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