Kay Sun

A Computationally Efficient Formal Optimization of Regional Myocardial Contractility in a Sheep With Left Ventricular Aneurysm

A non-invasive method for estimating regional myocardial contractility in vivo would be of great value in the design and evaluation of new surgical and medical strategies to treat and/or prevent infarction-induced heart failure. As a first step towards developing such a method, an explicit finite element (FE) model-based formal optimization of regional myocardial contractility in a sheep with left ventricular (LV) aneurysm was performed using tagged magnetic resonance (MR) images and cardiac catheterization pressures. From the tagged MR images, 3-dimensional (3D) myocardial strains, LV volumes and geometry for the animal-specific 3D FE model of the LV were calculated, while the LV pressures provided physiological loading conditions. Active material parameters (T(max_B) and T(max_R)) in the non-infarcted myocardium adjacent to the aneurysm (borderzone) and in myocardium remote from the aneurysm were estimated by minimizing the errors between FE model-predicted and measured systolic strains and LV volumes using the successive response surface method for optimization. The significant depression in optimized T(max_B) relative to T(max_R) was confirmed by direct ex vivo force measurements from skinned fiber preparations. The optimized values of T(max_B) and T(max_R) were not overly sensitive to the passive material parameters specified. The computation time of less than 5 hours associated with our proposed method for estimating regional myocardial contractility in vivo makes it a potentially very useful clinical tool.

Comparison of the Young-Laplace Law and Finite Element Based Calculation of Ventricular Wall Stress: Implications for Postinfarct and Surgical Ventricular Remodeling

BACKGROUND Both the Young-Laplace law and finite element (FE) based methods have been used to calculate left ventricular wall stress. We tested the hypothesis that the Young-Laplace law is able to reproduce results obtained with the FE method. METHODS Magnetic resonance imaging scans with noninvasive tags were used to calculate three-dimensional myocardial strain in 5 sheep 16 weeks after anteroapical myocardial infarction, and in 1 of those sheep 6 weeks after a Dor procedure. Animal-specific FE models were created from the remaining 5 animals using magnetic resonance images obtained at early diastolic filling. The FE-based stress in the fiber, cross-fiber, and circumferential directions was calculated and compared to stress calculated with the assumption that wall thickness is very much less than the radius of curvature (Young-Laplace law), and without that assumption (modified Laplace). RESULTS First, circumferential stress calculated with the modified Laplace law is closer to results obtained with the FE method than stress calculated with the Young-Laplace law. However, there are pronounced regional differences, with the largest difference between modified Laplace and FE occurring in the inner and outer layers of the infarct borderzone. Also, stress calculated with the modified Laplace is very different than stress in the fiber and cross-fiber direction calculated with FE. As a consequence, the modified Laplace law is inaccurate when used to calculate the effect of the Dor procedure on regional ventricular stress. CONCLUSIONS The FE method is necessary to determine stress in the left ventricle with postinfarct and surgical ventricular remodeling.

Dor procedure for dyskinetic anteroapical myocardial infarction fails to improve contractility in the border zone

BACKGROUND Endoventricular patch plasty (Dor) is used to reduce left ventricular volume after myocardial infarction and subsequent left ventricular remodeling. METHODS AND RESULTS End-diastolic and end-systolic pressure-volume and Starling relationships were measured, and magnetic resonance images with noninvasive tags were used to calculate 3-dimensional myocardial strain in 6 sheep 2 weeks before and 2 and 6 weeks after the Dor procedure. These experimental results were previously reported. The imaging data from 1 sheep were incomplete. Animal specific finite element models were created from the remaining 5 animals using magnetic resonance images and left ventricular pressure obtained at early diastolic filling. Finite element models were optimized with 3-dimensional strain and used to determine systolic material properties, T(max,skinned-fiber), and diastolic and systolic stress in remote myocardium and border zone. Six weeks after the Dor procedure, end-diastolic and end-systolic stress in the border zone were substantially reduced. However, although there was a slight increase in T(max,skinned-fiber) in the border zone near the myocardial infarction at 6 weeks, the change was not significant. CONCLUSIONS The Dor procedure decreases end-diastolic and end-systolic stress but fails to improve contractility in the infarct border zone. Future work should focus on measures that will enhance border zone function alone or in combination with surgical remodeling.

Effect of Adjustable Passive Constraint on the Failing Left Ventricle: A Finite-Element Model Study

BACKGROUND Passive constraint is used to prevent left ventricular dilation and subsequent remodeling. However, there has been concern about the effect of passive constraint on diastolic left ventricular chamber stiffness and pump function. This study determined the relationship between constraint, diastolic wall stress, chamber stiffness, and pump function. We tested the hypothesis that passive constraint at 3 mm Hg reduces wall stress with minimal change in pump function. METHODS A three-dimensional finite-element model of the globally dilated left ventricle based on left ventricular dimensions obtained in dogs that had undergone serial intracoronary microsphere injection was created. The model was adjusted to match experimentally observed end-diastolic left ventricular volume and midventricular wall thickness. The experimental results used to create the model were previously reported. A pressure of 3, 5, 7, and 9 mm Hg was applied to the epicardium. Fiber stress, end-diastolic pressure-volume relationship, end-systolic pressure-volume relationship, and the stroke volume-end-diastolic pressure (Starling) relationship were calculated. RESULTS As epicardial constraint pressure increased, fiber stress decreased, the end-diastolic pressure-volume relationship shifted to the left, and the Starling relationship shifted down and to the right. The end-systolic pressure-volume relationship did not change. A constraining pressure of 2.3 mm Hg was associated with a 10% reduction in stroke volume, and mean end-diastolic fiber stress was reduced by 18.3% (inner wall), 15.3% (mid wall), and 14.2% (outer wall). CONCLUSIONS Both stress and cardiac output decrease in a linear fashion as the amount of passive constraint is increased. If the reduction in cardiac output is to be less than 10%, passive constraint should not exceed 2.3 mm Hg. On the other hand, this amount of constraint may be sufficient to reverse eccentric hypertrophy after myocardial infarction.

The Benefit of Enhanced Contractility in the Infarct Borderzone: A Virtual Experiment

Objectives: Contractile function in the normally perfused infarct borderzone (BZ) is depressed. However, the impact of reduced BZ contractility on left ventricular (LV) pump function is unknown. As a consequence, there have been no therapies specifically designed to improve BZ contractility. We tested the hypothesis that an improvement in borderzone contractility will improve LV pump function. Methods: From a previously reported study, magnetic resonance imaging (MRI) images with non-invasive tags were used to calculate 3D myocardial strain in five sheep 16 weeks after anteroapical myocardial infarction. Animal-specific finite element (FE) models were created using MRI data and LV pressure obtained at early diastolic filling. Analysis of borderzone function using those FE models has been previously reported. Chamber stiffness, pump function (Starling’s law) and stress in the fiber, cross fiber, and circumferential directions were calculated. Animal-specific FE models were performed for three cases: (a) impaired BZ contractility (INJURED); (b) BZ-contractility fully restored (100% BZ IMPROVEMENT); or (c) BZ-contractility partially restored (50% BZ IMPROVEMENT). Results: 100% BZ IMPROVEMENT and 50% BZ IMPROVEMENT both caused an upward shift in the Starling relationship, resulting in a large (36 and 26%) increase in stroke volume at LVPED = 20 mmHg (8.0 ml, p < 0.001). Moreover, there were a leftward shift in the end-systolic pressure volume relationship, resulting in a 7 and 5% increase in LVPES at 110 mmHg (7.7 ml, p < 0.005). It showed that even 50% BZ IMPROVEMENT was sufficient to drive much of the calculated increase in function. Conclusion: Improved borderzone contractility has a beneficial effect on LV pump function. Partial improvement of borderzone contractility was sufficient to drive much of the calculated increase in function. Therapies specifically designed to improve borderzone contractility should be developed.

In Vivo Left Ventricular Geometry and Boundary Conditions

The first basic biomechanics modeling step outlined in the introductory chapter is to define the geometric configuration. In Chapters 12 and 14 we demonstrate the application of either simple (i.e., axisymmetric truncated ellipsoid) or complex (i.e., fully 3-D) left ventricular (LV) geometric models or finite element (FE) meshes. This chapter is primarily concerned with an instructive review of the methodology we have used to create both types of FE meshes, which relies on the “parametric” meshing software TrueGrid®. Since TrueGrid is rather expensive, Section 1.6 describes the use of free software executables available from the Pacific Northwest National Laboratory. The second basic biomechanics modeling step (determine mechanical properties) is addressed in the next three chapters. The third and fourth basic biomechanics modeling steps (governing equations and boundary conditions) are discussed briefly at the end of this chapter.

Determination of Myocardial Material Properties by Optimization

The previous chapter includes a computationally efficient strain energy function for describing the three-dimensional relationship between stress and strain in passive myocardial material properties, the material parameters of which were formally optimized using left ventricular pressure and epicardial strain measurements in a cylindrical model. Results from such a model are confined at best to the equatorial region of the left ventricle. A finite element model of the entire left ventricle is required to determine regional variations in myocardial material properties. The most important or at least interesting finding from such a study is that myocardial contractility in the (border zone) region adjacent to a myocardial infarction is much less than (typically only half) that in regions remote from the myocardial infarction. This finding has been confirmed with active stress measurements in skinned muscle fibers dissected from these regions. This chapter is concerned with brief descriptions of the studies from our laboratory that have led up to our current knowledge concerning regional variations of myocardial contractility in infarcted left ventricles.

Constitutive Equations and Model Validation

Of the four basic biomechanics modeling steps outlined in the Introduction, determining the constitutive equations for cardiovascular tissue is often the most difficult step, especially when the tissue properties vary with time and sarcomere length history, as is the case with contracting myocardium. Using a cylindrical model to study transmural variations in stress and strain rather than a finite element model of the entire left ventricle allows for the implementation of a time- and sarcomere length history-dependent constitutive equation. The cylindrical model simulations can then be repeated with progressively simpler constitutive equations and the resulting transmural stress and strain distributions compared to determine under what conditions the most computationally efficient constitutive equations are valid. This chapter is primarily concerned with an instructive review of the constitutive equations we have implemented in cylindrical and finite element models of the passive and beating left ventricle, including that of diseased and surgically treated hearts. The last section of this chapter is concerned with experimental measurements that we have used to validate these models.

Residual Stress Impairs Pump Function After Surgical Ventricular Remodeling: A Finite Element Analysis

BACKGROUND Surgical ventricular restoration (Dor procedure) is generally thought to reduce left ventricular (LV) myofiber stress (FS) but to adversely affect pump function. However, the underlying mechanism is unclear. The goal of this study was to determine the effect of residual stress (RS) on LV FS and pump function after the Dor procedure. METHODS Previously described finite element models of the LV based on magnetic resonance imaging data obtained in 5 sheep 16 weeks after anteroapical myocardial infarction were used. Simulated polyethylene terephthalate fiber (Dacron) patches that were elliptical and 25% of the infarct opening area were implanted using a virtual suture technique (VIRTUAL-DOR). In each case, diastole and systole were simulated, and RS, FS, LV volumes, systolic and diastolic function, and pump (Starling) function were calculated. RESULTS VIRTUAL-DOR was associated with significant RS that was tensile (2.89 ± 1.31 kPa) in the remote myocardium and compressive (234.15 ± 65.53 kPa) in the border zone. VIRTUAL-DOR+RS (compared with VIRTUAL-DOR-NO-RS) was associated with further reduction in regional diastolic and systolic FS, with the greatest change in the border zone (43.5-fold and 7.1-fold, respectively; p < 0.0001). VIRTUAL-DOR+RS was also associated with further reduction in systolic and diastolic volumes (7.9%; p = 0.0606, and 10.6%; p = 0.0630, respectively). The resultant effect was a further reduction in pump function after VIRTUAL-DOR+RS. CONCLUSIONS Residual stress that occurs after the Dor procedure is positive (tensile) in the remote myocardium and negative (compressive) in the border zone and associated with reductions in FS and LV volumes. The resultant effect is a further reduction in LV pump (Starling) function.

Surgical Left Ventricular Remodeling Procedures

Perhaps the most straightforward clinical application of validated regional ventricular mechanics models for diseased hearts is the simulation of a novel surgical procedure or medical device for treating heart failure or ischemic cardiomyopathy. In each study our cardiac biomechanics laboratory uses one of two different approaches: (1) an axisymmetric truncated ellipsoidal model with left ventricular (LV) cavity and wall volumes typical of the failing human heart or animal model of heart failure to determine efficacy of the surgical procedure or device; or (2) an animal- or patient-specific fully 3-D model of the infarcted LV created using echocardiography or MRI to optimize the design of the surgical procedure or device. This chapter is concerned with brief descriptions of the studies from our laboratory that provide the best examples of these two approaches.