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 hydraulic library. Details can be found in the Supplemental Files.
	<ol>
		<li>Navigate the hydraulics library to find the required elements: hydraulic pipeline, constant volume hydraulic chamber, linear resistance, centrifugal pump, check valve, variable area orifice, and the custom hydraulic fluid.
		<ol>
			<li>Drop the hydraulic pipeline elements into the workspace. 
			&#8203;NOTE: These account for frictional losses as well as wall compliance and fluid compressibility in blood vessels and heart chambers. Through this block, the pressure loss is calculated using the Darcy-Weisbach law, whereas the change in diameter due to wall compliance depends on the compliance proportionality constant, the luminal pressure, and the time constant. Finally, fluid compressibility is defined by the bulk modulus of the medium.</li>
			<li>Insert the constant volume hydraulic chamber elements to define wall compliance and fluid compressibility. 
			&#8203;NOTE: This block does not take into account pressure losses due to friction.</li>
			<li>Add the linear resistance elements to define resistance to flow. 
			NOTE: This is independent of the geometrical properties of the vasculature, analogously to the resistive element used in electrical analog Windkessel models. Other blocks, such as the centrifugal pump, the check valve, the variable-area orifice, and the custom hydraulic fluid elements should be inserted to generate the desired pressure input to the system, model the effects of heart valves on blood flow, and define the mechanical properties of blood. Through these elements, the behavior of the cardiovascular system in both physiology and disease can be fully captured. The input signal for the centrifugal pump can be found in Figure S1A.</li>
			<li>Model the contractility of each heart chamber through the custom variable-compliance compliance chamber element. 
			NOTE: This accepts compliance as a time-varying user-defined input signal and is based on the time-varying elastance model (Figure S1B-D).</li>
		</ol>
		</li>
		<li>Provide the parameters relative to each element, as shown in Table S1, also found in Rosalia et al.15</li>
		<li>Insert a Physical Signal (PS) Repeating Sequence element for each of the blocks that require a time-varying user-defined input signal: the LV pump, the variable-compliance compliance elements, and the variable-area orifice blocks. 
		NOTE: Input signals utilized for this simulation can be found in Figure S1.</li>
		<li>Select the default ODE 23t implicit solver and run the simulation for 100 s to reach a steady state.</li>
	</ol>
	</li>
</ol>
2. The FEA model
<ol>
	<li>Simulation setup 
	NOTE: The FEA Model utilizes a coupled electrical-mechanical analysis in sequence. In this model, the electrical analysis is conducted first; then the resulting electric potentials are used as the excitation source in the following mechanical analysis. Therefore, the simulation setup contains two work domains: the electrical (ELEC) and the mechanical (MECH) domains, that are predefined in the FEA simulation software (Table of Materials)18. Hence, the following section only describes the analysis workflow. The FEA model uses the following user subroutines HETVAL, VUANISOHYPER, and UAMP for the electrical and mechanical material modeling18.
	<ol>
		<li>Navigate the ELEC domain to perform electrical analysis using the predefined temperature procedure in the Standard module.
		<ol>
			<li>Use a single-analysis step named BEAT. Set the duration of the cardiac cycle to 500 ms and apply an electrical potential pulse to a node set representing the sinoatrial (SA) node (node set: R_Atrium-1.SA_NODE).</li>
			<li>Review the default electrical waveform, which ranges from -80 mV to 20 mV over 200 ms with the smooth step amplitude definition, as described in the model guide18. Use the default values of material constants in the electrical analysis to adjust the AV delay.</li>
			<li>Launch the Job module, and create a job named heart-elec.</li>
		</ol>
		</li>
		<li>Once the electrical analysis setup is completed, navigate the MECH domain to perform the fluid cavity-based mechanical analysis. 
		NOTE: The mechanical simulation is performed after the electrical analysis, and the resulting electric potentials are used as the excitation source for the mechanical analysis. The mechanical analysis contains multiple steps.
		<ol>
			<li>Use the three main steps named PRE-LOAD, BEAT1, AND RECOVERY1. In the PRE-LOAD step, review the boundary conditions of the pre-stressed state of the heart. Use 0.3 s as the step time to linearly ramp up the pressure in the fluid chambers. 
			NOTE: The predefined fluid cavity pressure values are shown in Table S3. The pre-stressed state of the heart was already defined in the normal heart simulation setup, and the initial node conditions are provided in the external simulation files, as listed in Table S5. Recalculation of the zero-stress state using the inverse mechanical simulation is required whenever the boundary condition is modified, as explained in steps 3.2.2-3.2.4.</li>
			<li>In the BEAT1 step, use 0.5 s as the step time to simulate contraction.</li>
			<li>In the RECOVERY1 step, select 0.5 s for cardiac relaxation and ventricular filling for a heart rate of 60 bpm.</li>
			<li>Enable the subsequent steps, BEATX and RECOVERYX, to simulate more than one cardiac cycle to reach a steady state. 
			NOTE: Three cardiac cycles will be sufficient to reach steady state. One cycle of the simulation is completed in ~8 h on a 24-core processor (3.2 GHz x 24).</li>
			<li>Launch the Job module, and create a job named heart-mech, enabling the double precision option.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Review the simplified lumped-parameter Windkessel model 
	NOTE: The mechanical domain of the FEA model has a blood flow model, which is based on a simplified lumped-parameter circuit and is created as a combination of surface-based fluid cavities and fluid exchanges as seen in Figure 218.
	<ol>
		<li>Use the Windkessel representation mentioned in the above note to run the simulation. Review the blood flow model representation to adjust the values of the resistive and capacitive elements for flow resistances and structural compliances, respectively.</li>
		<li>Review the 3D finite element representation of four heart chambers, and ensure their geometrical positions are accurate.</li>
		<li>Check the heart assembly, and switch to the Interaction module to adjust the compliance and contractility values of each of the four heart chambers. 
		NOTE: The default values in the Interaction module are configured to simulate an idealized healthy human heart beat cycle18.</li>
		<li>Review the following hydrostatic fluid cavities in the Interaction module, CAV-AORTA, CAV-LA, CAV-LV, CAV-PULMONARY_TRUNK, CAV-RA, CAV-RV, CAV-SVC, CAV-ARTERIAL-COMP, CAV-PULMONARY-COMP, and CAV-VENOUS-COMP (Table S3).</li>
		<li>Use the compliance chambers (CAV-ARTERIAL-COMP, CAV-PULMONARY-COMP, and CAV-VENOUS-COMP) as cubic volumes as they represent the compliance of the arterial, venous, and pulmonary circulations.</li>
		<li>Attach three compliance cubic volumes to a grounded spring, and review the stiffness value to model the pressure-volume response in the arterial, venous, and pulmonary circulations.</li>
		<li>Check the following fluid exchange definitions between the hydrostatic fluid cavities: arterial-venous, venous-right atrium, right atrium-right ventricle, right ventricle-pulmonary system, pulmonary system-left atrium, left atrium-left ventricle, and left ventricle-aorta (Table S4).</li>
		<li>Adjust the viscous resistance coefficient to modify the blood flow model in each fluid exchange link (see Supplemental files for more information about the viscous resistance effect).</li>
	</ol>
	</li>
	<li>Multiphysics simulation
	<ol>
		<li>Locate the CAE database file in the working directory. 
		NOTE: The FEA Model in this protocol is delivered in the database and is named as LH-Human-Model-Beta-V2_1.cae.</li>
		<li>Insert the input, object, and library files to the working directory to run the simulation. See Table S5 for the full list of input and library files.</li>
		<li>Launch the FEA model simulation software (see the Table of Materials). 
		NOTE: Consult the software provider for compatibility with later versions18.</li>
		<li>Review the parts, assembly, and boundary conditions in both ELEC and MECH domains, as described in sections 2.2 and 2.3.</li>
		<li>First, run the electrical simulation job named heart-elec, as described in section 2.1.1.3. Visually inspect the electrical potential results to verify that the heart-elec simulation ran as expected. Then, ensure that the result file heart-elec.odb is in the working directory.</li>
		<li>Move to the second simulation phase by switching to the MECH domain. Review the values of the material constants used in the mechanical simulation to model the desired passive and active cardiac response.</li>
		<li>Ensure that the material library files for the mechanical analysis use the HYBRID- string name. To modify the material response of the heart chambers, adjust the appropriate hybrid material file, or replace the entire material response by defining a new material behavior in the Materials section in the CAE module. 
		NOTE: Detailed information about the built-in constitutive laws can be found in the user guide18.</li>
		<li>In the PRE-LOAD step, set the pressures of the hydrostatic cavities to obtain the desired physiologic behavior. Use the built-in smooth amplitude option to ramp up from zero to the desired pressure level as described in step 2.1.2.1.</li>
		<li>Disable the pressure boundary conditions defined in 2.1.2.1 to run the blood flow model with a constant overall blood volume within the circulation system. Run the simulation job named heart-mech, as described in section 2.1.2.5.</li>
	</ol>
	</li>
</ol>
3. Aortic valve stenosis
NOTE: Aortic stenosis is often a driver of HFpEF as it leads to pressure overload and ultimately, to concentric remodeling and compliance loss of the left ventricular wall. The hemodynamics observed in aortic stenosis often progress to those seen in HFpEF.
<ol>
	<li>The lumped-parameter model
	<ol>
		<li>Modify the input signal in the PS repeating sequence element relative to the aortic valve, located in the left ventricular compartment. Simulate a reduction of the orifice area equal to 70% compared to baseline (Table S6). 
		NOTE: The input values will represent the orifice area of the stenotic valve during each heartbeat. The orifice area value can be easily adjusted by multiplying the start output values vector of the aortic valve PS element by a decimal value corresponding to the final orifice area with respect to its original value. In this work, a factor of 0.3 was used to achieve 70% constriction.</li>
	</ol>
	</li>
	<li>The FEA model
	<ol>
		<li>Modify the fluid exchange definition of the LINK-LV-ARTERIAL parameter. 
		NOTE: This parameter possesses a viscous resistance coefficient tuned to the blood flow between the left ventricle and the aorta. The effective exchange area can be modified to adjust the blood flow and create the appropriate aortic stenosis model (Table S7).</li>
		<li>Locate the toolbox folder and copy the files inside that folder to the main working directory.</li>
		<li>Perform an inverse mechanical simulation by executing the toolbox files18. To this end, change the suction pressures of the left ventricle and left atrium to 6 mmHg in the fluid cavity to adjust their initial volumetric state for the aortic stenosis model. Execute the inversePreliminary.py function. 
		&#8203;NOTE:Recalculation of the zero-stress state using the inverse mechanical simulation is required whenever the boundary condition is modified.</li>
		<li>Once the inverse mechanical simulation is completed, run the post-processing functions: calcNodeCoords.py and straight_mv_chordae.py. Use the default values for the other flow parameters, and run a new mechanical simulation as described in section 2.1.2.5.</li>
	</ol>
	</li>
</ol>
4. HFpEF hemodynamics
NOTE: To simulate the effects of chronic remodeling, the mechanical properties of the left heart were modified.
<ol>
	<li>The lumped-parameter model
	<ol>
		<li>Modify the left ventricular diastolic compliance of the LV compliance element to mimic wall stiffening due to pressure-overload, using the value of end-diastolic compliance in Table S8. 
		NOTE: Assume compliance to drop linearly from end-systole to end-diastole.</li>
		<li>Increase the leak resistance of the LV pump to 18 &#215; 106 Pa s m-3 (Table S8) to capture the elevated left ventricular pressures observed in HFpEF.</li>
	</ol>
	</li>
	<li>The FEA model
	<ol>
		<li>Edit the active material properties of the left ventricle geometry. Increase the stiffness component to tune the active tissue response affecting the stress components in the fiber and sheet directions in the constitutive model.
		<ol>
			<li>Modify the material response of the left ventricle in the mech-mat-LV_ACTIVE file. 
			&#8203;NOTE: The magnitude of stiffness for the left ventricular chamber can be tuned to provide the appropriate diastolic compliance effects.</li>
			<li>Increase the stiffness parameters a and b in the anisotropic hyperelastic formulation to capture the increased stiffness response for the HFpEF physiology.</li>
			<li>In the PRE-LOAD step, set the fluid cavity pressures of the left ventricle and left atrium to 20 mmHg.</li>
			<li>Perform an inverse mechanical simulation to obtain the volumetric state of the left ventricle and atrium. Export the nodal coordinates from the heart-mech-inverse.odb file18.</li>
			<li>Execute the post-processing functions: calcNodeCoords.py and straight_mv_chordae.py, as described in step 3.2.4. Locate the new nodal input files in the working directory and perform a new mechanical simulation, as described in section 2.1.2.5.</li>
		</ol>
		</li>
	</ol>
	</li>
</ol>

There are no conflicts of interest associated with this work.

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><tbody><tr><td>Abaqus Software</td><td>Dassault Syst&amp;egrave;mes Simulia Corp.</td><td></td><td>Version used: 2018; FEA simulation software</td></tr><tr><td>HETVAL</td><td>Dassault Syst&amp;egrave;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&amp;egrave;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>Version used: 2020a, object-oriented numerical solver</td></tr><tr><td>SIMSCAPE FLUIDS</td><td>MathWorks</td><td></td><td></td></tr><tr><td>UAMP</td><td>Dassault Syst&amp;egrave;mes Simulia Corp.</td><td></td><td>Version used: 2018</td></tr><tr><td>VUANISOHYPER</td><td>Dassault Syst&amp;egrave;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...

Watch this Scientific Journal Video about Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction at JoVE.com

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 ...

lumped-parameter-finite-element-modeling-heart-failure-with-preserved

Research

JoVE Journal

Engineering

6.4K Views.  Massachusetts Institute of Technology. Dit protocol kan worden gebruikt om acute drukbelasting te heroveren, evenals chronisch verlies van ventriculaire naleving om de effecten van hartfalen met geconserveerde ejectiefractie op cardiovasculaire hemodynamica te onderzoeken. Ons Lumped-Parameter model is zeer rekenkundig efficiënt en de financiële bedragbenadering integreert het elektrische en structurele domein voor een nauwkeurigere modellering van cardiovasculaire hemodynamica. Er is een sterke technische behoefte aan effectiev...

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

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Patient-specific simulations of heart (dys)function aimed at personalizing cardiac therapy are hampered by the absence of in vivo imaging technology for clinically acquiring myocardial fiber orientations. The objective of this project was to develop a methodology to estimate cardiac fiber orientations from in vivo images of patient heart geometries. An accurate representation of ventricular geometry and fiber orientations was reconstructed, respectively, from high-resolution ex vivo structural magnetic resonance (MR) and diffusion tensor (DT) MR images of a normal human heart, referred to as the atlas. Ventricular geometry of a patient heart was extracted, via semiautomatic segmentation, from an in vivo computed tomography (CT) image. Using image transformation algorithms, the atlas ventricular geometry was deformed to match that of the patient. Finally, the deformation field was applied to the atlas fiber orientations to obtain an estimate of patient fiber orientations. The accuracy of the fiber estimates was assessed using six normal and three failing canine hearts. The mean absolute difference between inclination angles of acquired and estimated fiber orientations was 15.4 &deg;. Computational simulations of ventricular activation maps and pseudo-ECGs in sinus rhythm and ventricular tachycardia indicated that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.The new insights obtained from the project will pave the way for the development of patient-specific models of the heart that can aid physicians in personalized diagnosis and decisions regarding electrophysiological interventions.

A methodology to estimate ventricular fiber orientations from in vivo images of patient heart geometries for personalized modeling is described. Validation of the methodology performed using normal and failing canine hearts demonstrate that that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.

Patient-specific  simulations of heart (dys)function aimed at personalizing cardiac therapy are hampered  by the absence of in vivo imaging technology for ...

Bioengineering

Reduction in Left Ventricular Wall Stress and Improvement in Function in Failing Hearts using Algisyl-LVR

Injection of Algisyl-LVR, a treatment under clinical development, is intended to treat patients with dilated cardiomyopathy. This treatment was recently used for the first time in patients who had symptomatic heart failure. In all patients, cardiac function of the left ventricle (LV) improved significantly, as manifested by consistent reduction of the LV volume and wall stress. Here we describe this novel treatment procedure and the methods used to quantify its effects on LV wall stress and function.
Algisyl-LVR is a biopolymer gel consisting of Na+-Alginate and Ca2+-Alginate. The treatment procedure was carried out by mixing these two components and then combining them into one syringe for intramyocardial injections. This mixture was injected at 10 to 19 locations mid-way between the base and apex of the LV free wall in patients.
Magnetic resonance imaging (MRI), together with mathematical modeling, was used to quantify the effects of this treatment in patients before treatment and at various time points during recovery. The epicardial and endocardial surfaces were first digitized from the MR images to reconstruct the LV geometry at end-systole and at end-diastole. Left ventricular cavity volumes were then measured from these reconstructed surfaces.
Mathematical models of the LV were created from these MRI-reconstructed surfaces to calculate regional myofiber stress. Each LV model was constructed so that 1) it deforms according to a previously validated stress-strain relationship of the myocardium, and 2) the predicted LV cavity volume from these models matches the corresponding MRI-measured volume at end-diastole and end-systole. Diastolic filling was simulated by loading the LV endocardial surface with a prescribed end-diastolic pressure. Systolic contraction was simulated by concurrently loading the endocardial surface with a prescribed end-systolic pressure and adding active contraction in the myofiber direction. Regional myofiber stress at end-diastole and end-systole was computed from the deformed LV based on the stress-strain relationship.

This article describes procedures for implanting a novel hydrogel in failing hearts and quantifying its effect on left ventricular wall stress and function. These procedures have been successfully applied in dogs and humans.

Injection of  Algisyl-LVR, a treatment under clinical development, is intended to treat  patients with dilated cardiomyopathy. This treatment was recently ...

Medicine

Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology

With the advent of three-dimensional (3D) imaging technologies such as electron tomography, serial-block-face scanning electron microscopy and confocal microscopy, the scientific community has unprecedented access to large datasets at sub-micrometer resolution that characterize the architectural remodeling that accompanies changes in cardiomyocyte function in health and disease. However, these datasets have been under-utilized for&#160;investigating the role of cellular architecture remodeling in cardiomyocyte function. The purpose of this protocol is to outline how to create an accurate finite element model of a cardiomyocyte using high resolution electron microscopy and confocal microscopy images. A detailed and accurate model of cellular architecture has significant potential to provide new insights into cardiomyocyte biology, more than experiments alone can garner. The power of this method lies in its ability to computationally fuse information from two disparate imaging modalities of cardiomyocyte ultrastructure to develop one unified and detailed model of the cardiomyocyte. This protocol outlines steps to integrate electron tomography and confocal microscopy images of adult male Wistar (name for a specific breed of albino rat) rat cardiomyocytes to develop a half-sarcomere finite element model of the cardiomyocyte. The procedure generates a 3D finite element model that contains an accurate, high-resolution depiction (on the order of ~35 nm) of the distribution of mitochondria, myofibrils and ryanodine receptor clusters that release the necessary calcium for cardiomyocyte contraction from the sarcoplasmic reticular network (SR) into the myofibril and cytosolic compartment. The model generated here as an illustration does not incorporate details of the transverse-tubule architecture or the sarcoplasmic reticular network and is therefore a minimal model of the cardiomyocyte. Nevertheless, the model can already be applied in simulation-based investigations into the role of cell structure in calcium signaling and mitochondrial bioenergetics, which is illustrated and discussed using two case studies that are presented following the detailed protocol.

This protocol outlines a novel method to create a spatially detailed finite element model of the intracellular architecture of cardiomyocytes from electron microscopy and confocal microscopy images. The power of this spatially detailed model is demonstrated using case studies in calcium signaling and bioenergetics.

With the advent of three-dimensional (3D) imaging technologies such as electron tomography, serial-block-face scanning electron microscopy and confocal ...

 IVUS-Based Computational Method to Quantify Coronary Mechanical Properties

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery

Quantifying the mechanical properties of coronary arterial walls could provide meaningful information for the diagnosis, management, and treatment of coronary artery diseases. Since patient-specific coronary samples are not available for patients requiring continuous monitoring, direct experimental testing of vessel material properties becomes impossible. Current coronary models typically use material parameters from available literature, leading to significant mechanical stress/strain calculation errors. Here, we would introduce a finite element model-based updating approach (FEMBUA) to quantify patient-specific in vivo material properties of coronary arteries based on medical images. In vivo cine intravascular ultrasound (IVUS) and virtual histology (VH)-IVUS images of coronary arteries were acquired from a patient with coronary artery disease. Cine IVUS images showing the vascular movement over one cardiac cycle were segmented, and two IVUS frames with maximum and minimum lumen circumferences were selected to represent the coronary geometry under systolic and diastolic pressure conditions, respectively. VH-IVUS image was also segmented to obtain the vessel contours, and a layer thickness of 0.05 cm was added to the VH-IVUS contours to reconstruct the coronary geometry. A computational finite element model was created with an anisotropic Mooney-Rivlin material model used to describe the vessel's mechanical properties and pulsatile blood pressure conditions prescribed to the coronary luminal surface to make it contract and expand. Then, an iterative updating approach was employed to determine the material parameters of the anisotropic Mooney-Rivlin model by matching minimum and maximum lumen circumferences from the computational finite element model with those from cine IVUS images. This image-based finite element model-based updating approach could be successfully extended to determine the material properties of arterial walls in various vascular beds and holds the potential for risk assessment of cardiovascular diseases.

In vivo cine intravascular ultrasound images show the coronary cross-sectional movement corresponding to different pressure loading conditions. Based on a finite element model, an iterative scheme was employed to determine the patient-specific mechanical properties of coronary arteries in vivo by matching coronary motion from the computational model and medical images.

Quantifying the mechanical properties of coronary arterial walls could provide meaningful information for the diagnosis, management, and treatment of ...

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

In this paper, we present a complete workflow for the biomechanical analysis of atherosclerotic plaque in the coronary vasculature. With atherosclerosis as one of the leading causes of global death, morbidity and economic burden, novel ways of analyzing and predicting its progression are needed. One such computational method is the use of fluid-structure interaction (FSI) to analyze the interaction between the blood flow and artery/plaque domains. Coupled with in vivo imaging, this approach could be tailored to each patient, assisting in differentiating between stable and unstable plaques. We outline the three-dimensional reconstruction process, making use of intravascular Optical Coherence Tomography (OCT) and invasive coronary angiography (ICA). The extraction of boundary conditions for the simulation, including replicating the three-dimensional motion of the artery, is discussed before the setup and analysis is conducted in a commercial finite element solver. The procedure for describing the highly nonlinear hyperelastic properties of the artery wall and the pulsatile blood velocity/pressure is outlined along with setting up the system coupling between the two domains. We demonstrate the procedure by analyzing a non-culprit, mildly stenotic, lipid-rich plaque in a patient following myocardial infarction. Established and emerging markers related to atherosclerotic plaque progression, such as wall shear stress and local normalized helicity, respectively, are discussed and related to the structural response in the artery wall and plaque. Finally, we translate the results to potential clinical relevance, discuss limitations, and outline areas for further development. The method described in this paper shows promise for aiding in the determination of sites at risk of atherosclerotic progression and, hence, could assist in managing the significant death, morbidity, and economic burden of atherosclerosis.

There is a need to determine which atherosclerotic lesions will progress in the coronary vasculature to guide intervention before myocardial infarction occurs. This article outlines the biomechanical modeling of arteries from Optical Coherence Tomography using fluid-structure interaction techniques in a commercial finite element solver to help predict this progression.

In this paper, we present a complete workflow for the biomechanical analysis of atherosclerotic plaque in the coronary vasculature. With atherosclerosis ...

In Silico Clinical Trials for Cardiovascular Disease

The SILICOFCM project mainly aims to develop a computational platform for in silico clinical trials of familial cardiomyopathies (FCMs). The unique characteristic of the platform is the integration of patient-specific biological, genetic, and clinical imaging data. The platform allows the testing and optimization of medical treatment to maximize positive therapeutic outcomes. Thus, adverse effects and drug interactions can be avoided, sudden cardiac death can be prevented, and the time between the commencement of drug treatment and the desired result can be shortened. This article presents a parametric model of the left ventricle automatically generated from patient-specific ultrasound images by applying an electromechanical model of the heart. Drug effects were prescribed through specific boundary conditions for inlet and outlet flow, ECG measurements, and calcium function for heart muscle properties. Genetic data from patients were incorporated through the material property of the ventricle wall. Apical view analysis involves segmenting the left ventricle using a previously trained U-net framework and calculating the bordering rectangle based on the length of the left ventricle in the diastolic and systolic cycle. M-mode view analysis includes bordering of the characteristic areas of the left ventricle in the M-mode view. After extracting the dimensions of the left ventricle, a finite elements mesh was generated based on mesh options, and a finite element analysis simulation was run with user-provided inlet and outlet velocities. Users can directly visualize on the platform various simulation results such as pressure-volume, pressure-strain, and myocardial work-time diagrams, as well as animations of different fields such as displacements, pressures, velocity, and shear stresses.

In Silico Clinical Trials for Cardiovascular Disease

This protocol demonstrates the workflow of the SILICOFCM platform for automatically generating a parametric model of the left ventricle from patient-specific ultrasound images by applying a multi-scale electromechanical model of the heart. This platform enables in silico clinical trials intended to reduce real clinical trials and maximize positive therapeutic outcomes.

The SILICOFCM project mainly aims to develop a computational platform for in silico clinical trials of familial cardiomyopathies (FCMs). The unique ...

A Rat Model of Pressure Overload Induced Moderate Remodeling and Systolic Dysfunction as Opposed to Overt Systolic Heart Failure

In response to an injury, such as myocardial infarction, prolonged hypertension or a cardiotoxic agent, the heart initially adapts through the activation of signal transduction pathways, to counteract, in the short-term, for the cardiac myocyte loss and or the increase in wall stress. However, prolonged activation of these pathways becomes detrimental leading to the initiation and propagation of cardiac remodeling leading to changes in left ventricular geometry and increases in left ventricular volumes; a phenotype seen in patients with systolic heart failure (HF). Here, we describe the creation of a rat model of pressure overload induced moderate remodeling and early systolic dysfunction (MOD) by ascending aortic banding (AAB) via a vascular clip with an internal area of 2 mm2. The surgery is performed in 200 g Sprague-Dawley rats. The MOD HF phenotype develops at 8-12 weeks after AAB and is characterized noninvasively by means of echocardiography. Previous work suggests the activation of signal transduction pathways and altered gene expression and post-translational modification of proteins in the MOD HF phenotype that mimic those seen in human systolic HF; therefore, making the MOD HF phenotype a suitable model for translational research to identify and test potential therapeutic anti-remodeling targets in HF. The advantages of the MOD HF phenotype compared to the overt systolic HF phenotype is that it allows for the identification of molecular targets involved in the early remodeling process and the early application of therapeutic interventions. The limitation of the MOD HF phenotype is that it may not mimic the spectrum of diseases leading to systolic HF in human. Moreover, it is a challenging phenotype to create, as the AAB surgery is associated with high mortality and failure rates with only 20% of operated rats developing the desired HF phenotype.

We describe the creation of a rat model of pressure overload induced moderate remodeling and early systolic dysfunction where signal transduction pathways involved in the initiation of the remodeling process are activated. This animal model will aid in identifying molecular targets for applying early therapeutic anti-remodeling strategies for heart failure.

In response to an injury, such as myocardial infarction, prolonged hypertension or a cardiotoxic agent, the heart initially adapts through the activation ...

Revealing Subtle Changes in Cardiac Function using Transthoracic Dobutamine Stress Echocardiography in Mice

Left ventricular (LV) dysfunction paves the final pathway for a multitude of cardiac disorders. With the non-invasive high-frequency transthoracic dobutamine stress echocardiography in humans, a reductionist investigation approach to unmask subtle changes in cardiac function has become possible. Here, we provide a protocol for using this technique in mice to facilitate expanded analysis of LV architecture and function in physiology and pathology enabling the observation of alterations in models of cardiac disease hidden in unstressed hearts. This investigation can be performed in one and the same animal and allows both, basal and pharmacologically stress-induced measurements. We outline detailed criteria for appropriate anesthesia, imaging-based LV analysis, consideration of intra- and interobserver variability, and obtaining positive inotrope response that can be attained in mice after intraperitoneal injection of dobutamine under near physiological conditions. To recapitulate the characteristics of human physiology and disease in small animal models, we highlight critical pitfalls in evaluation, e.g., a pronounced Bowditch effect in mice. To further meet translational objectives, we compare stress-induced effects in humans and mice. When used in translational studies, attention must be paid to physiological differences between mice and human. Experimental rigor dictates that some parameters assessed in patients can only be used with caution due to restrictions in spatial and temporal resolution in mouse models.

Left ventricular dysfunction constitutes the final common pathway for a host of cardiac disorders. We here provide a detailed protocol of transthoracic dobutamine stress echocardiography approach for comprehensive evaluation of the left ventricular function of mouse models of cardiac disease as well as cardiac phenotyping.

Left ventricular (LV) dysfunction paves the final pathway for a multitude of cardiac disorders. With the non-invasive high-frequency transthoracic ...

A New Model of Heart Failure Post-Myocardial Infarction in the Rat

Ligation of the left anterior descending (LAD) coronary artery has been widely used to establish the rat model of heart failure (HF) post myocardial infarction (MI). However, the disadvantages of this model include high mortality rate after ligation and larger variations both in the infarct size and the degree of impaired cardiac function. In addition, a ventilator or exteriorization of the heart is indispensable for the previous models, which complicates the procedure during the ligation. In this study, we developed a reliable and reproducible model without the ventilator or exteriorization of the heart by ligating the LAD coronary artery. Four weeks after the procedure, we found that the serum concentrations of CK-MB, NT-proBNP, and Renin, which were used to assist diagnoses of MI and HF, were significantly higher in the MI group compared to the sham group. In contrast, the value of left ventricle ejection fraction (LVEF) in the MI group was obviously less than in the sham group. Furthermore, the infarct size and cardiac fibrosis area were individually confirmed and quantitatively analyzed by TTC staining and Masson's trichrome staining. Smaller variations were found in either infarct size or fibrosis area in the MI group, which helped to develop a reliable and reproducible model of HF post-MI. This new model of HF post-MI in the rat is vital for studying the potential mechanisms of MI and HF. This new method can be used to develop the new drug for treatment of MI and HF in rats by using pharmacological strategies.

We successfully developed a reliable and reproducible model of heart failure post-myocardial infarction in the rat without ventilation or exteriorization of the heart. This simplifies the procedure and benefits the further studies about the potential mechanisms behind the heart failure.

Ligation of the left anterior descending (LAD) coronary artery has been widely used to establish the rat model of heart failure (HF) post myocardial ...

A Surgical Model of Heart Failure with Preserved Ejection Fraction in Tibetan Minipigs

More than half of heart failure (HF) cases are classified as heart failure with preserved ejection fraction (HFpEF) worldwide. Large animal models are limited for investigating the fundamental mechanisms of HFpEF and identifying potential therapeutic targets. This work provides a detailed description of the surgical procedure of descending aortic constriction (DAC) in Tibetan minipigs to establish a large animal model of HFpEF. This model used a precisely controlled constriction of the descending aorta to induce chronic pressure overload in the left ventricle. Echocardiography was used to evaluate the morphological and functional changes in the heart. After 12 weeks of DAC stress, the ventricular septum was hypertrophic, but the thickness of the posterior wall was significantly reduced, accompanied by dilation of the left ventricle. However, the LV ejection fraction of the model hearts was maintained at &gt;50% during the 12-week period. Furthermore, the DAC model displayed cardiac damage, including fibrosis, inflammation, and cardiomyocyte hypertrophy. Heart failure marker levels were significantly elevated in the DAC group. This DAC-induced HFpEF in minipigs is a powerful tool for investigating molecular mechanisms of this disease and for preclinical testing.

The present protocol describes a step-by-step procedure to establish a minipig model of heart failure with preserved ejection fraction using descending aortic constriction. The methods for evaluating cardiac morphology, histology, and function of this disease model are also presented.

More than half of heart failure (HF) cases are classified as heart failure with preserved ejection fraction (HFpEF) worldwide. Large animal models are ...

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

Samenvatting

Meer video's verkennen