Novel mathematical modeling approaches to assess ischemic stroke lesion evolution on medical imaging
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.
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