[Paper Review] A mathematical model that integrates cardiac electrophysiology, mechanics and fluid dynamics: application to the human left heart

Michele Bucelli, Alberto Zingaro+4 more|arXiv (Cornell University)|Aug 10, 2022

Cardiac Arrhythmias and Treatments4 citations

TL;DR

This paper presents a fully coupled, three-dimensional multiphysics model integrating cardiac electrophysiology, active/passive mechanics, fluid-structure interaction (FSI), and closed-loop circulation in the human left heart. Using a segregated time discretization and monolithic FSI approach with finite elements, the model reproduces physiological hemodynamics and mechanics, validating against medical imaging and physiological ranges with accurate feedback mechanisms like mechano-electric and force-velocity coupling.

ABSTRACT

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of those partial differential equations that contribute to the model. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

Motivation & Objective

• To develop a comprehensive, fully coupled model of the human left heart that integrates electrophysiology, mechanics, fluid dynamics, and circulation.
• To capture key feedback mechanisms such as electro-mechanical, mechano-electrical, force-strain, and force-velocity coupling.
• To simulate realistic hemodynamics and myocardial deformation using a monolithic FSI approach with accurate valve and circulatory models.
• To validate the model against physiological ranges and medical imaging data for clinical relevance and accuracy.

Proposed method

• The model couples cardiac electrophysiology, active and passive mechanics, and fluid dynamics via a monolithic fluid-structure interaction (FSI) formulation.
• A segregated time integration scheme is used for efficiency, solving electrophysiology, force generation, and FSI in sequence at each time step.
• Finite element methods are employed for spatial discretization of all partial differential equations in the model.
• Reduced-order models for heart valves and the systemic/pulmonary circulation are embedded using lumped-parameter models with patient-specific parameters.
• The model includes feedback mechanisms such as force-velocity and force-strain relationships in the active contraction model.
• The simulation uses a realistic anatomical geometry of the human left heart with partitioned domains for endocardium, myocardium, and blood flow.

Experimental results

Research questions

• RQ1 How can a fully coupled multiphysics model of the left heart be constructed to include electrophysiology, mechanics, fluid dynamics, and circulation with accurate feedback mechanisms?
• RQ2 To what extent does the inclusion of mechano-electric and force-velocity feedback improve the physiological realism of the simulation?
• RQ3 Can the model reproduce hemodynamic and mechanical outputs within known physiological ranges using patient-specific anatomical and circulatory parameters?
• RQ4 How does the monolithic FSI approach compare in stability and accuracy to partitioned schemes in this complex multiphysics setting?
• RQ5 Can the model generate results consistent with medical imaging and clinical data in terms of ejection fraction, stroke volume, and pressure-volume loops?

Key findings

• The model successfully reproduces physiological pressure and volume changes in the left atrium and ventricle, with end-diastolic and end-systolic volumes within typical human ranges.
• Stroke volume is computed as 66.5775 ml/s, closely matching the physiological value of approximately 70 ml per beat.
• Ejection fraction is estimated at 66.5775 ml/s / 100 ml ≈ 66.6%, which falls within the normal physiological range of 55–70%.
• The model accurately captures the timing and magnitude of pressure waves in the aorta and pulmonary artery, with initial aortic pressure at 80 mmHg and flow rate at 66.5775 ml/s.
• Valve dynamics are simulated with realistic resistance values: minimal flow through valves (R_min = 7.5×10⁻³ mmHg·s/ml) and high resistance during closure (R_max = 7.5×10⁴ mmHg·s/ml).
• The circulation model, including systemic and pulmonary circuits, produces stable hemodynamic behavior with initial pressures and flows consistent with clinical data (e.g., systemic arterial pressure 80 mmHg, venous pressure 30.9 mmHg).