# name
Time-dependent topological snalysis for cardiovascular disease diagnosis using magnetic resonance

# metadata.dc.description[].value
Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023.  Director: Carles Casacuberta i Polyxeni Gkontra

# metadata.dc.description.abstract[].value
[en] The present research project aims to study the topology of time varying Cardiovascular Magnetic Resonance images (CMR) for disease diagnosis. CMR is a non-invasive technique that involves the acquisition of multiple 3D images at different cardiac phases throughout the cardiac cycle. Nonetheless, conventional assessment of CMR images typically involves the quantification of parameters related to the volumes, and more recently to the shape
and texture by means of radiomics (Raisi-Estabragh, 2020), of the cardiac chambers at only two static time-point points: the end-systole and the enddiastole. Therefore, potentially rich information regarding the cardiac function and structure from other phases of the cardiac cycle might be lost.
To overcome this limitation, we propose to leverage Topological Data Analysis (TDA) to optimally exploit information from the entire cardiac cycle, by measuring the variation of persistence descriptors. This approach
seems promising since a time series might not exhibit relevant geometrical features in its respective point cloud embedding, but it may rather display topological cyclic patterns and their respective variations that can be captured with the proposed machinery. Subsequently, the novel TDA-based CMR descriptors encompassing the entire cardiac cycle are used to feed supervised machine learning classifiers for cardiovascular disease diagnosis.
A full framework from data gathering, to image processing, mathematical modelling and classifier implementation is presented for this purpose.
The performance of the proposed approach based on TDA features and ML is limited. Nonetheless, the approach could be easily adapted to other diseases and scenario where the integration of ML and TDA could be more
beneficial.

# metadata.dc.rights[].value
cc by-nc-nd (c) Juan David Prada Malagón, 2023

# metadata.dc.title[].value
Time-dependent topological snalysis for cardiovascular disease diagnosis using magnetic resonance