Finite Volume Informed Graph Neural Network for Myocardial Perfusion Simulation

Raoul Sallé de Chou, Matthew Sinclair, Sabrina Lynch, Nan Xiao, Laurent Najman, Irene Vignon-Clementel, Hugues Talbot
Proceedings of The 7nd International Conference on Medical Imaging with Deep Learning, PMLR 250:276-288, 2024.

Abstract

Medical imaging and numerical simulation of partial differential equations (PDEs) representing biophysical processes, have been combined in the past few decades to provide noninvasive diagnostic and treatment prediction tools for various diseases. Most approaches involve solving computationally expensive PDEs, which can hinder their effective deployment in clinical settings. To overcome this limitation, deep learning has emerged as a promising method to accelerate numerical solvers. One challenge persists however in the generalization abilities of these models, given the wide variety of patient morphologies. This study addresses this challenge by introducing a physics-informed graph neural network designed to solve Darcy equations for the simulation of myocardial perfusion. Leveraging a finite volume discretization of the equations as a p̈hysics-informed\"{loss}, our model was successfully trained and tested on a 3D synthetic dataset, namely meshes representing simplified myocardium shapes. Subsequent evaluation on a genuine myocardium mesh, extracted from patient Computed Tomography images, demonstrated promising results and generalized capabilities. Such a fast solver, within a differentiable learning framework will enable to tackle inverse problems based on $\text{H}_2$O-PET perfusion imaging data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v250-chou24a, title = {Finite Volume Informed Graph Neural Network for Myocardial Perfusion Simulation}, author = {de Chou, Raoul Sall\'e and Sinclair, Matthew and Lynch, Sabrina and Xiao, Nan and Najman, Laurent and Vignon-Clementel, Irene and Talbot, Hugues}, booktitle = {Proceedings of The 7nd International Conference on Medical Imaging with Deep Learning}, pages = {276--288}, year = {2024}, editor = {Burgos, Ninon and Petitjean, Caroline and Vakalopoulou, Maria and Christodoulidis, Stergios and Coupe, Pierrick and Delingette, Hervé and Lartizien, Carole and Mateus, Diana}, volume = {250}, series = {Proceedings of Machine Learning Research}, month = {03--05 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v250/main/assets/chou24a/chou24a.pdf}, url = {https://proceedings.mlr.press/v250/chou24a.html}, abstract = {Medical imaging and numerical simulation of partial differential equations (PDEs) representing biophysical processes, have been combined in the past few decades to provide noninvasive diagnostic and treatment prediction tools for various diseases. Most approaches involve solving computationally expensive PDEs, which can hinder their effective deployment in clinical settings. To overcome this limitation, deep learning has emerged as a promising method to accelerate numerical solvers. One challenge persists however in the generalization abilities of these models, given the wide variety of patient morphologies. This study addresses this challenge by introducing a physics-informed graph neural network designed to solve Darcy equations for the simulation of myocardial perfusion. Leveraging a finite volume discretization of the equations as a p̈hysics-informed\"{loss}, our model was successfully trained and tested on a 3D synthetic dataset, namely meshes representing simplified myocardium shapes. Subsequent evaluation on a genuine myocardium mesh, extracted from patient Computed Tomography images, demonstrated promising results and generalized capabilities. Such a fast solver, within a differentiable learning framework will enable to tackle inverse problems based on $\text{H}_2$O-PET perfusion imaging data.} }
Endnote
%0 Conference Paper %T Finite Volume Informed Graph Neural Network for Myocardial Perfusion Simulation %A Raoul Sallé de Chou %A Matthew Sinclair %A Sabrina Lynch %A Nan Xiao %A Laurent Najman %A Irene Vignon-Clementel %A Hugues Talbot %B Proceedings of The 7nd International Conference on Medical Imaging with Deep Learning %C Proceedings of Machine Learning Research %D 2024 %E Ninon Burgos %E Caroline Petitjean %E Maria Vakalopoulou %E Stergios Christodoulidis %E Pierrick Coupe %E Hervé Delingette %E Carole Lartizien %E Diana Mateus %F pmlr-v250-chou24a %I PMLR %P 276--288 %U https://proceedings.mlr.press/v250/chou24a.html %V 250 %X Medical imaging and numerical simulation of partial differential equations (PDEs) representing biophysical processes, have been combined in the past few decades to provide noninvasive diagnostic and treatment prediction tools for various diseases. Most approaches involve solving computationally expensive PDEs, which can hinder their effective deployment in clinical settings. To overcome this limitation, deep learning has emerged as a promising method to accelerate numerical solvers. One challenge persists however in the generalization abilities of these models, given the wide variety of patient morphologies. This study addresses this challenge by introducing a physics-informed graph neural network designed to solve Darcy equations for the simulation of myocardial perfusion. Leveraging a finite volume discretization of the equations as a p̈hysics-informed\"{loss}, our model was successfully trained and tested on a 3D synthetic dataset, namely meshes representing simplified myocardium shapes. Subsequent evaluation on a genuine myocardium mesh, extracted from patient Computed Tomography images, demonstrated promising results and generalized capabilities. Such a fast solver, within a differentiable learning framework will enable to tackle inverse problems based on $\text{H}_2$O-PET perfusion imaging data.
APA
de Chou, R.S., Sinclair, M., Lynch, S., Xiao, N., Najman, L., Vignon-Clementel, I. & Talbot, H.. (2024). Finite Volume Informed Graph Neural Network for Myocardial Perfusion Simulation. Proceedings of The 7nd International Conference on Medical Imaging with Deep Learning, in Proceedings of Machine Learning Research 250:276-288 Available from https://proceedings.mlr.press/v250/chou24a.html.

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