Robust and efficient fixed-point algorithm for the inverse elastostatic problem to identify myocardial passive material parameters and the unloaded reference configuration

Multi-physics simulations reveal hemodynamic impacts of patient-derived fibrosis-related changes in left atrial tissue mechanics

Stroke is a leading cause of death and disability worldwide. Atrial myopathy, including fibrosis, is associated with an increased risk of ischemic stroke, but the mechanisms underlying this association are poorly understood. Fibrosis modifies myocardial structure, impairing electrical propagation and tissue biomechanics, and creating stagnant flow regions where clots could form. Fibrosis can be mapped non-invasively using late gadolinium enhancement magnetic resonance imaging (LGE-MRI). However, fibrosis maps are not currently incorporated into stroke risk calculations or computational electro-mechano-fluidic models. We present multi-physics simulations of left atrial (LA) myocardial motion and hemodynamics using patient-specific anatomies and fibrotic maps from LGE-MRI. We modify tissue stiffness and active tension generation in fibrotic regions and investigate how these changes affect LA flow for different fibrotic burdens. We find that fibrotic regions and, to a lesser extent, non-fibrotic regions experience reduced myocardial strain, resulting in decreased LA emptying fraction consistent with clinical observations. Both fibrotic tissue stiffening and hypocontractility independently reduce LA function, but together, these two alterations cause more pronounced effects than either one alone. Fibrosis significantly alters flow patterns throughout the atrial chamber, and particularly, the filling and emptying jets of the left atrial appendage (LAA). The effects of fibrosis in LA flow are largely captured by the concomitant changes in LA emptying fraction except inside the LAA, where a multi-factorial behavior is observed. This work illustrates how high-fidelity, multi-physics models can be used to study thrombogenesis mechanisms in patient-specific anatomies, shedding light onto the links between atrial fibrosis and ischemic stroke.

Key points

Left atrial (LA) fibrosis is associated with arrhythmogenesis and increased risk of ischemic stroke; its extent and pattern can be quantified on a patient-specific basis using late gadolinium enhancement magnetic resonance imaging.Current stroke risk prediction tools have limited personalization, and their accuracy could be improved by incorporating patient-specific information like fibrotic maps and hemodynamic patterns.We present the first electro-mechano-fluidic multi-physics computational simulations of LA flow, including fibrosis and anatomies from medical imaging. Mechanical changes in fibrotic tissue impair global LA motion, decreasing LA and left atrial appendage (LAA) emptying fractions, especially in subjects with higher fibrosis burdens. Fibrotic-mediated LA motion impairment alters LA and LAA flow near the endocardium and the whole cavity, ultimately leading to more stagnant blood regions in the LAA.

Personalized evaluation of the passive myocardium in ischemic cardiomyopathy via computational modeling using Bayesian optimization

Biomechanics-based patient-specific modeling is a promising approach that has proved invaluable for its clinical potential to assess the adversities caused by ischemic heart disease (IHD). In the present study, we propose a framework to find the passive material properties of the myocardium and the unloaded shape of cardiac ventricles simultaneously in patients diagnosed with ischemic cardiomyopathy (ICM). This was achieved by minimizing the difference between the simulated and the target end-diastolic pressure-volume relationships (EDPVRs) using black-box Bayesian optimization, based on the finite element analysis (FEA). End-diastolic (ED) biventricular geometry and the location of the ischemia were determined from cardiac magnetic resonance (CMR) imaging. We employed our pipeline to model the cardiac ventricles of three patients aged between 57 and 66 years, with and without the inclusion of valves. An excellent agreement between the simulated and the target EDPVRs has been reached. Our results revealed that the incorporation of valvular springs typically leads to lower hyperelastic parameters for both healthy and ischemic myocardium, as well as a higher fiber Green strain in the viable regions compared to models without valvular stiffness. Furthermore, the addition of valve-related effects did not result in significant changes in myofiber stress after optimization. We concluded that more accurate results could be obtained when cardiac valves were considered in modeling ventricles. The present novel and practical methodology paves the way for developing digital twins of ischemic cardiac ventricles, providing a non-invasive assessment for designing optimal personalized therapies in precision medicine.

Differential effects of mechano-electric feedback mechanisms on whole-heart activation, repolarization, and tension

The human heart is subject to highly variable amounts of strain during day-to-day activities and needs to adapt to a wide range of physiological demands. This adaptation is driven by an autoregulatory loop that includes both electrical and the mechanical components. In particular, mechanical forces are known to feed back into the cardiac electrophysiology system, which can result in pro- and anti-arrhythmic effects. Despite the widespread use of computational modelling and simulation for cardiac electrophysiology research, the majority of in silico experiments ignore this mechano-electric feedback entirely due to the high computational cost associated with solving cardiac mechanics. In this study, we therefore use an electromechanically coupled whole-heart model to investigate the differential and combined effects of electromechanical feedback mechanisms with a focus on their physiological relevance during sinus rhythm. In particular, we consider troponin-bound calcium, the effect of deformation on the tissue diffusion tensor, and stretch-activated channels. We found that activation of the myocardium was only significantly affected when including deformation into the diffusion term of the monodomain equation. Repolarization, on the other hand, was influenced by both troponin-bound calcium and stretch-activated channels and resulted in steeper repolarization gradients in the atria. The latter also caused afterdepolarizations in the atria. Due to its central role for tension development, calcium bound to troponin affected stroke volume and pressure. In conclusion, we found that mechano-electric feedback changes activation and repolarization patterns throughout the heart during sinus rhythm and lead to a markedly more heterogeneous electrophysiological substrate. KEY POINTS: The electrophysiological and mechanical function of the heart are tightly interrelated by excitation-contraction coupling (ECC) in the forward direction and mechano-electric feedback (MEF) in the reverse direction. While ECC is considered in many state-of-the-art computational models of cardiac electromechanics, less is known about the effect of different MEF mechanisms. Accounting for calcium bound to troponin increases stroke volume and delays repolarization. Geometry-mediated MEF leads to more heterogeneous activation and repolarization with steeper gradients. Both effects combine in an additive way. Non-selective stretch-activated channels as an additional MEF mechanism lead to heterogeneous diastolic transmembrane voltage, higher developed tension and delayed repolarization or afterdepolarizations in highly stretched parts of the atria. The differential and combined effects of these three MEF mechanisms during sinus rhythm activation in a human four-chamber heart model may have implications for arrhythmogenesis, both in terms of substrate (repolarization gradients) and triggers (ectopy).

Personalized computational electro-mechanics simulations to optimize cardiac resynchronization therapy

In this study, we present a computational framework designed to evaluate virtual scenarios of cardiac resynchronization therapy (CRT) and compare their effectiveness based on relevant clinical biomarkers. Our approach involves electro-mechanical numerical simulations personalized, for patients with left bundle branch block, by means of a calibration obtained using data from Electro-Anatomical Mapping System (EAMS) measures acquired by cardiologists during the CRT procedure, as well as ventricular pressures and volumes, both obtained pre-implantation. We validate the calibration by using EAMS data coming from right pacing conditions. Three patients with fibrosis and three without are considered to explore various conditions. Our virtual scenarios consist of personalized numerical experiments, incorporating different positions of the left electrode along reconstructed epicardial veins; different locations of the right electrode; different ventriculo-ventricular delays. The aim is to offer a comprehensive tool capable of optimizing CRT efficiency for individual patients. We provide preliminary answers on optimal electrode placement and delay, by computing some relevant biomarkers such as d P / d t max , ejection fraction, stroke work. From our numerical experiments, we found that the latest activated segment during sinus rhythm is an effective choice for the non-fibrotic cases for the location of the left electrode. Also, our results showed that the activation of the right electrode before the left one seems to improve the CRT performance for the non-fibrotic cases. Last, we found that the CRT performance seems to improve by positioning the right electrode halfway between the base and the apex. This work is on the line of computational works for the study of CRT and introduces new features in the field, such as the presence of the epicardial veins and the movement of the right electrode. All these studies from the different research groups can in future synergistically flow together in the development of a tool which clinicians could use during the procedure to have quantitative information about the patient's propagation in different scenarios.

Modeling drug transport and absorption in subcutaneous injection of monoclonal antibodies: Impact of tissue deformation, devices, and physiology

The pharmaceutical industry has experienced a remarkable increase in the use of subcutaneous injection of monoclonal antibodies (mAbs), attributed mainly to its advantages in reducing healthcare-related costs and enhancing patient compliance. Despite this growth, there is a limited understanding of how tissue mechanics, physiological parameters, and different injection devices and techniques influence the transport and absorption of the drug. In this work, we propose a high-fidelity computational model to study drug transport and absorption during and after subcutaneous injection of mAbs. Our numerical model includes large-deformation mechanics, fluid flow, drug transport, and blood and lymphatic uptake. Through this computational framework, we analyze the tissue material responses, plume dynamics, and drug absorption. We analyze different devices, injection techniques, and physiological parameters such as BMI, flow rate, and injection depth. Finally, we compare our numerical results against the experimental data from the literature.

Simulating impaired left ventricular-arterial coupling in aging and disease: a systematic review

Aortic stenosis, hypertension, and left ventricular hypertrophy often coexist in the elderly, causing a detrimental mismatch in coupling between the heart and vasculature known as ventricular-vascular (VA) coupling. Impaired left VA coupling, a critical aspect of cardiovascular dysfunction in aging and disease, poses significant challenges for optimal cardiovascular performance. This systematic review aims to assess the impact of simulating and studying this coupling through computational models. By conducting a comprehensive analysis of 34 relevant articles obtained from esteemed databases such as Web of Science, Scopus, and PubMed until July 14, 2022, we explore various modeling techniques and simulation approaches employed to unravel the complex mechanisms underlying this impairment. Our review highlights the essential role of computational models in providing detailed insights beyond clinical observations, enabling a deeper understanding of the cardiovascular system. By elucidating the existing models of the heart (3D, 2D, and 0D), cardiac valves, and blood vessels (3D, 1D, and 0D), as well as discussing mechanical boundary conditions, model parameterization and validation, coupling approaches, computer resources and diverse applications, we establish a comprehensive overview of the field. The descriptions as well as the pros and cons on the choices of different dimensionality in heart, valve, and circulation are provided. Crucially, we emphasize the significance of evaluating heart-vessel interaction in pathological conditions and propose future research directions, such as the development of fully coupled personalized multidimensional models, integration of deep learning techniques, and comprehensive assessment of confounding effects on biomarkers.

Implementing new computational methods for the study of JCT and SC inner wall basement membrane biomechanics and hydrodynamics

PURPOSE

The conventional aqueous outflow pathway, which includes the trabecular meshwork (TM), juxtacanalicular tissue (JCT), and the inner wall endothelium of Schlemm's canal (SC), regulates intraocular pressure (IOP) by controlling the aqueous humor outflow resistance. Despite its importance, our understanding of the biomechanics and hydrodynamics within this region remains limited. Fluid-structure interaction (FSI) offers a way to estimate the biomechanical properties of the JCT and SC under various loading and boundary conditions, providing valuable insights that are beyond the reach of current imaging techniques.

METHODS

In this study, a normal human eye was fixed at a pressure of 7 mm Hg, and two radial wedges of the TM tissues, which included the SC inner wall basement membrane and JCT, were dissected, processed, and imaged using 3D serial block-face scanning electron microscopy (SBF-SEM). Four different sets of images were used to create 3D finite element (FE) models of the JCT and inner wall endothelial cells of SC with their basement membrane. The outer JCT portion was carefully removed as the outflow resistance is not in that region, leaving only the SCE inner wall and a few µm of the tissue, which does contain the resistance. An inverse iterative FE algorithm was then utilized to calculate the unloaded geometry of the JCT/SC complex at an aqueous humor pressure of 0 mm Hg. Then in the model, the intertrabecular spaces, pores, and giant vacuole contents were replaced by aqueous humor, and FSI was employed to pressurize the JCT/SC complex from 0 to 15 mm Hg.

RESULTS

In the JCT/SC complex, the shear stress of the aqueous humor is not evenly distributed. Areas proximal to the inner wall of SC experience larger stresses, reaching up to 10 Pa, while those closer to the JCT undergo lower stresses, approximately 4 Pa. Within this complex, giant vacuoles with or without I-pore behave differently. Those without I-pores experience a more significant strain, around 14%, compared to those with I-pores, where the strain is roughly 9%.

CONCLUSIONS

The distribution of aqueous humor wall shear stress is not uniform within the JCT/SC complex, which may contribute to our understanding of the underlying selective mechanisms in the pathway.

Advancing clinical translation of cardiac biomechanics models: a comprehensive review, applications and future pathways

Cardiac mechanics models are developed to represent a high level of detail, including refined anatomies, accurate cell mechanics models, and platforms to link microscale physiology to whole-organ function. However, cardiac biomechanics models still have limited clinical translation. In this review, we provide a picture of cardiac mechanics models, focusing on their clinical translation. We review the main experimental and clinical data used in cardiac models, as well as the steps followed in the literature to generate anatomical meshes ready for simulations. We describe the main models in active and passive mechanics and the different lumped parameter models to represent the circulatory system. Lastly, we provide a summary of the state-of-the-art in terms of ventricular, atrial, and four-chamber cardiac biomechanics models. We discuss the steps that may facilitate clinical translation of the biomechanics models we describe. A well-established software to simulate cardiac biomechanics is lacking, with all available platforms involving different levels of documentation, learning curves, accessibility, and cost. Furthermore, there is no regulatory framework that clearly outlines the verification and validation requirements a model has to satisfy in order to be reliably used in applications. Finally, better integration with increasingly rich clinical and/or experimental datasets as well as machine learning techniques to reduce computational costs might increase model reliability at feasible resources. Cardiac biomechanics models provide excellent opportunities to be integrated into clinical workflows, but more refinement and careful validation against clinical data are needed to improve their credibility. In addition, in each context of use, model complexity must be balanced with the associated high computational cost of running these models.

Physical model of end-diastolic and end-systolic pressure-volume relationships of a heart

Left ventricular stiffness and contractility, characterized by the end-diastolic pressure-volume relationship (EDPVR) and the end-systolic pressure-volume relationship (ESPVR), are two important indicators of the performance of the human heart. Although much research has been conducted on EDPVR and ESPVR, no model with physically interpretable parameters combining both relationships has been presented, thereby impairing the understanding of cardiac physiology and pathology. Here, we present a model that evaluates both EDPVR and ESPVR with physical interpretations of the parameters in a unified framework. Our physics-based model fits the available experimental data and in silico results very well and outperforms existing models. With prescribed parameters, the new model is used to predict the pressure-volume relationships of the left ventricle. Our model provides a deeper understanding of cardiac mechanics and thus will have applications in cardiac research and clinical medicine.

A biomechanics-based parametrized cardiac end-diastolic pressure-volume relationship for accurate patient-specific calibration and estimation

A simple power law has been proposed in the pioneering work of Klotz et al. (Am J Physiol Heart Circ Physiol 291(1):H403-H412, 2006) to approximate the end-diastolic pressure-volume relationship of the left cardiac ventricle, with limited inter-individual variability provided the volume is adequately normalized. Nevertheless, we use here a biomechanical model to investigate the sources of the remaining data dispersion observed in the normalized space, and we show that variations of the parameters of the biomechanical model realistically account for a substantial part of this dispersion. We therefore propose an alternative law based on the biomechanical model that embeds some intrinsic physical parameters, which directly enables personalization capabilities, and paves the way for related estimation approaches.

A coupling strategy for a first 3D-1D model of the cardiovascular system to study the effects of pulse wave propagation on cardiac function

A key factor governing the mechanical performance of the heart is the bidirectional coupling with the vascular system, where alterations in vascular properties modulate the pulsatile load imposed on the heart. Current models of cardiac electromechanics (EM) use simplified 0D representations of the vascular system when coupling to anatomically accurate 3D EM models is considered. However, these ignore important effects related to pulse wave transmission. Accounting for these effects requires 1D models, but a 3D-1D coupling remains challenging. In this work, we propose a novel, stable strategy to couple a 3D cardiac EM model to a 1D model of blood flow in the largest systemic arteries. For the first time, a personalised coupled 3D-1D model of left ventricle and arterial system is built and used in numerical benchmarks to demonstrate robustness and accuracy of our scheme over a range of time steps. Validation of the coupled model is performed by investigating the coupled system's physiological response to variations in the arterial system affecting pulse wave propagation, comprising aortic stiffening, aortic stenosis or bifurcations causing wave reflections. Our first 3D-1D coupled model is shown to be efficient and robust, with negligible additional computational costs compared to 3D-0D models. We further demonstrate that the calibrated 3D-1D model produces simulated data that match with clinical data under baseline conditions, and that known physiological responses to alterations in vascular resistance and stiffness are correctly replicated. Thus, using our coupled 3D-1D model will be beneficial in modelling studies investigating wave propagation phenomena.