The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function 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. 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. 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.
Individualized computer models of the geometry of the human heart are often based on mag- netic resonance images (MRI) or computed tomography (CT) scans. The stress distribution in the imaged state cannot be measured but needs to be estimated from the segmented geometry, e.g. by an iterative algorithm. As the convergence of this algorithm depends on different geometrical conditions, we system- atically studied their influence. Beside various shape alterations, we investigated the chamber volume, as well as the effect of material parameters. We found a marked influence of passive material parameters: increasing the model stiffness by a factor of ten halved the residual norm in the first iteration. Flat and concave areas led to a reduced robustness and convergence rate of the unloading algorithm. With this study, the geometric effects and modeling aspects governing the unloading algorithm’s convergence are identified and can be used as a basis for further improvement.
Mitral regurgitation alters the flow conditions in the left ventricle. To account for quantitative changes and to investigate the behavior of different flow components, a realistic computational model of the whole human heart was employed in this study. While performing fluid dynamics simulations, a scalar transport equation was solved to analyze vortex formation and ventricular wash-out for different regurgitation severities. Additionally, a particle tracking algorithm was implemented to visualize single components of the blood flow. We confirmed a significantly lowered volume of the direct flow component as well as a higher vorticity in the diseased case.
In order to be used in a clinical context, numerical simulation tools have to strike a balance between accuracy and low computational effort. For re- producing the pumping function of the human heart numerically, the physical domains of cardiac continuum mechanics and fluid dynamics have a significant relevance. In this context, fluid-structure interaction between the heart muscle and the blood flow is particularly important: Myocardial tension development and wall deformation drive the blood flow. However, the degree to which the blood flow has a retrograde effect on the cardiac mechanics in this multi-physics problem remains unclear up to now. To address this question, we implemented a cycle-to-cycle coupling based on a finite element model of a patient-specific whole heart geometry. The deforma- tion of the cardiac wall over one heart cycle was computed using our mechanical simulation framework. A closed loop circulatory system model as part of the simulation delivered the chamber pressures. The displacement of the endo- cardial surfaces and the pressure courses of one cycle were used as boundary conditions for the fluid solver. After solving the Navier-Stokes equations, the relative pressure was extracted for all endocardial wall elements from the three dimensional pressure field. These local pressure deviations were subsequently returned to the next iteration of the continuum mechanical simulation, thus closing the loop of the iterative coupling procedure. Following this sequential coupling approach, we simulated three iterations of mechanic and fluid simulations. To characterize the convergence, we evaluated the time course of the normalized pressure field as well as the euclidean distance between nodes of the mechanic simulation in subsequent iterations. For the left ventricle (LV), the maximal euclidean distance of all endocardial wall nodes was smaller than 2mm between the first and second iteration. The maximal distance between the second and third iteration was 70μm, thus the limit of necessary cycles was already reached after two iterations. In future work, this iterative coupling approach will have to prove its abil- ity to deliver physiologically accurate results also for diseased heart models. Altogether, the sequential coupling approach with its low computational effort delivered promising results for modeling fluid-structure interaction in cardiac simulations.