An atlas-based geometry pipeline for cardiac Hermite model construction and diffusion tensor reorientation

Modeling material transport regulation and traffic jam in neurons using PDE-constrained optimization

The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of transport. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in complex geometries of neurons. The transport is controlled to avoid traffic jam of materials by minimizing a pre-defined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using isogeometric analysis (IGA). Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neuron.

A clinically applicable strategy to estimate the in vivo distribution of mechanical material properties of the right ventricular wall

A clinically applicable approach to estimate the in vivo mechanical material properties of the heart wall is presented. This optimization-based inverse estimation approach applies a shape-based objective functional combined with rigid body registration and incremental parameterization of heterogeneity to use standard clinical imaging data along with simplified representations of cardiac function to provide consistent and physically meaningful solution estimates. The capability of the inverse estimation algorithm is evaluated through application to two clinically obtained human datasets to estimate the passive elastic mechanical properties of the heart wall, with an emphasis on the right ventricle. One dataset corresponded to a subject with normal heart function, while the other corresponded to a subject with severe pulmonary hypertension, and therefore expected to have a substantially stiffer right ventricle. Patient-specific pressure-driven bi-ventricle finite element analysis was used as the forward model and the endocardial surface of the right ventricle was used as the target data for the inverse problem. By using the right ventricle alone as the target of the inverse problem the relative sensitivity of the objective function to the right ventricle properties is increased. The method was able to identify material properties to accurately match the corresponding shape of the simplified forward model to the clinically obtained target data, and the properties obtained for the example cases are consistent with the clinical expectation for the right ventricle. Additionally, the material property estimates indicate significant heterogeneity in the heart wall for both subjects, and more so for the subject with pulmonary hypertension.

A finite element model of the cardiac ventricles with coupled circulation: Biventricular mesh generation with hexahedral elements, airbags and a functional mockup interface to the circulation

INTRODUCTION

Finite element (FE) mechanics models of the heart are becoming more sophisticated. However, there is lack of consensus about optimal element type and coupling of FE models to the circulation. We describe biventricular (left (LV) and right (RV) ventricles) FE mechanics model creation using hexahedral elements, airbags and a functional mockup interface (FMI) to lumped-parameter models of the circulation.

METHODS

Cardiac MRI (CMR) was performed in two healthy volunteers and a single patient with ischemic heart disease (IHD). CMR images were segmented and surfaced, meshing with hexahedral elements was performed with a "thin butterfly with septum" topology. LV and RV inflow and outflow airbags were coupled to lumped-parameter circulation models with an FMI interface. Pulmonary constriction (PAC) and vena cava occlusion (VCO) were simulated and end-systolic pressure-volume relations (ESPVR) were calculated.

RESULTS

Mesh construction was prompt with representative contouring and mesh adjustment requiring 32 and 26 min Respectively. The numbers of elements ranged from 4104 to 5184 with a representative Jacobian of 1.0026 ± 0.4531. Agreement between CMR-based surfaces and mesh was excellent with root-mean-squared error of 0.589 ± 0.321 mm. The LV ESPVR slope was 3.37 ± 0.09 in volunteers but 2.74 in the IHD patient. The effect of PAC and VCO on LV ESPVR was consistent with ventricular interaction (p = 0.0286).

CONCLUSION

Successful co-simulation using a biventricular FE mechanics model with hexahedral elements, airbags and an FMI interface to lumped-parameter model of the circulation was demonstrated. Future studies will include comparison of element type and study of cardiovascular pathologies and device therapies.

Deep learning of material transport in complex neurite networks

Neurons exhibit complex geometry in their branched networks of neurites which is essential to the function of individual neuron but also brings challenges to transport a wide variety of essential materials throughout their neurite networks for their survival and function. While numerical methods like isogeometric analysis (IGA) have been used for modeling the material transport process via solving partial differential equations (PDEs), they require long computation time and huge computation resources to ensure accurate geometry representation and solution, thus limit their biomedical application. Here we present a graph neural network (GNN)-based deep learning model to learn the IGA-based material transport simulation and provide fast material concentration prediction within neurite networks of any topology. Given input boundary conditions and geometry configurations, the well-trained model can predict the dynamical concentration change during the transport process with an average error less than 10% and [Formula: see text] times faster compared to IGA simulations. The effectiveness of the proposed model is demonstrated within several complex neurite networks.

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.

3D Hermite Transform Optical Flow Estimation inLeft Ventricle CT Sequences

Heart diseases are the most important causes of death in the world and over the years, thestudy of cardiac movement has been carried out mainly in two dimensions, however, it is important toconsider that the deformations due to the movement of the heart occur in a three-dimensional space.The 3D + t analysis allows to describe most of the motions of the heart, for example, the twistingmotion that takes place on every beat cycle that allows us identifying abnormalities of the heartwalls. Therefore, it is necessary to develop algorithms that help specialists understand the cardiacmovement. In this work, we developed a new approach to determine the cardiac movement inthree dimensions using a differential optical flow approach in which we use the steered Hermitetransform (SHT) which allows us to decompose cardiac volumes taking advantage of it as a model ofthe human vision system (HVS). Our proposal was tested in complete cardiac computed tomography(CT) volumes ( 3D + t), as well as its respective left ventricular segmentation. The robustness tonoise was tested with good results. The evaluation of the results was carried out through errors inforwarding reconstruction, from the volume at time t to time t + 1 using the optical flow obtained(interpolation errors). The parameters were tuned extensively. In the case of the 2D algorithm, theinterpolation errors and normalized interpolation errors are very close and below the values reportedin ground truth flows. In the case of the 3D algorithm, the results were compared with another similarmethod in 3D and the interpolation errors remained below 0.1. These results of interpolation errorsfor complete cardiac volumes and the left ventricle are shown graphically for clarity. Finally, a seriesof graphs are observed where the characteristic of contraction and dilation of the left ventricle isevident through the representation of the 3D optical flow.

A framework for biomechanics simulations using four-chamber cardiac models

Computational cardiac models have been extensively used to study different cardiac biomechanics; specifically, finite-element analysis has been one of the tools used to study the internal stresses and strains in the cardiac wall during the cardiac cycle. Cubic-Hermite finite element meshes have been used for simulating cardiac biomechanics due to their convergence characteristics and their ability to capture smooth geometries compactly-fewer elements are needed to build the cardiac geometry-compared to linear tetrahedral meshes. Such meshes have previously been used only with simple ventricular geometries with non-physiological boundary conditions due to challenges associated with creating cubic-Hermite meshes of the complex heart geometry. However, it is critical to accurately capture the different geometric characteristics of the heart and apply physiologically equivalent boundary conditions to replicate the in vivo heart motion. In this work, we created a four-chamber cardiac model utilizing cubic-Hermite elements and simulated a full cardiac cycle by coupling the 3D finite element model with a lumped circulation model. The myocardial fiber-orientations were interpolated within the mesh using the Log-Euclidean method to overcome the singularity associated with interpolation of orthogonal matrices. Physiologically equivalent rigid body constraints were applied to the nodes along the valve plane and the accuracy of the resulting simulations were validated using open source clinical data. We then simulated a complete cardiac cycle of a healthy heart and a heart with acute myocardial infarction. We compared the pumping functionality of the heart for both cases by calculating the ventricular work. We observed a 20% reduction in acute work done by the heart immediately after myocardial infarction. The myocardial wall displacements obtained from the four-chamber model are comparable to actual patient data, without requiring complicated non-physiological boundary conditions usually required in truncated ventricular heart models.

Cardiac image modelling: Breadth and depth in heart disease

With the advent of large-scale imaging studies and big health data, and the corresponding growth in analytics, machine learning and computational image analysis methods, there are now exciting opportunities for deepening our understanding of the mechanisms and characteristics of heart disease. Two emerging fields are computational analysis of cardiac remodelling (shape and motion changes due to disease) and computational analysis of physiology and mechanics to estimate biophysical properties from non-invasive imaging. Many large cohort studies now underway around the world have been specifically designed based on non-invasive imaging technologies in order to gain new information about the development of heart disease from asymptomatic to clinical manifestations. These give an unprecedented breadth to the quantification of population variation and disease development. Also, for the individual patient, it is now possible to determine biophysical properties of myocardial tissue in health and disease by interpreting detailed imaging data using computational modelling. For these population and patient-specific computational modelling methods to develop further, we need open benchmarks for algorithm comparison and validation, open sharing of data and algorithms, and demonstration of clinical efficacy in patient management and care. The combination of population and patient-specific modelling will give new insights into the mechanisms of cardiac disease, in particular the development of heart failure, congenital heart disease, myocardial infarction, contractile dysfunction and diastolic dysfunction.

DTI template-based estimation of cardiac fiber orientations from 3D ultrasound

PURPOSE

Cardiac muscle fibers directly affect the mechanical, physiological, and pathological properties of the heart. Patient-specific quantification of cardiac fiber orientations is an important but difficult problem in cardiac imaging research. In this study, the authors proposed a cardiac fiber orientation estimation method based on three-dimensional (3D) ultrasound images and a cardiac fiber template that was obtained from magnetic resonance diffusion tensor imaging (DTI).

METHODS

A DTI template-based framework was developed to estimate cardiac fiber orientations from 3D ultrasound images using an animal model. It estimated the cardiac fiber orientations of the target heart by deforming the fiber orientations of the template heart, based on the deformation field of the registration between the ultrasound geometry of the target heart and the MRI geometry of the template heart. In the experiments, the animal hearts were imaged by high-frequency ultrasound, T1-weighted MRI, and high-resolution DTI.

RESULTS

The proposed method was evaluated by four different parameters: Dice similarity coefficient (DSC), target errors, acute angle error (AAE), and inclination angle error (IAE). Its ability of estimating cardiac fiber orientations was first validated by a public database. Then, the performance of the proposed method on 3D ultrasound data was evaluated by an acquired database. Their average values were 95.4% ± 2.0% for the DSC of geometric registrations, 21.0° ± 0.76° for AAE, and 19.4° ± 1.2° for IAE of fiber orientation estimations. Furthermore, the feasibility of this framework was also performed on 3D ultrasound images of a beating heart.

CONCLUSIONS

The proposed framework demonstrated the feasibility of using 3D ultrasound imaging to estimate cardiac fiber orientation of in vivo beating hearts and its further improvements could contribute to understanding the dynamic mechanism of the beating heart and has the potential to help diagnosis and therapy of heart disease.

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

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

High-order finite element methods for cardiac monodomain simulations

Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.

Left Ventricular Diastolic and Systolic Material Property Estimation from Image Data: LV Mechanics Challenge

Cardiovascular simulations using patient-specific geometries can help researchers understand the mechanical behavior of the heart under different loading or disease conditions. However, to replicate the regional mechanics of the heart accurately, both the nonlinear passive and active material properties must be estimated reliably. In this paper, automated methods were used to determine passive material properties while simultaneously computing the unloaded reference geometry of the ventricles for stress analysis. Two different approaches were used to model systole. In the first, a physiologically-based active contraction model [1] coupled to a hemodynamic three-element Windkessel model of the circulation was used to simulate ventricular ejection. In the second, developed active tension was directly adjusted to match ventricular volumes at end-systole while prescribing the known end-systolic pressure. These methods were tested in four normal dogs using the data provided for the LV mechanics challenge [2]. The resulting end-diastolic and end-systolic geometry from the simulation were compared with measured image data.

Atlas-based quantification of cardiac remodeling due to myocardial infarction

Myocardial infarction leads to changes in the geometry (remodeling) of the left ventricle (LV) of the heart. The degree and type of remodeling provides important diagnostic information for the therapeutic management of ischemic heart disease. In this paper, we present a novel analysis framework for characterizing remodeling after myocardial infarction, using LV shape descriptors derived from atlas-based shape models. Cardiac magnetic resonance images from 300 patients with myocardial infarction and 1991 asymptomatic volunteers were obtained from the Cardiac Atlas Project. Finite element models were customized to the spatio-temporal shape and function of each case using guide-point modeling. Principal component analysis was applied to the shape models to derive modes of shape variation across all cases. A logistic regression analysis was performed to determine the modes of shape variation most associated with myocardial infarction. Goodness of fit results obtained from end-diastolic and end-systolic shapes were compared against the traditional clinical indices of remodeling: end-diastolic volume, end-systolic volume and LV mass. The combination of end-diastolic and end-systolic shape parameter analysis achieved the lowest deviance, Akaike information criterion and Bayesian information criterion, and the highest area under the receiver operating characteristic curve. Therefore, our framework quantitatively characterized remodeling features associated with myocardial infarction, better than current measures. These features enable quantification of the amount of remodeling, the progression of disease over time, and the effect of treatments designed to reverse remodeling effects.

Atlas-based Anatomical Modeling and Analysis of Heart Disease

Heart shape and function are major determinants of disease severity and predictors of future morbidity and mortality. Many studies now rely on non-invasive cardiac imaging techniques to quantify structural and functional changes. Statistical anatomical modeling of heart shape and motion provides a new tool for the quantification and evaluation of heart disease. This review surveys recent progress in the evaluation of statistical shape measures across populations and sub-cohorts, and highlights collaborative efforts to facilitate data sharing and atlas-based shape analysis.

Automatic 4D reconstruction of patient-specific cardiac mesh with 1-to-1 vertex correspondence from segmented contours lines

We propose an automatic algorithm for the reconstruction of patient-specific cardiac mesh models with 1-to-1 vertex correspondence. In this framework, a series of 3D meshes depicting the endocardial surface of the heart at each time step is constructed, based on a set of border delineated magnetic resonance imaging (MRI) data of the whole cardiac cycle. The key contribution in this work involves a novel reconstruction technique to generate a 4D (i.e., spatial-temporal) model of the heart with 1-to-1 vertex mapping throughout the time frames. The reconstructed 3D model from the first time step is used as a base template model and then deformed to fit the segmented contours from the subsequent time steps. A method to determine a tree-based connectivity relationship is proposed to ensure robust mapping during mesh deformation. The novel feature is the ability to handle intra- and inter-frame 2D topology changes of the contours, which manifests as a series of merging and splitting of contours when the images are viewed either in a spatial or temporal sequence. Our algorithm has been tested on five acquisitions of cardiac MRI and can successfully reconstruct the full 4D heart model in around 30 minutes per subject. The generated 4D heart model conforms very well with the input segmented contours and the mesh element shape is of reasonably good quality. The work is important in the support of downstream computational simulation activities.

Mapping Cardiac Fiber Orientations from High-Resolution DTI to High-Frequency 3D Ultrasound

The orientation of cardiac fibers affects the anatomical, mechanical, and electrophysiological properties of the heart. Although echocardiography is the most common imaging modality in clinical cardiac examination, it can only provide the cardiac geometry or motion information without cardiac fiber orientations. If the patient's cardiac fiber orientations can be mapped to his/her echocardiography images in clinical examinations, it may provide quantitative measures for diagnosis, personalized modeling, and image-guided cardiac therapies. Therefore, this project addresses the feasibility of mapping personalized cardiac fiber orientations to three-dimensional (3D) ultrasound image volumes. First, the geometry of the heart extracted from the MRI is translated to 3D ultrasound by rigid and deformable registration. Deformation fields between both geometries from MRI and ultrasound are obtained after registration. Three different deformable registration methods were utilized for the MRI-ultrasound registration. Finally, the cardiac fiber orientations imaged by DTI are mapped to ultrasound volumes based on the extracted deformation fields. Moreover, this study also demonstrated the ability to simulate electricity activations during the cardiac resynchronization therapy (CRT) process. The proposed method has been validated in two rat hearts and three canine hearts. After MRI/ultrasound image registration, the Dice similarity scores were more than 90% and the corresponding target errors were less than 0.25 mm. This proposed approach can provide cardiac fiber orientations to ultrasound images and can have a variety of potential applications in cardiac imaging.

An automatic service for the personalization of ventricular cardiac meshes

Computational cardiac physiology has great potential to improve the management of cardiovascular diseases. One of the main bottlenecks in this field is the customization of the computational model to the anatomical and physiological status of the patient. We present a fully automatic service for the geometrical personalization of cardiac ventricular meshes with high-order interpolation from segmented images. The method is versatile (able to work with different species and disease conditions) and robust (fully automatic results fulfilling accuracy and quality requirements in 87% of 255 cases). Results also illustrate the capability to minimize the impact of segmentation errors, to overcome the sparse resolution of dynamic studies and to remove the sometimes unnecessary anatomical detail of papillary and trabecular structures. The smooth meshes produced can be used to simulate cardiac function, and in particular mechanics, or can be used as diagnostic descriptors of anatomical shape by cardiologists. This fully automatic service is deployed in a cloud infrastructure, and has been made available and accessible to the scientific community.

Mathematical model of the anatomy and fibre orientation field of the left ventricle of the heart

Background

One of the main factors affecting propagation of electrical waves and contraction in ventricles of the heart is anisotropy of cardiac tissue. Anisotropy is determined by orientation of myocardial fibres. Determining fibre orientation field and shape of the heart is important for anatomically accurate modelling of electrical and mechanical function of the heart. The aim of this paper is to introduce a theoretical rule-based model for anatomy and fibre orientation of the left ventricle (LV) of the heart and to compare it with experimental data. We suggest explicit analytical formulae that allow us to obtain the left ventricle form and its fibre direction field. The ventricle band concept of cardiac architecture given by Torrent-Guasp is chosen as the model postulate.

Methods

In our approach, anisotropy of the heart is derived from some general principles. The LV is considered as a set of identical spiral surfaces, each of which can be produced from the other by rotation around one vertical axis. Each spiral surface is filled with non-intersecting curves which represent myocardial fibres.

For model verification, we use experimental data on fibre orientation in human and canine hearts.

Results

LV shape and anisotropy are represented by explicit analytical expressions in a curvilinear 3-D coordinate system. The derived fibre orientation field shows good qualitative agreement with experimental data. The model reveals the most thorough quantitative simulation of fibre angles at the LV middle zone.

Conclusions

Our analysis shows that the band concept can generate realistic anisotropy of the LV. Our model shows good qualitative agreement between the simulated fibre orientation field and the experimental data on LV anisotropy, and the model can be used for various numerical simulations to study the effects of anisotropy on cardiac excitation and mechanical function.

Multi-parametric MRI as an indirect evaluation tool of the mechanical properties of in-vitro cardiac tissues

Background

Early detection of heart failure is essential to effectively reduce related mortality. The quantification of the mechanical properties of the myocardium, a primordial indicator of the viability of the cardiac tissue, is a key element in patient’s care. Despite an incremental utilization of multi-parametric magnetic resonance imaging (MRI) for cardiac tissue characteristics and function, the link between multi-parametric MRI and the mechanical properties of the heart has not been established. We sought to determine the parametric relationship between the myocardial mechanical properties and the MR parameters. The specific aim was to develop a reproducible evaluative quantitative tool of the mechanical properties of cardiac tissue using multi-parametric MRI associated to principal component analysis.

Methods

Samples from porcine hearts were submitted to a multi-parametric MRI acquisition followed by a uniaxial tensile test. Multi linear regressions were performed between dependent (Young’s modulus E) and independent (relaxation times T1, T2 and T2*, magnetization transfer ratio MTR, apparent diffusion coefficient ADC and fractional anisotropy FA) variables. A principal component analysis was used to convert the set of possibly correlated variables into a set of linearly uncorrelated variables.

Results

Values of 46.1±12.7 MPa for E, 729±21 ms for T1, 61±6 ms for T2, 26±7 for T2*, 35±5% for MTRx100, 33.8±4.7 for FAx10^-2, and 5.85±0.21 mm²/s for ADCx10^-4 were measured. Multi linear regressions showed that only 45% of E can be explained by the MRI parameters. The principal component analysis reduced our seven variables to two principal components with a cumulative variability of 63%, which increased to 80% when considering the third principal component.

Conclusions

The proposed multi-parametric MRI protocol associated to principal component analysis is a promising tool for the evaluation of mechanical properties within the left ventricle in the in vitro porcine model. Our in vitro experiments will now allow us focused in vivo testing on healthy and infracted hearts in order to determine useful quantitative MR-based biomarkers.

A three-dimensional finite element model of human atrial anatomy: new methods for cubic Hermite meshes with extraordinary vertices

High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 mm, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology.