---
title: Biventricular Electromechanical Heart Model
url: https://www.emergentmind.com/topics/biventricular-electromechanical-human-heart-model
type: topic
---

# Biventricular Electromechanical Heart Model

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 [2108.01907], a “whole human heart electromechanics” formulation with four 3D chambers [2207.12460], and ventricular electromechanics integrated with a deformable torso for ECG and BSPM synthesis [2402.06308]. Closely related works also include left-ventricular-only 3D electromechanics embedded in four-chamber circulation [2110.13212], 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” [2108.01907], 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” [2207.12460], 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 [2402.06308].

| Representative paper | 3D cardiac domain | Scope note |
|---|---|---|
| “3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics” [2108.01907] | LV, RV, septum | Human biventricular ventricles with 0D atria and circulation |
| “A comprehensive and biophysically detailed computational model of the whole human heart electromechanics” [2207.12460] | RA, LA, LV, RV | Four-chamber human electromechanics |
| “An integrated heart-torso electromechanical model for the simulation of electrophysiogical outputs accounting for myocardial deformation” [2402.06308] | LV, RV | Biventricular electromechanics plus torso conduction |
| “A machine learning method for real-time numerical simulations of cardiac electromechanics” [2110.13212] | 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” [2106.12811] | LV only | Patient-specific LV electromechanics with 0D whole circulation |
| “A comprehensive mathematical model for cardiac perfusion” [2303.13914] | 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 [2110.13212], 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 [2106.12811], the 3D model is patient-specific LV only, while the RV appears only in the 0D loop. In [2303.13914], 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 [2108.01907], 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 [2207.12460], 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 [2108.01907], 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 \(\alpha_{\mathrm{epi,LV}}=-60^\circ\), \(\alpha_{\mathrm{endo,LV}}=+60^\circ\), \(\alpha_{\mathrm{epi,RV}}=-25^\circ\), \(\alpha_{\mathrm{endo,RV}}=+90^\circ\), \(\beta_{\mathrm{epi,LV}}=+20^\circ\), \(\beta_{\mathrm{endo,LV}}=-20^\circ\), \(\beta_{\mathrm{epi,RV}}=+20^\circ\), and \(\beta_{\mathrm{endo,RV}}=0^\circ\) [2108.01907]. In [2207.12460], 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” [1809.08297] 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 \(\Phi\) with Dirichlet values \(-2\) on LV endocardium, \(1\) on RV endocardium, and \(0\) on epicardium, which explicitly encodes the statement that approximately two thirds of the septum belong to the LV and one third to the RV [1809.08297]. 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” [2501.04504] 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” [2503.03706] 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 [2108.01907], the ventricular electrical system is
$$
J \chi_m \left[ C_m \frac{\partial u}{\partial t} + I_{\mathrm{ion}}(u,\boldsymbol{w}) \right] - \nabla \cdot \left( J F^{-1} D F^{-T} \nabla u \right) = J \chi_m I_{\mathrm{app}}(t),
$$
with ionic state equation
$$
\frac{\partial \boldsymbol{w}}{\partial t} - H(u,\boldsymbol{w}) = \boldsymbol{0},
$$
and homogeneous Neumann boundary conditions [2108.01907]. The ventricular ionic model is ten Tusscher–Panfilov 2006, and conduction anisotropy is encoded by a conductivity tensor aligned with \(\mathbf f_0\), \(\mathbf s_0\), and \(\mathbf n_0\). The reported fast-layer conductivities are \((4.28,1.96,0.64)\ \mathrm{mS/cm}\), whereas the myocardial values are \((1.07,0.49,0.16)\ \mathrm{mS/cm}\), with a surrogate fast endocardial layer thickness \(\epsilon=0.01\) [2108.01907].

The whole-heart model in [2207.12460] generalizes the same deformation-aware monodomain structure to atria and ventricles, with chamber-specific ionic systems:
$$
J \chi_m \left[ C_m \frac{\partial u}{\partial t} + I_{\mathrm{ion}}(u,\mathbf{w}_1,\mathbf{w}_2) \right] - \nabla \cdot \left( J F^{-1} D F^{-T} \nabla u \right) = J \chi_m I_{\mathrm{app}}(t),
$$
using Courtemanche–Ramirez–Nattel in atria and TTP06 in ventricles [2207.12460]. Ventricular conduction includes a fast endocardial layer acting as a Purkinje surrogate, with conductivities \((8.00,4.40,2.20)\times 10^{-4}\ \mathrm{m}^2/\mathrm{s}\) in that layer and \((2.00,1.10,0.55)\times 10^{-4}\ \mathrm{m}^2/\mathrm{s}\) in ventricular myocardium [2207.12460].

Activation sequence modeling varies by model scope. In [2108.01907], five endocardial pacing sites and a fast endocardial layer surrogate the Purkinje system, yielding a total activation time of about \(120\ \mathrm{ms}\). In [2207.12460], applied spherical impulses represent SAN initiation, atrial propagation, AV delay, and slightly earlier LV than RV endocardial stimulation, with \(T_{\mathrm{hb}}=0.8\ \mathrm{s}\), \(\delta t=3\ \mathrm{ms}\), \(r=3\times10^{-3}\ \mathrm{m}\), LV stimulus times \((160,160,160)\ \mathrm{ms}\), and RV stimulus times \((165,172)\ \mathrm{ms}\) [2207.12460]. For torso-integrated simulations, [2402.06308] 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” [2112.12854] 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 [2108.01907], the mechanical balance is
$$
\rho_s \frac{\partial^2 d}{\partial t^2} - \nabla \cdot P(d,a(s)) = \boldsymbol{0},
$$
with
$$
P(d,a) = \frac{\partial \mathcal{W}(F)}{\partial F} + a(\xi,s) \left[ n_f \frac{F\mathbf{f}_0\otimes \mathbf{f}_0}{\sqrt{I_{4f}}} + n_s \frac{F\mathbf{s}_0\otimes \mathbf{s}_0}{\sqrt{I_{4s}}} + n_n \frac{F\mathbf{n}_0\otimes \mathbf{n}_0}{\sqrt{I_{4n}}} \right],
$$
and a passive orthotropic Guccione law
$$
\mathcal{W} = \frac{\kappa}{2}(J-1)\log J + \frac{a}{2}(e^Q - 1)
$$
with \(a=0.88\times10^3\ \mathrm{Pa}\), \(\kappa=50\times10^3\ \mathrm{Pa}\), \(b_{ff}=8\), \(b_{ss}=6\), \(b_{nn}=3\), \(b_{fs}=12\), \(b_{fn}=3\), and \(b_{sn}=3\) [2108.01907]. The active-force generation model is an ANN-based surrogate of RDQ18, driven by intracellular calcium and sarcomere length, with baseline \(n_f=0.7\), \(n_s=0\), and \(n_n=0.3\). The same paper reports that sheet-direction active stress counteracts myofiber contraction, whereas sheet-normal active stress enhances cardiac work [2108.01907].

The four-chamber human model in [2207.12460] uses the RDQ20 model of Regazzoni–Dede’–Quarteroni, where
$$
\frac{\partial z}{\partial t} = K\!\left(z,\,w_{Ca},\,SL,\,\frac{\partial SL}{\partial t}\right),
$$
and tissue-level active tension is
$$
a(z,SL)=a_{\mathrm{XB}}^{\,i}\, G(z,SL).
$$
The passive law is the Usyk et al. exponential law plus volumetric penalization,
$$
\mathcal{W}(F) = \frac{C^i}{2}\left(e^Q-1\right) + \frac{B}{2}(J-1)\log J,
$$
with chamber-specific stiffness \(C^V=0.88\times10^3\ \mathrm{Pa}\), \(C^{RA}=1.47\times10^3\ \mathrm{Pa}\), \(C^{LA}=1.76\times10^3\ \mathrm{Pa}\), bulk modulus \(B=50\times10^3\ \mathrm{Pa}\), and active stress directional shares \((n_f,n_s,n_n)=(1,0,0.4)\) [2207.12460]. 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 [2207.12460].

An alternative formulation appears in [2106.12811], where patient-specific LV ischemic cardiomyopathy is modeled with an active strain decomposition \(F=F_EF_A\). The same spatial heterogeneity coefficient \(\eta(\mathbf{x})\) modifies electrical conductivity, ionic conductances, activation, and passive stiffness, with
$$
\bar{C} = C[\eta + (1-\eta)4.56],
$$
which increases passive stiffness in scarred regions [2106.12811]. 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” [2509.04024], which combines a monodomain reaction-diffusion model, voltage-dependent active stress,
$$
\frac{\partial S_a}{\partial t} = \epsilon(\phi)\left(k(\phi-\phi_r)-S_a\right),
$$
orthotropic projection
$$
S_{act}=S_a\left(V_f\, f\otimes f + V_s\, s\otimes s + V_n\, n\otimes n\right),
$$
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 [2509.04024].

## 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 [2108.01907], 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
$$
V_{\mathrm{LV}}^{0D}(c(t)) = V_{\mathrm{LV}}^{3D}(d(t)), \qquad
V_{\mathrm{RV}}^{0D}(c(t)) = V_{\mathrm{RV}}^{3D}(d(t)),
$$
while \(p_{\mathrm{LV}}(t)\) and \(p_{\mathrm{RV}}(t)\) act as Lagrange multipliers enforcing these constraints [2108.01907]. This makes the circulation-biventricle interface fundamentally pressure–volume based rather than flux- or displacement-prescribed.

The same principle is generalized in [2207.12460] to all four chambers:
$$
V_{RA}^{3D}(\mathbf{d}(t)) = V_{RA}^{0D}(c(t)),\quad
V_{LA}^{3D}(\mathbf{d}(t)) = V_{LA}^{0D}(c(t)),\quad
V_{RV}^{3D}(\mathbf{d}(t)) = V_{RV}^{0D}(c(t)),\quad
V_{LV}^{3D}(\mathbf{d}(t)) = V_{LV}^{0D}(c(t)).
$$
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 [2207.12460]. 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 [2402.06308], 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 [2402.06308]. The second is true 3D ventricular blood interaction. In [2509.04024], intraventricular blood is modeled as incompressible Newtonian fluid in ALE form, coupled to the myocardium by the standard interface conditions
$$
v_{fluid}=\dot u_{solid},\qquad \sigma_{fluid}n=\sigma_{solid}n,
$$
and integrated into systemic and pulmonary 0D circulation [2509.04024]. This is a stronger treatment of intracavitary loading than pressure-only cavity models.

Perfusion provides a different extension axis. In [2303.13914], 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 [2303.13914].

## 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 [2108.01907], the Segregated-Intergrid-Staggered method uses \(\mathbb{Q}_1\) 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 [2108.01907]. In [2207.12460], 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 [2207.12460].

A second acceleration route is surrogate modeling. “A machine learning method for real-time numerical simulations of cardiac electromechanics” [2110.13212] constructs a non-intrusive ANN-based reduced-order model in which the reduced state \(z(t)\) satisfies
$$
\frac{dz(t)}{dt} = NN\!\left( z(t), p_{\mathrm{LV}}(t), \cos\!\left(\frac{2\pi t}{\tau_{\mathrm{HB}}}\right), \sin\!\left(\frac{2\pi t}{\tau_{\mathrm{HB}}}\right), \boldsymbol\mu_M; w \right).
$$
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 [2110.13212]. 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 [2503.03706], 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 [2503.03706]. This suggests that large-scale in silico trials with biventricular ventricular models are becoming operationally feasible.

Validation remains strongly dependent on the target output. [2108.01907] reports simulated EDV, ESV, EF, systolic pressure, longitudinal fractional shortening, and wall thickening within reported literature ranges for both ventricles. [2207.12460] emphasizes simultaneous agreement of pressure-volume loops, time evolution of pressures, volumes and fluxes, and three-dimensional deformation across all heart chambers. [2402.06308] validates at the level of physiologic Wiggers synchronization and deformation-induced changes in ECG and BSPM, whereas [2509.04024] validates regional ventricular motion against Cine MRI and identifies the RV basal and mid free walls as the regions with the largest motion [2509.04024].

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” [2604.00881], 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 [2110.13212]. Third, whole-heart fidelity introduces additional dependencies on atrial contraction, AV-plane motion, and stabilization strategies that are not present in isolated ventricular models [2207.12460].

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 [2108.01907].

Source: https://www.emergentmind.com/topics/biventricular-electromechanical-human-heart-model