Reduced left ventricular dynamics modeling based on a cylindrical assumption

Abstract

Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full‐order finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, for example, for pre‐calibration of full‐order models, fast predictions, real‐time applications, and so forth. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of Guccione, McCulloch, & Waldman (1991); Guccione, Waldman, & McCulloch (1993), albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open‐loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel aswell, with consistent spatial (finite element) and time discretizations. Finally, we analyze the sensitivity of the model response to various numerical and physical parameters, and study its physiological response.

A biomechanics-based parametrized cardiac end-diastolic pressure–volume relationship for accurate patient-specific calibration and estimation

“…The second limitation concerns the model used here, in particular due to the spherical approximation made for the geometry in order to avoid the complexity of a 3D model. Other types of reduced models—such as those proposed in 15 , 16 —could be considered to verify that our findings are not significantly impacted. A 3D computational model could also be employed and calibrated as in 6 against the data of Klotz et al, albeit it is well-known that 3D models are very sensitive to the specific design of their artificial boundary conditions where the geometric model is truncated, and therefore would not necessarily produce more trustworthy EDPVRs in practice.…”