The mathematical models to the reconstruction of cardiac muscle fiber architecture in
biventricular geometries and the development of a 3D cardiac electromechanical
(EM) model coupled with a 0D closed-loop model for the cardiovascular system.
Here is an overview of the mathematical models discussed in the document:
1. Fiber Generation Methods: The document
outlines the methods used to reconstruct the cardiac muscle fiber architecture
in biventricular geometries. Specifically, Laplace-Dirichlet-Rule-Based-Methods
(LDRBMs) are employed to generate realistic fiber orientations within the
heart. These methods involve solving Laplace boundary-value problems to
determine the orientation of myocardial fibers based on boundary conditions on
the heart's surfaces.
2. 3D Cardiac EM Model: The document presents
a detailed 3D cardiac electromechanical model that captures the biophysical
processes involved in heart function. This model integrates aspects of
electrophysiology, active contraction of cardiomyocytes, tissue mechanics, and
blood circulation within the heart chambers. By considering these components,
the model can simulate the electromechanical behavior of the heart in a
comprehensive manner.
3. 0D Closed-Loop Model: In addition to the 3D
cardiac EM model, the document discusses the incorporation of a 0D closed-loop
model for the cardiovascular system. This model represents the hemodynamics of
the entire circulatory system using lumped parameters to simulate blood flow
dynamics, pressure-volume relationships, and systemic interactions. The
coupling of the 3D EM model with the 0D closed-loop model enables a holistic
simulation of the heart's electromechanical activity in the context of
circulatory dynamics.
4. Numerical Approximation: The document also
covers the numerical discretization strategies employed to solve the coupled
3D-0D model. This includes space and time discretizations using the Finite
Element Method (FEM) with different mesh resolutions to handle the varying
scales of electromechanical and hemodynamic processes. The
Segregated-Intergrid-Staggered (SIS) approach is utilized to sequentially solve
the core models contributing to cardiac EM and blood circulation.
Overall, the mathematical models presented in the
document provide a framework for simulating biventricular electromechanics and
studying the complex interactions between the heart and the circulatory system.
These models enable researchers to investigate cardiac function,
electromechanical behavior, and hemodynamic responses in a comprehensive and
integrated manner.
Piersanti, R., Regazzoni, F.,
Salvador, M., Corno, A. F., Dede', L., Vergara, C., & Quarteroni, A.
(2021). 3D-0D closed-loop model for the simulation of cardiac biventricular
electromechanics. *arXiv preprint arXiv:2108.01907*.
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