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Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction

Published: February 13th, 2021



1Institute for Medical Engineering and Science, Massachusetts Institute of Technology, 2Health Science and Technology Program, Harvard/Massachusetts Institute of Technology, 3Department of Mechanical Engineering, Massachusetts Institute of Technology
* These authors contributed equally

This work introduces two computational models of heart failure with preserved ejection fraction based on a lumped-parameter approach and finite element analysis. These models are used to evaluate the changes in the hemodynamics of the left ventricle and related vasculature induced by pressure overload and diminished ventricular compliance.

Scientific efforts in the field of computational modeling of cardiovascular diseases have largely focused on heart failure with reduced ejection fraction (HFrEF), broadly overlooking heart failure with preserved ejection fraction (HFpEF), which has more recently become a dominant form of heart failure worldwide. Motivated by the paucity of HFpEF in silico representations, two distinct computational models are presented in this paper to simulate the hemodynamics of HFpEF resulting from left ventricular pressure overload. First, an object-oriented lumped-parameter model was developed using a numerical solver. This model is based on a zero-dimensional (0D) Windkessel-like network, which depends on the geometrical and mechanical properties of the constitutive elements and offers the advantage of low computational costs. Second, a finite element analysis (FEA) software package was utilized for the implementation of a multidimensional simulation. The FEA model combines three-dimensional (3D) multiphysics models of the electro-mechanical cardiac response, structural deformations, and fluid cavity-based hemodynamics and utilizes a simplified lumped-parameter model to define the flow exchange profiles among different fluid cavities. Through each approach, both the acute and chronic hemodynamic changes in the left ventricle and proximal vasculature resulting from pressure overload were successfully simulated. Specifically, pressure overload was modeled by reducing the orifice area of the aortic valve, while chronic remodeling was simulated by reducing the compliance of the left ventricular wall. Consistent with the scientific and clinical literature of HFpEF, results from both models show (i) an acute elevation of transaortic pressure gradient between the left ventricle and the aorta and a reduction in the stroke volume and (ii) a chronic decrease in the end-diastolic left ventricular volume, indicative of diastolic dysfunction. Finally, the FEA model demonstrates that stress in the HFpEF myocardium is remarkably higher than in the healthy heart tissue throughout the cardiac cycle.

Heart failure is a leading cause of death worldwide, which occurs when the heart is unable to pump or fill adequately to keep up with the metabolic demands of the body. The ejection fraction, i.e., the relative amount of blood stored in the left ventricle that is ejected with each contraction is used clinically to classify heart failure into (i) heart failure with reduced ejection fraction (HFrEF) and (ii) heart failure with preserved ejection fraction (HFpEF), for ejection fractions less than or greater than 45%, respectively1,2,3. Symptoms of HFpEF often develop in response....

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1. 0D lumped-parameter model

  1. Simulation setup
    NOTE: In the numerical solver environment (see the Table of Materials), construct the domain as shown in Figure 1. This is composed of the 4-chamber heart, the upper body, abdominal, lower body, and thoracic compartments, as well as the proximal vasculature, including the aorta, the pulmonary artery, and the superior and inferior venae cavae. The standard elements used in this simulation are part of the default.......

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Results from the baseline simulations are illustrated in Figure 3. This depicts the pressure and volume waveforms of the left ventricle and the aorta (Figure 3A) as well as the left ventricular PV loop (Figure 3B). The two in silico models show similar aortic and left ventricular hemodynamics, which are within the physiologic range. Minor differences in the response predicted by the two platforms can be noticed during the ventricula.......

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The lumped-parameter and FEA platforms proposed in this work recapitulated the cardiovascular hemodynamics under physiologic conditions, both in the acute phase of stenosis-induced pressure overload and in chronic HFpEF. By capturing the role that pressure overload plays in the acute and chronic phases of HFpEF development, the results from these models are in agreement with the clinical literature of HFpEF, including the onset of a transaortic pressure gradient due to aortic stenosis, an increase in the left ventricular.......

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We acknowledge funding from the Harvard-Massachusetts Institute of Technology Health Sciences and Technology program, and the SITA Foundation Award from the Institute for Medical Engineering and Science.


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Name Company Catalog Number Comments
Abaqus Software Dassault Systèmes Simulia Corp. Version used: 2018; FEA simulation software
HETVAL Dassault Systèmes Simulia Corp. Version used: 2018
Hydraulic (Isothermal) library MathWorks Version used: 2020a
Living Heart Human Model Dassault Systèmes Simulia Corp. Version used: V2_1, anatomically accurate FEA platform of 4-chamber adult human heart
MATLAB MathWorks Version used: 2020a, object-oriented numerical solver
UAMP Dassault Systèmes Simulia Corp. Version used: 2018
VUANISOHYPER Dassault Systèmes Simulia Corp. Version used: 2018

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