PhD thesis

My PhD was completed at the University of Edinburgh (Edinburgh, UK), where my supervisors were Mark Bastin (Medical Physics) and Amos Storkey (Informatics). I also spent a very humid three months at Brown University (Providence, RI, USA) in the summer of 2006, where I worked in David Laidlaw’s group.

The entire thesis is available as a large pdf file (14,364 KiB), or chapter-by-chapter in smaller files (see below).

Tractography graphic


J.D. Clayden (2008). Comparative analysis of connection and disconnection in the human brain using diffusion MRI: New methods and applications. PhD thesis, University of Edinburgh.


Diffusion magnetic resonance imaging (dMRI) is a technique that can be used to examine the diffusion characteristics of water in the living brain. A recently developed application of this technique is “tractography”, in which information from brain images obtained using dMRI is used to reconstruct the pathways which connect regions of the brain together. Proxy measures for the integrity, or coherence, of these pathways have also been defined using dMRI-derived information.

The “disconnection hypothesis” suggests that specific neurological impairments can arise from damage to these pathways as a consequence of the resulting interruption of information flow between relevant areas of cortex. The development of dMRI and tractography have generated a considerable amount of renewed interest in the disconnectionist thesis, since they promise a means for testing the hypothesis in vivo in any number of pathological scenarios. However, in order to investigate the effects of pathology on particular pathways, it is necessary to be able to reliably locate them in three-dimensional dMRI images.

The aim of the work described in this thesis is to improve upon the robustness of existing methods for segmenting specific white matter “tracts” from image data, using tractography, and to demonstrate the utility of the novel methods for the comparative analysis of white matter integrity in groups of subjects.

The thesis begins with an overview of probability theory, which will be a recurring theme throughout what follows, and its application to machine learning. After reviewing the principles of magnetic resonance in general, and dMRI and tractography in particular, we then describe existing methods for segmenting particular tracts from group data, and introduce a novel approach. Our innovation is to use a reference tract to define the topological characteristics of the tract of interest, and then search a group of “candidate” tracts in the target brain volume for the best match to this reference. In order to assess how well two tracts match we define a heuristic but quantitative tract similarity measure.

In later chapters we demonstrate that this method is capable of successfully segmenting tracts of interest in both young and old, healthy and unhealthy brains; and then describe a formalised version of the approach which uses machine learning methods to match tracts from different subjects. In this case the similarity between tracts is represented as a matching probability under an explicit model of topological variability between equivalent tracts in different brains. Finally, we examine the possibility of comparing the integrity of groups of white matter structures at a level more fine-grained than a whole tract.


  1. Introduction [pdf (812 KiB)]
    • Problem statement
  2. Probability and machine learning principles [pdf (404 KiB)]
    • Fundamentals of probability theory
    • Probability distributions
    • Inference and learning
    • Maximum likelihood
    • Expectation–Maximisation
    • Sampling methods
      • Rejection sampling
      • Markov chain Monte Carlo
    • Summary
  3. Magnetisation, excitation and relaxation [pdf (808 KiB)]
    • State and spin
    • Protons in a magnetic field
    • The NMR signal
    • Pulse sequences
    • On ghosts and pile-ups
    • Summary
  4. Diffusion magnetic resonance imaging [pdf (788 KiB)]
    • The Einstein picture
    • Diffusion tensor imaging
    • A more general displacement distribution
    • The role of registration
    • Diffusion MRI in the clinic
    • Summary
  5. White matter fibre tracking [pdf (5848 KiB)]
    • Streamlines
    • Fast marching
    • High angular resolution methods
      • Using q-space
      • Spherical deconvolution
    • Applications and challenges
    • Summary
  6. Neighbourhood tractography [pdf (2696 KiB)]
    • Group comparison in white matter
    • Tract-specific comparison
    • Similarity and matching
      • The reduced tract
      • A similarity measure
    • Validation and application
    • How many seeds?
    • Evaluation of the similarity measure
    • The next step
  7. Applications [pdf (1080 KiB)]
    • Tractography in the ageing brain
    • Old versus young
    • Improving the reference tracts
    • A schizophrenia study
    • Conclusions
  8. Model-based tract matching [pdf (2520 KiB)]
    • B-splines
    • Tract representation revisited
    • Comparing spline tracts
    • Training and using the model
    • Advantages and limitations
    • An unsupervised approach
    • Conclusions
  9. Anisotropy profiling [pdf (328 KiB)]
    • A single profile
    • The median tube
    • Intersubject tube alignment
    • Comparative profiling
    • Discussion
  10. Conclusions [pdf (92 KiB)]
    • Tract segmentation
    • Comparative analysis
    • Final remarks
  11. Appendices and bibliography [pdf (180 KiB)]