Tumor ablation due to inhomogeneous anisotropic diffusion in generic three-dimensional topologies

In recent decades computer-aided technologies have become prevalent in medicine, however, cancer drugs are often only tested on in vitro cell lines from biopsies. We derive a full three-dimensional model of inhomogeneous -anisotropic diffusion in a tumor region coupled to a binary population model, which simulates in vivo scenarios faster than traditional cell-line tests. The diffusion tensors are acquired using diffusion tensor magnetic resonance imaging from a patient diagnosed with glioblastoma multiform. Then we numerically simulate the full model with finite element methods and produce drug concentration heat maps, apoptosis hotspots, and dose-response curves. Finally, predictions are made about optimal injection locations and volumes, which are presented in a form that can be employed by doctors and oncologists

Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries

This two-volume set LNCS 12962 and 12963 constitutes the thoroughly refereed proceedings of the 7th International MICCAI Brainlesion Workshop, BrainLes 2021, as well as the RSNA-ASNR-MICCAI Brain Tumor Segmentation (BraTS) Challenge, the Federated Tumor Segmentation (FeTS) Challenge, the Cross-Modality Domain Adaptation (CrossMoDA) Challenge, and the challenge on Quantification of Uncertainties in Biomedical Image Quantification (QUBIQ). These were held jointly at the 23rd Medical Image Computing for Computer Assisted Intervention Conference, MICCAI 2020, in September 2021. The 91 revised papers presented in these volumes were selected form 151 submissions. Due to COVID-19 pandemic the conference was held virtually. This is an open access book

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

High-grade glioma diffusive modeling using statistical tissue information and diffusion tensors extracted from atlases

Summarization: Glioma, especially glioblastoma, is a leading cause of brain cancer fatality involving highly invasive and neoplastic growth. Diffusive models of glioma growth use variations of the diffusion-reaction equation in order to simulate the invasive patterns of glioma cells by approximating the spatiotemporal change of glioma cell concentration. The most advanced diffusive models take into consideration the heterogeneous velocity of glioma in gray and white matter, by using two different discrete diffusion coefficients in these areas. Moreover, by using diffusion tensor imaging (DTI), they simulate the anisotropic migration of glioma cells, which is facilitated along white fibers, assuming diffusion tensors with different diffusion coefficients along each candidate direction of growth. Our study extends this concept by fully exploiting the proportions of white and gray matter extracted by normal brain atlases, rather than discretizing diffusion coefficients. Moreover, the proportions of white and gray matter, as well as the diffusion tensors, are extracted by the respective atlases; thus, no DTI processing is needed. Finally, we applied this novel glioma growth model on real data and the results indicate that prognostication rates can be improved.Presented on: IEEE Transactions on Information Technology in Biomedicin

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal