Conference Agenda

Patient-specific cardiac simulations require the calibration of physical model parameters from measurements of the patient's physiology. Parameter estimation in the heart has been conducted so far using measurements in the myocardium, typically displacement surrogates obtained from MRI. To the best of the authors' knowledge, parameter estimation in cardiac mechanics using velocity images of the ventricular blood flow has remained unexplored. This study assesses the use of Eulerian volumetric velocity images of the ventricular blood flow for estimating material properties of a physiological fully-dimensional fluid–structure interaction (FSI) model of the systolic phase of the heart contraction.
The myocardium is modeled as a hyperelastic material using the standard Holzapfel-Ogden constitutive model with an active contribution to the stress, accounting the contraction of the heart. A fractional step scheme is used to simulate the blood flow efficiently, splitting the Navier–Stokes equations governing the fluid into a tentative velocity step and a projection step to be solved for the fluid pressure. Writing the problem in the Arbitrary Lagrange–Eulerian formalism avoids remeshing the deforming fluid domain at every timestep. In the FSI algorithm, the solid and the fluid problems are coupled in a semi-implicit fashion. In particular, the fluid mesh update and the velocity step are carried out explicitly, depending on the solid displacement of the previous timestep. The fluid's projection step is coupled implicitly to the solid problem, which gives rise to a nonlinear problem, solved with a Krylov–Newton method.
The study considers the left and right ventricles extracted from medical images of a patient. Valve dynamics are not included, as the semilunar valves are considered wide open and the atrioventricular valves closed during systole.
Synthetic measurements of both the solid displacement and the fluid velocity are generated by computing a solution of the FSI problem with fixed ground truth parameters, subsampling the solution in time and adding noise at levels typical for medical images.
The cardiac mechanics model parameters estimated from these measurements are (a) the myocardial tissue contractility, controlling the active contraction, and (b) the epicardial stiffness, characterizing the epicardial wall boundary condition by accounting for the external tissue support. Sequential data assimilation, namely a reduced-order unscented Kalman filter, is employed to estimate the parameters from (i) solid displacement measurements only, (ii) fluid velocity measurements only, or (iii) a combination of both.
Our findings indicate that the accuracy of the estimated parameters with respect to the ground truth strongly depends on the temporal resolution of the data, with only high resolution data allowing for accurate parameter estimates. Using combined fluid and solid measurements reduces the sensitivity of the estimation to measurement noise. The contractility estimation result is closest to the ground truth when using fluid measurements only, whereas the epicardial stiffness is recovered more accurately when using only solid measurements.

Accurate estimation of electrophysiological parameters is crucial for understanding and modeling the dynamic behavior of cardiac tissues across the cardiac cycle, which includes phases of depolarization, repolarization, and refractory periods. These phases underpin the generation and propagation of action potentials that coordinate rhythmic contractions of the heart. In this study, we propose a robust parameter estimation framework based on Differential Evolution (DE) to infer hidden parameters of nonlinear cardiac models. DE, a population-based global optimization algorithm, is particularly suited for handling the nonlinearity and high dimensionality inherent in biological systems. We first demonstrate the effectiveness of DE using the Van der Pol oscillator, a simplified excitable system that mimics the cyclical behavior of cardiac cells. Building on this foundation, we apply our method to more detailed and physiologically relevant models, including the FitzHugh-Nagumo model, which captures essential features of excitability and recovery in cardiac membranes, and the O'Hara-Rudy (ORd) model, which represents detailed ion channel kinetics, intracellular calcium handling, and membrane potential dynamics in human ventricular myocytes. These models are critical for simulating normal and pathological conditions such as early afterdepolarizations, arrhythmias, and conduction blocks. Our results show that DE can accurately recover key parameters even in the presence of sparse or noisy measurements. This highlights DE's value as a powerful tool for inverse modeling in computational cardiology, enabling deeper insight into the mechanisms of cardiac excitability, arrhythmogenesis, and potential therapeutic interventions.

In computational biomedicine, model geometry generation is commonly based on images, which are typically assumed to be at rest and free from external stimuli. However, biological structures are often in mechanical equilibrium under various forces or transitioning between states, necessitating a more dynamic modeling approach. We present a framework that extends the classical formulation of stress-free geometry computation, known as the inverse elasticity problem (IEP), to fully nonlinear poroelastic media. Our approach involves expressing the governing equations in terms of the reference porosity and defining a time-dependent problem where the steady-state solution corresponds to the reference porosity. We introduce Anderson acceleration as a means to significantly enhance computational speed, achieving up to an 80% reduction in the number of iterations. Furthermore, we identify an inconsistency in the primal formulation of the nonlinear mass conservation equations, arising from second-order derivatives of the strain, which we resolve using appropriate mixed formulations.