610 research outputs found
Unified Topological Inference for Brain Networks in Temporal Lobe Epilepsy Using the Wasserstein Distance
Persistent homology can extract hidden topological signals present in brain
networks. Persistent homology summarizes the changes of topological structures
over multiple different scales called filtrations. Doing so detect hidden
topological signals that persist over multiple scales. However, a key obstacle
of applying persistent homology to brain network studies has always been the
lack of coherent statistical inference framework. To address this problem, we
present a unified topological inference framework based on the Wasserstein
distance. Our approach has no explicit models and distributional assumptions.
The inference is performed in a completely data driven fashion. The method is
applied to the resting-state functional magnetic resonance images (rs-fMRI) of
the temporal lobe epilepsy patients collected at two different sites:
University of Wisconsin-Madison and the Medical College of Wisconsin. However,
the topological method is robust to variations due to sex and acquisition, and
thus there is no need to account for sex and site as categorical nuisance
covariates. We are able to localize brain regions that contribute the most to
topological differences. We made MATLAB package available at
https://github.com/laplcebeltrami/dynamicTDA that was used to perform all the
analysis in this study
Topological Learning for Brain Networks
This paper proposes a novel topological learning framework that can integrate
networks of different sizes and topology through persistent homology. This is
possible through the introduction of a new topological loss function that
enables such challenging task. The use of the proposed loss function bypasses
the intrinsic computational bottleneck associated with matching networks. We
validate the method in extensive statistical simulations with ground truth to
assess the effectiveness of the topological loss in discriminating networks
with different topology. The method is further applied to a twin brain imaging
study in determining if the brain network is genetically heritable. The
challenge is in overlaying the topologically different functional brain
networks obtained from the resting-state functional MRI (fMRI) onto the
template structural brain network obtained through the diffusion MRI (dMRI)
A persistent homology-based topological loss function for multi-class CNN segmentation of cardiac MRI
With respect to spatial overlap, CNN-based segmentation of short axis
cardiovascular magnetic resonance (CMR) images has achieved a level of
performance consistent with inter observer variation. However, conventional
training procedures frequently depend on pixel-wise loss functions, limiting
optimisation with respect to extended or global features. As a result, inferred
segmentations can lack spatial coherence, including spurious connected
components or holes. Such results are implausible, violating the anticipated
topology of image segments, which is frequently known a priori. Addressing this
challenge, published work has employed persistent homology, constructing
topological loss functions for the evaluation of image segments against an
explicit prior. Building a richer description of segmentation topology by
considering all possible labels and label pairs, we extend these losses to the
task of multi-class segmentation. These topological priors allow us to resolve
all topological errors in a subset of 150 examples from the ACDC short axis CMR
training data set, without sacrificing overlap performance.Comment: To be presented at the STACOM workshop at MICCAI 202
From Mathematics to Medicine: A Practical Primer on Topological Data Analysis (TDA) and the Development of Related Analytic Tools for the Functional Discovery of Latent Structure in fMRI Data
fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent. “Structure” within fMRI data is determined by dynamic fluctuations in spatially distributed signals over time, and TDA is well positioned to help researchers better characterize mass dynamics of the signal by rigorously capturing shape within it. To accurately motivate this idea, we a) survey an established method in TDA (“persistent homology”) to reveal and describe how complex structures can be extracted from data sets generally, and b) describe how persistent homology can be applied specifically to fMRI data. We provide explanations for some of the mathematical underpinnings of TDA (with expository figures), building ideas in the following sequence: a) fMRI researchers can and should use TDA to extract structure from their data; b) this extraction serves an important role in the endeavor of functional discovery, and c) TDA approaches can complement other established approaches toward fMRI analyses (for which we provide examples). We also provide detailed applications of TDA to fMRI data collected using established paradigms, and offer our software pipeline for readers interested in emulating our methods. This working overview is both an inter-disciplinary synthesis of ideas (to draw researchers in TDA and fMRI toward each other) and a detailed description of methods that can motivate collaborative research
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