Combining physics-based modeling with data-driven methods is critical to enabling the translation of computational methods to clinical use in cardiology. The use of rigorous differential equations combined with machine learning tools allows for model personalization with uncertainty quantification in time frames compatible with clinical practice. However, accurate and efficient surrogate models of cardiac function, built from physics-based numerical simulation, are still mostly geometry-specific and require retraining for different patients and pathological conditions. We propose a novel computational pipeline to embed cardiac anatomies into full-field surrogate models. We generate a dataset of electrophysiology simulations using an accurate multi-scale mathematical model coupling partial and ordinary differential equations. We adopt Branched Latent Neural Maps (BLNMs) as a computationally efficient scientific machine learning method to encode activation maps extracted from physics-based numerical simulations into a neural network. Leveraging large deformation diffeomorphic metric mappings, we build a biventricular anatomical atlas and parametrize the anatomical variability of a small and challenging cohort of 13 pediatric patients affected by Tetralogy of Fallot. We propose a novel z-score sampling approach based on statistical shape modeling to generate a new synthetic cohort of 52 biventricular geometries that are compatible with the original geometrical variability. This synthetic cohort acts as the training set for BLNMs. Our surrogate model demonstrates robustness and great generalization across the complex original patient cohort, achieving an average adimensional mean squared error of 0.0034. The Python implementation of our BLNM model is publicly available under MIT License at https://github.com/StanfordCBCL/BLNM.

Understanding the physiological condition of the vascular system is critical to explain, treat, and manage vascular disease. Numerous experimental and computational studies characterize the mechanical behavior of arterial tissue under controlled laboratory conditions. However, translating this knowledge into physiologically realistic conditions remains challenging. Key difficulties include selecting suitable and relevant test methods, minimizing uncertainty, and ensuring robust model validation. Here, we present a novel integrative approach to translate laboratory experiments on arterial samples into clinically relevant pressure-diameter behavior. We perform controlled planar-biaxial tests on carotid arteries under three stretch ratios and generate axial and circumferential stress-stretch data to calibrate a fiber-reinforced soft tissue model. Using an analytical thick-walled cylindrical model, we predict subject-specific pressure-diameter behavior, informed by arterial prestretches from ring opening experiments. We systematically compare predictions against extension-inflation experiments on tubes from the same artery by applying controlled pairs of axial stretch and inner pressure, while recording outer diameter. We quantify prediction error in absolute and relative stretch regimes and evaluate the importance of the load-free reference dimensions. Results show how planar-biaxial tests probe different stretch regimes compared to extension-inflation deformations, leading to extrapolation of model predictions. We demonstrate how the constitutive material parameters can be fitted to different biomechanical loading conditions, and we assess the sensitivity of the simulations to axial stretch and circumferential prestretch. Only when those key model parameters are accurately captured and their uncertainty propagated, planar-biaxial stress-stretch data can reliably predict arterial pressure-diameter behavior.

The intricate three-dimensional organization of cardiac myofibers and sheetlets plays a critical role in the mechanical behavior of the human heart. Despite extensive research and the development of various rule-based myofiber architecture surrogate models, the precise arrangement of these structures and their impact on cardiac function remain subjects of debate. In this study, we present a novel myofiber architecture surrogate inspired by Streeter’s nested tori conjecture, modeling the left ventricle as a series of smoothly twisting toroidal surfaces populated by continuous myofiber and sheetlet fields. Leveraging high-fidelity cardiac computational modeling approaches, we systematically evaluated the biomechanical performance of this nested tori architecture against conventional rule-based nested ellipsoidal models. Our results demonstrate that the nested tori architecture aligns more closely with experimental data on physiological myofiber and sheetlet angles. Notably, it enhances sheetlet mobility—a key mechanism for effective cardiac pumping—resulting in higher ejection fraction, greater global deformation, and a more physiological wall rotation pattern. Additionally, it produces a more homogeneous myofiber stress distribution and increased myofiber shortening during ejection. These findings suggest that the nested tori architecture provides a compelling alternative to conventional nested ellipsoidal models, offering a more physiologically consistent representation of myocardial structure and its functional implications. By enabling improved biomechanical performance in silico, this approach supports further investigation into how detailed myoarchitectural continuity shapes cardiac function. Ultimately, it may open promising avenues for advancing cardiac diagnosis, guiding the design of bioinspired implants and devices, and deepening our understanding of both healthy and diseased cardiac mechanics.

In cardiovascular mechanics, reaching consensus in simulation results within a physiologically relevant range of parameters is essential for reproducibility purposes. Although currently available benchmarks contain some of the features that cardiac mechanics models typically include, some important modeling aspects are missing. Therefore, we propose a new set of cardiac benchmark problems and solutions for assessing passive and active material behavior, viscous effects, and pericardial boundary condition. The problems proposed include simplified analytical fiber definitions and active stress models on a monoventricular and biventricular domains, allowing straightforward testing and validation with already developed solvers.

Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these trade-offs, we present monotonic Input-Convex Kolmogorov-Arnold Networks (ICKANs) for learning polyconvex hyperelastic constitutive laws. ICKANs leverage the Kolmogorov-Arnold representation, decomposing the model into compositions of trainable univariate spline-based activation functions for rich expressivity. We introduce trainable monotonic input-convex splines within the KAN architecture, ensuring physically admissible polyconvex models for isotropic compressible hyperelasticity. The resulting models are both compact and interpretable, enabling explicit extraction of analytical constitutive relationships through a monotonic input-convex symbolic regression technique. Through unsupervised training on full-field strain data and limited global force measurements, ICKANs accurately capture nonlinear stress–strain behavior across diverse strain states. Finite element simulations of unseen geometries with trained ICKAN hyperelastic constitutive models confirm the framework's robustness and generalization capability.

The fields of mechanobiology and biomechanics are expanding our understanding of the complex behavior of soft biological tissues across multiple scales. Given the intricate connection between tissue microstructure and its macroscale mechanical behavior, unraveling this mechanistic relationship remains an ongoing challenge. Reconstituted fiber networks serve as valuable in vitro models to simplify the intricacy of in vivo systems for targeted investigations. Concurrently, advances in imaging enable microstructure visualization and, through generative pipelines, modeling as discrete element networks. These mesoscale (μm) models provide insights into macroscale (mm) tissue behavior. However, there is still no clear way to systematically incorporate detailed experimentally observed microstructural changes into in silico models of biological networks. In this work, we develop a novel framework to generate topologically-driven discrete fiber networks using high-resolution images that account for how environmental changes during polymerization influence the resulting structure. Leveraging these networks, we generate models of interconnected load-bearing fiber components that exhibit softening under compression and are bending-resistant. The generative topology framework enables control over network-level features, such as fiber volume fraction and cross-link density, along with fiber-level properties, like length distribution, to simulate changes driven by different polymerization conditions. We validate the robustness of our simulations against experimental data in a collagen-specific study case where we examine nonlinear elastic responses of collagen networks across varying conditions. TopoGEN provides a versatile tool for tissue biomechanics and engineering, helping to bridge microstructural insights and bulk mechanical behavior by linking image-derived microstructural topological organization to soft tissue mechanics.

Accurate modeling of cardiovascular tissues is crucial for understanding and predicting their behavior in various physiological and pathological conditions. In this study, we specifically focus on the pulmonary artery in the context of the Ross procedure, using neural networks to discover the most suitable material model. The Ross procedure is a complex cardiac surgery where the patient’s own pulmonary valve is used to replace the diseased aortic valve. Ensuring the successful long-term outcomes of this intervention requires a detailed understanding of the mechanical properties of pulmonary tissue. Constitutive artificial neural networks offer a novel approach to capture such complex stress–strain relationships. Here, we design and train different constitutive neural networks to characterize the hyperelastic, anisotropic behavior of the main pulmonary artery. Informed by experimental biaxial testing data under various axial-circumferential loading ratios, these networks autonomously discover the inherent material behavior, without the limitations of predefined mathematical models. We regularize the model discovery using cross-sample feature selection and explore its sensitivity to the collagen fiber distribution. Strikingly, we uniformly discover an isotropic exponential first-invariant term and an anisotropic quadratic fifth-invariant term. We show that constitutive models with both these terms can reliably predict arterial responses under diverse loading conditions. Our results provide crucial improvements in experimental data agreement, and enhance our understanding into the biomechanical properties of pulmonary tissue. The model outcomes can be used in a variety of computational frameworks of autograft adaptation, ultimately improving the surgical outcomes after the Ross procedure.

This work presents a novel approach for characterizing the mechanical behavior of atrial tissue using constitutive neural networks. Based on experimental biaxial tensile test data of healthy human atria, we automatically discover the most appropriate constitutive material model, thereby overcoming the limitations of traditional, pre-defined models. This approach offers a new perspective on modeling atrial mechanics and is a significant step towards improved simulation and prediction of cardiac health.

Cardiac deformation is a crucial biomarker for the evaluation of cardiac function. Current methods for estimating cardiac strain might underestimate local deformation due to through-plane motion and segmental averaging. Mesh-based mapping methods are gaining interest for localized analysis of cardiac motion and strain, yet they often do not consider important properties of cardiac tissue. In this work, we propose an extension of the large deformation diffeomorphic metric mapping framework to incorporate near incompressibility into the loss function that guides the mapping. As such, our mechanically regularized mLDDMM allows for accurate and mechanically coherent estimation of volume displacement and strain tensors from time-resolved three-dimensional meshes. We benchmark our method against the results of a finite element simulation of cardiac contraction and find a very good agreement between our estimation and the simulated ground truth. Our method forms a promising technique to extract volume displacement and strain tensors from time-resolved meshes while accounting for the incompressibility of cardiac tissue.

Abstract: Sex-based differences in cardiovascular disease are well documented, yet the precise nature and extent of these discrepancies in cardiac anatomy remain incompletely understood. Traditional scaling models often fail to capture the interplay of age, blood pressure and body size, prompting a more nuanced investigation. Here we use statistical shape modelling in a healthy subset (n = 456) of the UK Biobank to explore sex-specific variations in biventricular anatomy. We reconstruct 3D meshes and perform multivariate analyses of shape coefficients, controlling for age, blood pressure and various body size metrics. Our findings reveal that sex alone explains at least 25% of morphological variability, with strong discrimination between men and women (AUC = 0.96–0.71) persisting even after correction for confounders. Notably, the most discriminative modes highlight pronounced differences in cardiac chamber volumes, the anterior–posterior width of the right ventricle and the relative positioning of the cardiac chambers. These results underscore that sex has a fundamental influence on cardiac morphology, which may have important clinical implications for differing cardiac structural assessments in men and women. Future work should investigate how these anatomical differences manifest in various cardiovascular conditions, ultimately paving the way for more precise risk stratification and personalised therapeutic strategies for both men and women. (Figure presented.). Key points: Men's and women's hearts differ significantly in overall shape and size, but an in-depth quantification of these sex differences in healthy cardiac anatomy is lacking. We used a three-dimensional statistical shape modelling approach that goes beyond standard clinical measurements to capture subtle anatomical features. Our findings show that sex alone accounts for at least 25% of the natural variation in heart structure, even after correcting for age, blood pressure and various body size metric confounders. Female hearts consistently present smaller chambers and different inter-chamber positioning compared with male hearts. Our findings highlight the importance of sex-specific anatomical insights for better diagnosis, treatment and research on heart disease.

In recent years, blending mechanistic knowledge with machine learning has had a major impact in digital healthcare. In this work, we introduce a computational pipeline to build certified digital replicas of cardiac electrophysiology in paediatric patients with congenital heart disease. We construct the patient-specific geometry by means of semi-automatic segmentation and meshing tools. We generate a dataset of electrophysiology simulations covering cell-to-organ level model parameters and using rigorous mathematical models based on differential equations. We previously proposed Branched Latent Neural Maps (BLNMs) as an accurate and efficient means to recapitulate complex physical processes in a neural network. Here, we employ BLNMs to encode the parametrized temporal dynamics of in silico 12-lead electrocardiograms (ECGs). BLNMs act as a geometry-specific surrogate model of cardiac function for fast and robust parameter estimation to match clinical ECGs in paediatric patients. Identifiability and trustworthiness of calibrated model parameters are assessed by sensitivity analysis and uncertainty quantification.

Personalized computational simulations have emerged as a vital tool to understand the biomechanical factors of a disease, predict disease progression, and design personalized intervention. Material modeling is critical for realistic biomedical simulations, and poor model selection can have life-threatening consequences for the patient. However, selecting the best model requires a profound domain knowledge and is limited to a few highly specialized experts in the field. Here we explore the feasibility of eliminating user involvement and automate the process of material modeling in finite element analyses. We leverage recent developments in constitutive neural networks, machine learning, and artificial intelligence to discover the best constitutive model from thousands of possible combinations of a few functional building blocks. We integrate all discoverable models into the finite element workflow by creating a universal material subroutine that contains more than 60,000 models, made up of 16 individual terms. We prototype this workflow using biaxial extension tests from healthy human arteries as input and stress and stretch profiles across the human aortic arch as output. Our results suggest that constitutive neural networks can robustly discover various flavors of arterial models from data, feed these models directly into a finite element simulation, and predict stress and strain profiles that compare favorably to the classical Holzapfel model. Replacing dozens of individual material subroutines by a single universal material subroutine—populated directly via automated model discovery—will make finite element simulations more user-friendly, more robust, and less vulnerable to human error. Democratizing finite element simulation by automating model selection could induce a paradigm shift in physics-based modeling, broaden access to simulation technologies, and empower individuals with varying levels of expertise and diverse backgrounds to actively participate in scientific discovery and push the boundaries of biomedical simulation.

Constitutive modeling is the cornerstone of computational and structural mechanics. In a finite element analysis, the constitutive model is encoded in the material subroutine, a function that maps local strains onto stresses. This function is called within every finite element, at each integration point, within every time step, at each Newton iteration. Today's finite element packages offer large libraries of material models to choose from. However, the scientific criteria for appropriate model selection remain highly subjective and prone to user bias. Here we fully automate the process of model selection, autonomously discover the best model and parameters from experimental data, encode all possible discoverable models into a single material subroutine, and seamlessly integrate this universal material subroutine into a finite element analysis. We prototype this strategy for incompressible, isotropic, hyperelastic soft matter systems that we characterize through a combination of twelve possible terms. These terms feature the first and second invariants, raised to the first and second powers, embedded in the identity, exponential, and logarithmic functions, generating 2^2×2×3= 4096 models in total. We demonstrate how to integrate these models into a single universal material subroutine that features the classical neo Hooke, Blatz Ko, Mooney Rivlin, Demiray, Gent, and Holzapfel models as special cases. Finite element simulations with our new universal material subroutine show that it specializes well to these widely used models, generalizes well to newly discovered models, and agrees excellently with both experimental data and previous simulations. It also performs well within realistic finite element simulations and accurately predicts stress concentrations in the human brain for six different head impact scenarios. We anticipate that integrating automated model discovery into a universal material subroutine will generalize naturally to more complex compressible, anisotropic, inelastic materials and to other nonlinear finite element platforms. Replacing dozens of individual material subroutines by a single universal material subroutine that is populated directly via automated model discovery – entirely without human interaction – makes finite element analyses more accessible, more robust, and less vulnerable to human error. This could forever change how we simulate materials and structures. Our source code, data, and examples are available at https://github.com/LivingMatterLab.

For more than half a century, scientists have developed mathematical models to understand the behavior of the human heart. Today, we have dozens of heart tissue models to choose from, but selecting the best model is limited to expert professionals, prone to user bias, and vulnerable to human error. Here we take the human out of the loop and automate the process of model discovery. Towards this goal, we establish a novel incompressible orthotropic constitutive neural network to simultaneously discover both, model and parameters, that best explain human cardiac tissue. Notably, our network features 32 individual terms, 8 isotropic and 24 anisotropic, and fully autonomously selects the best model, out of more than 4 billion possible combinations of terms. We demonstrate that we can successfully train the network with triaxial shear and biaxial extension tests and systematically sparsify the parameter vector with L₁-regularization. Strikingly, we robustly discover a four-term model that features a quadratic term in the second invariant I₂, and exponential quadratic terms in the fourth and eighth invariants I_4f, I_4n, and I_8fs. Importantly, our discovered model is interpretable by design and has parameters with well-defined physical units. We show that it outperforms popular existing myocardium models and generalizes well, from homogeneous laboratory tests to heterogeneous whole heart simulations. This is made possible by a new universal material subroutine that directly takes the discovered network weights as input. Automating the process of model discovery has the potential to democratize cardiac modeling, broaden participation in scientific discovery, and accelerate the development of innovative treatments for cardiovascular disease. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.

Personalized treatment informed by computational models has the potential to markedly improve the outcome for patients with a type B aortic dissection. However, existing computational models of dissected walls significantly simplify the characteristic false lumen, tears and/or material behavior. Moreover, the patient-specific wall thickness and stiffness cannot be accurately captured non-invasively in clinical practice, which inevitably leads to assumptions in these wall models. It is important to evaluate the impact of the corresponding uncertainty on the predicted wall deformations and stress, which are both key outcome indicators for treatment optimization. Therefore, a physiology-inspired finite element framework was proposed to model the wall deformation and stress of a type B aortic dissection at diastolic and systolic pressure. Based on this framework, 300 finite element analyses, sampled with a Latin hypercube, were performed to assess the global uncertainty, introduced by 4 uncertain wall thickness and stiffness input parameters, on 4 displacement and stress output parameters. The specific impact of each input parameter was estimated using Gaussian process regression, as surrogate model of the finite element framework, and a δ moment-independent analysis. The global uncertainty analysis indicated minor differences between the uncertainty at diastolic and systolic pressure. For all output parameters, the 4^th quartile contained the major fraction of the uncertainty. The parameter-specific uncertainty analysis elucidated that the material stiffness and relative thickness of the dissected membrane were the respective main determinants of the wall deformation and stress. The uncertainty analysis provides insight into the effect of uncertain wall thickness and stiffness parameters on the predicted deformation and stress. Moreover, it emphasizes the need for probabilistic rather than deterministic predictions for clinical decision making in aortic dissections.

Soft materials play an integral part in many aspects of modern life including autonomy, sustainability, and human health, and their accurate modeling is critical to understand their unique properties and functions. Today’s finite element analysis packages come with a set of pre-programmed material models, which may exhibit restricted validity in capturing the intricate mechanical behavior of these materials. Regrettably, incorporating a modified or novel material model in a finite element analysis package requires non-trivial in-depth knowledge of tensor algebra, continuum mechanics, and computer programming, making it a complex task that is prone to human error. Here we design a universal material subroutine, which automates the integration of novel constitutive models of varying complexity in non-linear finite element packages, with no additional analytical derivations and algorithmic implementations. We demonstrate the versatility of our approach to seamlessly integrate innovative constitutive models from the material point to the structural level through a variety of soft matter case studies: a frontal impact to the brain; reconstructive surgery of the scalp; diastolic loading of arteries and the human heart; and the dynamic closing of the tricuspid valve. Our universal material subroutine empowers all users, not solely experts, to conduct reliable engineering analysis of soft matter systems. We envision that this framework will become an indispensable instrument for continued innovation and discovery within the soft matter community at large.

The lack of sex-specific cardiovascular disease criteria contributes to the underdiagnosis of women compared to that of men. For more than half a century, the Framingham Risk Score has been the gold standard to estimate an individual’s risk of developing cardiovascular disease based on the age, sex, cholesterol levels, blood pressure, diabetes status, and the smoking status. Now, machine learning can offer a much more nuanced insight into predicting the risk of cardiovascular diseases. The UK Biobank is a large database that includes traditional risk factors and tests related to the cardiovascular system: magnetic resonance imaging, pulse wave analysis, electrocardiograms, and carotid ultrasounds. Here, we leverage 20,542 datasets from the UK Biobank to build more accurate cardiovascular risk models than the Framingham Risk Score and quantify the underdiagnosis of women compared to that of men. Strikingly, for a first-degree atrioventricular block and dilated cardiomyopathy, two conditions with non-sex-specific diagnostic criteria, our study shows that women are under-diagnosed 2× and 1.4× more than men. Similarly, our results demonstrate the need for sex-specific criteria in essential primary hypertension and hypertrophic cardiomyopathy. Our feature importance analysis reveals that out of the top 10 features across three sexes and four disease categories, traditional Framingham factors made up between 40% and 50%; electrocardiogram, 30%–33%; pulse wave analysis, 13%–23%; and magnetic resonance imaging and carotid ultrasound, 0%–10%. Improving the Framingham Risk Score by leveraging big data and machine learning allows us to incorporate a wider range of biomedical data and prediction features, enhance personalization and accuracy, and continuously integrate new data and knowledge, with the ultimate goal to improve accurate prediction, early detection, and early intervention in cardiovascular disease management. Our analysis pipeline and trained classifiers are freely available at https://github.com/LivingMatterLab/CardiovascularDiseaseClassification.

Computational heart modeling is a promising approach for improving the prognosis of patients born with congenital heart defects. To create accurate physics-based digital cardiac twins of this population, it is crucial to accurately represent the highly diverse and unique subject-specific heart geometry. In young pediatric patients, this is a challenging endeavor given the lack of high-spatial-resolution imaging data and the risk of slice misalignment. In this study, we set up a multistep shape morphing and slice correction approach to accommodate these challenges and establish a population of biventricular heart models for a variety of healthy, Fallot, and Fontan pediatric patients.

Impaired cardiac filling in response to increased passive myocardial stiffness contributes to the pathophysiology of heart failure. By leveraging cardiac MRI data and ventricular pressure measurements, we can estimate in vivo passive myocardial stiffness using personalized inverse finite element models. While it is well-known that this approach is subject to uncertainties, only few studies quantify the accuracy of these stiffness estimates. This lack of validation is, at least in part, due to the absence of ground truth in vivo passive myocardial stiffness values. Here, using 3D printing, we created soft, homogenous, isotropic, hyperelastic heart phantoms of varying geometry and stiffness and simulate diastolic filling by incorporating the phantoms into an MRI-compatible left ventricular inflation system. We estimate phantom stiffness from MRI and pressure data using inverse finite element analyses based on a Neo-Hookean model. We demonstrate that our identified softest and stiffest values of 215.7 and 512.3 kPa agree well with the ground truth of 226.2 and 526.4 kPa. Overall, our estimated stiffnesses revealed a good agreement with the ground truth (< 5.8 % error) across all models. Our results suggest that MRI-driven computational constitutive modeling can accurately estimate synthetic heart material stiffnesses in the range of 200–500 kPa.

Single ventricle patients, including those with hypoplastic left heart syndrome (HLHS), typically undergo three palliative heart surgeries culminating in the Fontan procedure. HLHS is associated with high rates of morbidity and mortality, and many patients develop arrhythmias, electrical dyssynchrony, and eventually ventricular failure. However, the correlation between ventricular enlargement and electrical dysfunction in HLHS physiology remains poorly understood. Here we characterize the relationship between growth and electrophysiology in HLHS using computational modeling. We integrate a personalized finite element model, a volumetric growth model, and a personalized electrophysiology model to perform controlled in silico experiments. We show that right ventricle enlargement negatively affects QRS duration and interventricular dyssynchrony. Conversely, left ventricle enlargement can partially compensate for this dyssynchrony. These findings have potential implications on our understanding of the origins of electrical dyssynchrony and, ultimately, the treatment of HLHS patients.