonal membrane or myelin sheet, shifts in the ratio between extra- and intracellular space, or any of the many other possible mechanisms; 2) by definition, fibre configu-rations cannot be resolved beyond the voxel resolution, i.e. the spatial relation between the separate axon segments that make up the full ensemble of axons occupying a white matter voxel is unknown. Hence, the interpretation of the DWI measurement in voxels with complex fibre configurations is inherently ambiguous. This is commonly known as the kissing-crossing problem, a term that does not quite capture the full extent of the problem as the ambiguity generalizes to a wider range of possible configurations. Validation is concerned with verifying the interpretations given to these ambiguous data.</p>
<p>Contributing to the disambiguation and validation of in vivo diffusion MRI methods is the principal aim of this thesis. Two principles are used to achieve this. Foremost, by zooming in to the structures of interest, anatomical observations on scales inaccessible to the usual DWI measurements assist in the interpretation of data at the lower resolu-tion. For the work in this thesis, this entails DWI measurements of ex vivo tissue samples at a magnetic field strength much higher than customary for measuring human fibre anatomy in vivo. Measurement of multiple modalities is the second principle relied on in this thesis. This principle can be used for disambiguation (e.g. integrate two MR modalities to harness the strength of the independent modalities) as well as validation. As it appears that ambiguity is inherent in the diffusion MRI measurement, the most promising validation approach employs independent measures of the same microstructure. Microscop-ic measurements of fibre architecture in histologically processed tissue are the obvious candidate. These approaches can serve as a bridge between the microscopic and macroscopic scales of connectivity. To link the two is important for two reasons. The multiscale organization of the brain calls for a multilevel description, where the links between the levels are crucial for understanding how higher-level network properties emerge from the lower levels. Furthermore, linking the body of microscale animal tract tracing literature to the now-feasible macroscale human investigations constitutes an important validation of the human structural connectome in its own right.</p>
<p>Connectional neuroanatomy is a field with a long history. It has taught us a great deal about how neurons communicate and affect each other. At present, we have the opportunity to consider the dynamics of the human brain in action. The anatomical substrate of connections is tremendously relevant as it constrains this dynamic behaviour. Fortu-nately, many investigators realize that the cumbersome anatomical work of past and present, as well as the structural connectome derived from diffusion MRI are indispensible ingredients in the mix of methods in order to draw sensible conclusions from functional data. In effect, anatomy is all-encompassing.
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<h3 class="phdthesis-title" id="Sec12">1.2 Thesis outline</h3>
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<p>This thesis contains a triplet of introductory chapters that will prepare you for the quintet of research chapters.</p>
<p>To provide a solid base and historical perspective on the main subject, i.e. connectional neuroanatomy, the scientific thesis contains an essay on how scholars have investigated the brain throughout the ages (<a href="phdthesis.html#Chapter02">Chapter 2</a>). In this essay, special emphasis will be placed on anatomical research on nerve fibres. Central concepts of fibre architecture in grey and white matter that have resulted from the efforts of the early neuroanatomical researchers is summarized in Boxes as a convenient reference for later research chapters. <a href="phdthesis.html#Chapter02">Chapter 2</a> also includes a brief overview of histological methods with a spotlight on the staining protocols used in <a href="phdthesis.html#Chapter06">Chapter 6</a> of this thesis.</p>
<p>In <a href="phdthesis.html#Chapter03">Chapter 3</a>, the concept of how nuclear magnetic resonance can be used in MRI to probe tissue properties is introduced as well as how a three-dimensional image reflecting these properties can be acquired noninvasively. The main MRI technique used in this thesis is DWI. The biophysics, acquisition methods, local diffusion models and tractog-raphy are explained in detail. More particular to this thesis, the specific opportunities and difficulties of ex vivo and high field (diffusion) MRI are discussed. In addition to diffusion MRI, susceptibility imaging is also central to <a href="phdthesis.html#Chapter04">Chapter 4</a>. Therefore, the relevant aspects of this method will be dealt with briefly.</p>
<p><a href="phdthesis.html#Chapter04">Chapter 4</a> describes a newly developed approach to DWI tractography in the white matter of the brain. In this chapter, it is explored whether fibre pathway reconstructions can be improved by integrating diffusion and susceptibility imaging, exploiting their respective advantages in angular and spatial resolution as well as their different contrast mechanisms.</p>
<p>In the subsequent chapters, the focus is shifted to cortical anatomy. Because recent high resolution diffusion MRI studies have shown radial fibre organization in the neocortex<a href="phdthesis.html#ref015"><sup>15</sup></a><sup>,</sup><a href="phdthesis.html#ref016"><sup>16</sup></a>, we set out to characterize the diffusion properties of the neocortex. The well-established laminar subdivisions of the cortex (described in <a href="phdthesis.html#Box23">Box 2.3</a>) suggest that a much richer (than homogeneously radial) non-invasive description of the neocortex is feasible with diffusion imaging. <a href="phdthesis.html#Chapter05">Chapter 5</a> reports on the first demonstration of this notion. The research discussed in <a href="phdthesis.html#Chapter06">Chapter 6</a> expands the work described in <a href="phdthesis.html#Chapter05">Chapter 5</a>. The methods used (high-field, ex vivo imaging using powerful gradient coils) present possibilities to not only demonstrate laminar characteristics, but to quantify cortical fibre architecture using advanced diffusion models. In addition, in <a href="phdthesis.html#Chapter06">Chapter 6</a> the ex vivo MRI results are validated with classical histological methods.</p>
<p>The results established in Chapters <a href="phdthesis.html#Chapter05">5</a> and <a href="phdthesis.html#Chapter06">6</a> gave confidence in the approach of mapping cortical fibre architecture with diffusion imaging. Therefore, it was attempted to extend the approach to the human brain in vivo. To bring out these features (that are certainly not readily apparent in typical DWI), high-resolution data of the cortical sheet was acquired at high field strength. The results of this investigation are included in <a href="phdthesis.html#Chapter07">Chapter 7</a>.</p>
<p>The final research paper in <a href="phdthesis.html#Chapter08">Chapter 8</a> provides an excellent example of how old and new techniques can amplify each other. It describes an approach to teach white matter anatomy. For educational purposes, a three-dimensional mental image of relations between fibre bundles is very important. This is still best achieved through dissection specimens. The new technique of specimen plastination permits safe handling by many students. Next to highlighting aspects of the anatomy not easily achieved with dissection, the combination with tractography of the same fibre bundles provides the link to modern-day clinical imaging methods, which is crucial to future radiologists, for example.</p>
<p>To conclude, <a href="phdthesis.html#Chapter09">Chapter 9</a> summarizes the contributions to the field of connectional anatomy reported in the thesis. The work is discussed in the light of recent advances and the probable future directions in the brain mapping community. Specifically, the implications of the present work regarding mapping brain networks at the mesoscopic level are discussed.</p>
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<h2 class="phdthesis-title">Chapter 2</h2>
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<h2 class="phdthesis-title">A historical essay on connectional neuroanatomy<a href="phdthesis.html#footnote2a"><sup>a</sup></a></h2>
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<h5>Introductory remarks</h5>
<p class="abstract">This chapter will give an introduction on the methods and discoveries of brain investigators throughout the ages. Although the first mention of the brain is in the Edwin Smith surgical papyrus of which the original content is dated ~3000BC, we start our journey in Greek antiquity when the notion of the brain as an information-processing device first appeared. We will visit scientists wielding their ever-improving tools to conquer the mystery of the brain. How connectional neuroanatomy fits into their quest will be given due attention. We arrive at modern day neuroscience equipped with the knowledge, experimental methods and thinking tools as they were accumulated over 2500 years. What have we learned about the white matter, and can we still learn from them?</p>
<p class="abstract">It is not the goal of this chapter to give a comprehensive account of the history of white matter research. In this short sketch, it is unavoidable that many excellent scientists are, unjustly, left out. For a more comprehensive overview, the reader is referred to the books listed below. Rather, the chapter aims to honour the efforts of the many contributors to the field by sketching the progress that has been made by leaps and bounds. Furthermore, the aim is to create awareness that knowledge does not come from books, but from the people who have written and published books and papers over the past centuries. These giants whose shoulders we stand on are easily neglected. In the modern scientific discipline, we are often forced to look after personal short-term gains. It should not be forgotten that visionary insight requires the wisdom from the past as leverage for the achievements of the future.</p>
<h5>Sources</h5>
<p class="abstract">The primary source of this chapter is the book ‘The Human Brain and Spinal Cord: A Historical Study Illustrated by Writings from Antiquity to the Twentieth Century’ by E. Clarke and C.D. O’Malley<a href=phdthesis.html#Eq017><sup>17</sup></a>. It is a fine selection of passages (including a section on the cerebral white matter), commented with clarity, and providing an informative background on the quoted scholars. The secondary source is the book ‘Fiber Pathways of the Brain’ by J.D. Schmahmann and D.N. Pandya<a href=phdthesis.html#Eq018><sup>18</sup></a>. It presents the fruit of a decade of tracing experiments in the macaque brain. Insightful conclusions about the anatomical and functional characteristics of the various major tracts are given in Part IV of the book, which also relates their findings to human anatomy (see <a href=phdthesis.html#Box21>Box 2.1</a>). Part I is an historical overview like the present chapter, but with a length that cannot be accommodated in this thesis. It complements early history with a stunning collection of reproductions of early white matter drawings and a summary of tracing studies of the twentieth century. The primary source of the information in <a href=phdthesis.html#Box23>Box 2.3</a> is the neuroanatomy textbook by Nieuwenhuys, Voogd and van Huijzen<a href=phdthesis.html#Eq018><sup>19</sup></a>. In fact, this book has been essential for most discussions concerning neuroanatomy throughout this thesis. The collections of articles in Stricker and Power (1872)<a href=phdthesis.html#Eq018><sup>20</sup></a> and Von Bonin (1960)<a href=phdthesis.html#Eq018><sup>21</sup></a> provided English translations of influential papers from the early histologists and crucial publications on the human neocortex, respectively.</p>
<h5>Abbreviations</h5>
<table class="abstract">
<tr>
<td>HE
<td>hematoxylin & eosin
</tr>
<tr>
<td>LFB
<td>Luxol Fast Blue
</tr>
<tr>
<td>SLF
<td>superior longitudinal fasciculus
</tr>
</table>
</div>
<h3 class="phdthesis-title" id="Sec21">2.1 Birth of neuroanatomy</h3>
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<p>The role of the brain (brechmos; βρεχμος) as the centre of sensation and cognition seems to have been first put forward by Alcmaeon of Croton (~500BC). He held the notion that humans were distinct from animals in the capacity of their brains. In his view, the brains of both animals and humans were responsible for sensations flowing through channels (poroi; ποροτ) that connected the sense organs to the brain. Whereas animals could only combine sensory information by correlation, the human brain was able to make inferences based on the sensory input to achieve understanding<a href=phdthesis.html#Eq022><sup>22</sup></a>. Alcmaeon is sometimes credited with the invention of dissection. His observation of poroi in the optic nerve suggests an empirical attitude, but it is debated whether he systematically applied the dissection technique. Furthermore, it is unknown whether Alcmaeon investigated multiple sensory pathways and traced the entire optical pathway from eyes to brain, or that he based his general conclusions on the excision of the eyeball alone<a href=phdthesis.html#Eq022><sup>22</sup></a>.</p>
<p>The elements (earth, water, air and fire) and humours (blood, phlegm, yellow and black bile) of Hippocratic theory could already be recog-nized in Alcmaeon’s ideas and are illustrative of the Greeks’ conception of the interactions between the external world and the body. For example, the elements of water and fire in the eyes were responsible for vision; air resounding in the auditory canal resulted in auditory perception. In line with Alcmaeon’s beliefs, the Hippocratic School (~400BC) taught that the brain was responsible for sensation, emotion and intelligence. The Hippocratic stance on medicine—that illness was caused by imbalance of the humours—was also applied to pathology of the brain. Epilepsy, for instance, was demystified as the sacred disease by proposing blockage of the phlegm produced by the brain as its cause. Although the Hippocratic School rejected all superstition and embraced scrupulous clinical observation, there was little interest in anatomical observations and therefore no furtherance of neuroanatomy.</p>
<p>Importantly, Plato, in the Timaeus (~360BC), also supported the cephalocentric view put forward by Alcmaeon. As Plato was not a naturalist, the resemblance of the head to the perfect figure—the sphere—was his reason to adopt cephalocentrism. This manner of reasoning was quite common for these days. Democritus, who devel-oped the atomistic theory of matter, ascribed the smallest and most perfectly spherical atoms to the brain.</p>
<p>Unfortunately for posterity, the view of the brain as the centre of cognition faced heavy competition from the cardiocentric hypothesis. According to this view, the heart is the seat of cognition and consciousness. Before Alcmaeon, this had been the dominant hypothesis for millennia in many cultures (e.g. Chinese and Egyptian). It was invigorated by Aristotle and the Sicilian / southern Italian schools around 350BC. Aristotle regarded the brain (amongst other organs) as a device to merely cool the hot organ of the heart. In spite of rejecting the cephalocentric hypothesis, Aristotle still believed the brain to be an organ of primary importance to the whole body<a href=phdthesis.html#Eq023><sup>23</sup></a>. The animal dissections he performed allowed him a number of important neuroanatomical observations. For example, he described two membranes covering the brain and gave a first account of its bilateral nature.</p>
<p>Whereas cultural beliefs prohibited human dissections throughout antiquity, the Alexandrian Ptolemaic period was an exception. It is asserted that even vivisection of convicted criminals was practiced<a href=phdthesis.html#Eq024><sup>24</sup></a>. As a proponent of the empirical method, Aristotle paved the way for founding the Musaeum of Alexandria by his student Ptolemy I Soter<a href=phdthesis.html#Eq023><sup>23</sup></a>. It was among this impressive gathering of scientists, that systematic investigations of human (neuro)anatomy were first undertaken between ~300-250BC. A duo of highly knowledgeable physicians named Herophilus and Erasistratus have significantly advanced the field of medicine, and neuroanatomy in particular. Herophilus identified various cranial nerves and made the important distinction between motor and sensory nerve roots. Erasistratus delivered a blow to proponents of the cardiocentric view by establishing the pumping function of the heart. Furthermore, his descriptions of the gross anatomy of the brain were unparalleled, describing the ventricles unabridged, and making a clear distinction between the cerebrum and cerebellum ascribing separate functions to each. An account of the relations between the parts of the nervous system was provided by Rufus of Ephesus (~100AD), who was heavily influenced by the Alexandrian scholars.</p>
<p>The idea of the nervous system as a unit was shared by Galen of Pergamum (129-199AD). He is the last and also the most influential physician of antiquity. Beside his anatomical, physiological and clinical observations, Galen has greatly advanced medicine by taking a definite experimentalist stance. Although human dissection was prohibited under Roman law, Galen extensively practiced animal dissection, vivisection and artery/nerve ligation studies<a href=phdthesis.html#Eq025><sup>25</sup></a>. This allowed him to gather a wealth of experimental evidence against the cardiocentric hypothesis, to which he was very strongly opposed. Galen is well known for his accurate and meticulous description of the ventricles, but he stressed the importance of brain tissue itself, contrary to a common belief that he originated the theory that the ventricles are the seat of the soul<a href=phdthesis.html#Eq026><sup>26</sup></a>. He described the white matter structures of the fornix and corpus callosum (that included the white matter of the hemispheres). A final essential concept that emerges from his work—inspired by the concurrent investigations of physiology and anatomy—is that structure and function are intimately linked. The quest to elucidate this relation still pervades neuroscience today.</p>
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<h3 class="phdthesis-title" id="Sec22">2.2 Scientific darkness</h3>
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<p>During the Middle Ages, as in all branches of science and art, few new discoveries were made regarding the brain and its connections. The Arab scholars, with Ibn Sina / Avicenna as their most influential figure, preserved the works of the ancient Greeks, but did not contribute significantly to neuroanatomy themselves. Despite the strong influence of Galen’s writings on medical issues, the cardiocentric view persisted throughout the Middle Ages. The few proponents of cephalocentrism supported the ventricular hypothesis. Moreover, the empirical method did not stand in high regard among the medieval thinkers. Dogma ruled the western world. Anticipating the dawn of better times for science, the practice of human dissection was reinstated by Mondino de Luzzi at the turn of the 13th century<a href=phdthesis.html#Eq027><sup>27</sup></a>. Although this is important in itself, his descriptions of neuroanatomy are rather obscure and no breakthroughs were achieved until the Renaissance anatomists took the stage.</p>
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<h3 class="phdthesis-title" id="Sec23">2.3 Brain dissection renaissance: sculpting the white matter</h3>
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<p>Modern day art expositions themed around human anatomy are numerous. Informative exhibits displaying human and animal specimens travel around the globe. Displays of man-machine interactions form a popular means for commenting on current trends in society and artistic shock-effects are easily obtained by juxtaposing human anatomy with characteristically materialistic objects. Anatomy is essential for many figurative art forms. It is for this reason that anatomy was one of sciences at the forefront of the Age of Enlightenment. Already during the Renaissance, artists sought to improve their work by studying anatomy and practicing dissection. The anatomical drawings of Leonardo Da Vinci are a famous product of this modus operandi. Vesalius, the exponent of the Renaissance anatomists, was a physician rather than an artist. Nonetheless, he learned enough from Da Vinci’s work to include his methods in his magnum opus from 1543: De Humani Corporis Fabrica<a href=phdthesis.html#Eq028><sup>28</sup></a>. Vesalius’ brain dissections form the cornerstone of all neuroanatomical teachings today.</p>
<p>The first scholar to make the distinction between the cortical grey and the underlying white matter (medulla) was Archangelo Piccolomini in 1586. He made the subdivision on the basis of the macroscopic appearance of the tissue, describing the colour (ashen-coloured vs. white) and consistency (soft vs. compact) of the two tissue types. In the 17th century, the essential discovery about the nature of the white matter was that it is composed of fibres. Using a rudimentary microscope, Marcello Malpighi traced white matter fibres from the brainstem to the cerebral hemispheres where he observed that they inserted into the cortex. As a biologist, he provided the apt analogy of plants rooting in the earth. Malpighi observed that fibres run in distinct bundles—e.g. he identified the pons and middle cerebellar peduncles as a bundle covering the brainstem—that sometimes meet and diverge again.</p>
<p>This discovery paved the way for other scientists to start unravelling the brain’s connections. The Enlightenment brought progress in all branches of science, including connectional neuroanatomy using the new tool of white matter dissection. With this technique specific white matter pathways are exposed by scraping along the fibres and removing the surrounding bundles/structures. It was proposed by Nicolas Steno, first practiced by Thomas Willis and systematically applied by Raymond de Vieussens. In the centuries after white matter dissection was first used, the method has been progressively refined by various pre-processing steps. The early white matter investigators boiled the brain in water (Malpighi) or oil (Vieussens), or hardened it in alcohol (Félix Vicq d’Azyr) to facilitate dissection. The advent of tissue preservation methods with fixation chemicals brought new opportunities in the 19th century: the white matter dissections of Reil, Gall & Spurzheim, Burdach and Gratiolet demonstrated the fibre bundles and connections with much more clarity than the early efforts. A selection of these fibre bundles as they have been identified with dissection techniques is discussed in <a href=phdthesis.html#Box21>Box 2.1</a>. The last major advance in white matter dissection was made in the twentieth century by Ludwig Klingler, who invented loosening tissue structure by freezing and thawing the specimens after fixation. In this form (Klingler dissection) white matter dissection is still practiced to date, for research purposes<a href=phdthesis.html#Eq029><sup>29</sup></a>, mapping surgical approaches<a href=phdthesis.html#Eq030><sup>30</sup></a> as well as the preparation of educational specimens (this thesis, <a href=phdthesis.html#chapter08>Chapter 8</a>).</p>
<div class="Boxes" id="Box21">
<h4 class="phdthesis-title">Box 2.1 Cerebral white matter fibre bundles</h4>
<a href="phdthesisfiles/Ch02/MK_Ch02_Box1.png" title="MK_Ch02_Box1_thumb" id="MK_Ch02_Box1_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch02/MK_Ch02_Box1_thumb.jpg" alt="MK_Ch02_Box1_thumb.jpg"/></a>
<h5 class="phdthesis-title">COMMISSURES</h5>
<p>The <b>corpus callosum</b> is the massive fibre bundle that connects the hemispheres. The corpus callosum can be safely regarded as the most well known and investigated fibre bundle in the brain. It has been since antiquity. What was regarded as the corpus callosum in the days of Galen (who named it) does not correspond with what is meant by it now. As no methods were invented to distin-guish bundles before the era of white matter dissection, the corpus callosum usually included the white matter mass within the hemispheres. Today, the corpus callosum is the arced set of fibres crossing the midline in the telencephalon. It is separate from the other commissures. The anatomical subdivision that is usually made in this massive fibre tract is over its rostrocaudal axis: the rostrum, genu, body and splenium of the corpus callosum contain interhemispheric connections of various lobes of the brain in a topographic manner. In terms of function, the corpus callosum carries both homotopic (i.e. axons connecting bilateral homologous areas) and heterotopic fibres. As such, the corpus callosum appears to be in-volved in the coordination of perception and action as well as interhemispheric cross-modality integration. Evidently, the functional significance of such a massive tract extends beyond perceptual and motor processes. This can also be deduced from the wide array of clinical symptoms associated with callosal agenesis where—contrary to early beliefs—not only basic perceptual and motor deficits are observed, but also social/emotional cognition is affected<a href=phdthesis.html#Eq031><sup>31</sup></a>. Furthermore, the surgical procedure of callosotomy—sporadically applied to relieve refractory epilepsy and resulting in a ‘split brain’—has provided invaluable insights into hemispheric specialization as well as functional integration of mental processes<a href=phdthesis.html#Eq032><sup>32</sup></a>.</p>
<p>The <b>anterior commissure</b> is much less bulky than the corpus callosum. On the midline, it is a small well-circumscribed cord of fibres wedged between the diencephalon and the columns of the fornix. The anterior commissure tapers out to both sides over the inferior aspects of the temporal lobes. It is a dynamic bundle that undergoes heavy pruning of connections during development leading to considerable variation in size between individuals. In mammals, the bundle is less important than in other vertebrates (that lack cerebral hemispheres and a corpus callosum). This position in phylogeny provides hints to its anatomical and functional significance in primates: connecting pre-isocortical and amygdalar regions of the brain and interhemispheric processing of emotionally and mnemonical-ly relevant visual and auditory stimuli<a href=phdthesis.html#Eq018><sup>18</sup></a>.</p>
<h5 class="phdthesis-title">ASSOCIATION TRACTS</h5>
<p>In the posterior portion of the brain, the distinction between various tracts has proven to be difficult to establish. It is well established that a projection system carries fibres from the thalamus to the visual areas and that this system is contained within the sagittal stratum. The anatomy of the associative systems in the occipital lobe, however, has seeded some controversies in the past. In short, the localization and existence of the <b>inferior longitudinal fasciculus</b> (ILF) and <b>inferior fronto-occipital fasciculus</b> (IFOF) has been a matter of debate (reviewed in Schmahmann and Pandya (2006)<a href=phdthesis.html#Eq018><sup>18</sup></a>, whose conclu-sions will be adopted here). The inferior longitudinal fasciculus is the visual association system connecting the extrastriate areas of the occipital lobe to the temporal lobe. Its central bundle is located ventrolaterally to the sagittal stratum. The putatively non-existent inferior fronto-occipital fasciculus—found by means of fibre dissection and MRI tractography, but not consistently in animal tracer studies—would overlap with the inferior longitudinal fasciculus, or would be situated in between the sagittal stratum and inferior longitudinal fasciculus over its posterior extent. Anteriorly, the bundle would run ventral to the apex of the insula and alongside the fibres of the uncinate fasciculus to the ventral aspect of the frontal lobe.</p>
<p>The association tract connecting the frontal cortex with parietal association areas is the <b>superior longitudinal fasciculus</b> (SLF). It has three subcomponents (SLF I, II and III) distinguished over the mediodorsal-to-lateroventral axis<a href=phdthesis.html#Eq018><sup>18</sup></a><sup>,</sup><a href=phdthesis.html#Eq033><sup>33</sup></a>. The superior longitudinal fasciculus is thought to serve functions such as sensorimotor integration (SLF I), visuospatial awareness (SLF II) and imitation (SLF III). The arcuate fasciculus connects the caudal superior temporal lobe with the dorsal prefrontal cortex (in non-human primates). Over its dorsal extent, it runs alongside SLF II. Historically, the <b>arcuate fasciculus</b> has been regarded as a bundle connecting the language areas for articulation (Broca’s) and comprehension (Wernicke’s). Because there is little evidence that the bundle connects to Broca’s area this is no longer tenable. Because the bundle connects auditory regions to prefrontal areas it is now thought to be the auditory counterpart of the SLF II, serving audiospatial attention<a href=phdthesis.html#Eq018><sup>18</sup></a>.</p>
<p><b>U-fibres</b> form a thin sheet covering the cortical mantle on the inside. These short association fibres connect cortical neurons over small distances, e.g. homologous neurons in a topographic hierarchy or integration across cortical columns. In cross-section, the convexities and concavities of the cerebral convolutions make them appear (inversely) u-shaped<a href=phdthesis.html#Eq034><sup>34</sup></a>, hence their name. Neighbourhood association fibres (neighbourhood SA) form the shell of fibres between the u-fibres and the deep white matter. They span multiple gyri, e.g. connecting lobules.</p>
<p>The <b>cingulum</b> lies within the cingulate and parahippocampal gyri. It forms a continuous arc around the corpus callosum on the dorsal side and extends to the temporal lobe on the ventral side. Fibres enter and fan out of the bundle over its entire course. They arise mostly from pyramidal neurons in the cingulate gyrus comprising association, projection (to the striatum) as well as commissural fibres. The cingulum forms part of Papez’ circuit<a href=phdthesis.html#Eq035><sup>35</sup></a>. As such, it is an important constituent of the limbic system, playing a central role in emotion. The cingulum branches dorsally to multimodal sensory association areas and connects these to the limbic lobe. Affective stimuli might get their valence through this connection. Memory systems are also linked by the cingulum: working memory in the dorsolateral prefrontal cortex, spatial memory in the parietal region and declarative memory in the hippocampal systems. The cingulum is furthermore implicated with internally oriented behaviour in linking the regions that make up the default mode network found with fMRI during the resting-state<a href=phdthesis.html#Eq036><sup>36</sup></a>.</p>
<h5 class="phdthesis-title">PROJECTION TRACTS</h5>
<p>The <b>fornix</b> contains the efferent fibres of the hippocampus (which it leaves as the alveus, then fimbria) that project to the basal forebrain and the diencephalon. The body of the fornix arches over the posterior part of the third ventricle separating anteriorly into the bilateral columns of the fornix and posteriorly into the bilateral crura. In the body of the fornix, part of the fibres cross to the contralateral hemispheres and hence the fornix is both a projection and commissural tract. The columns of the fornix split around the anterior commissure. The precommissural fornix (projecting to the septal nuclei and nucleus accumbens) is involved in emotional and motivational processing. The postcommissural fornix projects to the mammillary bodies of the hypothalamus and the thalamus’ limbic nuclei. It complements the cingulum in Papez’ circuit and has a role in memory processes. For example, damage to the diencephalic circuit seems to specifically impair memory recall, but not recognition<a href=phdthesis.html#Eq037><sup>37</sup></a>.</p>
<p>The <b>corona radiata</b> contains fibres projecting from all over the hemispheres to various subcortical structures including the thalamus, brainstem and pontine nuclei. It is continuous with the <b>internal capsule</b> (red) that carries these fibres in between the lentiform nucleus laterally and the caudate nucleus and thalamus medially. Observed in sagittal view, it has the shape of a wedge with its apex in the brainstem and fibres ‘radiating’ upward. In the centrum semiovale, the bundle crosses association fibres and the corpus callosum. The internal capsule can be anatomically subdivided in an anterior limb, a genu and a posterior limb. The anterior limb includes mostly cortico-thalamic fibres from the anterior portion of the thalamus to the frontal lobe. The posterior limb of the internal capsule includes many axons of the motor and sensory systems. Hence, the most common clinical symptom involving damage to the internal capsule is hemiparesis after lacunar infarction.</p>
<p>In the posterior part of the cerebral hemispheres, the <b>sagittal stratum</b> contains the visual projection system. It encapsulates the occipital horn of the lateral ventricle on all sides but the medial one. The sagittal stratum can be divided in an internal and an external shell. The sagittal stratum externa contains corticopetal fibres from the lateral geniculate nucleus of the thalamus. It is synonymous with the <b>optic radiation</b>. A notable feature of the tract is the Flechsig-Meyer loop that curves through the temporal lobe in its course towards the lower bank of the calcarine sulcus. Clinically, this anatomical peculiarity is relevant, because sectioning the loop in surgical treatment of temporal lobe epilepsy often leads to visual field defects. The sagittal stratum interna contains the corticofugal fibres of the reciprocal pathway from visual cortex to the pulvinar of the thalamus and other subcortical structures.</p>
</div>
<p>The discovery of the heterogeneity of the white matter was followed by the observation of the laminated structure of the surrounding grey matter of the cortex. Francesco di Gennari first identified the eponymous line in the primary visual cortex<a href=phdthesis.html#Eq038><sup>38</sup></a>. Independent confirmation of this cortical feature was provided by Vicq d’Azyr. The discovery was further generalized to multiple layers throughout the cortex by Jules Baillarger (1840)<a href=phdthesis.html#Eq039><sup>39</sup></a>. The significance of cortical heterogeneity was only realized much later in the era of histology (<a href=phdthesis.html#Sec25>Section 2.5</a>; and see also <a href=phdthesis.html#Chapter05>Chapter 5</a> for an in-depth discussion of this history and the current state of laminar neuroanatomy research techniques).</p>
<p>The functional interpretation that was given to the discovery of the fibrous structure of the white matter by the Renaissance anatomists still leaned heavily on the Galenic view. Naturally, the fibrous nature of the white matter fit in perfectly with being conduits (as in Alcmaeon’s poroi) for animal spirits flowing on “a broad, almost a royal, highway … [which] are carried to all the nervous parts of the body”<a href=phdthesis.html#Eq040><sup>40</sup></a>. Also Rene Descartes, in his Treatise of Man, adhered to the idea of animal spirits flowing through hollow fibres (tuyeaux) mechanically opened by the nerves. Ideas, however, can change quickly. Descartes' authoritative ideas were already under serious attack some years after publication. The experimentalist Nicolas Steno, although generally an admirer of Descartes<a href=phdthesis.html#Eq041><sup>41</sup></a>, already referred to animal spirits as “words without any meaning”<a href=phdthesis.html#Eq042><sup>42</sup></a>. The irritability of nervous tissue (observed by Francis Glisson in 1654; ignored for a century; and reintroduced by Albrecht von Haller) called for new explanations of nerve function. However, none were found in the 18th century. It was only after Luigi Galvani’s landmark experiments in ‘animal electricity’ that the function of the fibres in the white matter as electrophysiological impulse conductors became widely accepted.</p>
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<h3 class="phdthesis-title" id="Sec24">2.4 Functional specialization: surgical ablation, clinicopathological correlation and electrical stimulation</h3>
<div class="box">
<p>In the 19th century, the notions about brain function changed dramatically with the idea that specific mental functions were localized in specific areas of the cortex. Before these times, functional divisions that were made were crude and based on conjecture (e.g. the ventricular doctrine; or the pineal gland as Descartes’ door of the soul). Albrecht von Haller’s equipotentiality hypothesis (i.e. the cortex is functionally homogeneous) prevailed until Franz Joseph Gall formed his ideas about the localization of mental faculties to cortical organs. In Gall’s framework, the cerebral convolutions were “expansions of the cerebral fibrils and of the fibre bundles”<a href=phdthesis.html#Eq043><sup>43</sup></a>. These fibre bundles formed intra-hemispheric association tracts, both long- and short-range, that connected the various functionally specialized areas. The association fibres included the commissures, but were distinguished from the projection system connecting cortical organs with subcortical structures and the spinal cord. The specialization hypothesis and the distinction between the fibre systems were largely based on correlations between observed brain damage with functional loss: the primary means to study functional specialization in that age.</p>
<p>Gall exercised another means of investigation. Next to advancing the fruitful idea that the cortex is central to human brain function and providing descriptions of the cerebral white matter that still prove to be accurate today, Gall and his collaborator Johann Kaspar Spurzheim formed many of the misguided ideas of phrenology. According to the phrenologists, hypertrophy or atrophy of cortical organs, and therefore mental faculties, could be measured by the morphology of the skull. This position was rightly met with scepticism by most of the scientific community, but gained popularity in 19th century society nonetheless. Phrenologists believed the cerebral convolutions to be the seat of certain propensities, sentiments and intellectual faculties. For example, the phrenologist George Combe located philoprogenitiveness (love of offspring) in the occipital pole, because the skull overlying this region—the occiput—would be more prominent in primates and women<a href=phdthesis.html#Eq044><sup>44</sup></a>. Notwithstanding the now obvious absurdity of these premises, the phrenological era does mark the start of investigations into the functional specialization of cortical regions.</p>
<p>French opposition closed the book on phrenology. Many followed the holistic view of Jean Pierre Flourens, the most eminent scientist of the time. The holistic stance implies that the entire brain participates in any cognitive process. Jean-Baptiste Bouillaud, Ernest Aubertin and Pierre Paul Broca adhered to localisationist theory. In 1861, Broca provided the most convincing account that articulate speech functions are localized in the frontal lobe, likely on the inferior frontal gyrus, through autopsy of aphasia patient Monsieur LeBorgne, also known as “Tan”<a href=phdthesis.html#Eq045><sup>45</sup></a>.</p>
<p>The specificity of cortical localization by clinicopathological correlation was greatly enhanced by tract degeneration methods, for example those developed by Augustus Waller<a href=phdthesis.html#Eq046><sup>46</sup></a>. The axonal degeneration by damage to a tract, sense organ or cortical area can be followed (anterogradely) through the white matter to its destination area. Evidently, this can provide a wealth of information on the connections between regions. The degeneration method allowed Ludwig Türck to trace the divisions of the corticospinal tract in brain-damaged individuals<a href=phdthesis.html#Eq047><sup>47</sup></a>. Importantly, whereas white matter dissections are biased by expectations about the white matter anatomy in locations where fibre bundles cross, tract degeneration studies are not complicated by this at all. The degeneration technique thus enabled Bernard von Gudden to describe intricate fibre crossings in the brain such as the optic chiasm<a href=phdthesis.html#Eq048><sup>48</sup></a>.</p>
<p>Some years prior to this, Bartolomeo Panizza already used the degen-eration technique to demonstrate that visual functions are located in the occipital lobe. Panizza used both surgical ablation techniques in animals as well as human clinical observations to support his claim. Refinement of the lesioning techniques at the turn of the 19th century allowed comprehensive descriptions of the gross anatomy of the visual system. Through clinocopathological correlations in brain-damaged World War I soldiers, this lay-out could be verified in humans as well. The large number of war casualties even lead to the first retinotopic maps<a href=phdthesis.html#Eq042><sup>49</sup></a>.</p>
<p>Localization specificity was further enhanced by electrophysiological stimulation methods, although these could only be applied in animals and had a limited range with respect to the regions that could be investigated. The initial successful investigations in electrophysiology have been performed by Eduard Hitzig and Gustav Fritsch<a href=phdthesis.html#Eq050><sup>50</sup></a>. Stimulating a dog’s frontal lobes, they noticed the contractions of specific muscle groups on the contralateral half of the body. The method led to the first functional topographic map of an area of the brain and forms the basis of modern day electrophysiology.</p>
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<h3 class="phdthesis-title" id="Sec25">2.5 Milestones in microstructure</h3>
<div class="box">
<p>One of the great scientific advances in history, the invention of the microscope, has benefitted neuroscience like no other tool has. The investigation of the microscopic structure of the nervous system has its origin in observations by Antoni van Leeuwenhoek, who described the bovine optic nerve as containing “filamentous particles”<a href=phdthesis.html#Eq051><sup>51</sup></a>. Within the brain, the first microscopic accounts were given by Marcello Malpighi<a href=phdthesis.html#Eq052><sup>52</sup></a>. His cortical “glands” in the grey matter were a first step in imaging microscopic brain structure. It should be realized that many of these early observations are likely to have been artefacts owing to the limited accuracy of the tools. Significant progress was made after achromatic compound microscopes became available in the 1820’s. For instance, in 1836 Robert Remak used it to accurately describe myelinated and unmyelinated nerve fibres. Furthermore, his observations lead him to believe that the fibres were connected to the nerve cell, a year before cell theory was formed by Theodor Schwann in 1839. A decade later, Waller’s degeneration studies established a functional division between the two, implicating the cell body as the trophic centre of the cells. The degeneration of the distal portion of a nerve fibre when detached from the cell body is still referred to as Wallerian degeneration.</p>
<div class="Boxes" id="Box22">
<h4 class="phdthesis-title">Box 2.2 Staining methods</h4>
<p>After the industrial revolution in the first half of the 19th century, Germany’s chemical industry was booming. The availability of a wide range of dyes facilitated the discovery of chemical compounds suitable for staining biological materials for investigating them with a micro-scope. Carmine was the prime stain for the nervous system (used extensively by Joseph von Gerlach), colouring the cytoplasm a bright red. Using this dense stain, the boundaries of individual neurons could not be determined. Improvement came with the silver staining method, perfected by Golgi, resulting in a “black reaction” for a small percentage of neurons in their entirety. The next step consisted in staining specific cell parts, e.g. the methylene blue stain for axons (Ehrlich), Weigert’s myelin stain and the Nissl stain for nuclei. Over the past century, a plethora of staining methods have been proposed that have an affinity for various neural components. Three of them are used in his thesis.</p>
<p>Hematoxylin specifically stains the cell body; it is the workhorse of histology. Its oxidation product hematein is combined with the mordant (i.e. a metal salt that acts as a chain-link between the dye and the tissue) aluminium to form hemalum: a basic dye. Hemalum renders cell bodies intensely blue/purple because it reacts with basophilic structures (e.g. DNA/RNA). It is often used in combination with the acidic counterstain eosin. Eosin stains most other cell components (e.g. acidophilic proteins in the cytoplasm) in varying shade of red. The combination is termed the H&E or HE section. It is a stain well suited to investigate nuclear morphology and it gives a global impression of the cytoplasm.</p>
<a href="phdthesisfiles/Ch02/MK_Ch02_Box21.png" title="MK_Ch02_Box21_thumb" id="MK_Ch02_Box21_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch02/MK_Ch02_Box21_thumb.jpg" alt="MK_Ch02_Box21_thumb.jpg"/></a>
<p>The LFB stain for myelin was developed by Klüver and Barrera; its combination with the cresyl violet counter-stain is referred to as the Klüver-Barrera method<a href=phdthesis.html#Eq053><sup>53</sup></a>. It uses the Luxol Fast Blue MBS salt to stain the myelin sheet blue. In ethanol solution, the salts’ anion (copper phthalocyanine) binds to the cationic elements of the tissue. A differentiation step with lithium carbonate can remove weakly bound anions from the grey matter substance, while the stronger ionic bonds with the lipoproteins in the myelin sheet stay intact. Interestingly, owing to the paramagnetic copper atom in the salt, the method also appears to work as a contrast agent for specific MRI applications<a href=phdthesis.html#Eq054><sup>54</sup></a><sup>,</sup><a href=phdthesis.html#Eq055><sup>55</sup></a>. However, it should be noted that differentiation can be inhomogeneous and unverifiable in tissue blocks (as opposed to thin histological sections) used in ex vivo MR-microscopy<a href=phdthesis.html#Eq055><sup>55</sup></a>.</p>
<a href="phdthesisfiles/Ch02/MK_Ch02_Box22.png" title="MK_Ch02_Box22_thumb" id="MK_Ch02_Box22_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch02/MK_Ch02_Box22_thumb.jpg" alt="MK_Ch02_Box22_thumb.jpg"/></a>
<p>In the central nervous system, the Bodian method stains axons and neurofibrils black<a href=phdthesis.html#Eq056><sup>56</sup></a>. It is a argyrophilic silver staining method, i.e. silver ions from a silver proteinate solution bind to neurofilaments in the cytoskeleton<a href=phdthesis.html#Eq057><sup>57</sup></a> and with the help of a reducing reagent (hydroquinone) metallic silver particles are formed. The silver is then replaced by metallic gold from a gold chloride solution (using oxalic acid as reductant), a process known as toning. In the Bodian method, the silver proteinate is combined with metallic copper. The silver protein oxidizes the metallic copper and both are reduced onto the section by hydroquinone. During the toning stage both silver and copper are replaced by gold, hence resulting in a more intense staining<a href=phdthesis.html#Eq058><sup>58</sup></a>.</p>
<a href="phdthesisfiles/Ch02/MK_Ch02_Box23.png" title="MK_Ch02_Box23_thumb" id="MK_Ch02_Box23_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch02/MK_Ch02_Box23_thumb.jpg" alt="MK_Ch02_Box23_thumb.jpg"/></a>
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<p>The 19th century delivered methods for the preservation of tissues. This was another prerequisite for microstructural investigations of the nervous system. Important contributions in this respect were hardening the brain in alcohol<a href=phdthesis.html#Eq059><sup>59</sup></a> or chromic acid<a href=phdthesis.html#Eq060><sup>60</sup></a> and tissue fixation with formaldehyde<a href=phdthesis.html#Eq061><sup>61</sup></a>. A final indispensible ingredient for unravelling the microscopic structure of the neuron was the staining technique (<a href=phdthesis.html#Box22>Box 2.2</a>). With this methodological triplet—the microscope, tissue fixation, and dyes—the neuroanatomists of the second half of the 19th century were well equipped to tackle problems at the scale of the basic building blocks of the nervous system.</p>
<p>The debate that dominated neuroscience in the last decades of the 19th century concerned the structure of the brain network: is it continuous or is it built of units? The discussion was sparked by Joseph von Gerlach, who put forward the idea of the nerve net after observing a network of interlacing fibrils in his carmine-stained sections<a href=phdthesis.html#Eq062><sup>62</sup></a>. His theory implied that dendrites, described 7 years earlier by Otto Deiters, formed a continuous network connecting all neurons<a href=phdthesis.html#Eq063><sup>63</sup></a>, while the axonal network was separate and more sparse. Camillo Golgi adapted von Gerlach’s nerve net theory, finding only evidence for the axonal network in his superior stainings, but becoming its greatest advocate nonetheless. The opposing theory was brought forward by Wilhelm His. Building on Paul Ehrlich’s work on nerve endings, His deduced from the outgrowth of processes during cellular development that cells remained separate entities not in direct contact with each other<a href=phdthesis.html#Eq064><sup>64</sup></a>. This later became the well-known neuron doctrine, arguably the most influential doctrine in neuroscience today. Independent confirmation of the validity of the neuron doctrine came only three months later by August-Henri Forel. Using the very different approach of von Gudden’s retrograde nerve degeneration studies, Forel showed that atrophy is confined to nerve cells with actual peripheral damage<a href=phdthesis.html#Eq065><sup>65</sup></a>. The final blow for nerve net theory came from Santiago Ramón y Cajal, who provided yet another independent account of the unity of the nerve cell. A synthesis of the work relating to the debate was provided by Wilhelm Waldeyer, who gave the neuron its name<a href=phdthesis.html#Eq066><sup>66</sup></a>.</p>
<p>Next to basic neuron morphology, the structure of the cortex (<a href=phdthesis.html#Box23>Box 2.3</a>) was intensively investigated. The preliminary microscopic examinations of van Leeuwenhoek and Malpighi were followed by the crucial macroscopic observations of Gennari and Baillarger, establishing that the cerebral cortex is a layered sheet. Using the newly developed histological tools, numerous neuronal cell types were discovered in the decades around 1900 (Purkinje cells, Betz cells, Cajal-Retzius cells; to name a few that are eponymous with their discoverers). The combination of the two opens the field of cortical cytoarchitecture: the anatomical study of the distribution of cell types over the cortical depth. The exponent of this method was Theodore Meynert. Next to providing the first detailed survey of the cytoarchitecture of the cerebral cortex, Meynert grounded the division of white matter into association, projection and commissural fibres as it is still used today. The ramification of these fibres in the cortical grey matter has been exquisitely described by Ramón y Cajal. This forms the basis for the related field of myeloarchitectonics: the variation in myelinated fibre content over the depth of the cortex.</p>
<p>Meynert laid the foundations for the most significant neuroscientific endeavour of the first quarter of the 20th century. Cortical mapping became popular because it had been realized that the structural divisions found in the cortex were likely to be related to functional specialization of cortical areas (as discussed in <a href=phdthesis.html#Sec24>Section 2.4</a>). Cyto- and myeloarchitectonic maps galore—with Alfred Walter Campbell, Grafton Elliot Smith, Korbinian Brodmann, Cecile and Oskar Vogt, and Constantin von Economo and Georg Koskinas as their most prominent inventors—exhibiting a range of parcellation scales, taxonomies and claims. In retrospect, it can be concluded that Brodmann ‘won’, because his map is most widely used today. However, consensus on an appropriate parcellation has never been reached—and therefore investigators often choose a parcellation to suit their needs.</p>
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<h3 class="phdthesis-title" id="Sec26">2.6 Tracing progress through the 20th century</h3>
<div class="box">
<p>Although the investigative focus might have been on cyto-and myeloarchitecture of the cortex in the decades around 1900, white matter research was not abandoned. Some of the most important principles of brain connectivity were uncovered during this period. Much of the basic knowledge of the white matter that can be found in textbooks can be traced back to investigators that had their productive years during this period.</p>
<p>Paul Emil Flechsig investigated the sequence in which various fibre systems myelinate during pre- and postnatal development. This myelogenesis method led him to some brilliant insights about connectivity and the nature of brain organization. Flechsig not only determined important functional subdivisions within otherwise anatomically indistinguishable tracts (e.g. in the internal capsule and the corticospinal tract), based on the myelogenetic observations he also posed the more general subdivision of the cerebral cortex in primary, secondary and association areas.</p>
<p>Around 1900, the couple Joseph Jules Dejerine and Augusta Dejerine-Klumpke published the perhaps most influential work on fibre systems in history<a href=phdthesis.html#Eq067><sup>67</sup></a><sup>,</sup><a href=phdthesis.html#Eq068><sup>68</sup></a>. The Anatomie des Centres Nerveux contained the fruit of meticulous staining and serial sectioning of the human brain, building a near-comprehensive atlas of the white matter illustrated with many wonderfully accurate drawings. Further, Jules Dejerine was an excellent clinician who classified many neurological syndromes for the first time<a href=phdthesis.html#Eq069><sup>69</sup></a>. His wife Augusta, the first female intern in a French hospital, had the same gift topped with a heart for the injured soldiers of World War I<a href=phdthesis.html#Eq070><sup>70</sup></a>.</p>
<div class="Boxes" id="Box23">
<h4 class="phdthesis-title">Box 2.3 Cortical anatomy and function</h4>
<p>The cytoarchitecture, functional organization and fibre architecture of the primary visual cortex (V1) is visualized in the figure below. A) Nissl staining (adapted from <a href="http://webvision.med.utah.edu/imageswv/Nissl-CO.jpg">http://webvision.med.utah.edu/imageswv/Nissl-CO.jpg</a>); B<a href=phdthesis.html#Eq075><sup>75</sup></a>) schematic drawing of cell distribution in V1; C<a href=phdthesis.html#Eq076><sup>76</sup></a>) simple functional model of laminar processing in the V1 microcircuit: the granular layer (4C) receives feedforward input from the thalamus that is forwarded to the supragranular layers (2-4B) and modulated by infragranular layers (5, 6); the visual stream continues in extrastriate areas through feedforward projections from the supragranular layers; D<a href=phdthesis.html#Eq077><sup>77</sup></a>) minicolumn model showing cell stacks and dendritic bundles: minicolumnar anatomy could be an important organizational feature for cortical processing, in particular lateral integration, because the neurons composing a cellular minicolumn send their apical dendrites to different interposed dendritic bundles (or pyramidal cell modules<a href=phdthesis.html#Eq078><sup>78</sup></a>); neurons belonging to the same dendritic bundle, however, project to the same distant target; dendritic bundles with different targets but common inputs can be grouped into ‘cortical output units’; how minicolumns relate to functional macrocolumns<a href=phdthesis.html#Eq079><sup>79</sup></a> is as of yet unknown; E<a href=phdthesis.html#Eq075><sup>75</sup></a>) schematic drawing of myelinated axons in V1; F<a href=phdthesis.html#Eq080><sup>80</sup></a>) inhibitory neurons (blue) and infragranular pyramidal cells (red) in minicolumns showing dendritic arborisations.</p>
<a href="phdthesisfiles/Ch02/MK_Ch02_Box3.png" title="MK_Ch02_Box3_thumb" id="MK_Ch02_Box3_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch02/MK_Ch02_Box3_thumb.jpg" alt="MK_Ch02_Box3_thumb.jpg"/></a>
<p>The opposite page lists the cytoarchitectural (left column) and fibrearchitectural (right column) particulars of the cortical layers (i.e. all layers feature many other cell types and processes not listed here), where [+,±,-] gives an appreciation of the presence within a layer; [|,=,⊥] denotes radial, tangential, radial+tangential fibre orientations with respect to the cortical sheet.</p>
<hr><br>
<table class="table">
<tr>
<p><b>Layer I: lamina molecularis</b><a href=phdthesis.html#Eq081><sup>81</sup></a></p>
</tr>
<tr>
<p><i>integration of cortico-cortical (and cortico-thalamic) feedback signals</i></p>
</tr>
<tr>
<td><p>+ Astrocytes</p></td>
<td><p>= Dendritic tufts</p></td>
</tr>
<tr>
<td><p>- neurons (80% GABAergic)</p></td>
<td><p>⊥ Axons</p></td>
</tr>
<tr>
<td><p>- Cajal-Retzius cells</p></td>
<td><p>= Cajal-Retzius process</p></td>
</tr>
</table>
<hr><br>
<table class="table">
<tr>
<p><b>Layer II: lamina granularis externa</b></p>
</tr>
<tr>
<p><i>integration of feedforward and feedback; efferents to extrastriate areas (comm+ass)</i></p>
</tr>
<tr>
<td><p>± Pyramidal cells</p></td>
<td><p>| Apical dendrites</p></td>
</tr>
<tr>
<td><p>+ Stellate cells (GABA)</p></td>
<td><p>= Horizontal connections</p></td>
</tr>
<tr>
<td><p></p></td>
<td><p>| Asc/Desc axons</p></td>
</tr>
</table>
<hr><br>
<table class="table">
<tr>
<p><b>Layer III: lamina pyramidalis externa</b></p>
</tr>
<tr>
<p><i>integration of feedforward and feedback; efferents to extrastriate areas (comm+ass)</i></p>
</tr>
<tr>
<td><p>+ Pyramidal cells</p></td>
<td><p>| Apical dendrites</p></td>
</tr>
<tr>
<td><p></p></td>
<td><p>= Horizontal connections</p></td>
</tr>
<tr>
<td><p></p></td>
<td><p>| Asc/Desc axons</p></td>
</tr>
</table>
<hr><br>
<table class="table">
<tr>
<p><b>Layer IV: lamina granularis interna</b></p>
</tr>
<tr>
<p><i>receives feedforward input from thalamus; intracortical projection to superior layers</i></p>
</tr>
<tr>
<td><p>+ granule cells (IVA)</p></td>
<td><p>| Apical dendrites</p></td>
</tr>
<tr>
<td><p>+ outer Meynert cells (IVB)</p></td>
<td><p>= Ext. band of Baillarger (IVB)</p></td>
</tr>
<tr>
<td><p>+ spiny stellate cells (IVC)</p></td>
<td><p>| Asc/Desc axons</p></td>
</tr>
</table>
<hr><br>
<table class="table">
<tr>
<p><b>Layer V: lamina pyramidalis interna</b></p>
</tr>
<tr>
<p><i>receives projection from supragranular layers; efferents to basal ganglia, brainstem, spinal cord</i></p>
</tr>
<tr>
<td><p>+ Pyramidal cells</p></td>
<td><p>| Apical dendrites</p></td>
</tr>
<tr>
<td><p></p></td>
<td><p>= Int. band of Baillarger (IVB)</p></td>
</tr>
<tr>
<td><p></p></td>
<td><p>| Asc/Desc axons</p></td>
</tr>
</table>
<hr><br>
<table class="table">
<tr>
<p><b>Layer IV: lamina multiformis</b></p>
</tr>
<tr>
<p><i>receives projection from supragranular layers; cortical efferents to thalamus</i></p>
</tr>
<tr>
<td><p>+ small Meynert cells (VIA)</p></td>
<td><p>= Collaterals desc axons</p></td>
</tr>
<tr>
<td><p>+ transition zone (VIB)</p></td>
<td><p>= Int. band of Baillarger (IVB)</p></td>
</tr>
<tr>
<td><p></p></td>
<td><p>| Asc/Desc axons</p></td>
</tr>
</table>
<hr><br>
<table class="table">
<tr>
<p><i>comm = commisural; ass = association; asc = ascending; desc = descending; int = internal; ext = external</i></p>
</tr>
</table>
</div>
<p>After World War II, tracing methods applied in living animals progressively improved, permitting highly specific connectivity research. Before these methods became available, the Marchi method was reliant on myelin degradation and hence missed the (often unmyelinated) cortical extension of the axons. The Bielchowsky silver impregnation was rather unpredictable, even after the improvements in the second half of the 20th century<a href=phdthesis.html#Eq018><sup>18</sup></a>. The realization that active transport mechanisms in the cell could be used for delivery of a dye meant a leap in specificity and reliability in the 1970’s. The subsequent development of many variants of the tracing methods resulted in enormous flexibility to answer experimental questions on connectivity pertaining directionality (retro- vs. anterograde), co-localization (fluorescent double-labelling), synaptic morphology, trans-synaptic connectivity (viral tracers), function (tracing in combination with in situ hybridization), etc<a href=phdthesis.html#Eq071><sup>71</sup></a>.</p>
<p>The wealth of information on specific individual projections that these approaches have produced is most valuable when their interactions in the networks of the brain are considered. The hierarchy of the visual system of the macaque by Felleman and Van Essen<a href=phdthesis.html#Eq072><sup>72</sup></a> is the famous example of a network-level description of tracing data. There are others. The connectome of Caenorhabditis elegans has been mapped in its entirety with serial-section electron microscopy<a href=phdthesis.html#Eq073><sup>73</sup></a>. The extensive collection of macaque tracing results in the CoCoMac database can nowadays be conveniently queried online<a href=phdthesis.html#Eq074><sup>74</sup></a>. The major drawback of the active tracing method, however, is that it is not applicable in humans. Here is where the journey through history ends. We have arrived at the modern technique of tracking fibres in the human brain with diffusion MRI, the topic of the next chapter.</p>
</div>
<div class="boxhdr">Footnotes</div>
<div class="box">
<p class="footnote" id="footnote2a"><sup>a</sup> preprint version</p>
</div>
</div>
<div class="boxhdr"><span><a href="phdthesis.html#pagetop">▲back to top</a></span></div>
<br><hr><div id="Chapter03" class="equalcolumn21">
<br>
<h2 class="phdthesis-title">Chapter 3</h2>
<hr>
<h2 class="phdthesis-title">Magnetic resonance imaging of fibre architecture</h2>
<hr>
<div class="box">
<h5>Introductory remarks</h5>
<p class="abstract">Technological advances have opened up avenues to investigate fibre architecture in the living human brain. The most prominent methods for visualizing fibre systems in vivo are specific flavours of magnetic resonance imaging (MRI). MRI is nowadays widely used in the clinical setting to image soft tissues. The technique is very versatile in its ability to characterize the microscopic magnetic environment of (water) molecules. This chapter first introduces the physics involved in acquiring an image of the brain. Then, it provides a detailed description of the two MRI-methods sensitive to fibre architecture that are used in the remaining chapters of this thesis.</p>
<h5>Abbreviations</h5>
<table class="abstract">
<tr>
<td>ADC
<td>apparent diffusion coefficient
</tr>
<tr>
<td>BOLD
<td>blood oxygen level dependent
</tr>
<tr>
<td>CSF
<td>cerebrospinal fluid
</tr>
<tr>
<td>dHb
<td>deoxyhemoglobin
</tr>
<tr>
<td>dODF
<td>diffusion orientation distribution function
</tr>
<tr>
<td>DKI
<td>diffusion kurtosis imaging
</tr>
<tr>
<td>DT
<td>diffusion tensor
</tr>
<tr>
<td>DTI
<td>diffusion tensor imaging
</tr>
<tr>
<td>DSI
<td>diffusion spectrum imaging
</tr>
<tr>
<td>DWI
<td>diffusion weighted imaging
</tr>
<tr>
<td>EPI
<td>echo planar imaging
</tr>
<tr>
<td>FA
<td>fractional anisotropy
</tr>
<tr>
<td>FACT
<td>fibre assignment by continuous tracking
</tr>
<tr>
<td>FID
<td>free induction decay
</tr>
<tr>
<td>fMRI
<td>functional magnetic resonance imaging
</tr>
<tr>
<td>fODF
<td>fibre orientation distribution function
</tr>
<tr>
<td>FOV
<td>field of view
</tr>
<tr>
<td>GE
<td>gradient echo
</tr>
<tr>
<td>M1
<td>primary motor cortex
</tr>
<tr>
<td>MD
<td>mean diffusivity
</tr>
<tr>
<td>MRI
<td>magnetic resonance imaging
</tr>
<tr>
<td>MR
<td>magnetic resonance
</tr>
<tr>
<td>NMR
<td>nuclear magnetic resonance
</tr>
<tr>
<td>NODDI
<td>neurite orientation dispersion and density imaging
</tr>
<tr>
<td>ODF
<td>orientation distribution function
</tr>
<tr>
<td>RF
<td>radiofrequency
</tr>
<tr>
<td>S1
<td>primary somatosensory cortex
</tr>
<tr>
<td>SAR
<td>specific absorption rate
</tr>
<tr>
<td>SE
<td>spin echo
</tr>
<tr>
<td>SNR
<td>signal-to-noise ratio
</tr>
<tr>
<td>SWI
<td>susceptibility weighted imaging
</tr>
<tr>
<td>TE
<td>echo time
</tr>
<tr>
<td>TR
<td>repetition time
</tr>
<tr>
<td>PAS
<td>persistent angular structure
</tr>
<tr>
<td>PBS
<td>phosphate buffered saline
</tr>
<tr>
<td>PGSE
<td>pulsed gradient spin echo
</tr>
<tr>
<td>QSM
<td>quantitative susceptibility mapping
</tr>
</table>
</div>
<h3 class="phdthesis-title" id="Sec31">3.1 Introduction to magnetic resonance imaging</h3>
<div class="box">
<h4 class="phdthesis-title" id="Sec311">3.1.1 Nuclear magnetic resonance</h4>
<p>After exposing an ensemble of excitable nuclei in a magnetic field to a second transverse magnetic field rotating at the appropriate frequency, the return to the equilibrium state is accompanied by detectable changes in the field. This principle is known as nuclear magnetic resonance (NMR). We can use this property to probe the excited nucleus’ environment that influences the process of return to equilibrium. This is not only widely used in MRI, but also in NMR spectroscopy. By means of spectroscopy the physical and chemical properties of (organic) molecules can be investigated without obtaining information about the spatial distribution of the molecules.</p>
<p>The ground-breaking research on NMR was performed in the 1930’s and 1940’s, after quantum theory was developed. NMR could only have been discovered in the age of quantum mechanics, because it uses manipulation of quantum states of the nuclei under investigation by exposing them to a magnetic field. This approach is rooted in the experiments by Gerlach and Stern in the 1920’s<a href="phdthesis.html#ref082"><sup>82</sup></a>. They used inhomo-geneous magnetic fields to deflect spin-bearing nuclei in a molecular beam. One of their important discoveries was that a discrete spectrum is obtained, which is direct evidence for a quantized angular momentum of the nuclei. This experiment directly relates to the discovery of the NMR phenomenon. This same experimental approach—using a molecular beam of spin-bearing nuclei in a magnetic field—was used by Rabi et al.<a href="phdthesis.html#ref083"><sup>83</sup></a> when they first reported on the basic principle of NMR: manipulation of the angular momentum of nuclei in a magnetic field by radiofrequency excitation. Bloch<a href="phdthesis.html#ref084"><sup>84</sup></a> and Purcell, Torrey and Pound<a href="phdthesis.html#ref085"><sup>85</sup></a> showed in 1946 that the same principles of excitation can be applied to liquids and solids. Several Nobel prizes have been awarded to the pioneers in both NMR (Isidor Rabi<sup>†1988</sup>, Felix Bloch<sup>†1983</sup>, Edward Purcell<sup>†1997</sup>) and MRI (Paul Lauterbur<sup>†2007</sup>, Sir Peter Mansfield), emphasizing the importance of the field.</p>
<h5 class="phdthesis-title" id="Sec3111">3.1.1.1 Protons in a magnetic field</h5>
<p>The quantum mechanical property spin is associated with all elementary particles. A nucleus with an odd atomic and/or mass number, and hence nonzero spin, possesses an angular moment. In case the nucleus in question has a net charge, this angular moment \(\mathbf{I}\) causes it to have a dipolar magnetic moment \(\mathbf{\mu}\), which are related through the gyromagnetic ratio \(\gamma\) </p>
<!--
<div class="EqBox">
<span class="Eq">\[\mathbf{ \mu} = \gamma \mathbf{I}\]</span>
<span class="EqNo" id="Eq31">3.1</span>
</div>
-->
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\mathbf{ \mu} = \gamma \mathbf{I}\]</td>
<td class="EqNo" id="Eq31">3.1</td>
</tr>
</table>
<p>The gyromagnetic ratio is nucleus-specific and equals 42.58 MHz·T<sup>-1</sup> for the hydrogen atom <sup>1</sup>H composed of a single proton with spin ½—the nucleus relevant for the present considerations. Henceforth, the term proton will refer to the proton of the hydrogen atom <sup>1</sup>H and will be used as the model system. Note, however, that most principles explained below can be applied to any nucleus with nonzero spin and charge such as <sup>13</sup>C and <sup>31</sup>P that are widely used in NMR spectroscopy.</p>
<p>For a proton in an external magnetic field \(\mathbf{B}_0\)—the direction that conventionally defines the z-axis of the coordinate system in NMR and MRI—two possible energy states (eigenstates) exist in which the magnetic moments have an angle of ± 54.44° with the direction of the field. In the transverse plane, the magnetic moment vector describes a circular path: it is said to precess about \(\mathbf{B}_0\). The frequency \(\omega_0\) at which it precesses is given by </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\omega_0 = \gamma \mathbf{B}_0\]</td>
<td class="EqNo" id="Eq32">3.2</td>
</tr>
</table>
<p>and is termed the Larmor-frequency.</p>
<p>In MRI, we are we are generally not concerned with a single nucleus, but with a large set of nuclei of the same type, i.e. precessing with the same Larmor-frequency (in a homogeneous field). For the present purpose, the collection of protons in the brain will be referred to as the spin system. In such a spin system, a classical description of NMR phenomena is warranted.</p>
<p>In a spin system with spin quantum number \(I\), the distribution of protons in the parallel vs. the anti-parallel state is dictated by the Boltzmann distribution, resulting in slightly more protons aligning with the field than against it. The spin system hence has a net bulk magnetization \(\mathbf{M}_0\) in the direction of the external magnetic field \(\mathbf{B}_0\) that is proportional to the proton density \(\rho_0\) and quantified by </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\rho_0 \propto \mathbf{M}_0 = {{N \hbar^2 \gamma^2 I(I+1) \mathbf{B}_0} \over {3 \mu_0 k_B T}}\]</td>
<td class="EqNo" id="Eq33">3.3</td>
</tr>
</table>
<p>where \(N\) is the number of protons per volume, \(k_B\) is Boltzmann’s constant, \(\hbar\) is Planck’s constant, \(\mu_0\) is the permeability of free space and \(T\) is the temperature. It is important to note for this thesis that the magnetization is directly proportional to the magnetic field, the proton density as well as inversely proportional to temperature. As the orientation of the transverse component of the magnetic moment \(\mathbf\mu\) is random for any proton, the spin system in equilibrium does not display net magnetization in the transverse plane.</p>
<h5 class="phdthesis-title" id="Sec3112">3.1.1.2 Excitation and relaxation</h5>
<p>The equilibrium magnetization vector \(\mathbf{M}_0\) of the spin system in the presence of an external magnetic field \(\mathbf{B}_0\) can be manipulated by supplying a magnetic field at the appropriate frequency. The resonance frequency is equal to the Larmor-frequency. For protons in the magnetic fields commonly used in NMR (1-30 T) and MRI (1-7 T) the resonance frequency is in the radiofrequency range and hence radiofrequency (RF) pulses are used for excitation of the protons. An RF pulse is an oscillating magnetic field (the \(\mathbf{B}_1\) field) transverse to the main magnetic field that tips the magnetization away from the z-axis when applied on-resonance (i.e. oscillating at the Larmor-frequency). The magnetization can be tipped by an arbitrary flip angle α by using an appropriate RF pulse power. Provided that α ≠ [0,180,360,…]°, the on-resonance RF pulse results in a magnetization \(\mathbf{M}_{xy}\) in the transverse plane (<a href=phdthesis.html#MK_Ch03_F01_thumb>Figure 3.1</a>).
<p>As the spin system is no longer in equilibrium after excitation, interactions of the protons with the environment will inevitably lead to a release of energy to return to the equilibrium state \(\mathbf{M}_0\). Two relaxation mechanisms play a significant role in NMR: spin-lattice relaxation with time constant \(T_1\) and spin-spin relaxation with time constant \(T_2\).</p>
<a href="phdthesisfiles/Ch03/MK_Ch03_F01.png" title="MK_Ch03_F01_thumb" id="MK_Ch03_F01_thumb" target="_blank"><img class="FigThumb" src="phdthesisfiles/Ch03/MK_Ch03_F01_thumb.jpg" alt="MK_Ch03_F01_thumb.jpg"/></a>
<p class="FigCaption">Figure 3.1. Magnetization during excitation with an RF pulse with 90° flip angle. a) in the laboratory frame of reference the magnetization \(\mathbf{M}_0\) oscillates from its equilibrium position on the z-axis to the transverse plane resulting in a transverse magnetization \(\mathbf{M}_{xy}\). b) shows the same process as in a), but seen from the rotating frame of reference rotating about z at the resonance frequency. Click image to play animation.</p>
<p>The evolution of the magnetization is described by the Bloch equations<a href="phdthesis.html#ref084"><sup>84</sup></a> </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[{dM_x \over dt} = \gamma M_x \times B_x - {M_x \over T_2}\]</td>
<td class="EqNo" id="Eq34">3.4</td>
</tr>
</table>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[{dM_y \over dt} = \gamma M_y \times B_y - {M_y \over T_2}\]</td>
<td class="EqNo" id="Eq35">3.5</td>
</tr>
</table>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[{dM_z \over dt} = \gamma M_z \times B_z - {M_z - M_0 \over T_1}\]</td>
<td class="EqNo" id="Eq36">3.6</td>
</tr>
</table>
<p>or combined in vector form:</p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[{d \mathbf M \over dt} = \gamma \mathbf M \times \mathbf B - { \mathbf {M}_x \vec i + \mathbf {M}_y \vec j \over T_2} - {( \mathbf {M}_z - \mathbf {M}_0) \vec k \over T_1}\]</td>
<td class="EqNo" id="Eq37">3.7</td>
</tr>
</table>
<p>The first term on the right-hand side of the Bloch equations describes the precession about the field. It is convenient to define a rotating frame of reference that rotates about the z-axis at the Larmor-frequency. An excitation with 90° flip angle in the rotating frame of reference is illustrated in <a href=phdthesis.html#MK_Ch03_F01_thumb>Figure 3.1b</a>. The relaxation process can then be described in the rotating frame of reference only considering the second terms on the right-hand side of <a href=phdthesis.html#Eq34>Eq 3.4</a>-<a href=phdthesis.html#Eq36>3.6</a> and solutions to the Bloch equations are greatly simplified.</p>
<p>In spin-lattice relaxation the energy difference between \(\mathbf{M}_z\) and \(\mathbf{M}_0\) is released into the lattice of the spin system’s environment by thermal interactions, returning the magnetization to the equilibrium state (and causing an increase in sample temperature). It is an exponential process characterized by time constant \(T_1\). In the rotating frame of reference the Bloch equation is </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[{d \mathbf{M}_z \over dt} = {{\mathbf{M}_0 - \mathbf{M}_z(t)} \over T_1}\]</td>
<td class="EqNo" id="Eq38">3.8</td>
</tr>
</table>
<p>yielding the expression </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\mathbf{M}_{z}(t) = \mathbf{M}_0 \left( 1 - e^{-t \over T_1} \right) + \mathbf{M}_{z}(0) e^{-t \over T_1}\]</td>
<td class="EqNo" id="Eq39">3.9</td>
</tr>
</table>
<p>for the evolution of longitudinal magnetization.</p>
<p>After application of an RF pulse, there will be phase coherence in the precession about \(\mathbf{B}_0\) of the protons in the spin system, i.e. there is net magnetization \(\mathbf{M}_{xy}\) in the transverse plane. Due to interaction between the protons experiencing slightly different magnetic environments, the theoretically single Larmor-frequency of static protons in a homogeneous field will rather be a range of Larmor-frequencies. As protons are precessing at different frequencies, the spin system dephases. The speed at which this dephasing occurs, and therefore the speed at which \(\mathbf{M}_{xy}\) returns to zero, is captured by time constant \(T_2\). The Bloch equation </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[{d \mathbf{M}_{xy} \over dt} = {\mathbf{M}_{xy}(t) \over T_2}\]</td>
<td class="EqNo" id="Eq310">3.10</td>
</tr>
</table>
<p>has the solution </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\mathbf{M}_{xy}(t) = \mathbf{M}_{xy}(0) e^{-t \over T_2}\]</td>
<td class="EqNo" id="Eq311">3.11</td>
</tr>
</table>
<p>for transverse magnetization.</p>
<p>The decay of transverse magnetization with \(T_2\) only holds in a perfectly homogeneous field. However, in the technical and biological systems dealt with in MRI, non-negligible static field variations occur due to inhomogeneity of \(\mathbf{B}_0\) as well as field perturbations by differences in magnetic susceptibility between tissue types included in the measurement volume (see also <a href=phdthesis.html#Sec314>Section 3.1.4</a> and <a href=phdthesis.html#Sec33>Section 3.3</a>). These static field variations cause an additional dephasing with time constant \(T_{2}'\) characterized by: </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[T_{2}' = {2\pi \over {\gamma \Delta B_0}}\]</td>
<td class="EqNo" id="Eq312">3.12</td>
</tr>
</table>
<p>Thus, rather than pure \(T_2\)-decay, the transverse magnetization decays with a relaxation rate \(R_{2}^*\)</p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[R_{2}^* = R_{2} + R_{2}'\]</td>
<td class="EqNo" id="Eq313">3.13</td>
</tr>
</table>
<p>or, equivalently, with time constant \(T_{2}^*\)</p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[{1 \over T_{2}^*} = {1 \over T_{2}} + {1 \over T_{2}'}\]</td>
<td class="EqNo" id="Eq314">3.14</td>
</tr>
</table>
<p>which can substitute \(T_2\) in <a href=phdthesis.html#Eq311>Eq 3.11</a>:</p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\mathbf{M}_{xy}(t) = \mathbf{M}_{xy}(0) e^{-t \over T_{2}'}\]</td>
<td class="EqNo" id="Eq315">3.15</td>
</tr>
</table>
<h4 class="phdthesis-title" id="Sec312">3.1.2 Where NMR turns into MRI</h4>
<p>The essential difference between an NMR system and an MRI system is the gradient set included in the MRI scanner. This gradient set provides the possibility to add magnetic fields that vary with spatial position. The resulting gradient field is roughly two orders of magnitude smaller than the main magnetic field, but also orders of magnitude larger than the static magnetic field inhomogeneity. This allows accurate encoding of spatial position. To acquire the images, elaborate pulse sequences are used combining successions of RF pulses of varying flip angles and magnetic field gradients in various directions to manipulate image contrast and resolution. The basic principles of image acquisition relevant for this thesis will be introduced in this section.</p>
<h5 class="phdthesis-title" id="Sec3121">3.1.2.1 Magnetic field gradients</h5>
<p>In MRI, the static main magnetic field \(\mathbf{B}_0\) is complemented by a magnetic field \(G\) in the direction of \(\mathbf{B}_0\) originating from three separate gradient coils: </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\mathbf{G} = \mathbf{G}_x + \mathbf{G}_y + \mathbf{G}_z\]</td>
<td class="EqNo" id="Eq316">3.16</td>
</tr>
</table>
<p>where \(\mathbf{G}_x\), \(\mathbf{G}_y\) and \(\mathbf{G}_z\) are linear functions of spatial position through the origin. Consequently, the Larmor-frequency is preserved in the magnet isocenter, but has an offset \(\Delta\omega\) for other locations</>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\Delta\omega (\mathbf{r}) = \gamma \mathbf{r} \mathbf{G}\]</td>
<td class="EqNo" id="Eq317">3.17</td>
</tr>
</table>
<p>with the position-dependent Larmor-frequency</p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\omega (\mathbf{r}) = \gamma (\mathbf{B}_0 + \mathbf{r} \mathbf{G})\]</td>
<td class="EqNo" id="Eq318">3.18</td>
</tr>
</table>
<h5 class="phdthesis-title" id="Sec3122">3.1.2.2 k-space formalism</h5>
<p>In MRI, the acquired complex signal \(S(t)\) is composed of a range of frequencies \([\omega_0 - \Delta\omega ; \omega_0 + \Delta\omega]\) as a result of the gradient field. The proton density function \(\rho(\mathbf{r})\) of the sample under study is related to \(S(t)\) by </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[S(t) = \int {\rho(\mathbf{r}) e^{i \int_0^t G(t') dt'\mathbf{r}} d^3} \int {\rho(\mathbf{r}) e^{i \int_0^t G(t') dt\mathbf{r}} d^{3}\mathbf{r}} \]</td>
<td class="EqNo" id="Eq319">3.19</td>
</tr>
</table>
<p>Conveniently defining \(k\) as the time integral of the gradient \(\mathbf{G}\)</p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[k = \gamma \int_0^t {\mathbf{G}(t')dt'} \int_0^t {\mathbf{G}(t)dt}\]</td>
<td class="EqNo" id="Eq320">3.20</td>
</tr>
</table>
<p>we arrive at </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[S(k) = \int {\rho(\mathbf{r}) e^{ik\mathbf{r}}dk}\]</td>
<td class="EqNo" id="Eq321">3.21</td>
</tr>
</table>
<p>and it’s conjugate </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\rho(\mathbf{r}) = S(k) \int { e^{-ik\mathbf{r}}dk}\]</td>
<td class="EqNo" id="Eq322">3.22</td>
</tr>
</table>
<p>The Fourier pair links the image domain to the domain in which the data are acquired, which is called \(k\textrm{-space}\). Thus, the proton density function \(\rho(\mathbf{r})\) can be obtained by inverse Fourier transform of \(S(k)\). This transform can be easily computed when \(S\) is (re)sampled on a Cartesian grid in \(k\textrm{-space}\). The traversal of \(k\textrm{-space}\) can be achieved by careful design of sequences of magnetic field gradients (<a href=phdthesis.html#Sec313>Section 3.1.3</a>). The number of samples taken over a particular \(k\textrm{-space}\) area determines the field-of-view (FOV) of the corresponding dimension of the reconstructed image: </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\Delta k = {1 \over {FOV}}\]</td>
<td class="EqNo" id="Eq323">3.23</td>
</tr>
</table>
<p>As the Nyquist criterion—which dictates the sampling rate \(1 / \Delta k\) to be twice the maximum frequency to be resolved—has to be observed for \(k\textrm{-space}\), signal coming from parts of the sample outside the FOV will alias into the image and can manifest itself as folding-in of these parts into the image.</p>
<p>Likewise, the \(k\textrm{-space}\) range sampled determine the spatial frequencies that can be resolved in the image. The centre of \(k\textrm{-space}\) harbours the low spatial frequencies (i.e. the contours), while the edges of \(k\textrm{-space}\) contain higher spatial frequencies (i.e. the edges in the image). Thus, one can obtain a higher resolution image by covering a larger extent of \(k\)-space.</p>
<p>Further, it is relevant to mention that \(k\textrm{-space}\) displays conjugate symmetry </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[S(-k) = S(k)^*\]</td>
<td class="EqNo" id="Eq324">3.24</td>
</tr>
</table>
<p>making it in principle possible to reconstruct the image from only half of \(k\textrm{-space}</span> using the redundancy obtained from sampling the complex signal to perform ‘partial Fourier’ imaging.</p>
<h4 class="phdthesis-title" id="Sec313">3.1.3 Image formation</h4>
<h5 class="phdthesis-title" id="Sec3131">3.1.3.1 Free induction decay, spin echo and gradient echo</h5>
<p>After excitation, the magnetization vector oscillates in the transverse plane (in the laboratory frame of reference). A coil placed over the sample will thus experience a change in magnetic flux which according to Faraday’s law will generate an electromagnetic force in the coil proportional to the transverse magnetization of the sample under study, i.e. oscillating with frequency \(\omega_0\) and decaying with a \(T_{2}^*\) envelope. This constitutes the basic free induction decay (FID) experiment. As only the transverse component is detectable, it follows that an on-resonance RF pulse with flip angle of 90° creates the maximal signal that can be obtained with a single excitation.</p>
<p>The spin echo (SE) method (<a href=phdthesis.html#MK_Ch03_F02_thumb>Figure 3.2</a>) was proposed by Hahn in 1950<a href="phdthesis.html#ref086"><sup>86</sup></a>. It was the first echo formation technique for NMR and has been widely used since. A spin echo is achieved by applying two RF pulses: an excitation pulse and a refocusing pulse. The excitation pulse tips magnetization in the transverse plane. In the time between the excitation pulse and the refocusing pulse, the protons dephase according to \(T_{2}^*\). After a certain time, an 180° refocusing pulse flips the magnetization within the transverse plane. Allowing the same time to rephase, the maximal phase coherence is achieved: an echo has formed at echo time TE. The magnetization has decayed stochastically according to \(T_{2}\), because the dephasing due to static magnetic field variations (\(T_{2}'\)) is fully reversible. This is one of the big advantages of the spin echo sequence: it is relatively insensitive to static magnetic field inhomogeneities.</p>
<p>A gradient echo (GE) is achieved by a single excitation pulse and a bipolar gradient (<a href=phdthesis.html#MK_Ch03_F03_thumb>Figure 3.3</a>). The first lobe of the (readout) gradient causes dephasing. The second lobe, of opposite polarity, compensates for the dephasing caused by the first gradient lobe and rephases the protons. Dephasing due to \(T_{2}^*\) is not compensated, making GE sequences sensitive to static field inhomogeneities. The gradient echo has the advantage over the spin echo technique that no refocusing pulse has to be applied. This allows short intervals between multiple excitations (repetition time TR), especially when using low flip angles.</p>
<a href="phdthesisfiles/Ch03/MK_Ch03_F02.png" title="MK_Ch03_F02_thumb" id="MK_Ch03_F02_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch03/MK_Ch03_F02_thumb.jpg" alt="MK_Ch03_F02_thumb.jpg"/></a>
<p class="FigCaption">Figure 3.2. Sequence diagram and phase evolution in the transverse plane for the basic spin echo sequence. Gs, Gp and Gr are the gradients applied in the slice, phase and read direction, respectively. Click image to play animation.</p>
<a href="phdthesisfiles/Ch03/MK_Ch03_F03.png" title="MK_Ch03_F03_thumb" id="MK_Ch03_F03_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch03/MK_Ch03_F03_thumb.jpg" alt="MK_Ch03_F03_thumb.jpg"/></a>
<p class="FigCaption">Figure 3.3. Sequence diagram and phase evolution in the transverse plane for the basic gradient echo sequence. Gs, Gp, Gr are the gradient applied in the slice, phase and read direction, respectively. Click image to play animation.</p>
<h5 class="phdthesis-title" id="Sec3132">3.1.3.2 Sampling k-space</h5>
<p>MR images are acquired in \(k\textrm{-space}\), where the resolution and field-of-view are determined by the \(k\textrm{-space}\) extent and sampling density, respectively (<a href=phdthesis.html#Sec3122>Section 3.1.2.2</a>). The image acquisition sequence determines the trajectory by which the points in \(k\textrm{-space}\) are sampled. The traversal of a certain \(k\textrm{-space}\) trajectory is achieved by playing out imaging gradients. This trajectory is extremely important as it has profound effects on the final image quality.</p>
<p>In a typical sequence, a single line in 3D \(k\textrm{-space}\) is read per RF excitation. In a 2D sequence, the RF pulse is accompanied by a slice-select gradient that ensures that only protons within a particular slice of the volume are excited. This gradient has two lobes of opposite polarity to rewind the induced dephasing (Gs in <a href=phdthesis.html#MK_Ch03_F02_thumb>Figure 3.2</a>; <a href=phdthesis.html#MK_Ch03_F03_thumb>Figure 3.3</a>). The slice thickness and slice location are controlled by the RF frequency in combination with the strength of the slice-select gradient. A phase-encode gradient is then applied to pre-phase the protons and move to a particular line in \(k\textrm{-space}\) within the selected slice (<a href=phdthesis.html#MK_Ch03_F04_thumb>Figure 3.4a</a>). For the gradient-echo sequence, the gradient that encodes position on the \(k\textrm{-space}\) line in the read-out direction has two lobes of opposite polarity. The first lobe dephases the spin system, while the second lobe rephases the spin system. By choosing the second lobe twice the duration as the first and centring the signal readout under this lobe, the gradient recalled echo occurs at the centre of the readout window. A whole slice is sampled by repeating this sequence for multiple excitations, but with different amplitude of the phase-encode gradient, while slices at different positions can be obtained by varying the frequency of the RF excitation pulse. Because the spin echo has a different echo formation mechanism, the basic sequence to acquire a spin echo is somewhat different. An additional slice-select gradient can be necessary under the refocusing pulse. After the excitation pulse, the phase-encode gradient and a dephasing gradient in the read-out direction are applied. The second read-out gradient that rewinds the position in the read-out direction is of the same polarity as the dephasing read-out gradient, because \(\mathbf{M}_{xy}\) was flipped in the transverse plane by the refocusing pulse. To perform the readout under the echo, this gradient is centered on TE. A whole slice is sampled by repeating this sequence for multiple excitations, but with different amplitude of the phase-encode gradient, while slices at different positions can be obtained by varying the frequency of the RF excitation pulse.</p>
<a href="phdthesisfiles/Ch03/MK_Ch03_F04.png" title="MK_Ch03_F04_thumb" id="MK_Ch03_F04_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch03/MK_Ch03_F04_thumb.jpg" alt="MK_Ch03_F04_thumb.jpg"/></a>
<p class="FigCaption">Figure 3.4. Trajectories through k-space for the acquisition of a slice. a) acquiring a slice line-by-line; b) acquiring a slice with EPI readout.</p>
<p>For some specific applications it is important to be fast. There can be multiple reasons for wanting this, e.g. sampling physiological signals at an adequate rate in functional MRI or reduction of artefacts in diffusion imaging (<a href=phdthesis.html#Sec323>Section 3.2.3</a>). In these instances, echo-planar imaging (EPI) can be used for fast sampling of \(k\textrm{-space}\)<a href="phdthesis.html#ref087"><sup>87</sup></a>. EPI can acquire a whole brain volume in seconds (nowadays even within 50 ms; see e.g. Boyacioğlu and Barth, 2012<a href="phdthesis.html#ref088"><sup>88</sup></a>). Unfortunately, fast acquisition comes with a trade-off in signal-to-noise ratio and, potentially, spatial resolution. Furthermore, the EPI acquisition is associated with particular artefacts. These are discussed in <a href="phdthesis.html#Box31">Box 3.1</a>.</p>
<p>In EPI, a full slice is read out after a single excitation. Slice-selection is achieved in a similar manner to the conventional sequences. A phase-encoding gradient and readout gradient then moves the acquisition out to one of the far corners of \(k\textrm{-space}\). To read out the slice, gradient lobes of alternating polarity in the readout direction are combined with gradient ‘blips’ in the phase-encoding direction. The resulting \(k\textrm{-space}\) trajectory zigzags effectively through the slice (<a href=phdthesis.html#MK_Ch03_F04_thumb>Figure 3.4b</a>). A positive lobe of the readout gradient moves over a line in the \(+k_x\) direction, a phase-encode blip shifts one line up in the \(+k_y\) direction, a negative readout lobe moves over a line in the \(-k_x\) direction, another phase-encode blip shifts one line up, etc., until \(k\textrm{-space}\) is filled. The series of echoes formed under each readout gradient lobe is referred to as the echo-train.</p>
<h5 class="phdthesis-title" id="Sec3133">3.1.3.3 Manipulating contrast in the brain</h5>
<p>In combination with the strength of the main magnetic field (<a href=phdthesis.html#Sec314>Section 3.1.4</a>), the composition (cellular, chemical) and structure (molecular, macroscopic) determine the relaxation rates \(T_{1}\), \(T_{2}\) and \(T_{2}^*\). As these quantities are different for the various brain tissue types a well-considered choice of imaging parameters can maximize the difference in relaxation between tissues, hence optimize the contrast in the final image. The main parameters that influence image contrast are repetition time (TR), echo time (TE) and flip angle. The repetition time is the time between successive excitations of the tissue by the RF pulse. The echo time is the time between excitation and the readout of the signal. The flip angle is determined by the RF power and controls how much of the magnetization is tipped in the transverse plane. The basic contrasts and their origin are discussed shortly. Specific contrast mechanisms most relevant for this thesis are discussed in <a href=phdthesis.html#Sec32>Sections 3.2</a> and <a href=phdthesis.html#Sec33>3.3</a>.</p>
<h6 class="phdthesis-title">Proton density contrast</h6>
<p>The proton density is the amount of protons per unit volume of tissue. The transverse magnetization after excitation is directly proportional to the proton density. To be maximally sensitive to the proton density, any relaxation should be minimized. This can be achieved by using a sequence with a long TR and short TE. Proton density imaging is mainly used in body imaging (bone, water, fat have different proton densities).</p>
<h6 class="phdthesis-title">T1 contrast</h6>
<p>The T1 constant can be conceptualized as the rate at which a material can be magnetized. Likewise, \(T_{1}\) relaxation is the rate at which magnetization is absorbed into the tissue. This absorption is due to thermal interactions between protons and their environment. For tissues that have thermal motion at a frequency close to the Larmor frequency, \(T_{1}\) relaxation is fast. T1-weighting can be achieved by using long TE or inversion-recovery methods.</p>
<p>Protons in cerebrospinal fluid (CSF) have a thermal frequency much higher than the Larmor-frequency at common field strengths and therefore CSF has a long \(T_{1}\). Protons in the white matter, on the other hand, have a lower frequency (interaction with the macromolecules of myelin slows them down considerably). The \(T_{1}\) of grey matter is considerably higher than that of white matter. Therefore, \(T_{1}\)-weighted imaging provides excellent contrast for anatomical brain imaging. Allowing a certain time for \(T_{1}\)-relaxation, the longitudinal magnetization will have recovered more for the grey matter as compared to the white matter. Hence, the grey matter appears hypointense with respect to the white matter on a \(T_{1}\)-weighted image (<a href=phdthesis.html#MK_Ch03_F05_thumb>Figure 3.5a</a>). In this thesis, the excellent grey-white matter contrast in \(T_{1}\)-weighted images makes them a very suitable go-between for registering other images (<a href=phdthesis.html#Chapter04>Chapter 4</a>). Furthermore, owing to the high grey-white matter contrast, the \(T_{1}\)-weighted image is used to reconstruct the surfaces bounding the cortical sheet (<a href=phdthesis.html#Chapter07>Chapter 7</a>).</p>
<h6 class="phdthesis-title">T2 contrast</h6>
<p>After excitation of the spin system, protons precess in phase. Magnetic interaction between protons results in a loss of coherence. The DC-component of the local field facilitates \(T_{2}\) relaxation. In rapid tumbling molecules (e.g. in CSF) this is inefficient, whereas in large stationary ones (e.g. proteins in white matter) it is efficient. A \(T_{2}\)-weighted image is typically acquired by spin echo experiments with a short TE.</p>
<a href="phdthesisfiles/Ch03/MK_Ch03_F05.png" title="MK_Ch03_F05_thumb" id="MK_Ch03_F05_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch03/MK_Ch03_F05_thumb.jpg" alt="MK_Ch03_F05_thumb.jpg"/></a>
<p class="FigCaption">Figure 3.5. Conventional MRI contrasts of an axial slice of the brain. a) \(T_{1}\)-weighted; b) \(T_{2}\)-weighted; c) \(T_{2}^*\)-weighted.</p>
<p>In the brain, the \(T_{2}\)-effect is most evident in the contrast between cerebrospinal fluid and brain tissue (<a href=phdthesis.html#MK_Ch03_F05_thumb>Figure 3.5b</a>). The CSF has a very long \(T_{2}\) in comparison to the parenchyma. Thus, \(T_{2}\) relaxation in CSF is slow, leaving the bulk of the transverse magnetization intact at the moment when the image is acquired. Hence, the CSF is very bright in the \(T_{2}\)-weighted image. The \(T_{2}\) of healthy grey and white matter are similar and do not show much \(T_{2}\)-contrast. In many cases, pathological tissue states alter the \(T_{2}\)-value of the tissue due to a change in water content. This is used in clinical MRI, e.g. for imaging oedema where fluid is accumulated in the extracellular space. In all scientific chapters of this thesis, the \(T_{2}\)-weighted image is used in the context of diffusion imaging (<a href=phdthesis.html#Sec32>Section 3.2</a>), in which it serves as the reference image.</p>
<h6 class="phdthesis-title">T2* contrast</h6>
<p>Additional dephasing of the excited spin system occurs due to inhomogeneities in the magnetic field. Spatial inhomogeneities stem from imperfections in the magnet and magnetic susceptibility differences between and within regions in the subject/sample. In some instances there is a temporal component as well, e.g. in functional MRI and subject motion. The variance in the field within an imaging voxel results in a range of Larmor-frequencies causing dephasing according to \(T_{2}^*\). \(T_{2}^*\)-weighting is obtained by gradient echo sequences with long TE and long TR.</p>
<p>An important application of the \(T_{2}^*\)-effect is functional MRI (fMRI). In fMRI, the blood-oxygen-level-dependent (BOLD) signal is measured. The BOLD signal arises from field perturbations around blood vessels that result from the presence of deoxyhemoglobin (dHb) in the veins. Deoxyhemoglobin is paramagnetic with respect to tissue and leads to a field inhomogeneity around a vessel. This field perturbation is bipolar due to the cylindrical geometry of the blood vessel. The concentration of deoxyhemoglobin, and hence the \(T_{2}^*\)-dephasing, is as a measure of brain activation, because neural activity is metabolically expensive. The neurovascular unit (i.e. a neuron, astrocyte and capillary) responds to the oxygen consumption (increasing [dHb]) associated with changes in the dendritic polarization of the postsynaptic neuron with dilation of the capillaries (increasing [dHb]) and an increase in blood flow (decreasing [dHb]). As the blood flow effect is the dominant mechanism in neurovascular coupling, the counterintuitive net effect is a decrease in dHb per unit volume of activated tissue. Activated tissue therefore has a higher signal intensity compared to a baseline condition (“rest”) in a \(T_{2}^*\)-weighted image. Although the effect is small (~1-4% compared to the baseline condition), it is reliably measurable when appropriate activation paradigms are used. Without a paradigm, useful information can still be obtained about spatiotemporal correlations in the BOLD signal: the resting-state fMRI method.</p>
<p>In this thesis, the \(T_{2}^*\)-effect is used for anatomical imaging (susceptibility imaging, explained in <a href=phdthesis.html#Sec33>Section 3.3</a>). Brain nuclei and fibre tracts display a range of magnetic susceptibility values as a result of their chemical composition (concentrations of diamagnetic and paramagnetic proteins as well as iron storage and accumulation). The field variations that result from these tissue characteristics in these brain regions can yield exquisite contrast, showing detailed anatomical structures (<a href=phdthesis.html#MK_Ch03_F05_thumb>Figure 3.5c</a>). The method is used in multiple scientific chapters in this thesis and is particularly relevant for <a href=phdthesis.html#Chapter04>Chapter 4</a>.</p>
<h4 class="phdthesis-title" id="Sec314">3.1.4 Some considerations for high field MRI</h4>
<p>Over the past two decades, a steady trend of increasing field strength is evident for both human and animal MR systems. There are a few—very significant—advantages associated with increasing the field strength in MRI, but also numerous challenges. The work presented in this thesis has mostly been performed on MR systems that can be considered high field (i.e. ≥7T). This warrants a discussion of issues that are specifically relevant to high field MRI.</p>
<p>The first consideration is the primary reason to image at high field: signal. The equilibrium magnetization is proportional to the main magnetic field \(\mathbf{B}_0\) (<a href=phdthesis.html#Eq33>Eq 3.3</a>). Going to higher field strength, therefore also increases the signal available after excitation. Theoretically, the signal-to-noise ratio increases linearly with field strength<a href="phdthesis.html#ref089"><sup>89</sup></a>. Evidently, when wanting to image at high resolution, scanning on a high field system is highly beneficial.</p>
<p>The second consideration is that the effect of magnetic susceptibility variations increases with field strength. This is both a curse (susceptibility artefacts increase in severity; see <a href="phdthesis.html#Box31">Box 3.1</a>) and a blessing. The blessing is that this can be used in susceptibility-based imaging methods. For BOLD imaging (<a href=phdthesis.html#Sec3133>Section 3.1.3.3</a>), for example, the contrast between baseline and activation is significantly increased. The same goes for the contrasts between tissue types in anatomical susceptibility imaging (discussed in <a href=phdthesis.html#Sec33>Section 3.3</a>). Therefore, susceptibility and BOLD imaging have an advantage over and above ‘just’ increased signal when performed at high field strength.</p>
<p>This relates to the general finding that the relaxation behaviour of tissues changes with field strength. At high field, the \(T_{1}\) of brain tissue increases<a href="phdthesis.html#ref090"><sup>90</sup></a>. Transverse relaxation constants decrease with field strength. The \(T_{2}\) decrease is linear, while the \(T_{2}'\) decreases nonlinearly<a href="phdthesis.html#ref091"><sup>91</sup></a>. Importantly, this has considerable impact (i.e. rapid signal loss) for sequences that use a long echo time, such as diffusion imaging (<a href=phdthesis.html#Sec32>Section 3.2</a>).</p>
<p>The RF characteristics are also different at high field strength. The RF power required for excitation increases with field strength, although fortunately not with the theoretically expected \(\mathbf{B}_{0}^2\)-dependence<a href="phdthesis.html#ref092"><sup>92</sup></a>. Nevertheless, this limits the range of sequences that can be used at high field—or complicates their implementation, because RF-intensive sequences quickly exceed the specific-absorption-rate (SAR) limits set for MR imaging (3.2 W/kg in the European Union). This is particularly problematic for spin echo sequences that employ many 180° pulses. To reduce SAR in these cases, one can opt for increasing the repetition time or acquire only a specific region-of-interest. The latter option was chosen in <a href=phdthesis.html#Chapter07>Chapter 7</a> for the acquisition of diffusion-weighted data. For gradient echo sequences lacking the 180° pulses, SAR is usually less of a problem at high field, also because of the customary low flip angles used.
<p>Additionally, the RF field is not nearly as homogeneous over the brain as compared to lower field strengths. This \(\mathbf{B}_{1}\)-inhomogeneity arises from the dielectric properties of the brain and is inherent for frequencies above 200 MHz<a href="phdthesis.html#ref093"><sup>93</sup></a>. As the RF pulse wavelength approaches the dimension of the body at high field, destructive interference patterns occur manifesting as a high intensity in the centre of the brain with respect to the periphery<a href="phdthesis.html#ref094"><sup>94</sup></a>. Various approaches have been proposed to ameliorate the effect, including RF shimming<a href="phdthesis.html#ref094"><sup>94</sup></a>, the use of dielectric pads<a href="phdthesis.html#ref095"><sup>95</sup></a> and the use of multiple transmit channels<a href="phdthesis.html#ref096"><sup>96</sup></a><sup>,</sup><a href="phdthesis.html#ref097"><sup>97</sup></a>.</p>
<p>Animal MR systems have smaller bore dimensions compared to clinical scanners. This is of great significance for the system’s performance. A smaller bore means that a homogeneous field can be more easily obtained over the bore in comparison to large-bore systems of the same field strength. The reduced \(\mathbf{B}_{0}\)-inhomogeneity allows scanning at a higher resolution. Alternatively, higher field strengths (7-21T) are customary for these systems, with the standard becoming 9.4T.</p>
<p>A second important advantage of small-bore systems is that much larger gradient fields can be maintained (up to 1-2 T/m). As will be detailed in <a href=phdthesis.html#Sec323>Section 3.2.3</a>, diffusion-weighting gradients are best kept short to avoid signal loss due to \(T_{2}\) decay. Using the powerful gradients in animal systems allows strong diffusion weighting and yet short gradient pulses. Both characteristics of small-bore systems have proven highly beneficial for the work in Chapters <a href=phdthesis.html#Chapter05>5</a> and <a href=phdthesis.html#Chapter06>6</a> of this thesis.</p>
<p>Furthermore, for the small volumes scanned on these animal systems small receive coils are appropriate. The sensitivity of a coil increases with decreasing diameter. In many MR spectroscopy applications the use of microcoils are optimal<a href="phdthesis.html#ref098"><sup>98</sup></a>. Rodent brain MRI uses coils with a diameter on the order of 1 cm. A fairly recent innovation has greatly enhanced the capability of coils of these dimensions. The cryogenic probe, originally proposed by Hoult and Richards (1976)<a href="phdthesis.html#ref099"><sup>99</sup></a>, is a coil that is cooled to low temperatures. The electronics involved in tuning-and-matching, transmit-receive switching and preamplification are cooled as well. The noise owing to random thermal motion of electrons in the system is significantly reduced at these temperatures and the conductivity of the electronics increases. As a result, a considerable gain in SNR can be achieved in comparison to similar room-temperature systems<a href="phdthesis.html#ref100"><sup>100</sup></a>. A cryogenic probe was employed in the work of <a href=phdthesis.html#Chapter06>Chapter 6</a>.</p>
</div>
<h3 class="phdthesis-title" id="Sec32">3.2 Diffusion weighted imaging</h3>
<div class="box">
<p>The image contrasts obtained by probing \(T_{1}\), \(T_{2}\) and \(T_{2}^*\) relaxation processes provide indispensible insight in many processes influencing the molecular environment in the brain. However, it does not provide many clues on the geometric architecture of the tissue. To understand the organization of the brain, the dimensions and arrangement of neurons and supportive cell types is of high importance. Although unable to infer connectivity or geometry of individual cells directly, diffusion weighted imaging (DWI) is an imaging technique unequalled in its capability to probe tissue microstructure in the living human brain.</p>
<p>The applications of DWI are many. It is the clinical workhorse of stroke imaging. Immediately at the onset of cerebral infarction the oedematous tissue has a hyperintense appearance in the diffusion weighted image. As fast detection and characterization is of utmost importance for treatment decisions, the value of diffusion imaging cannot be understated. In research, diffusion imaging is best known for distinguishing between fibre tracts in the white matter. As the only available technique to infer anatomical connectivity between regions in the human brain in vivo, DWI may be regarded as one of the primary investigative tools in cognitive neuroscience. A relatively young and upcoming branch of diffusion MRI methods is microstructure imaging. It aims to provide an accurate quantification of a diversity of microstructural tissue parameters. Although the basic principles and first (ex vivo) experimental results have been reported more than two decades ago, advances in MR (gradient) systems, pulse sequences and tissue models have brought this field into the realm of the living human brain.</p>
<h4 class="phdthesis-title" id="Sec321">3.2.1 Physics of diffusion</h4>
<p>In the aqueous environment of the brain protons are far from static. The water molecules containing most of the protons constantly move about in a random walk. This random walk of particles is known as Brownian motion (or self-diffusion, in contrast to diffusion in the presence of a concentration gradient). In an isotropic medium, the particle displacement can be statistically described by the diffusion coefficient \(D\) through the Einstein relation </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[D = {1 \over 6\tau} \langle {\mathbf{R}^{T}\mathbf{R}} \rangle\]</td>
<td class="EqNo" id="Eq325">3.25</td>
</tr>
</table>
<p>where \(\tau\) is the diffusion time and \(\mathbf{R}=\mathbf{r}-\mathbf{r}_0\) is the relative particle displacement. \(\langle ... \rangle\) indicates averaging over particles. In 3D, the diffusion coefficient thus relates to the characteristic step length of the random walk </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[l = \sqrt {6 D \tau}\]</td>
<td class="EqNo" id="Eq326">3.26</td>
</tr>
</table>
<p>In terms of the interactions with the environment in a homogeneous medium, the Stokes-Einstein equation applies to diffusion of particles with radius \(r\) </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[D = {{k_{B} T} \over {6 \pi \eta r}}\]</td>
<td class="EqNo" id="Eq327">3.27</td>
</tr>
</table>
<p>where \(k_B\) is Boltzmanns constant, \(T\) is the temperature and \(\eta\) is the viscosity of the medium.</p>
<p>It is instructive to consider the diffusion process in terms of the diffusion propagator \(P\), because the relations above only hold for—as will be elaborately discussed in the following sections—the very limited set of situations where diffusion is Gaussian. The diffusion propagator is the probability distribution of particle displacements in three-dimensional space. Thus, in the context of diffusion MRI it describes the probability of protons traveling from position \(\mathbf{r}_0\) to \(\mathbf{r}\) in a diffusion time \(\tau\). In an isotropic homogeneous medium, the proton displacements follow a Gaussian distribution and an analytic expression can be given for \(P\): </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[P(\mathbf{r}_{0},\mathbf{r}) = {1 \over (4 \pi D \tau)^{3/2}} e^{-{{(\mathbf{r} - \mathbf{r}_{0})^{2}} \over {4 D \tau}}}\]</td>
<td class="EqNo" id="Eq328">3.28</td>
</tr>
</table>
<h4 class="phdthesis-title" id="Sec322">3.2.2 Biophysics of diffusion in the brain</h4>
<p>In the brain, the cerebrospinal fluid in can be considered an isotropic medium and Eqs <a href=phdthesis.html#Eq325>3.25</a>-<a href=phdthesis.html#Eq328>3.28</a> hold. Brain parenchyma, however, is far from homogeneous. It consists of neurons and glia of all shapes and sizes. The macromolecular components that compose these cells form barriers to diffusion. Protons therefore diffuse with an apparent diffusion coefficient (ADC). Not only do the cells slow down diffusion as in a viscous isotropic medium, some components of the cell form impassable barriers to the protons. In particular, the lipid bilayer of the cell membrane that separates the cell’s interior from the exterior can be an impenetrable boundary to diffusion. The neuronal membrane, for example, is almost impermeable to water. The water permeability of the astrocytic membrane, on the other hand, is orders of magnitude larger due to aquaporins in the lipid bilayer<a href="phdthesis.html#ref101"><sup>101</sup></a>. Because the composition and geometry of the intra- and extracellular space differ qualitatively, the diffusion characteristics of these spaces are very dissimilar. For many applications, this warrants separate discussion of intra- and extracellular diffusion.</p>
<a href="phdthesisfiles/Ch03/MK_Ch03_F06.png" title="MK_Ch03_F06_thumb" id="MK_Ch03_F06_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch03/MK_Ch03_F06_thumb.jpg" alt="MK_Ch03_F06_thumb.jpg"/></a>
<p class="FigCaption">Figure 3.6. Schematics of myelinated axons in cross-section with random walks of three protons in the extracellular space (orange, green & blue) and one intra-axonally (magenta; in axon B). a) perpendicular cross-section illustrates the tortuous paths taken around axon A (image courtesy of Karla Miller); b) anisotropic diffusion along the length of the axons.</p>
<h5 class="phdthesis-title" id="Sec3221">3.2.2.1 Diffusivity in the intra- and extracellular space</h5>
<p>Outside the cells, the interstitial fluid is similar in composition to the cerebrospinal fluid, although the macromolecules of the extracellular matrix increase the viscosity<a href="phdthesis.html#ref102"><sup>102</sup></a>. The distance between cells is on the order of 50 nm<a href="phdthesis.html#ref103"><sup>103</sup></a>, while cell body diameters are on the order of 1-100 μm and neuronal processes are an order of magnitude less than that. This geometry results in considerable tortuosity, i.e. protons diffusing around the tightly packed cells appear to move over smaller distances as compared to when they are free to diffuse over any path (see e.g. the green diffusion path moving around axon A in <a href=phdthesis.html#MK_Ch03_F06_thumb>Figure 3.6a</a>). The tortuosity λ relates to the ADC as </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[\lambda^2 = {ADC \over D}\]</td>
<td class="EqNo" id="Eq329">3.29</td>
</tr>
</table>
<p>The tortuosity of brain tissue is approximately 1.6, while the theoretical value given the geometry is 1.23<a href="phdthesis.html#ref102"><sup>102</sup></a>. Because the extracellular space is continuous—at least on the scale of the displacements in the MR diffusion experiment—protons can diffuse to any location within the extracellular space. However, dead-space microdomains that transiently trap protons in concave geometries contribute to the tortuosity<a href="phdthesis.html#ref104"><sup>104</sup></a>. Interactions with macromolecules in the extracellular matrix and on the neuronal membranes might also slow down protons and increase the viscosity<a href="phdthesis.html#ref102"><sup>102</sup></a>. Nevertheless, the proton displacement distribution of the extracellular space can be approximated reasonably well by a Gaussian diffusion propagator irrespective of the time the protons are diffusing.</p>
<p>The extracellular space accounts for approximately 20% of the volume fraction in adult healthy brain parenchyma<a href="phdthesis.html#ref102"><sup>102</sup></a>. The remaining 80% is occupied by cells. The cytosol within the cells’ interior is aqueous, but cytoskeletal filaments and microtubules prevent free diffusion of protons and results in a fourfold decrease of the diffusion coefficient<a href="phdthesis.html#ref105"><sup>105</sup></a><sup>,</sup><a href="phdthesis.html#ref106"><sup>106</sup></a>. To what extent the Gaussian approximation holds for intracellular diffusion without membrane interactions is unresolved. For cells with an impermeable membrane (i.e. assuming zero exchange with the extracellular compartment on the time scale of the MR diffusion experiment), protons are confined within the cell and the displacement of any proton cannot be larger than the cell’s dimensions (see e.g. the magenta diffusion path inside axon B in <a href=phdthesis.html#MK_Ch03_F06_thumb>Figure 3.6a</a>). Diffusion is said to be restricted. This, of course, has a major implication for the proton displacement distribution: restricted diffusion is non-Gaussian.</p>
<h5 class="phdthesis-title" id="Sec3222">3.2.2.2 Anisotropy</h5>
<p>Neurons have elongated processes. In the extreme case, the neuronal processes can be a meter long in humans. In most locations in the brain, neuronal processes are not oriented randomly, but are structured. They can be organized in bundles, sheets or grids. All these configurations have the consequence that proton diffusion is not equal in all directions, but larger along the long axis of neuronal processes as compared to the short axes: there is diffusion anisotropy (<a href=phdthesis.html#MK_Ch03_F06_thumb>Figure 3.6b</a>).</p>
<p>The anisotropy of diffusion in a hollow cylinder is determined by the ratio of its length and diameter. Assuming cylindrical neuronal processes with a long axis much longer and a diameter smaller than the root-mean-square proton displacement and no exchange with the extracellular compartment, it follows that the intracellular diffusion component is very directionally specific for the orientation of the neuronal process. Diffusion along the long axis of the process may be approximately Gaussian, but diffusion in the perpendicular directions is highly restricted by the cell membrane<a href="phdthesis.html#ref101"><sup>101</sup></a>. Outside of the cylinders, diffusion is also constrained by the cylindrical cell processes, especially when the processes are coherently organized. The anisotropy of the extracellular space depends on geometrical factors such as fibre coherence and packing density.</p>
<h5 class="phdthesis-title" id="Sec3223">3.2.2.3 Diffusion in different tissue types</h5>
<h6 class="phdthesis-title">White matter</h6>
<p>Diffusion anisotropy is most pronounced for the white matter. The white matter is composed of interareal axons, most of which are myelinated. These axons form fibre bundles, grouping together axons that share a destination. In between these axons, oligodendrocytes produce myelin sheets that wrap around the axons in multiple layers. Each oligodendrocyte myelinates a section of multiple axons. The axonal metabolism is low and therefore comparatively few astrocytes and blood vessels reside in the white matter. Within white matter, there is some variability in the diameter, packing density and myelination of the axons, which results in variation in anisotropy over the white matter. Generally, this is the anisotropy that one wants to infer on in DWI.</p>
<a href="phdthesisfiles/Ch03/MK_Ch03_F07.png" title="MK_Ch03_F07_thumb" id="MK_Ch03_F07_thumb" target="_blank" class="FigThumb"><img class="FigThumb" src="phdthesisfiles/Ch03/MK_Ch03_F07_thumb.jpg" alt="MK_Ch03_F07_thumb.jpg"/></a>
<p class="FigCaption">Figure 3.7. Schematic fibre configurations encountered in the white matter: a) linear; b) bending; c) fanning; d) crossing; e) kissing; and f) the cortical grey matter: tangential view.</p>
<p>A different source of variability in anisotropy is the fibre configuration (<a href=phdthesis.html#MK_Ch03_F07_thumb>Figure 3.7</a>). In general, fibres do not all share the same orientation within the voxel volume. A multitude of configurations is possible. What still might be considered a true source of variability in anisotropy (i.e. that persists when measured at the cellular scale) is the interdigitation of fibres of bundles with different orientations: the quintessential fibre crossing (<a href=phdthesis.html#MK_Ch03_F07_thumb>Figure 3.7d</a>). The grid that axons of two interdigitating bundles weave dictates that the proton displacement shows two peaks in the directions along the bundles. However, the peak proton displacement is much reduced in comparison to diffusion along a single coherent bundle (<a href=phdthesis.html#MK_Ch03_F07_thumb>Figure 3.7a</a>). Protons in the extracellular space that have the largest displacement along one of the fibre bundles, will have encountered many perpendicular axons of the other bundle on their path. Other configurations for which anisotropy is expected to persist microscopically are the bending (<a href=phdthesis.html#MK_Ch03_F07_thumb>Figure 3.7b</a>) and fanning (<a href=phdthesis.html#MK_Ch03_F07_thumb>Figure 3.7c</a>) configurations. In this thesis, the fanning configuration—in which a fibre bundle enters a voxel more coherently than it leaves the voxel—is investigated in <a href=phdthesis.html#Chapter06>Chapter 6</a>.</p>
<p>Complex fibre configurations can also arise purely from the limited resolution of the MR measurement. For example, two coherent fibre bundles with different orientations can occupy parts of the same voxel. This configuration shown in <a href=phdthesis.html#MK_Ch03_F07_thumb>Figure 3.7e</a> is termed fibre kissing and results from partial volume. It is a confound in data processing of all MR modalities, including DWI. As the smallest unit of measurement available, an imaging voxel is a black box with regard to the internal distribution of the sources that underlie the signal from within that voxel. Therefore, it cannot be inferred from the DWI measurement alone which of many possible configurations has generated an observed DWI signal. In <a href=phdthesis.html#Chapter04>Chapter 4</a>, a partial solution is presented to distinguish two of these configurations (crossing/kissing) in selective areas of the brain.</p>
<h6 class="phdthesis-title">Grey matter</h6>
<p>The composition of grey matter is very different from white matter. A far larger fraction of the volume is occupied by cell bodies, both neurons and glial cells. The diffusion in and around these cell bodies is nearly isotropic (and can also be restricted inside the cell body). This shift to a larger fraction of isotropic compartments thus results in a low diffusion anisotropy, as only the elongated cellular processes contribute to this. However, the grey matter is not devoid of all neuronal processes. In fact, the axons that form the white matter originate somewhere in grey matter. Additionally, intra-areal (myelinated and unmyelinated) axons provide short range communications within grey matter structures. Dendritic processes are found almost only in grey matter. The orientation of these processes is often highly specific, in particular for the neocortex.</p>
<p>The neocortex is a sheet composed of several layers (see also <a href="phdthesis.html#Box23">Box 2.3</a>). Traditionally, six layers are defined on the basis of cytoarchitecture. The intracortical circuit that is formed through the interaction between these layers is highly typical over the cortical sheet. Therefore, the connections between the layers through the neuronal processes also have a consistent anatomical arrangement. Because the cortex is a layered sheet, the fibres are arranged in a grid-like structure (<a href=phdthesis.html#MK_Ch03_F07_thumb>Figure 3.7f</a>). Fibres radial to the cortical sheet provide communications between the layers and regions, while fibres in the tangential plane of the cortical sheet provide lateral integration. In a simplified model, the radially oriented fibres are 1) axons entering and leaving the cortex for long-distance connectivity; 2) intracortical axons that provide interlaminar communications; 3) apical dendrites of pyramidal neurons ascending to the supragranular layers. The tangential fibres are 1) axon collaterals from long-range connections; 2) intra- and intercolumnar axons for lateral communication; 3) basal dendrites and apical dendritic tufts.</p>
<p>These two orthogonal components of the cortical fibre grid are not homogeneously distributed. As is the case for the cell bodies, the tangential fibres show a laminar pattern where some layers are high in fibre density, while other layers are characterized by low fibre content. For the radial fibres, there is also laminar variability (e.g. in the density and the fibre types) as the layers have specific functions and therefore specific connectivity. For example, the primary motor cortex (M1) sends myelinated fibres to the spinal cord from the voluminous infragranular layers, while thalamic input connections are sparse (the granular layer is virtually absent). Therefore, in M1 has low myelinated fibre content. In primary somatosensory cortex (S1), however, the innervation with myelinated fibres from the thalamus to the granular layer is much larger, leading to a higher myelin content throughout the infragranular and granular layers. Neither is the tangential distribution of radial fibres homogeneous. Rather, fibres co-ascend the cortical layers in small bundles of about 20 axons/dendrites<a href="phdthesis.html#ref078"><sup>78</sup></a>. Whether this influences the diffusion properties in the cortex as observed in DWI is unknown. Furthermore, fibre constituents of the cortex will also vary by cortical region.</p>
<h6 class="phdthesis-title">Ex vivo tissues</h6>
<p>Diffusion imaging has gained popularity because of its ability to measure brain connections in vivo. For some purposes, as will be seen in Chapters <a href=phdthesis.html#Chapter05>5</a> and <a href=phdthesis.html#Chapter06>6</a>, it is highly beneficial to image tissue samples ex vivo. However, after death, autolytic and putrefactic processes start degrading the neuronal membrane. For diffusion imaging, this membrane is the main source of contrast. To avoid tissue degradation, the tissue has to be fixed by a chemical compound, usually formaldehyde. Because autolysis starts immediately after death, it is important to start fixation as soon as possible. The fixation procedure is not without consequence for the tissue characteristics that we aim to measure with diffusion imaging. Apart from inhibiting the growth of moulds and bacteria to counter putrefaction, the fixation compound cross-links proteins of the cytoskeleton and in the extracellular space to inactivate the lysosomal enzymes responsible for autolysis. It thus increases the tissue’s rigidity and decreases the diffusivity. Moreover, tissue fixation can result in changes to the ratio of the intra- and extracellular volume fractions when the fixative solution is not isotonic.</p>
<p>Another consideration in ex vivo diffusion imaging concerns temperature. The diffusion coefficient increases with temperature (<a href=phdthesis.html#Eq327>Eq 3.27</a>). Our brains are maintained at a stable temperature of 37°C. The change to room temperature at which most ex vivo scanning is performed causes a considerable drop in the diffusion coefficient. Fortunately, the decreased diffusivity can be compensated by stronger diffusion sensitization. This is only feasible when using capable hardware (see <a href=phdthesis.html#Sec314>Section 3.1.4</a>).</p>
<p>Relaxation rates also change with tissue fixation<a href="phdthesis.html#ref107"><sup>107</sup></a><sup>,</sup><a href="phdthesis.html#ref108"><sup>108</sup></a>. Most relevant for diffusion imaging, the formaldehyde fixative has a short \(T_2\). Scanning the tissue in the formaldehyde solution is therefore inefficient with regard to signal-to-noise ratio (SNR). The \(T_2\) can be (partially) restored by soaking the sample in phosphate buffered saline (PBS)<a href="phdthesis.html#ref107"><sup>107</sup></a> before scanning. To avoid magnetic field inhomogeneities at the edges of the samples due to susceptibility differences between the fluid and the sample, it is beneficial to immerse the sample in a proton-free susceptibility-matched liquid during scanning.</p>
<h4 class="phdthesis-title" id="Sec323">3.2.3 Diffusion weighting in MRI</h4>
<p>The diffusion of protons in tissue is a given phenomenon. It occurs spontaneously without any external manipulation by the MR system. The MR signal is influenced by the process of diffusion in the presence of magnetic field gradients. This was already realized by Hahn (1950)<a href="phdthesis.html#ref086"><sup>86</sup></a> when he published the spin echo method. He attributed reductions in the spin echo to protons diffusing through local magnetic field inhomogeneities. Carr and Purcell (1954)<a href="phdthesis.html#ref109"><sup>109</sup></a> provided a rigorous mathematical framework for the diffusion effect and also proposed to introduce a magnetic field gradient throughout the spin echo measurement to deliberately sensitize the signal to diffusion. This was followed by the formal description of the effect on magnetization when Torrey (1956)<a href="phdthesis.html#ref110"><sup>110</sup></a> adapted the Bloch equation (<a href=phdthesis.html#Eq37>Eq 3.7</a>) to account for diffusion. The Bloch-Torrey equation (in the laboratory frame of reference) is </p>
<table style="width:100%;">
<colgroup><col style="width:350px"><col style="width:50px"></colgroup>
<tr>
<td class="Eq">\[{d \mathbf M \over dt} = \gamma \mathbf M \times \mathbf B - { \mathbf {M}_x \vec i + \mathbf {M}_y \vec j \over T_2} - {( \mathbf {M}_z - \mathbf {M}_0) \vec k \over T_1} + {\nabla \mathbf{D} \nabla \mathbf{M}}\]</td>
<td class="EqNo" id="Eq330">3.30</td>
</tr>
</table>
<p>In the first three terms on the right-hand side the classic Bloch equation can be recognized. The diffusion tensor D (<a href=phdthesis.html#Sec3241>Section 3.2.4.1</a>) is incorporated in the last term on the right-hand side. For isotropic diffusion, the Bloch-Torrey equation has the solution (in the rotating frame of reference) for the transverse magnetization </p>