Parallel transport for cardiac motion modeling: exploration of relative volume-preserving strategies
Nicolas Guigui  1@  
1 : Inria
Université Côte d'Azur (UCA)

In this talk, I will apply the tools developed in Lorenzi 2014 and Guigui 2021 to the study of the motion of the cardiac right ventricle under pressure or volume overload.
The difficulty of this task lies in the interactions between shape and deformation. The central idea of this work is to filter out these interactions using the parallel transport of deformations to a reference shape, where deformations are considered in the Large Deformations Diffeomorphic Metric Mapping (LDDMM) framework. It appears that parallel transport alone is not sufficient to normalize deformations when large volume differences occur.
We thus propose a normalization procedure for the amplitude of the deformation, and compare it with volume-preserving metrics. After normalization, we use a geodesic regression to represent the full cardiac contraction. The statistical analysis of the parameters of the model reveal insights into the dynamics of each disease.
The method is applied to 3D meshes of the right ventricle extracted from echocardiographic sequences of 314 patients divided into three disease categories and a control group.

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