Biventricular Electromechanical Heart Model

• Biventricular electromechanical heart models are 3D computational frameworks representing the LV, RV, and septum that integrate electrical activation with mechanical contraction and circulatory loading.
• They use anatomically realistic geometries and rule-based fiber architecture to capture myocardial anisotropy, accurately simulating tissue deformation and electrical propagation.
• Models range from strict 3D ventricular representations to comprehensive four-chamber systems, employing advanced numerical methods and coupling strategies for validation against physiological data.

A biventricular electromechanical human heart model is a computational model in which the left ventricle, right ventricle, and usually the interventricular septum are represented as a three-dimensional excitable and actively contracting continuum, then coupled to hemodynamic loading and circulation. In the current literature, this label spans several distinct scopes: an explicitly human “3D biventricular electromechanical model” of the ventricles coupled to a 0D closed loop (Piersanti et al., 2021), a “whole human heart electromechanics” formulation with four 3D chambers (Fedele et al., 2022), and ventricular electromechanics integrated with a deformable torso for ECG and BSPM synthesis (Zappon et al., 2024). Closely related works also include left-ventricular-only 3D electromechanics embedded in four-chamber circulation (Regazzoni et al., 2021), which makes the term “biventricular” partly dependent on whether it refers to the 3D myocardial domain or to the closed-loop cardiovascular setting.

1. Scope and model classes

The contemporary literature distinguishes between strict 3D biventricular ventricular models, broader four-chamber human electromechanics, and partial ventricular models embedded in multichamber circulation. The strict ventricular interpretation is exemplified by “3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics” (Piersanti et al., 2021), which represents the LV wall, RV wall, and interventricular septum in 3D and couples them to a 0D whole-circulation model. The broader whole-heart interpretation is exemplified by “A comprehensive and biophysically detailed computational model of the whole human heart electromechanics” (Fedele et al., 2022), where all four chambers are modeled in 3D and coupled to a closed-loop circulation. A further extension couples a human biventricular electromechanical heart to a deformable torso to study ECG and BSPM changes induced by myocardial motion (Zappon et al., 2024).

Representative paper	3D cardiac domain	Scope note
“3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics” (Piersanti et al., 2021)	LV, RV, septum	Human biventricular ventricles with 0D atria and circulation
“A comprehensive and biophysically detailed computational model of the whole human heart electromechanics” (Fedele et al., 2022)	RA, LA, LV, RV	Four-chamber human electromechanics
“An integrated heart-torso electromechanical model for the simulation of electrophysiogical outputs accounting for myocardial deformation” (Zappon et al., 2024)	LV, RV	Biventricular electromechanics plus torso conduction
“A machine learning method for real-time numerical simulations of cardiac electromechanics” (Regazzoni et al., 2021)	LV only	Single-chamber 3D LV embedded in four-chamber circulation
“Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia” (Salvador et al., 2021)	LV only	Patient-specific LV electromechanics with 0D whole circulation
“A comprehensive mathematical model for cardiac perfusion” (Zingaro et al., 2023)	Left-heart electromechanics; biventricular perfusion domain	Not a full biventricular electromechanical model

This classification resolves a common misconception. A model may report separate LV and RV pressure-volume outputs without containing a symmetric 3D biventricular myocardium. In (Regazzoni et al., 2021), the 3D full-order electromechanics is explicitly a single-chamber human LV, even though the coupled 0D circulation contains LA, RA, and RV and therefore yields separate RV hemodynamic outputs. In (Salvador et al., 2021), the 3D model is patient-specific LV only, while the RV appears only in the 0D loop. In (Zingaro et al., 2023), the electromechanics is left-heart-only, whereas the porous perfusion domain is biventricular. This makes “biventricular electromechanical human heart model” a term with a precise narrow meaning and a broader systems-level usage.

2. Anatomy, geometry, and fiber architecture

Human biventricular electromechanical models rely on anatomically realistic ventricular geometry, ventricular-specific fiber architecture, and explicit treatment of septal and basal regions. In (Piersanti et al., 2021), the reported simulations use a realistic biventricular geometry processed from the Zygote 3D heart, described as a CAD model representing an average healthy human heart reconstructed from high-resolution computed tomography. The computational 3D domain contains the LV wall, RV wall, and interventricular septum, with boundary subsets for epicardium, LV endocardium, RV endocardium, and a truncated basal plane. In (Fedele et al., 2022), the whole-heart geometry is also derived from the Zygote Solid 3D Heart Model and partitioned into atrial domains, a ventricular myocardial domain containing LV, RV, and septal continuity, arterial segments, valves represented as simplified insulating fibrous regions, and venous caps.

Fiber and sheet architecture are generally assigned by Laplace–Dirichlet rule-based methods. In (Piersanti et al., 2021), the ventricular geometry is endowed with transmural distance $\phi$, apico-basal distance $\psi$, and interventricular distance $\xi$, then rotated into $\mathbf f_0$, $\mathbf s_0$, and $\mathbf n_0$ using ventricular-specific helical and sheetlet angles. The baseline values are $\alpha_{\mathrm{epi,LV}}=-60^\circ$, $\alpha_{\mathrm{endo,LV}}=+60^\circ$, $\alpha_{\mathrm{epi,RV}}=-25^\circ$, $\alpha_{\mathrm{endo,RV}}=+90^\circ$, $\psi$0, $\psi$1, $\psi$2, and $\psi$3 (Piersanti et al., 2021). In (Fedele et al., 2022), the same LDRBM philosophy is extended to all four chambers, including ventricular outflow tracts and atrial bundles.

A major anatomical refinement for biventricular modeling is region-specific RV, septal, and outflow-tract fiber prescription. “A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts” (Doste et al., 2018) introduces the OT-RBM, in which LV and RV are treated separately, the RV sub-endocardium is longitudinal, outflow-tract sub-endocardium is longitudinal, outflow-tract sub-epicardium is circumferential, and the septum can be independently controlled. The method computes a transmural field $\psi$4 with Dirichlet values $\psi$5 on LV endocardium, $\psi$6 on RV endocardium, and $\psi$7 on epicardium, which explicitly encodes the statement that approximately two thirds of the septum belong to the LV and one third to the RV (Doste et al., 2018). This is directly relevant to biventricular electromechanics because fiber orientation affects both preferential electrical wave propagation and tissue contraction.

Population-scale anatomical infrastructure has also become available. “Integrating anatomy and electrophysiology in the healthy human heart: Insights from biventricular statistical shape analysis using universal coordinates” (Santvliet et al., 8 Jan 2025) constructs a healthy human biventricular statistical shape model from 271 high-resolution CT scans and releases 100 volumetric biventricular meshes with fibers and anatomical labels. “An Automated Computational Pipeline for Generating Large-Scale Cohorts of Patient-Specific Ventricular Models in Electromechanical In Silico Trials” (Doste et al., 5 Mar 2025) automates closure, labeling, volumetric meshing, coordinate-field generation, and biventricular rule-based fiber assignment for large virtual cohorts. These works do not themselves define a new electromechanical formulation, but they supply the anatomical and microstructural substrate required by one.

3. Electrophysiology and activation

The dominant tissue-scale electrophysiological formulation in human ventricular electromechanics is the monodomain equation coupled to ventricular ionic dynamics. In (Piersanti et al., 2021), the ventricular electrical system is

$\psi$8

with ionic state equation

$\psi$9

and homogeneous Neumann boundary conditions (Piersanti et al., 2021). The ventricular ionic model is ten Tusscher–Panfilov 2006, and conduction anisotropy is encoded by a conductivity tensor aligned with $\xi$0, $\xi$1, and $\xi$2. The reported fast-layer conductivities are $\xi$3, whereas the myocardial values are $\xi$4, with a surrogate fast endocardial layer thickness $\xi$5 (Piersanti et al., 2021).

The whole-heart model in (Fedele et al., 2022) generalizes the same deformation-aware monodomain structure to atria and ventricles, with chamber-specific ionic systems:

$\xi$6

using Courtemanche–Ramirez–Nattel in atria and TTP06 in ventricles (Fedele et al., 2022). Ventricular conduction includes a fast endocardial layer acting as a Purkinje surrogate, with conductivities $\xi$7 in that layer and $\xi$8 in ventricular myocardium (Fedele et al., 2022).

Activation sequence modeling varies by model scope. In (Piersanti et al., 2021), five endocardial pacing sites and a fast endocardial layer surrogate the Purkinje system, yielding a total activation time of about $\xi$9. In (Fedele et al., 2022), applied spherical impulses represent SAN initiation, atrial propagation, AV delay, and slightly earlier LV than RV endocardial stimulation, with $\mathbf f_0$0, $\mathbf f_0$1, $\mathbf f_0$2, LV stimulus times $\mathbf f_0$3, and RV stimulus times $\mathbf f_0$4 (Fedele et al., 2022). For torso-integrated simulations, (Zappon et al., 2024) adds a pseudo-bidomain recovery of extracellular potential and then solves a passive conduction problem in a deforming torso, which makes surface potentials sensitive to both myocardial activation and myocardial motion.

A distinct but complementary direction is high-fidelity whole-heart electrophysiology without mechanics. “A fast computational model for the electrophysiology of the whole human heart” (Corso et al., 2021) represents a single 3D ventricular myocardium containing LV and RV, a 1D fast conduction system, and a 2D Purkinje layer, with the ten Tusscher–Panfilov 2006 ventricular model and explicit left and right bundle branches. It is not an electromechanical model, but it provides an electrical backbone for later biventricular electromechanical integration.

4. Mechanics and excitation–contraction coupling

Human biventricular electromechanical models combine finite-strain passive mechanics with either active stress or active strain. In (Piersanti et al., 2021), the mechanical balance is

$\mathbf f_0$5

with

$\mathbf f_0$6

and a passive orthotropic Guccione law

$\mathbf f_0$7

with $\mathbf f_0$8, $\mathbf f_0$9, $\mathbf s_0$0, $\mathbf s_0$1, $\mathbf s_0$2, $\mathbf s_0$3, $\mathbf s_0$4, and $\mathbf s_0$5 (Piersanti et al., 2021). The active-force generation model is an ANN-based surrogate of RDQ18, driven by intracellular calcium and sarcomere length, with baseline $\mathbf s_0$6, $\mathbf s_0$7, and $\mathbf s_0$8. The same paper reports that sheet-direction active stress counteracts myofiber contraction, whereas sheet-normal active stress enhances cardiac work (Piersanti et al., 2021).

The four-chamber human model in (Fedele et al., 2022) uses the RDQ20 model of Regazzoni–Dede’–Quarteroni, where

$\mathbf s_0$9

and tissue-level active tension is

$\mathbf n_0$0

The passive law is the Usyk et al. exponential law plus volumetric penalization,

$\mathbf n_0$1

with chamber-specific stiffness $\mathbf n_0$2, $\mathbf n_0$3, $\mathbf n_0$4, bulk modulus $\mathbf n_0$5, and active stress directional shares $\mathbf n_0$6 (Fedele et al., 2022). A distinctive feature is fibers-stretch-rate feedback; the authors state that without this feedback semilunar valve fluxes become unphysiologically large despite apparently reasonable PV loops (Fedele et al., 2022).

An alternative formulation appears in (Salvador et al., 2021), where patient-specific LV ischemic cardiomyopathy is modeled with an active strain decomposition $\mathbf n_0$7. The same spatial heterogeneity coefficient $\mathbf n_0$8 modifies electrical conductivity, ionic conductances, activation, and passive stiffness, with

$\mathbf n_0$9

which increases passive stiffness in scarred regions (Salvador et al., 2021). Although this is LV-only in 3D, the constitutive and multiphysics architecture is directly transferable to a biventricular infarct model.

A more recent clinically oriented variant is “Electromechanical human heart modeling for predicting endocardial heart motion” (Hasani et al., 4 Sep 2025), which combines a monodomain reaction-diffusion model, voltage-dependent active stress,

$\alpha_{\mathrm{epi,LV}}=-60^\circ$0

orthotropic projection

$\alpha_{\mathrm{epi,LV}}=-60^\circ$1

and two-way fluid-structure interaction with actual 3D ventricular blood meshes. The reported validation against Cine MRI showed consistency in regional displacement patterns, especially in the RV free wall (Hasani et al., 4 Sep 2025).

5. Circulatory loading, closed-loop coupling, and multiphysics extensions

A defining feature of advanced biventricular electromechanics is 3D–0D coupling through cavity volume consistency and pressure loading. In (Piersanti et al., 2021), the 0D closed-loop circulation includes left atrium, right atrium, left ventricle, right ventricle, systemic arterial and venous compartments, pulmonary arterial and venous compartments, and valves modeled as non-ideal diodes. The ventricular 0D chambers are replaced by 3D ventricles using

$\alpha_{\mathrm{epi,LV}}=-60^\circ$2

while $\alpha_{\mathrm{epi,LV}}=-60^\circ$3 and $\alpha_{\mathrm{epi,LV}}=-60^\circ$4 act as Lagrange multipliers enforcing these constraints (Piersanti et al., 2021). This makes the circulation-biventricle interface fundamentally pressure–volume based rather than flux- or displacement-prescribed.

The same principle is generalized in (Fedele et al., 2022) to all four chambers:

$\alpha_{\mathrm{epi,LV}}=-60^\circ$5

The paper argues that realistic healthy biventricular function cannot be understood in isolation from atrial contraction, atrioventricular plane motion, and closed-loop circulation, because these determine ventricular preload, timing, and chamber interaction (Fedele et al., 2022). This extends the notion of a biventricular model from ventricular wall mechanics alone to ventricular function inside a four-chamber loop.

Two major multiphysics extensions have been added to this core architecture. The first is torso coupling. In (Zappon et al., 2024), cardiac displacement is transferred to the torso through a pseudo-deformation solve, and cardiac extracellular potential is imposed at the heart–torso interface. The authors report non-negligible effects of myocardial contraction on ECGs and BSPMs, especially in ventricular tachycardia, where deformation and mechano-electric feedback can alter the apparent arrhythmic phenotype (Zappon et al., 2024). The second is true 3D ventricular blood interaction. In (Hasani et al., 4 Sep 2025), intraventricular blood is modeled as incompressible Newtonian fluid in ALE form, coupled to the myocardium by the standard interface conditions

$\alpha_{\mathrm{epi,LV}}=-60^\circ$6

and integrated into systemic and pulmonary 0D circulation (Hasani et al., 4 Sep 2025). This is a stronger treatment of intracavitary loading than pressure-only cavity models.

Perfusion provides a different extension axis. In (Zingaro et al., 2023), left-heart electromechanics is coupled to left-heart and coronary hemodynamics plus a three-compartment Darcy perfusion model on a biventricular porous domain. The electromechanics is not itself biventricular, but the work shows how ventricular mechanics, aortic-root flow, coronary outlet conditions, and myocardial blood flow maps can be embedded in one framework (Zingaro et al., 2023).

6. Numerical strategies, validation, and unresolved issues

The numerical burden of human biventricular electromechanics is substantial, and the literature reflects several distinct acceleration strategies. In (Piersanti et al., 2021), the Segregated-Intergrid-Staggered method uses $\alpha_{\mathrm{epi,LV}}=-60^\circ$7 hexahedral finite elements, a fine electrophysiology mesh about four times finer than the mechanics mesh, BDF2 IMEX for electrophysiology, BDF1 explicit for activation, BDF1 fully implicit for mechanics and volume constraints, and explicit RK4 for circulation. A 3D-0D-3D V-cycle is used to accelerate convergence to the limit cycle, reducing the effective cost to about six 3D heartbeats (Piersanti et al., 2021). In (Fedele et al., 2022), the whole heart is discretized on a single tetrahedral mesh with different FE spaces for different physics, and stabilization of the segregated-intergrid-staggered formulation is emphasized as crucial in the four-chamber scenario (Fedele et al., 2022).

A second acceleration route is surrogate modeling. “A machine learning method for real-time numerical simulations of cardiac electromechanics” (Regazzoni et al., 2021) constructs a non-intrusive ANN-based reduced-order model in which the reduced state $\alpha_{\mathrm{epi,LV}}=-60^\circ$8 satisfies

$\alpha_{\mathrm{epi,LV}}=-60^\circ$9

The method requires only pressure and volume transients from the full model and achieves a speedup by more than three orders of magnitude, enabling global sensitivity analysis and Bayesian parameter estimation that would otherwise be unaffordable (Regazzoni et al., 2021). However, the underlying 3D full-order model in that paper is single-chamber LV only, not a 3D biventricular myocardium.

A third route is cohort automation. In (Doste et al., 5 Mar 2025), preprocessing from ventricular surface meshes to simulation-ready files takes approximately 10 minutes per case, and electromechanical simulations require approximately 2 hours real time per case on HPC. The pipeline automatically labels epicardium, LV endocardium, RV endocardium, RV septal endocardium, basal plane or valve rings, computes Laplace-derived coordinate fields, assigns biventricular rule-based fibers, and exports solver-ready files for Alya and MonoAlg3D (Doste et al., 5 Mar 2025). This suggests that large-scale in silico trials with biventricular ventricular models are becoming operationally feasible.

Validation remains strongly dependent on the target output. (Piersanti et al., 2021) reports simulated EDV, ESV, EF, systolic pressure, longitudinal fractional shortening, and wall thickening within reported literature ranges for both ventricles. (Fedele et al., 2022) emphasizes simultaneous agreement of pressure-volume loops, time evolution of pressures, volumes and fluxes, and three-dimensional deformation across all heart chambers. (Zappon et al., 2024) validates at the level of physiologic Wiggers synchronization and deformation-induced changes in ECG and BSPM, whereas (Hasani et al., 4 Sep 2025) validates regional ventricular motion against Cine MRI and identifies the RV basal and mid free walls as the regions with the largest motion (Hasani et al., 4 Sep 2025).

Several unresolved issues are recurrent. First, fiber architecture remains a dominant uncertainty. In the murine but structurally relevant study “The functional impact of myofiber macroscopic organization and disarray in computational models of the murine heart” (Guastamacchia et al., 1 Apr 2026), passive mechanics and electrophysiological activation are only weakly affected by fiber disarray, whereas active mechanics is highly sensitive to fiber architecture. This suggests that biventricular human models may tolerate rule-based fibers for activation timing more readily than for pump-function prediction. Second, the meaning of “biventricular” remains model-dependent: a system can be biventricular at the hemodynamic level while remaining LV-only in 3D myocardium (Regazzoni et al., 2021). Third, whole-heart fidelity introduces additional dependencies on atrial contraction, AV-plane motion, and stabilization strategies that are not present in isolated ventricular models (Fedele et al., 2022).

Taken together, the literature defines the biventricular electromechanical human heart model not as a single fixed architecture but as a family of progressively richer formulations. At one end lie 3D LV–RV ventricular continua coupled to 0D circulation; at the other lie four-chamber, torso-coupled, perfusion-coupled, or FSI-enhanced frameworks. The persistent core, across these variants, is the combination of anatomically structured ventricular geometry, anisotropic activation, finite-strain myocardial mechanics, excitation–contraction coupling, and pressure–volume-consistent interaction with the circulation (Piersanti et al., 2021).