A monolithic 3D‐0D coupled closed‐loop model of the heart and the vascular system: Experiment‐based parameter estimation for patient‐specific cardiac mechanics

Abstract

A model for patient-specific cardiac mechanics simulation is introduced, incorporating a 3-dimensional finite element model of the ventricular part of the heart, which is coupled to a reduced-order 0-dimensional closed-loop vascular system, heart valve, and atrial chamber model. The ventricles are modeled by a nonlinear orthotropic passive material law. The electrical activation is mimicked by a prescribed parameterized active stress acting along a generic muscle fiber orientation. Our activation function is constructed such that the start of ventricular contraction and relaxation as well as the active stress curve's slope are parameterized. The imaging-based patient-specific ventricular model is prestressed to low end-diastolic pressure to account for the imaged, stressed configuration. Visco-elastic Robin boundary conditions are applied to the heart base and the epicardium to account for the embedding surrounding. We treat the 3D solid-0D fluid interaction as a strongly coupled monolithic problem, which is consistently linearized with respect to 3D solid and 0D fluid model variables to allow for a Newton-type solution procedure. The resulting coupled linear system of equations is solved iteratively in every Newton step using 2 × 2 physics-based block preconditioning. Furthermore, we present novel efficient strategies for calibrating active contractile and vascular resistance parameters to experimental left ventricular pressure and stroke volume data gained in porcine experiments. Two exemplary states of cardiovascular condition are considered, namely, after application of vasodilatory beta blockers (BETA) and after injection of vasoconstrictive phenylephrine (PHEN). The parameter calibration to the specific individual and cardiovascular state at hand is performed using a 2-stage nonlinear multilevel method that uses a low-fidelity heart model to compute a parameter correction for the high-fidelity model optimization problem. We discuss 2 different low-fidelity model choices with respect to their ability to augment the parameter optimization. Because the periodic state conditions on the model (active stress, vascular pressures, and fluxes) are a priori unknown and also dependent on the parameters to be calibrated (and vice versa), we perform parameter calibration and periodic state condition estimation simultaneously. After a couple of heart beats, the calibration algorithm converges to a settled, periodic state because of conservation of blood volume within the closed-loop circulatory system. The proposed model and multilevel calibration method are cost-efficient and allow for an efficient determination of a patient-specific in silico heart model that reproduces physiological observations very well. Such an individual and state accurate model is an important predictive tool in intervention planning, assist device engineering and other medical applications.

Cardiovascular Function and Ballistocardiogram: A Relationship Interpreted via Mathematical Modeling

“…In particular, some works have highlighted the non-negligible effect of the feedback wave within a closed-loop circuit, see e.g. [31][32][33][34]. We have leveraged the knowledge available in the modeling literature to develop a novel closed-loop model for the cardiovascular system that includes sufficient elements to reproduce theoretically the BCG signal and predict changes in the signal associated with specific pathological conditions.…”

The importance of the pericardium for cardiac biomechanics: from physiology to computational modeling

“…The pericardial model we propose is based on [36] and is sketched in figure 3. Using our code it was also already applied to a two-chamber geometry in [37]. It consists of a spring and a dashpot in parallel acting in normal direction to the epicardial surface.…”

“…We thus expect that a global value of k p = 0.1 kPa/mm for pericardial stiffness yields good results for a biventricular geometry with ±60 • fibers. This value was also used in [37], although it was not really analyzed there, e.g. with respect to MRI.…”

Kinematic boundary conditions substantially impact in silico ventricular function

“…Despite the wide range of (bi) ventricular modeling studies found in literature, no consistent approach in incorporating the effect of external tissue support into these models could be found (we considered a non‐exhaustive subset of (bi) ventricular modeling studies (published over the last decade) where generic kinematic BCs were used:). Overall, most studies adopted the practice to apply Neumann BCs on the endocardial surface and to constrain basal out‐of‐plane motion by constraining the basal nodes not to move along the basal surface's normal direction (be it using an exact or penalty‐method based Dirichlet BC).…”

“…These epicardial BCs range from constraining the epicardium not to move along the surface normal 22 or in the circumferential direction 37 to elastic constraints, 40,46 viscoelastic constraints, 22 or both elastic and viscoelastic constraints (Robin-type BCs). 42 A few studies also constrained the movement of the apex, in all directions 15,23,43 or only in the lateral directions. 19 Table 1 gives an overview of the variety in BCs we found in the studies considered.…”