Novel mathematical modeling approaches to assess ischemic stroke lesion evolution on medical imaging
Abstract
Stroke is a major cause of disability and death worldwide. Although different clinical
studies and trials used Magnetic Resonance Imaging (MRI) to examine patterns of
change in different imaging modalities (eg: perfusion and diffusion), we still lack a clear
and definite answer to the question: “How does an acute ischemic stroke lesion grow?”
The inability to distinguish viable and dead tissue in abnormal MR regions in stroke
patients weakens the evidence accumulated to answer this question, and relying on static
snapshots of patient scans to fill in the spatio-temporal gaps by “thinking/guessing” make
it even harder to tackle. Different opposing observations undermine our understanding
of ischemic stroke evolution, especially at the acute stage: viable tissue transiting into
dead tissue may be clear and intuitive, however, “visibly” dead tissue restoring to full
recovery is still unclear.
In this thesis, we search for potential answers to these raised questions from a
novel dynamic modelling perspective that would fill in some of the missing gaps in the
mechanisms of stroke evolution. We divided our thesis into five parts. In the first part,
we give a clinical and imaging background on stroke and state the objectives of this
thesis. In the second part, we summarize and review the literature in stroke and medical
imaging. We specifically spot gaps in the literature mainly related to medical image
analysis methods applied to acute-subacute ischemic stroke. We emphasize studies that
progressed the field and point out what major problems remain. Noticeably, we have
discovered that macroscopic (imaging-based) dynamic models that simulate how stroke
lesion evolves in space and time were completely overlooked: an untapped potential
that may alter and hone our understanding of stroke evolution. Progress in the dynamic
simulation of stroke was absent –if not inexistent.
In the third part, we answer this new call and apply a novel current-based dynamic
model âpreviously applied to compare the evolution of facial characteristics between
Chimpanzees and Bonobos [Durrleman 2010] – to ischemic stroke. This sets a robust
numerical framework and provides us with mathematical tools to fill in the missing
gaps between MR acquisition time points and estimate a four-dimensional evolution
scenario of perfusion and diffusion lesion surfaces. We then detect two characteristics
of patterns of abnormal tissue boundary change: spatial, describing the direction of
change –outward as tissue boundary expands or inward as it contracts–; and kinetic,
describing the intensity (norm) of the speed of contracting and expanding ischemic
regions. Then, we compare intra- and inter-patients estimated patterns of change in
diffusion and perfusion data. Nevertheless, topology change limits this approach: it
cannot handle shapes with different parts that vary in number over time (eg: fragmented
stroke lesions, especially in diffusion scans, which are common).
In the fourth part, we suggest a new mathematical dynamic model to increase
rigor in the imaging-based dynamic modeling field as a whole by overcoming the
topology-change hurdle. Metamorphosis. It morphs one source image into a target one
[Trouvé 2005]. In this manuscript, we extend it into dealing with more than two time-indexed
images. We propose a novel extension of image-to-image metamorphosis into
longitudinal metamorphosis for estimating an evolution scenario of both scattered and
solitary ischemic lesions visible on serial MR. It is worth noting that the spatio-temporal
metamorphosis we developed is a generic model that can be used to examine intensity
and shape changes in time-series imaging and study different brain diseases or disorders.
In the fifth part, we discuss our main findings and investigate future directions to
explore to sharpen our understanding of ischemia evolution patterns.
The following license files are associated with this item: