Sequential Coupling Shows Minor Effects of Fluid Dynamics on Myocardial Deformation in a Realistic Whole-Heart Model

Abstract

Background: The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function in silico to reproduce physiological characteristics and diseases remains challenging. Especially the complex simulation of the blood's hemodynamics and its interaction with the myocardial tissue requires a high accuracy of the underlying computational models and solvers. These demanding aspects make whole-heart fully-coupled simulations computationally highly expensive and call for simpler but still accurate models. While the mechanical deformation during the heart cycle drives the blood flow, less is known about the feedback of the blood flow onto the myocardial tissue.Methods and Results: To solve the fluid-structure interaction problem, we suggest a cycle-to-cycle coupling of the structural deformation and the fluid dynamics. In a first step, the displacement of the endocardial wall in the mechanical simulation serves as a unidirectional boundary condition for the fluid simulation. After a complete heart cycle of fluid simulation, a spatially resolved pressure factor (PF) is extracted and returned to the next iteration of the solid mechanical simulation, closing the loop of the iterative coupling procedure. All simulations were performed on an individualized whole heart geometry. The effect of the sequential coupling was assessed by global measures such as the change in deformation and—as an example of diagnostically relevant information—the particle residence time. The mechanical displacement was up to 2 mm after the first iteration. In the second iteration, the deviation was in the sub-millimeter range, implying that already one iteration of the proposed cycle-to-cycle coupling is sufficient to converge to a coupled limit cycle.Conclusion: Cycle-to-cycle coupling between cardiac mechanics and fluid dynamics can be a promising approach to account for fluid-structure interaction with low computational effort. In an individualized healthy whole-heart model, one iteration sufficed to obtain converged and physiologically plausible results.

Global Sensitivity Analysis of Four Chamber Heart Hemodynamics Using Surrogate Models

“…In this study we create and validate a patient-specific model of blood flow across the four chambers of the heart using and extending the residual-based variational multiscale formulation (RBVMS) [22] of the arbitrary Lagrangian-Eulerian Navier-Stokes-Brinkman equations (ALE-NSB) [23] – [26] . We test the ability of machine learning-based GPEs, which approximate the model and estimate the uncertainty in the approximation, to provide a low-cost surrogate for the full physics-based model.…”

Reliable numerical treatment with Adams and BDF methods for plant virus propagation model by vector with impact of time lag and density

“…The dynamics of non-linear fluid dynamic models may be investigated in the future utilizing the strength of Adams predictor corrector method and BDF method [66][67][68][69].…”

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

“…Most of them focus on some specific feature of the heart function, by surrogating the remaining ones with models of reduced dimensionality: electrophysiology, 13–20 cardiac mechanics and electromechanics 2,21–33 or computational fluid dynamics (CFD) of the blood 4,34–43 . Only few works also consider the interplay between hemodynamics and cardiac mechanics in a fluid–structure interaction (FSI) framework, 44–48 while neglecting or simplifying the electrical processes generating the contraction 49–52 …”

“…4,[34][35][36][37][38][39][40][41][42][43] Only few works also consider the interplay between hemodynamics and cardiac mechanics in a fluid-structure interaction (FSI) framework, [44][45][46][47][48] while neglecting or simplifying the electrical processes generating the contraction. [49][50][51][52] Albeit each of the above-mentioned models can provide meaningful insight into the cardiac function in both healthy and pathological conditions, they often neglect the feedback mechanisms that relate the different components. Conversely, fully integrated models featuring multiphysics coupling of electrophysiology, mechanics and fluid dynamics 12,[53][54][55][56] can provide a very accurate description of the physics of the heart, at the price of a high model complexity and large computational cost.…”