A mathematical model for active contraction in healthy and failing myocytes and left ventricles

Effect of biomaterial stiffness on cardiac mechanics in a biventricular infarcted rat heart model with microstructural representation of in situ intramyocardial injectate

Intramyocardial delivery of biomaterials is a promising concept for treating myocardial infarction. The delivered biomaterial provides mechanical support and attenuates wall thinning and elevated wall stress in the infarct region. This study aimed at developing a biventricular finite element model of an infarcted rat heart with a microstructural representation of an in situ biomaterial injectate, and a parametric investigation of the effect of the injectate stiffness on the cardiac mechanics. A three-dimensional subject-specific biventricular finite element model of a rat heart with left ventricular infarct and microstructurally dispersed biomaterial delivered 1 week after infarct induction was developed from ex vivo microcomputed tomography data. The volumetric mesh density varied between 303 mm-3 in the myocardium and 3852 mm-3 in the injectate region due to the microstructural intramyocardial dispersion. Parametric simulations were conducted with the injectate's elastic modulus varying from 4.1 to 405,900 kPa, and myocardial and injectate strains were recorded. With increasing injectate stiffness, the end-diastolic median myocardial fibre and cross-fibre strain decreased in magnitude from 3.6% to 1.1% and from -6.0% to -2.9%, respectively. At end-systole, the myocardial fibre and cross-fibre strain decreased in magnitude from -20.4% to -11.8% and from 6.5% to 4.6%, respectively. In the injectate, the maximum and minimum principal strains decreased in magnitude from 5.4% to 0.001% and from -5.4% to -0.001%, respectively, at end-diastole and from 38.5% to 0.06% and from -39.0% to -0.06%, respectively, at end-systole. With the microstructural injectate geometry, the developed subject-specific cardiac finite element model offers potential for extension to cellular injectates and in silico studies of mechanotransduction and therapeutic signalling in the infarcted heart with an infarct animal model extensively used in preclinical research.

Estimation of left ventricular parameters based on deep learning method

Estimating material properties of personalized human left ventricular (LV) modelling is a central problem in biomechanical studies. In this work we use deep learning (DL) method to evaluating the passive myocardial mechanical properties inversely. In the first part of the paper, we establish a standardized geometric model of the LV. The geometric model parameters are optimized based on 27 different healthy volunteers. In the second part, we use statistical methods and Latin hypercube sampling (LHS) to obtain the geometric parameters data. The LV myocardium is described using a structure-based orthotropic Holzapfel-Ogden constitutive law. The LV diastolic pressure-volume (PV) curves are calculated by numerical simulation. Tn the third part, we establish the multiple neural networks to pblackict PV curve parameters. Then, instead of using constrained optimization problems to solve constitutive parameters, DL was used to establish the nonlinear mapping relationship of geometric parameters, PV curve parameters and constitutive parameters. The results show that the deep learning method can greatly improve the computational efficiency of numerical simulation and increase the possibility of its application in rapid feedback of clinical data.

Simulation of action potential propagation based on the ghost structure method

In this paper, a ghost structure (GS) method is proposed to simulate the monodomain model in irregular computational domains using finite difference without regenerating body-fitted grids. In order to verify the validity of the GS method, it is first used to solve the Fitzhugh-Nagumo monodomain model in rectangular and circular regions at different states (the stationary and moving states). Then, the GS method is used to simulate the propagation of the action potential (AP) in transverse and longitudinal sections of a healthy human heart, and with left bundle branch block (LBBB). Finally, we analyze the AP and calcium concentration under healthy and LBBB conditions. Our numerical results show that the GS method can accurately simulate AP propagation with different computational domains either stationary or moving, and we also find that LBBB will cause the left ventricle to contract later than the right ventricle, which in turn affects synchronized contraction of the two ventricles.

A geometric model for the human pulmonary valve in its fully open case

The human pulmonary valve, one of the key cardiac structures, plays an important role in circulatory system. However, there are few mathematical models to accurately simulate it. In this paper, we establish a geometric model of the normal human pulmonary valve from a mathematical perspective in the fully opening case. Based on the statistical data of the human pulmonary valves, we assume that the motions of the three cusps are symmetrical in the cardiac cycle. Thus, we first propose that each cusp is a part of the cylindrical shell according to its structure and physiological feature. The parameters for the pulmonary valve cusps in three-dimensional space are obtained by the fitting functions. We verify the accuracy of our results by comparing the areas of the pulmonary valve and pulmonary valve flap.

Sensitivity analysis revealing the effect of modulating ionic mechanisms on calcium dynamics in simulated human heart failure

Abnormal intracellular Ca²⁺ handling is the major contributor to the depressed cardiac contractility observed in heart failure. The electrophysiological remodeling associated with this pathology alters both the action potential and the Ca²⁺ dynamics, leading to a defective excitation-contraction coupling that ends in mechanical dysfunction. The importance of maintaining a correct intracellular Ca²⁺ concentration requires a better understanding of its regulation by ionic mechanisms. To study the electrical activity and ionic homeostasis of failing myocytes, a modified version of the O’Hara et al. human action potential model was used, including electrophysiological remodeling. The impact of the main ionic transport mechanisms was analyzed using single-parameter sensitivity analyses, the first of which explored the modulation of electrophysiological characteristics related to Ca²⁺ exerted by the remodeled parameters. The second sensitivity analysis compared the potential consequences of modulating individual channel conductivities, as one of the main effects of potential drugs, on Ca²⁺ dynamic properties under both normal conditions and in heart failure. The first analysis revealed the important contribution of the sarcoplasmic reticulum Ca²⁺-ATPase (SERCA) dysfunction to the altered Ca²⁺ homeostasis, with the Na⁺/Ca²⁺ exchanger (NCX) and other Ca²⁺ cycling proteins also playing a significant role. Our results highlight the importance of improving the SR uptake function to increase Ca²⁺ content and restore Ca²⁺ homeostasis and contractility. The second sensitivity analysis highlights the different response of the failing myocyte versus the healthy myocyte to potential pharmacological actions on single channels. The result of modifying the conductances of the remodeled proteins such as SERCA and NCX in heart failure has less impact on Ca²⁺ modulation. These differences should be taken into account when designing drug therapies.