Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

A Novel non-invasive optical framework for simultaneous analysis of contractility and calcium in single-cell cardiomyocytes

The use of a video method based on the Digital Image Correlation (DIC) algorithm from experimental mechanics to estimate the displacements, strain field, and sarcolemma length in a beating single-cell cardiomyocyte is proposed in this work. The obtained deformation is then correlated with the calcium signal, from calcium imaging where fluorescent dyes sensitive to calcium Ca2+ are used. Our proposed video-based method for simultaneous contraction and intracellular calcium analysis results in a low-cost, non-invasive, and label-free method. This technique has shown great advantages in long-term observations because this type of intervention-free measurement neutralizes the possible alteration in the beating cardiomyocyte introduced by other techniques for measuring cell contractility (e.g., Traction Force Microscopy, Atomic Force Microscopy, Microfabrication or Optical tweezers). Three tests were performed with synthetically augmented data from cardiomyocyte images to validate the robustness of the algorithm. First, a simulated rigid translation of a referenced image is applied, then a rotation, and finally a controlled longitudinal deformation of the referenced image, thus simulating a native realistic deformation. Finally, the proposed framework is evaluated with real experimental data. To validate contraction induced by intracellular calcium concentration, this signal is correlated with a new deformation measure proposed in this article, which is independent of cell orientation in the imaging setup. Finally, based on the displacements obtained by the DIC algorithm, the change in sarcolemma length in a contracting cardiomyocyte is calculated and its temporal correlation with the calcium signal is obtained.

Biomechanical modeling combined with pressure-volume loop analysis to aid surgical planning in patients with complex congenital heart disease

Patients with congenitally corrected transposition of the great arteries (ccTGA) can be treated with a double switch operation (DSO) to restore the normal anatomical connection of the left ventricle (LV) to the systemic circulation and the right ventricle (RV) to the pulmonary circulation. The subpulmonary LV progressively deconditions over time due to its connection to the low pressure pulmonary circulation and needs to be retrained using a surgical pulmonary artery band (PAB) for 6-12 months prior to the DSO. The subsequent clinical follow-up, consisting of invasive cardiac pressure and non-invasive imaging data, evaluates LV preparedness for the DSO. Evaluation using standard clinical techniques has led to unacceptable LV failure rates of ∼15 % after DSO. We propose a computational modeling framework to (1) reconstruct LV and RV pressure-volume (PV) loops from non-simultaneously acquired imaging and pressure data and gather model-derived mechanical indicators of ventricular function; and (2) perform in silico DSO to predict the functional response of the LV when connected to the high-pressure systemic circulation. Clinical datasets of six patients with ccTGA after PAB, consisting of cardiac magnetic resonance imaging (MRI) and right and left heart catheterization, were used to build patient-specific models of LV and RV - MbaselineLV and MbaselineRV. For in silico DSO the models of MbaselineLV and MbaselineRV were used while imposing the afterload of systemic and pulmonary circulations, respectively. Model-derived contractility and Pressure-Volume Area (PVA) - i.e., the sum of stroke work and potential energy - were computed for both ventricles at baseline and after in silico DSO. In silico DSO suggests that three patients would require a substantial augmentation of LV contractility between 54 % and 80 % and an increase in PVA between 38 % and 79 % with respect to the baseline values to accommodate the increased afterload of the systemic circulation. On the contrary, the baseline functional state of the remaining three patients is predicted to be adequate to sustain cardiac output after the DSO. This work demonstrates the vast variation of LV function among patients with ccTGA and emphasizes the importance of a biventricular approach to assess patients' readiness for DSO. Model-derived predictions have the potential to provide additional insights into planning of complex surgical interventions.

A Graph-Based Machine-Learning Approach Combined with Optical Measurements to Understand Beating Dynamics of Cardiomyocytes

The development of computational models for the prediction of cardiac cellular dynamics remains a challenge due to the lack of first-principled mathematical models. We develop a novel machine-learning approach hybridizing physics simulation and graph networks to deliver robust predictions of cardiomyocyte dynamics. Embedded with inductive physical priors, the proposed constraint-based interaction neural projection (CINP) algorithm can uncover hidden physical constraints from sparse image data on a small set of beating cardiac cells and provide robust predictions for heterogenous large-scale cell sets. We also implement an in vitro culture and imaging platform for cellular motion and calcium transient analysis to validate the model. We showcase our model's efficacy by predicting complex organoid cellular behaviors in both in silico and in vitro settings.

A model of mechanical loading of the lungs including gravity and a balancing heterogeneous pleural pressure

Recent years have seen the development of multiple in silico lung models, notably with the aim of improving patient care for pulmonary diseases. These models vary in complexity and typically only consider the implementation of pleural pressure, a depression that keeps the lungs inflated. Gravity, often considered negligible compared to pleural pressure, has been largely overlooked, also due to the complexity of formulating physiological boundary conditions to counterbalance it. However, gravity is known to affect pulmonary functions, such as ventilation. In this study, we incorporated gravity into a recent lung poromechanical model. To do so, in addition to the gravitational body force, we proposed novel boundary conditions consisting in a heterogeneous pleural pressure field constrained to counterbalance gravity to reach global equilibrium of applied forces. We assessed the impact of gravity on the global and local behavior of the model, including the pressure-volume response and porosity field. Our findings reveal that gravity, despite being small, influences lung response. Specifically, the inclusion of gravity in our model led to the emergence of heterogeneities in deformation and stress distribution, compatible with in vivo imaging data. This could provide valuable insights for predicting the progression of certain pulmonary diseases by correlating areas subjected to higher deformation and stresses with disease evolution patterns.

Modeling 3D Cardiac Contraction and Relaxation With Point Cloud Deformation Networks

Global single-valued biomarkers, such as ejection fraction, are widely used in clinical practice to assess cardiac function. However, they only approximate the heart's true 3D deformation process, thus limiting diagnostic accuracy and the understanding of cardiac mechanics. Metrics based on 3D shape have been proposed to alleviate these shortcomings. In this work, we present the Point Cloud Deformation Network (PCD-Net) as a novel geometric deep learning approach for direct modeling of 3D cardiac mechanics of the biventricular anatomy between the extreme ends of the cardiac cycle. Its encoder-decoder architecture combines a low-dimensional latent space with recent advances in point cloud deep learning for effective multi-scale feature learning directly on flexible and memory-efficient point cloud representations of the cardiac anatomy. We first evaluate the PCD-Net's predictive capability for both cardiac contraction and relaxation on a large UK Biobank dataset of over 10,000 subjects and find average Chamfer distances between the predicted and ground truth anatomies below the pixel resolution of the underlying image acquisition. We then show the PCD-Net's ability to capture subpopulation-specific differences in 3D cardiac mechanics between normal and myocardial infarction (MI) subjects and visualize abnormal phenotypes between predicted normal 3D shapes and corresponding observed ones. Finally, we demonstrate that the PCD-Net's learned 3D deformation encodings outperform multiple clinical and machine learning benchmarks by 11% in terms of area under the receiver operating characteristic curve for the tasks of prevalent MI detection and incident MI prediction and by 7% in terms of Harrell's concordance index for MI survival analysis.

Patient-specific closed-loop model of the fontan circulation: Calibration and validation

The Fontan circulation, designed for managing patients with a single functional ventricle, presents challenges in long-term outcomes. Computational methods offer potential solutions, yet their application in cardiology practice remains largely unexplored. Our aim was to assess the ability of a patient-specific, closed-loop, reduced-order blood flow model to simulate pulsatile blood flow in the Fontan circulation. Using one-dimensional models, we simulated the aorta, superior and inferior venae cavae, and right and left pulmonary arteries, while lumping heart chambers and remaining vessels into zero-dimensional models. The model was calibrated with patient-specific haemodynamic data from combined cardiac catheterisation and magnetic resonance exams, using a novel physics-based stepwise methodology involving simpler open-loop models. Testing on a 10-year-old, anesthetised patient, demonstrated the model's capability to replicate pulsatile pressure and flow in the larger vessels and ventricular pressure. Average relative errors in mean pressure and flow were 2.9 % and 3.6 %, with average relative point-to-point errors (RPPE) in pressure and flow at 5.2 % and 16.0 %. Comparing simulation results to measurements, mean aortic pressure and flow values were 50.7 vs. 50.4 mmHg and 41.6 vs. 41.9 ml/s, respectively, while ventricular pressure values were 28.7 vs. 27.4 mmHg. The model accurately described time-varying ventricular volume with a RPPE of 2.9 %, with mean, minimum, and maximum ventricular volume values for simulation results vs. measurements at 59.2 vs. 58.2 ml, 38.0 vs. 37.6 ml, and 76.0 vs. 74.4 ml, respectively. It provided physiologically realistic predictions of haemodynamic changes from pulmonary vasodilation and atrial fenestration opening. The new model and calibration methodology are freely available, offering a platform to virtually investigate the Fontan circulation's response to clinical interventions and explore potential mechanisms of Fontan failure. Future efforts will concentrate on broadening the model's applicability to a wider range of patient populations and clinical scenarios, as well as testing its effectiveness.

Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio-temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high-performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning-based operator approximation, which we refer to as Deep-HyROMnet technique. Our strategy combines a projection-based POD-Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper-reduction techniques employed in reduced-order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient-specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter-dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection-based ROMs, in terms of orders of magnitude of computational speed-up, and to return accurate pressure-volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

Reduced left ventricular dynamics modeling based on a cylindrical assumption

Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full-order finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, for example, for pre-calibration of full-order models, fast predictions, real-time applications, and so forth. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of Guccione, McCulloch, & Waldman (1991); Guccione, Waldman, & McCulloch (1993), albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open-loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel aswell, with consistent spatial (finite element) and time discretizations. Finally, we analyze the sensitivity of the model response to various numerical and physical parameters, and study its physiological response.

Advances in the design, generation, and application of tissue-engineered myocardial equivalents

Due to the limited regenerative ability of cardiomyocytes, the disabling irreversible condition of myocardial failure can only be treated with conservative and temporary therapeutic approaches, not able to repair the damage directly, or with organ transplantation. Among the regenerative strategies, intramyocardial cell injection or intravascular cell infusion should attenuate damage to the myocardium and reduce the risk of heart failure. However, these cell delivery-based therapies suffer from significant drawbacks and have a low success rate. Indeed, cardiac tissue engineering efforts are directed to repair, replace, and regenerate native myocardial tissue function. In a regenerative strategy, biomaterials and biomimetic stimuli play a key role in promoting cell adhesion, proliferation, differentiation, and neo-tissue formation. Thus, appropriate biochemical and biophysical cues should be combined with scaffolds emulating extracellular matrix in order to support cell growth and prompt favorable cardiac microenvironment and tissue regeneration. In this review, we provide an overview of recent developments that occurred in the biomimetic design and fabrication of cardiac scaffolds and patches. Furthermore, we sift in vitro and in situ strategies in several preclinical and clinical applications. Finally, we evaluate the possible use of bioengineered cardiac tissue equivalents as in vitro models for disease studies and drug tests.

The Potential of Deep Learning to Advance Clinical Applications of Computational Biomechanics

When combined with patient information provided by advanced imaging techniques, computational biomechanics can provide detailed patient-specific information about stresses and strains acting on tissues that can be useful in diagnosing and assessing treatments for diseases and injuries. This approach is most advanced in cardiovascular applications but can be applied to other tissues. The challenges for advancing computational biomechanics for real-time patient diagnostics and treatment include errors and missing information in the patient data, the large computational requirements for the numerical solutions to multiscale biomechanical equations, and the uncertainty over boundary conditions and constitutive relations. This review summarizes current efforts to use deep learning to address these challenges and integrate large data sets and computational methods to enable real-time clinical information. Examples are drawn from cardiovascular fluid mechanics, soft-tissue mechanics, and bone biomechanics. The application of deep-learning convolutional neural networks can reduce the time taken to complete image segmentation, and meshing and solution of finite element models, as well as improving the accuracy of inlet and outlet conditions. Such advances are likely to facilitate the adoption of these models to aid in the assessment of the severity of cardiovascular disease and the development of new surgical treatments.

A comprehensive mathematical model for cardiac perfusion

The aim of this paper is to introduce a new mathematical model that simulates myocardial blood perfusion that accounts for multiscale and multiphysics features. Our model incorporates cardiac electrophysiology, active and passive mechanics, hemodynamics, valve modeling, and a multicompartment Darcy model of perfusion. We consider a fully coupled electromechanical model of the left heart that provides input for a fully coupled Navier-Stokes-Darcy Model for myocardial perfusion. The fluid dynamics problem is modeled in a left heart geometry that includes large epicardial coronaries, while the multicompartment Darcy model is set in a biventricular myocardium. Using a realistic and detailed cardiac geometry, our simulations demonstrate the biophysical fidelity of our model in describing cardiac perfusion. Specifically, we successfully validate the model reliability by comparing in-silico coronary flow rates and average myocardial blood flow with clinically established values ranges reported in relevant literature. Additionally, we investigate the impact of a regurgitant aortic valve on myocardial perfusion, and our results indicate a reduction in myocardial perfusion due to blood flow taken away by the left ventricle during diastole. To the best of our knowledge, our work represents the first instance where electromechanics, hemodynamics, and perfusion are integrated into a single computational framework.

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.

GPU accelerated digital twins of the human heart open new routes for cardiovascular research

The recruitment of patients for rare or complex cardiovascular diseases is a bottleneck for clinical trials and digital twins of the human heart have recently been proposed as a viable alternative. In this paper we present an unprecedented cardiovascular computer model which, relying on the latest GPU-acceleration technologies, replicates the full multi-physics dynamics of the human heart within a few hours per heartbeat. This opens the way to extensive simulation campaigns to study the response of synthetic cohorts of patients to cardiovascular disorders, novel prosthetic devices or surgical procedures. As a proof-of-concept we show the results obtained for left bundle branch block disorder and the subsequent cardiac resynchronization obtained by pacemaker implantation. The in-silico results closely match those obtained in clinical practice, confirming the reliability of the method. This innovative approach makes possible a systematic use of digital twins in cardiovascular research, thus reducing the need of real patients with their economical and ethical implications. This study is a major step towards in-silico clinical trials in the era of digital medicine.

lifex-fiber: an open tool for myofibers generation in cardiac computational models

BACKGROUND

Modeling the whole cardiac function involves the solution of several complex multi-physics and multi-scale models that are highly computationally demanding, which call for simpler yet accurate, high-performance computational tools. Despite the efforts made by several research groups, no software for whole-heart fully-coupled cardiac simulations in the scientific community has reached full maturity yet.

RESULTS

In this work we present [Formula: see text]-fiber, an innovative tool for the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, which are the essential building blocks for modeling the electrophysiological, mechanical and electromechanical cardiac function, from single-chamber to whole-heart simulations. [Formula: see text]-fiber is the first publicly released module for cardiac simulations based on [Formula: see text], an open-source, high-performance Finite Element solver for multi-physics, multi-scale and multi-domain problems developed in the framework of the iHEART project, which aims at making in silico experiments easily reproducible and accessible to a wide community of users, including those with a background in medicine or bio-engineering.

CONCLUSIONS

The tool presented in this document is intended to provide the scientific community with a computational tool that incorporates general state of the art models and solvers for simulating the cardiac function within a high-performance framework that exposes a user- and developer-friendly interface. This report comes with an extensive technical and mathematical documentation to welcome new users to the core structure of [Formula: see text]-fiber and to provide them with a possible approach to include the generated cardiac fibers into more sophisticated computational pipelines. In the near future, more modules will be successively published either as pre-compiled binaries for x86-64 Linux systems or as open source software.

Imaging and biophysical modelling of thrombogenic mechanisms in atrial fibrillation and stroke

Atrial fibrillation (AF) underlies almost one third of all ischaemic strokes, with the left atrial appendage (LAA) identified as the primary thromboembolic source. Current stroke risk stratification approaches, such as the CHA₂DS₂-VASc score, rely mostly on clinical comorbidities, rather than thrombogenic mechanisms such as blood stasis, hypercoagulability and endothelial dysfunction-known as Virchow's triad. While detection of AF-related thrombi is possible using established cardiac imaging techniques, such as transoesophageal echocardiography, there is a growing need to reliably assess AF-patient thrombogenicity prior to thrombus formation. Over the past decade, cardiac imaging and image-based biophysical modelling have emerged as powerful tools for reproducing the mechanisms of thrombogenesis. Clinical imaging modalities such as cardiac computed tomography, magnetic resonance and echocardiographic techniques can measure blood flow velocities and identify LA fibrosis (an indicator of endothelial dysfunction), but imaging remains limited in its ability to assess blood coagulation dynamics. In-silico cardiac modelling tools-such as computational fluid dynamics for blood flow, reaction-diffusion-convection equations to mimic the coagulation cascade, and surrogate flow metrics associated with endothelial damage-have grown in prevalence and advanced mechanistic understanding of thrombogenesis. However, neither technique alone can fully elucidate thrombogenicity in AF. In future, combining cardiac imaging with in-silico modelling and integrating machine learning approaches for rapid results directly from imaging data will require development under a rigorous framework of verification and clinical validation, but may pave the way towards enhanced personalised stroke risk stratification in the growing population of AF patients. This Review will focus on the significant progress in these fields.

Modeling signaling pathways in biology with MaBoSS: From one single cell to a dynamic population of heterogeneous interacting cells

As a result of the development of experimental technologies and the accumulation of data, biological and molecular processes can be described as complex networks of signaling pathways. These networks are often directed and signed, where nodes represent entities (genes/proteins) and arrows interactions. They are translated into mathematical models by adding a dynamic layer onto them. Such mathematical models help to understand and interpret non-intuitive experimental observations and to anticipate the response to external interventions such as drug effects on phenotypes. Several frameworks for modeling signaling pathways exist. The choice of the appropriate framework is often driven by the experimental context. In this review, we present MaBoSS, a tool based on Boolean modeling using a continuous time approach, which predicts time-dependent probabilities of entities in different biological contexts. MaBoSS was initially built to model the intracellular signaling in non-interacting homogeneous cell populations. MaBoSS was then adapted to model heterogeneous cell populations (EnsembleMaBoSS) by considering families of models rather than a unique model. To account for more complex questions, MaBoSS was extended to simulate dynamical interacting populations (UPMaBoSS), with a precise spatial distribution (PhysiBoSS). To illustrate all these levels of description, we show how each of these tools can be used with a running example of a simple model of cell fate decisions. Finally, we present practical applications to cancer biology and studies of the immune response.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

The basic heart anatomy and physiology from the cardiologist's perspective: Toward a better understanding of left ventricular mechanics, systolic, and diastolic function

A comprehensive understanding of the cardiac structure-function relationship is essential for proper clinical cardiac imaging. This review summarizes the basic heart anatomy and physiology from the perspective of a heart imager focused on myocardial mechanics. The main issues analyzed are the left ventricular (LV) architecture, the LV myocardial deformation through the cardiac cycle, the LV diastolic function basic parameters and the basic parameters of the LV deformation used in clinical practice for the LV function assessment.

Data-driven computational models of ventricular-arterial hemodynamics in pediatric pulmonary arterial hypertension

Pulmonary arterial hypertension (PAH) is a complex disease involving increased resistance in the pulmonary arteries and subsequent right ventricular (RV) remodeling. Ventricular-arterial interactions are fundamental to PAH pathophysiology but are rarely captured in computational models. It is important to identify metrics that capture and quantify these interactions to inform our understanding of this disease as well as potentially facilitate patient stratification. Towards this end, we developed and calibrated two multi-scale high-resolution closed-loop computational models using open-source software: a high-resolution arterial model implemented using CRIMSON, and a high-resolution ventricular model implemented using FEniCS. Models were constructed with clinical data including non-invasive imaging and invasive hemodynamic measurements from a cohort of pediatric PAH patients. A contribution of this work is the discussion of inconsistencies in anatomical and hemodynamic data routinely acquired in PAH patients. We proposed and implemented strategies to mitigate these inconsistencies, and subsequently use this data to inform and calibrate computational models of the ventricles and large arteries. Computational models based on adjusted clinical data were calibrated until the simulated results for the high-resolution arterial models matched within 10% of adjusted data consisting of pressure and flow, whereas the high-resolution ventricular models were calibrated until simulation results matched adjusted data of volume and pressure waveforms within 10%. A statistical analysis was performed to correlate numerous data-derived and model-derived metrics with clinically assessed disease severity. Several model-derived metrics were strongly correlated with clinically assessed disease severity, suggesting that computational models may aid in assessing PAH severity.

From evidence-based medicine to digital twin technology for predicting ventricular tachycardia in ischaemic cardiomyopathy

Survivors of myocardial infarction are at risk of life-threatening ventricular tachycardias (VTs) later in their lives. Current guidelines for implantable cardioverter defibrillators (ICDs) implantation to prevent VT-related sudden cardiac death is solely based on symptoms and left ventricular ejection fraction. Catheter ablation of scar-related VTs is performed following ICD therapy, reducing VTs, painful shocks, anxiety, depression and worsening heart failure. We postulate that better prediction of the occurrence and circuit of VT, will improve identification of patients at risk for VT and boost preventive ablation, reducing mortality and morbidity. For this purpose, multiple time-evolving aspects of the underlying pathophysiology, including the anatomical substrate, triggers and modulators, should be part of VT prediction models. We envision digital twins as a solution combining clinical expertise with three prediction approaches: evidence-based medicine (clinical practice), data-driven models (data science) and mechanistic models (biomedical engineering). This paper aims to create a mutual understanding between experts in the different fields by providing a comprehensive description of the clinical problem and the three approaches in an understandable manner, leveraging future collaborations and technological innovations for clinical decision support. Moreover, it defines open challenges and gains for digital twin solutions and discusses the potential of hybrid modelling.

How viscous is the beating heart?: Insights from a computational study

Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress-relaxation curves, pressure-volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic.

Altered Aortic Hemodynamics and Relative Pressure in Patients with Dilated Cardiomyopathy

Ventricular-vascular interaction is central in the adaptation to cardiovascular disease. However, cardiomyopathy patients are predominantly monitored using cardiac biomarkers. The aim of this study is therefore to explore aortic function in dilated cardiomyopathy (DCM). Fourteen idiopathic DCM patients and 16 controls underwent cardiac magnetic resonance imaging, with aortic relative pressure derived using physics-based image processing and a virtual cohort utilized to assess the impact of cardiovascular properties on aortic behaviour. Subjects with reduced left ventricular systolic function had significantly reduced aortic relative pressure, increased aortic stiffness, and significantly delayed time-to-pressure peak duration. From the virtual cohort, aortic stiffness and aortic volumetric size were identified as key determinants of aortic relative pressure. As such, this study shows how advanced flow imaging and aortic hemodynamic evaluation could provide novel insights into the manifestation of DCM, with signs of both altered aortic structure and function derived in DCM using our proposed imaging protocol.

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.

A Poroelastic Approach for Modelling Myocardial Oedema in Acute Myocarditis

Myocarditis is a general set of mechanisms that manifest themselves into the inflammation of the heart muscle. In 2017, more than 3 million people were affected by this disease worldwide, causing about 47,000 deaths. Many aspects of the origin of this disease are well known, but several important questions regarding the disease remain open. One of them is why some patients develop a significantly localised inflammation while others develop a much more diffuse inflammation, reaching across large portions of the heart. Furthermore, the specific role of the pathogenic agent that causes inflammation as well as the interaction with the immune system in the progression of the disease are still under discussion. Providing answers to these crucial questions can have an important impact on patient treatment. In this scenario, computational methods can aid specialists to understand better the relationships between pathogens and the immune system and elucidate why some patients develop diffuse myocarditis. This paper alters a recently developed model to study the myocardial oedema formation in acute infectious myocarditis. The model describes the finite deformation regime using partial differential equations to represent tissue displacement, fluid pressure, fluid phase, and the concentrations of pathogens and leukocytes. A sensitivity analysis was performed to understand better the influence of the most relevant model parameters on the disease dynamics. The results showed that the poroelastic model could reproduce local and diffuse myocarditis dynamics in simplified and complex geometrical domains.

Meshless Electrophysiological Modeling of Cardiac Resynchronization Therapy—Benchmark Analysis with Finite-Element Methods in Experimental Data

Computational models of cardiac electrophysiology are promising tools for reducing the rates of non-response patients suitable for cardiac resynchronization therapy (CRT) by optimizing electrode placement. The majority of computational models in the literature are mesh-based, primarily using the finite element method (FEM). The generation of patient-specific cardiac meshes has traditionally been a tedious task requiring manual intervention and hindering the modeling of a large number of cases. Meshless models can be a valid alternative due to their mesh quality independence. The organization of challenges such as the CRT-EPiggy19, providing unique experimental data as open access, enables benchmarking analysis of different cardiac computational modeling solutions with quantitative metrics. We present a benchmark analysis of a meshless-based method with finite-element methods for the prediction of cardiac electrical patterns in CRT, based on a subset of the CRT-EPiggy19 dataset. A data assimilation strategy was designed to personalize the most relevant parameters of the electrophysiological simulations and identify the optimal CRT lead configuration. The simulation results obtained with the meshless model were equivalent to FEM, with the most relevant aspect for accurate CRT predictions being the parameter personalization strategy (e.g., regional conduction velocity distribution, including the Purkinje system and CRT lead distribution).

Engineering Models of the Heart Left Ventricle

Despite capturing the imagination of scientists for decades, the goal of creating an artificial heart for transplantation proved to be significantly more challenging than initially anticipated. Toward this goal, recent ground-breaking studies demonstrate the development of functional left ventricular (LV) models. LV models are artificially constructed 3D chambers that are capable of containing liquid within the engineered cavity and exhibit the functionality of native LV including contraction, ejection of fluid, and electrical impulse propagation. Various hydrogels and polymers have been used in manufacturing of LV models, relying on techniques such as electrospinning, bioprinting, casting, and molding. Most studies scaled down the models based on the dimensions of the human or rat ventricle. Initially, neonatal rat cardiomyocytes were the cell type of choice for construction the LV models. Yet, as the stem cell biology field advanced, recent studies focused on the use of cardiomyocytes derived from human induced pluripotent stem cells. In this review, we first describe the physiological characteristics of the human heart, to establish the parameter space for modeling. We then elaborate on current advances in the field and compare recently developed LV models among themselves and with the native human left ventricle. Fabrication methods, cell types, biomaterials, functional properties, and disease modeling capability are some of the major parameters that have distinguished these models. We also highlight some of the current challenges in this field, such as vascularization, cell composition and fidelity, and discuss potential solutions to overcome them.

Comparison of interpolation methods of predominant cardiomyocyte orientation from in vivo and ex vivo cardiac diffusion tensor imaging data

Cardiac electrophysiology and cardiac mechanics both depend on the average cardiomyocyte long-axis orientation. In the realm of personalized medicine, knowledge of the patient-specific changes in cardiac microstructure plays a crucial role. Patient-specific computational modelling has emerged as a tool to better understand disease progression. In vivo cardiac diffusion tensor imaging (cDTI) is a vital tool to non-destructively measure the average cardiomyocyte long-axis orientation in the heart. However, cDTI suffers from long scan times, rendering volumetric, high-resolution acquisitions challenging. Consequently, interpolation techniques are needed to populate bio-mechanical models with patient-specific average cardiomyocyte long-axis orientations. In this work, we compare five interpolation techniques applied to in vivo and ex vivo porcine input data. We compare two tensor interpolation approaches, one rule-based approximation, and two data-driven, low-rank models. We demonstrate the advantage of tensor interpolation techniques, resulting in lower interpolation errors than do low-rank models and rule-based methods adapted to cDTI data. In an ex vivo comparison, we study the influence of three imaging parameters that can be traded off against acquisition time: in-plane resolution, signal to noise ratio, and number of acquired short-axis imaging slices.

Simulation of the 3D Hyperelastic Behavior of Ventricular Myocardium using a Finite-Element Based Neural-Network Approach

High-fidelity cardiac models using attribute-rich finite element based models have been developed to a very mature stage. However, such finite-element based approaches remain time consuming, which have limited their clinical use. There remains a need for alternative methods for novel cardiac simulation methods of capable of high fidelity simulations in clinically relevant time frames. Surrogate models are one approach, which traditionally use a data-driven approach for training, requiring the generation of a sufficiently large number of simulation results as the training dataset. Alternatively, a physics-informed neural network can be trained by minimizing the PDE residuals or energy potentials. However, this approach does not provide for a general method to easily using existing finite element models. To address these challenges, we developed a hybrid approach that seamlessly bridged a neural network surrogate model with a differentiable finite element domain representation (NNFE). Given its importance in cardiac simulations, we applied this approach to simulations of the hyperelastic mechanical behavior of ventricular myocardium from recent 3D kinematic constitutive model (J Mech Behav Biomed Mater, 2020 doi: 10.1016/j.jmbbm.2019.103508). We utilized cuboidal domain and conducted numerical studies of individual myocardium specimens discretized by a finite element mesh and assigned with experimentally obtained myofiber architectures. Both parameterized Dirichlet and Neumann boundary conditions were studied. We developed a second-order Newton optimization method, instead of using stochastic gradient descent method, to train the neural network efficiently. The resulting trained neural network surrogate model demonstrated excellent agreement with the corresponding 'ground truth' finite element solutions over the entire physiological deformation range. More importantly, the NNFE approach provided a significantly decreased computational time for a range of finite element mesh sizes for online predictions. For example, as the finite element mesh sized increased from 2744 to 175615 elements the NNFE computational time increased from 0.1108 s to 0.1393 s, while the 'ground truth' FE model increased from 4.541 s to 719.9 s. These results suggests that NNFE run times can be significantly reduced compared with the traditional large-deformation based finite element solution methods. The trade off is to train the NNFE off-line within a range of anticipated physiological responses. However, training time would only have to be performed once before any number of application uses. Moreover, since the NNFE is an analytical function its computational performance will be amplified when the corresponding problem becomes more complex.

Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle

We consider parameter inference in cardio-mechanic models of the left ventricle, in particular the one based on the Holtzapfel-Ogden (HO) constitutive law, using clinical in vivo data. The equations underlying these models do not admit closed form solutions and hence need to be solved numerically. These numerical procedures are computationally expensive making computational run times associated with numerical optimisation or sampling excessive for the uptake of the models in the clinical practice. To address this issue, we adopt the framework of Bayesian optimisation (BO), which is an efficient statistical technique of global optimisation. BO seeks the optimum of an unknown black-box function by sequentially training a statistical surrogate-model and using it to select the next query point by leveraging the associated exploration-exploitation trade-off. To guarantee that the estimates based on the in vivo data are realistic also for high-pressures, unobservable in vivo, we include a penalty term based on a previously published empirical law developed using ex vivo data. Two case studies based on real data demonstrate that the proposed BO procedure outperforms the state-of-the-art inference algorithm for the HO constitutive law.

Estimation of Regional Pulmonary Compliance in Idiopathic Pulmonary Fibrosis Based On Personalized Lung Poromechanical Modeling

Pulmonary function is tightly linked to the lung mechanical behavior, especially large deformation during breathing. Interstitial lung diseases, such as Idiopathic Pulmonary Fibrosis (IPF), have an impact on the pulmonary mechanics and consequently alter lung function. However, IPF remains poorly understood, poorly diagnosed and poorly treated. Currently, the mechanical impact of such diseases is assessed by pressure-volume curves, giving only global information. We developed a poromechanical model of the lung that can be personalized to a patient based on routine clinical data. The personalization pipeline uses clinical data, mainly CT-images at two time steps and involves the formulation of an inverse problem to estimate regional compliances. The estimation problem can be formulated both in terms of "effective", i.e., without considering the mixture porosity, or "rescaled", i.e., where the first-order effect of the porosity has been taken into account, compliances. Regional compliances are estimated for one control subject and three IPF patients, allowing to quantify the IPF-induced tissue stiffening. This personalized model could be used in the clinic as an objective and quantitative tool for IPF diagnosis.

Machine Learning Prediction of Cardiac Resynchronisation Therapy Response From Combination of Clinical and Model-Driven Data

Background: Up to 30–50% of chronic heart failure patients who underwent cardiac resynchronization therapy (CRT) do not respond to the treatment. Therefore, patient stratification for CRT and optimization of CRT device settings remain a challenge.

Objective: The main goal of our study is to develop a predictive model of CRT outcome using a combination of clinical data recorded in patients before CRT and simulations of the response to biventricular (BiV) pacing in personalized computational models of the cardiac electrophysiology.

Materials and Methods: Retrospective data from 57 patients who underwent CRT device implantation was utilized. Positive response to CRT was defined by a 10% increase in the left ventricular ejection fraction in a year after implantation. For each patient, an anatomical model of the heart and torso was reconstructed from MRI and CT images and tailored to ECG recorded in the participant. The models were used to compute ventricular activation time, ECG duration and electrical dyssynchrony indices during intrinsic rhythm and BiV pacing from the sites of implanted leads. For building a predictive model of CRT response, we used clinical data recorded before CRT device implantation together with model-derived biomarkers of ventricular excitation in the left bundle branch block mode of activation and under BiV stimulation. Several Machine Learning (ML) classifiers and feature selection algorithms were tested on the hybrid dataset, and the quality of predictors was assessed using the area under receiver operating curve (ROC AUC). The classifiers on the hybrid data were compared with ML models built on clinical data only.

Results: The best ML classifier utilizing a hybrid set of clinical and model-driven data demonstrated ROC AUC of 0.82, an accuracy of 0.82, sensitivity of 0.85, and specificity of 0.78, improving quality over that of ML predictors built on clinical data from much larger datasets by more than 0.1. Distance from the LV pacing site to the post-infarction zone and ventricular activation characteristics under BiV pacing were shown as the most relevant model-driven features for CRT response classification.

Conclusion: Our results suggest that combination of clinical and model-driven data increases the accuracy of classification models for CRT outcomes.

Prediction of Ventricular Mechanics After Pulmonary Valve Replacement in Tetralogy of Fallot by Biomechanical Modeling: A Step Towards Precision Healthcare

Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient's pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSM_pre, and patient-specific models of the same patients created post-PVR (PSM_post)-both created in our previous published work. Using the PSM_pre and assuming cessation of the pulmonary regurgitation and a progressive decrease of RVOT resistance, we built relationships between the contractility and RVOT resistance post-PVR. The predictive value of such in silico obtained relationships were tested against the PSM_post, i.e. the models created from the actual post-PVR datasets. Our results show a linear 1-dimensional relationship between the in silico predicted contractility post-PVR and the RVOT resistance. The predicted contractility was close to the contractility in the PSM_post model with a mean (± SD) difference of 6.5 (± 3.0)%. The relationships between the contractility predicted by in silico PVR vs. RVOT resistance have a potential to inform clinicians about hypothetical mechanical response of the ventricle based on the degree of pre-operative RVOTO.

Engineering Microsphere-Loaded Non-mulberry Silk-Based 3D Bioprinted Vascularized Cardiac Patches with Oxygen-Releasing and Immunomodulatory Potential

A hostile myocardial microenvironment post ischemic injury (myocardial infarction) plays a decisive role in determining the fate of tissue-engineered approaches. Therefore, engineering hybrid 3D printed platforms that can modulate the MI microenvironment for improving implant acceptance has surfaced as a critical requirement for reconstructing an infarcted heart. Here, we have employed a non-mulberry silk-based conductive bioink comprising carbon nanotubes (CNTs) to bioprint functional 3D vascularized anisotropic cardiac constructs. Immunofluorescence staining, polymerase chain reaction-based gene expression studies, and electrophysiological studies showed that the inclusion of CNTs in the bioink played a significant role in upregulating matured cardiac biomarkers, sarcomere formation, and beating rate while promoting cardiomyocyte viability. These constructs were then microinjected with calcium peroxide and IL-10-loaded gelatin methacryloyl microspheres. Measurements of oxygen concentration revealed that these microspheres upheld the oxygen availability for maintaining cellular viability for at least 5 days in a hypoxic environment. Also, the ability of microinjected IL-10 microspheres to modulate the macrophages to anti-inflammatory M2 phenotype in vitro was uncovered using immunofluorescent staining and gene expression studies. Furthermore, in vivo subcutaneous implantation of microsphere-injected 3D constructs provided insights toward the extended time frame that was achieved for dealing with the hostile microenvironment for promoting host neovascularization and implant acceptance.

A viscoelastic model for human myocardium

Understanding the biomechanics of the heart in health and disease plays an important role in the diagnosis and treatment of heart failure. The use of computational biomechanical models for therapy assessment is paving the way for personalized treatment, and relies on accurate constitutive equations mapping strain to stress. Current state-of-the art constitutive equations account for the nonlinear anisotropic stress-strain response of cardiac muscle using hyperelasticity theory. While providing a solid foundation for understanding the biomechanics of heart tissue, most current laws neglect viscoelastic phenomena observed experimentally. Utilizing experimental data from human myocardium and knowledge of the hierarchical structure of heart muscle, we present a fractional nonlinear anisotropic viscoelastic constitutive model. The model is shown to replicate biaxial stretch, triaxial cyclic shear and triaxial stress relaxation experiments (mean error ∼7.68%), showing improvements compared to its hyperelastic (mean error ∼24%) counterparts. Model sensitivity, fidelity and parameter uniqueness are demonstrated. The model is also compared to rate-dependent biaxial stretch as well as different modes of biaxial stretch, illustrating extensibility of the model to a range of loading phenomena. STATEMENT OF SIGNIFICANCE: The viscoelastic response of human heart tissues has yet to be integrated into common constitutive models describing cardiac mechanics. In this work, a fractional viscoelastic modeling approach is introduced based on the hierarchical structure of heart tissue. From these foundations, the current state-of-the-art biomechanical models of the heart muscle are transformed using fractional viscoelasticity, replicating passive muscle function across multiple experimental tests. Comparisons are drawn with current models to highlight the improvements of this approach and predictive responses show strong qualitative agreement with experimental data. The proposed model presents the first constitutive model aimed at capturing viscoelastic nonlinear response across multiple testing regimes, providing a platform for better understanding the biomechanics of myocardial tissue in health and disease.

Biomechanical Modeling to Inform Pulmonary Valve Replacement in Tetralogy of Fallot Patients After Complete Repair

BACKGROUND

A biomechanical model of the heart can be used to incorporate multiple data sources (electrocardiography, imaging, invasive hemodynamics). The purpose of this study was to use this approach in a cohort of patients with tetralogy of Fallot after complete repair (rTOF) to assess comparative influences of residual right ventricular outflow tract obstruction (RVOTO) and pulmonary regurgitation on ventricular health.

METHODS

Twenty patients with rTOF who underwent percutaneous pulmonary valve replacement (PVR) and cardiovascular magnetic resonance imaging were included in this retrospective study. Biomechanical models specific to individual patient and physiology (before and after PVR) were created and used to estimate the RV myocardial contractility. The ability of models to capture post-PVR changes of right ventricular (RV) end-diastolic volume (EDV) and effective flow in the pulmonary artery (Q_eff) was also compared with expected values.

RESULTS

RV contractility before PVR (mean 66 ± 16 kPa, mean ± standard deviation) was increased in patients with rTOF compared with normal RV (38-48 kPa) (P < 0.05). The contractility decreased significantly in all patients after PVR (P < 0.05). Patients with predominantly RVOTO demonstrated greater reduction in contractility (median decrease 35%) after PVR than those with predominant pulmonary regurgitation (median decrease 11%). The model simulated post-PVR decreased EDV for the majority and suggested an increase of Q_eff-both in line with published data.

CONCLUSIONS

This study used a biomechanical model to synthesize multiple clinical inputs and give an insight into RV health. Individualized modeling allows us to predict the RV response to PVR. Initial data suggest that residual RVOTO imposes greater ventricular work than isolated pulmonary regurgitation.

Passive myocardial mechanical properties: meaning, measurement, models

Passive mechanical tissue properties are major determinants of myocardial contraction and relaxation and, thus, shape cardiac function. Tightly regulated, dynamically adapting throughout life, and affecting a host of cellular functions, passive tissue mechanics also contribute to cardiac dysfunction. Development of treatments and early identification of diseases requires better spatio-temporal characterisation of tissue mechanical properties and their underlying mechanisms. With this understanding, key regulators may be identified, providing pathways with potential to control and limit pathological development. Methodologies and models used to assess and mimic tissue mechanical properties are diverse, and available data are in part mutually contradictory. In this review, we define important concepts useful for characterising passive mechanical tissue properties, and compare a variety of in vitro and in vivo techniques that allow one to assess tissue mechanics. We give definitions of key terms, and summarise insight into determinants of myocardial stiffness in situ. We then provide an overview of common experimental models utilised to assess the role of environmental stiffness and composition, and its effects on cardiac cell and tissue function. Finally, promising future directions are outlined.

Neural network-based left ventricle geometry prediction from CMR images with application in biomechanics

Combining biomechanical modelling of left ventricular (LV) function and dysfunction with cardiac magnetic resonance (CMR) imaging has the potential to improve the prognosis of patient-specific cardiovascular disease risks. Biomechanical studies of LV function in three dimensions usually rely on a computerized representation of the LV geometry based on finite element discretization, which is essential for numerically simulating in vivo cardiac dynamics. Detailed knowledge of the LV geometry is also relevant for various other clinical applications, such as assessing the LV cavity volume and wall thickness. Accurately and automatically reconstructing personalized LV geometries from conventional CMR images with minimal manual intervention is still a challenging task, which is a pre-requisite for any subsequent automated biomechanical analysis. We propose a deep learning-based automatic pipeline for predicting the three-dimensional LV geometry directly from routinely-available CMR cine images, without the need to manually annotate the ventricular wall. Our framework takes advantage of a low-dimensional representation of the high-dimensional LV geometry based on principal component analysis. We analyze how the inference of myocardial passive stiffness is affected by using our automatically generated LV geometries instead of manually generated ones. These insights will inform the development of statistical emulators of LV dynamics to avoid computationally expensive biomechanical simulations. Our proposed framework enables accurate LV geometry reconstruction, outperforming previous approaches by delivering a reconstruction error 50% lower than reported in the literature. We further demonstrate that for a nonlinear cardiac mechanics model, using our reconstructed LV geometries instead of manually extracted ones only moderately affects the inference of passive myocardial stiffness described by an anisotropic hyperelastic constitutive law. The developed methodological framework has the potential to make an important step towards personalized medicine by eliminating the need for time consuming and costly manual operations. In addition, our method automatically maps the CMR scan into a low-dimensional representation of the LV geometry, which constitutes an important stepping stone towards the development of an LV geometry-heterogeneous emulator.

An Implementation of Patient-Specific Biventricular Mechanics Simulations With a Deep Learning and Computational Pipeline

Parameterised patient-specific models of the heart enable quantitative analysis of cardiac function as well as estimation of regional stress and intrinsic tissue stiffness. However, the development of personalised models and subsequent simulations have often required lengthy manual setup, from image labelling through to generating the finite element model and assigning boundary conditions. Recently, rapid patient-specific finite element modelling has been made possible through the use of machine learning techniques. In this paper, utilising multiple neural networks for image labelling and detection of valve landmarks, together with streamlined data integration, a pipeline for generating patient-specific biventricular models is applied to clinically-acquired data from a diverse cohort of individuals, including hypertrophic and dilated cardiomyopathy patients and healthy volunteers. Valve motion from tracked landmarks as well as cavity volumes measured from labelled images are used to drive realistic motion and estimate passive tissue stiffness values. The neural networks are shown to accurately label cardiac regions and features for these diverse morphologies. Furthermore, differences in global intrinsic parameters, such as tissue anisotropy and normalised active tension, between groups illustrate respective underlying changes in tissue composition and/or structure as a result of pathology. This study shows the successful application of a generic pipeline for biventricular modelling, incorporating artificial intelligence solutions, within a diverse cohort.

Applications of artificial intelligence in cardiovascular imaging

Research into artificial intelligence (AI) has made tremendous progress over the past decade. In particular, the AI-powered analysis of images and signals has reached human-level performance in many applications owing to the efficiency of modern machine learning methods, in particular deep learning using convolutional neural networks. Research into the application of AI to medical imaging is now very active, especially in the field of cardiovascular imaging because of the challenges associated with acquiring and analysing images of this dynamic organ. In this Review, we discuss the clinical questions in cardiovascular imaging that AI can be used to address and the principal methodological AI approaches that have been developed to solve the related image analysis problems. Some approaches are purely data-driven and rely mainly on statistical associations, whereas others integrate anatomical and physiological information through additional statistical, geometric and biophysical models of the human heart. In a structured manner, we provide representative examples of each of these approaches, with particular attention to the underlying computational imaging challenges. Finally, we discuss the remaining limitations of AI approaches in cardiovascular imaging (such as generalizability and explainability) and how they can be overcome.

Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator

The results of numerical simulations of cardiac electromechanics are typically characterized by a long transient before reaching a periodic solution known as limit cycle. This yields a serious computational overhead, as the only clinically relevant output is associated with such limit cycle. To accelerate the convergence to the limit cycle, we propose a strategy based on a surrogate model, wherein the computationally demanding 3D components are replaced by a 0D emulator, built through an automated data-driven algorithm on the basis of pressure-volume transients of as few as three heartbeats simulated with the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, can provide the 3D model with an initial guess, such that in just two heartbeats a solution is reached that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the 3D model. The 0D emulator is also recommended in many-query settings (e.g. when performing sensitivity analysis, parameter estimation and uncertainty quantification), that call for the repeated solution of the model for different values of the parameters. Indeed, the construction of the emulator does not have to be repeated when the parameters of the circulation model it is coupled with vary. Finally, should the parameters of the 3D electromechanical model vary as well, we propose a parametric emulator, obtained by interpolation of emulators constructed for given values of the parameters. This paper is accompanied by a Python library implementing the proposed algorithm, open to integration with existing cardiac solvers.

The impact of myocardial compressibility on organ-level simulations of the normal and infarcted heart

Myocardial infarction (MI) rapidly impairs cardiac contractile function and instigates maladaptive remodeling leading to heart failure. Patient-specific models are a maturing technology for developing and determining therapeutic modalities for MI that require accurate descriptions of myocardial mechanics. While substantial tissue volume reductions of 15-20% during systole have been reported, myocardium is commonly modeled as incompressible. We developed a myocardial model to simulate experimentally-observed systolic volume reductions in an ovine model of MI. Sheep-specific simulations of the cardiac cycle were performed using both incompressible and compressible tissue material models, and with synchronous or measurement-guided contraction. The compressible tissue model with measurement-guided contraction gave best agreement with experimentally measured reductions in tissue volume at peak systole, ventricular kinematics, and wall thickness changes. The incompressible model predicted myofiber peak contractile stresses approximately double the compressible model (182.8 kPa, 107.4 kPa respectively). Compensatory changes in remaining normal myocardium with MI present required less increase of contractile stress in the compressible model than the incompressible model (32.1%, 53.5%, respectively). The compressible model therefore provided more accurate representation of ventricular kinematics and potentially more realistic computed active contraction levels in the simulated infarcted heart. Our findings suggest that myocardial compressibility should be incorporated into future cardiac models for improved accuracy.

Multiscale modeling meets machine learning: What can we learn?

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

Personalising left-ventricular biophysical models of the heart using parametric physics-informed neural networks

We present a parametric physics-informed neural network for the simulation of personalised left-ventricular biomechanics. The neural network is constrained to the biophysical problem in two ways: (i) the network output is restricted to a subspace built from radial basis functions capturing characteristic deformations of left ventricles and (ii) the cost function used for training is the energy potential functional specifically tailored for hyperelastic, anisotropic, nearly-incompressible active materials. The radial bases are generated from the results of a nonlinear Finite Element model coupled with an anatomical shape model derived from high-resolution cardiac images. We show that, by coupling the neural network with a simplified circulation model, we can efficiently generate computationally inexpensive estimations of cardiac mechanics. Our model is 30 times faster than the reference Finite Element model used, including training time, while yielding satisfactory average errors in the predictions of ejection fraction (-3%), peak systolic pressure (7%), stroke work (4%) and myocardial strains (14%). This physics-informed neural network is well suited to efficiently augment cardiac images with functional data and to generate large sets of synthetic cases for training deep network classifiers while it provides efficient personalization to the specific patient of interest with a high level of detail.

Transverse isotropic modelling of left-ventricle passive filling: Mechanical characterization for epicardial biomaterial manufacturing

Biomaterials applied to the epicardium have been studied intensively in recent years for different therapeutic purposes. Their mechanical influence on the heart, however, has not been clearly identified. Most biomaterials for epicardial applications are manufactured as membranes or cardiac patches that have isotropic geometry, which is not well suited to myocardial wall motion. Myocardial wall motion during systole and diastole produces a complex force in different directions. Membrane or cardiac patches that cannot adapt to these specific directions will exert an inappropriate force on the heart, at the risk of overly restricting or dilating it. Accurately characterizing the mechanical properties of the myocardial wall is thus essential, through analysis of muscle orientation and elasticity. In this study, we investigated the Hertz contact theory for characterizing cardiac tissue, using nanoindentation measurements to distinguish different patterns in the local myocardium. We then evaluated the predictive accuracy of this model using Finite Element Analysis (FEA) to mimic the diastolic phase of the heart. Our results, extracted from instrumented nanoindentation experiments in a liquid environment using five pig hearts, revealed variations in elasticity according to the local orientation of the myocardial tissue. In addition, applying the Finite Element Method (FEM) in our model based on transverse isotropy and local tissue orientation proved able to accurately simulate the passive filling of a left ventricle (LV) in a representative 3D geometry. Our model enables improved understanding of the underlying mechanical properties of the LV wall and can serve as a guide for designing and manufacturing biomedical material better adapted to the local epicardial tissue.

Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function

In order to simulate the cardiac function for a patient-specific geometry, the generation of the computational mesh is crucially important. In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images. These surfaces need ad-hoc processing to be suitable for a volumetric mesh generation. In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process. In particular, we focus on different aspects of a cardiac mesh generation pipeline: (1) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs; (2) generation of accurate boundary tags; (3) definition of mesh-size functions dependent on relevant geometric quantities; (4) processing and connecting together several volumetric meshes. The new algorithms-implemented in the open-source software vmtk-can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled. Thanks to these features, the proposed tools can significantly speed-up the mesh generation process for a large range of cardiac applications, from single-chamber single-physics simulations to multi-chambers multi-physics simulations. We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.

Data integration for the numerical simulation of cardiac electrophysiology

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing therapies and interventions. In this direction, mathematical and numerical models provide a complementary relevant tool, able not only to reproduce patient-specific clinical indicators but also to predict and explore unseen scenarios. With this goal, clinical data are processed and provided as inputs to the mathematical model, which quantitatively describes the physical processes that occur in the cardiac tissue. In this paper, the process of integration of clinical data and mathematical models is discussed. Some challenges and contributions in the field of cardiac electrophysiology are reported.