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.

1. 0D lumped-parameter model
<ol>
	<li>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...

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...

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 to left ventricular pressure overload, which can be caused by several conditions including aortic stenosis, hypertension, and left ventricular outflow tract obstruction3,4,5,6,7. Pressure overload drives a cascade of molecular and cellular aberrations, leading to thickening of the left ventricular wall (concentric remodeling) and ultimately, to wall stiffening or loss of compliance8,9,10. These biomechanical changes profoundly affect cardiovascular hemodynamics as they result in an elevated end-diastolic pressure-volume relationship and in a reduction of the end-diastolic volume11.
Computational modeling of the cardiovascular system has advanced the understanding of blood pressures and flows in both physiology and disease and has fostered the development of diagnostic and therapeutic strategies12. In silico&#160;models are classified into low- or high-dimensional models, with the former utilizing analytical methods to evaluate global hemodynamic properties with low computational demand and the latter providing a more extensive multiscale and multiphysics description of cardiovascular mechanics and hemodynamics in the 2D or 3D domain13. The lumped-parameter Windkessel representation is the most common among the low-dimensional descriptions. Based on the electrical circuit analogy (Ohm&#39;s law), this mimics the overall hemodynamic behavior of the cardiovascular system through a combination of resistive, capacitive, and inductive elements14. A recent study by this group has proposed an alternative Windkessel model in the hydraulic domain that allows the modeling of changes in the geometry and mechanics of large vessels-heart chambers and valves-in a more intuitive way than traditional electrical analog models. This simulation is developed on an object-oriented numerical solver (see the Table of Materials) and can capture the normal hemodynamics, physiologic effects of cardiorespiratory coupling, respiratory-driven blood flow in single-heart physiology, and hemodynamic changes due to aortic constriction. This description expands upon the capabilities of lumped-parameter models by offering a physically intuitive approach to model a spectrum of pathologic conditions including heart failure15.
High-dimensional models are based on FEA to compute spatiotemporal hemodynamics and fluid-structure interactions. These representations can provide detailed and accurate descriptions of the local blood flow field; however, due to their low computational efficiency, they are not suitable for studies of the entire cardiovascular tree16,17. A software package (see the Table of Materials) was employed as an anatomically accurate FEA platform of the 4-chamber adult human heart, which integrates the electro-mechanical response, structural deformations, and fluid cavity-based hemodynamics. The adapted human heart model also comprises a simple lumped-parameter model that defines the flow exchange among the different fluid cavities, as well as a complete mechanical characterization of the cardiac tissue18,19.
Several lumped-parameter and FEA models of heart failure have been formulated to capture hemodynamic abnormalities and evaluate therapeutic strategies, particularly in the context of mechanical circulatory assist devices for HFrEF20,21,22,23,24. A broad array of 0D lumped-parameter models of various complexities has therefore successfully captured the hemodynamics of the human heart in physiological and HFrEF conditions via optimization of two or three-element electrical analog Windkessel systems20,21,23,24. The majority of these representations are uni- or biventricular models based on the time varying-elastance formulation to reproduce the contractile action of the heart and use a non-linear end-diastolic pressure-volume relationship to describe ventricular filling25,26,27. Comprehensive models, which capture the complex cardiovascular network and mimic both the atrial and ventricular pumping action, have been used as platforms for device testing. Nevertheless, although a significant body of literature exists around the field of HFrEF, very few in silico models of HFpEF have been proposed20,22,28,29,30,31.
A low-dimensional model of HFpEF hemodynamics, recently developed by Burkhoff et al.32 and Granegger et al.28, can capture the pressure-volume (PV) loops of the 4-chamber heart, fully recapitulating the hemodynamics of various phenotypes of HFpEF. Furthermore, they utilize their in silico platform to evaluate the feasibility of a mechanical circulatory device for HFpEF, pioneering computational research of HFpEF for physiology studies as well as device development. However, these models remain unable to capture the dynamic changes in blood flows and pressures observed during disease progression. A recent study by Kadry et al.30 captures the various phenotypes of diastolic dysfunction by adjusting the active relaxation of the myocardium and the passive stiffness of the left ventricle on a low-dimensional model. Their work provides a comprehensive hemodynamic analysis of diastolic dysfunction based on both the active and passive properties of the myocardium. Similarly, the literature of high-dimensional models has primarily focused on HFrEF19,33,34,35,36,37. Bakir et al.33 proposed a fully-coupled cardiac fluid-electromechanics FEA model to predict the HFrEF hemodynamic profile and the efficacy of a left-ventricular assist device (LVAD). This biventricular (or two-chamber) model utilized a coupled Windkessel circuit to simulate the hemodynamics of the healthy heart, HFrEF and HFrEF with LVAD support33,37.
Similarly, Sack et al.35 developed a biventricular model to investigate right ventricular dysfunction. Their biventricular geometry was obtained from a patient&#39;s magnetic resonance imaging (MRI) data, and the model&#39;s finite-element mesh was constructed using image segmentation to analyze the hemodynamics of a VAD-supported failing right ventricle35. Four-chamber FEA cardiac approaches have been developed to enhance the accuracy of models of the electromechanical behavior of the heart19,34. In contrast to biventricular descriptions, MRI-derived four-chamber models of the human heart provide a better representation of the cardiovascular anatomy18. The heart model employed in this work is an established example of a four-chamber FEA model. Unlike lumped-parameter and biventricular FEA models, this representation captures hemodynamic changes as they occur during disease progression34,37. Genet et al.34, for example, used the same platform to implement a numerical growth model of the remodeling observed in HFrEF and HFpEF. However, these models evaluate the effects of cardiac hypertrophy on structural mechanics only and do not provide a comprehensive description of the associated hemodynamics.
To address the lack of HFpEF in silico&#160;models in this work, the lumped-parameter model previously developed by this group15 and the FEA model were readapted to simulate the hemodynamic profile of HFpEF. To this end, the ability of each model to simulate cardiovascular hemodynamics at baseline will be first demonstrated. The effects of stenosis-induced left ventricular pressure overload and of diminished left ventricular compliance due to cardiac remodeling-a typical hallmark of HFpEF-will then be evaluated.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>Abaqus Software</td>
			<td>Dassault Syst&#232;mes Simulia Corp.</td>
			<td></td>
			<td>Version used: 2018; FEA simulation software</td>
		</tr>
		<tr>
			<td>HETVAL</td>
			<td>Dassault Syst&#232;mes Simulia Corp.</td>
			<td></td>
			<td>Version used: 2018</td>
		</tr>
		<tr>
			<td>Hydraulic (Isothermal) library</td>
			<td>MathWorks</td>
			<td></td>
			<td>Version used: 2020a</td>
		</tr>
		<tr>
			<td>Living Heart Human Model</td>
			<td>Dassault Syst&#232;mes Simulia Corp.</td>
			<td></td>
			<td>Version used: V2_1, anatomically accurate FEA platform of 4-chamber adult human heart</td>
		</tr>
		<tr>
			<td>MATLAB</td>
			<td>MathWorks</td>
			<td></td>
			<td rowspan="2">Version used: 2020a, object-oriented numerical solver</td>
		</tr>
		<tr>
			<td>SIMSCAPE FLUIDS</td>
			<td>MathWorks</td>
			<td></td>
		</tr>
		<tr>
			<td>UAMP</td>
			<td>Dassault Syst&#232;mes Simulia Corp.</td>
			<td></td>
			<td>Version used: 2018</td>
		</tr>
		<tr>
			<td>VUANISOHYPER</td>
			<td>Dassault Syst&#232;mes Simulia Corp.</td>
			<td></td>
			<td>Version used: 2018</td>
		</tr>
	</tbody>
</table>

lumped-parameter and finite element modeling of heart failure with preserved ejection fraction

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.

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

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 ...

This protocol can be used to recapitulate acute pressure load, as well as chronic loss of ventricular compliance to investigate the effects of heart failure with preserved ejection fraction on cardiovascular hemodynamics. Our Lumped-Parameter model is very computationally efficient and the financial amount approach integrates the electrical and structural domain for a more accurate modeling of cardiovascular hemodynamics. There is a strong technical need for effective treatments for EFPEF.Computational methods like ours, are paramount in the development and regulatory approval of medical devices and therapeutics. To set up a zero dimension Lumped-parameter model, after constructing a domain in the numerical solver environment as illustrated, navigate to the hydraulics library to find the required elements and drop the hydraulic pipeline elements into the workspace. Insert the constant volume hydraulic chamber elements to define the wall compliance and fluid compressibility.And add the linear resistance elements to define the resistance to flow. Model the contractility of each heart chamber through the custom variable compliance compliance chamber element and provide the parameters relative to each element as illustrated in the table. Then insert a physical signal repeating sequence element for each of the blocks that require a time varying user defined input signal, select the default ODE 23 T implicit solver and run the simulation for 100 seconds to reach a steady state.To set up a finite element analysis model, navigate to the electrical domain and select the standard module. Select the single analysis beat step. Set the duration of the cardiac cycle to 500 milliseconds and apply an electrical potential poles to a node set representing the sinoatrial node.After reviewing the default electrical wave form, launch the job module and create a heart electrical job. Once the electrical analysis setup is complete, navigate to the mechanical domain in the preload step. Review the boundary conditions of the pre-stressed state of the heart and select 0.3 seconds as the step time.In the beat one step, use 0.5 seconds as the step time to simulate contraction. In the recovery one step, select 0.5 seconds for cardiac relaxation and ventricular filling for a heart rate of 60 beats per minute. Launch the job module and create a heart mechanical job.Enable the double precision option. Review the simplified Lumped-parameter wind castle model and the blood flow model representation adjusting the values of the resistive and capacitive elements for the flow resistances and structural compliances, respectively as necessary. Review the 3D finite elements representation of the four heart chambers and confirm that their geometrical positions are accurate.After checking the heart assembly, switch to the interaction module to adjust the compliance and contractility values of each of the four heart chambers. Review the stiffness value to model the pressure volume response in the arterial, venus, and pulmonary circulations and adjust the viscous resistance coefficient to modify the blood flow model in each food exchange link. For a multi-physics simulation, insert the input, object, and library files into the working directory and launch the finite element analysis model simulation software.Run the electrical stimulation heart electrical job, and confirm that the resulting ODB file is in the working directory. Switch to the mechanical domain to move to the second simulation phase. In the preload step, use the built-in smooth amplitude option to increase the pressure level from zero to the desired level.Then disable the pressure boundary conditions to run the blood flow model with a constant overall blood volume within the circulation system and run the heart mic simulation job. To simulate aortic valve stenosis in a lumped parameter model, in the left ventricular compartment, modify the input signal relative to the aortic valve and simulate a reduction of the orifice area equal to 70%compared to baseline. To simulate aortic valve stenosis and the FEA model, modify the fluid exchange definition of the link left ventricle arterial parameter, and execute the toolbox files to perform an inverse mechanical simulation.Once the inverse mechanical simulation is complete, run the post-processing functions as indicated. Then watch the job module and create a heart mech job to run a new mechanical simulation as demonstrated To mimic wall stiffening due to pressure overload in the lumped-parameter model, modify the left ventricular diastolic compliance of the left ventricle compliance element and increase the leak resistance of the left ventricle pump to 18 times 10 to the six pascals per second per meter. To simulate the effects of chronic remodeling in the finite element analysis model, edit the active material properties of the left ventricle geometry and modify the material response of the left ventricle in the mechanical material left ventricle active file.To capture the increased stiffness response for the heart failure with preserved ejection fraction physiology, increase the A and B stiffness parameters in the anisotropic hyperelastic formulation. In the preload step, set the fluid cavity pressures of the left ventricle and left atrium to 20 millimeters of mercury and perform an inverse mechanical simulation to obtain the volumetric state of the left ventricle and atrium. Then execute the post-processing functions as indicated and perform a new mechanical simulation as demonstrated.The two in silico models to show similar aortic and left ventricular hemodynamics within the physiologic range. Under aortic stenosis conditions, pressure and volume wave forms demonstrate a 70%reduction of the aortic valve orifice area in both models. Both models are also able to capture the increase in the systolic left ventricular pressure due to the rise and afterload induced by aortic stenosis.Upon remodeling and left ventricular compliance loss, the end-diastolic pressure volume relationship becomes elevated resulting in higher end diastolic pressures and lower end diastolic volumes. These phenomena, which are due to the inability of the left ventricle to relax and feel adequately are successfully captured by the heart failure with preserved ejection fraction pressure volume loops in both the low and high dimensional models. The flow through the mitral valve data highlights both the early relaxation and atrial contraction phases.Compared to the normal and stenosis profiles, the heart failure with preserved ejection fraction flow was characterized by a slightly higher peak early relaxation phase mitral flow, and a significantly diminished peak atrial contraction phase flow. As illustrated in these myocardium stress maps, elevated stresses can be observed in the heart failure with preserved ejection fraction due to the characteristic loss of ventricular compliance. To model the chronic effects of pressure overload and thus recapitulate the hemodynamics of heart failure with preserved ejection fraction, it is critical to change the ventricular compliance in each simulation accordingly.The stolic stiffness can be parametrically investigated to simulate various phenotypes of diastolic dysfunction. This will enable us to more comprehensively characterize the effects of diminished compliance on disease. We hope that our work paves the way toward the creation of models that can advance our current understanding of heart failure with preserved ejection fraction and supports the development of therapies for this condition.

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6.1K visualizações.  Massachusetts Institute of Technology. Este protocolo pode ser usado para recapitular a carga de pressão aguda, bem como a perda crônica da conformidade ventricular para investigar os efeitos da insuficiência cardíaca com fração de ejeção preservada na hemodinâmica cardiovascular. Nosso modelo lumped-parameter é muito computacionalmente eficiente e a abordagem da quantidade financeira integra o domínio elétrico e estrutural para uma modelagem mais precisa da hemodinâmica cardiovascular. Há uma forte necessidade técn...