Jonathan F. Wenk

Numerical Modeling of Stress in Stenotic Arteries With Microcalcifications: A Micromechanical Approximation

Most finite element models of atherosclerotic arteries do not account for the heterogeneity of the plaque constituents at the microscale. Failure of plaque lesions has been shown to be a local event, linked to stress concentrations caused by cap thinning, inflammation, macroscopic heterogeneity, and recently, the presence of microcalcifications. There is growing evidence that microcalcifications exist in the fibrous cap of plaque lesions. However, their role is not yet fully understood. The goal of the present work is to investigate the effects of localized regions of microcalcifications on the stress field of atherosclerotic plaque caps in a section of carotid artery. This is achieved by performing finite element simulations of three-dimensional fluid-structure interaction models. The material response in the region of microcalcification is modeled using a combination of finite elements, homogenization theory, and a stress concentration function that approximates the average local stresses in the fibrous tissue and microcalcification phases. The results indicate that the circumferential stress in the fibrous tissue phase increases as the volume fraction of microcalcifications is increased, and that the stress exceeds a critical threshold when the fibrous cap thickness is decreased. Furthermore, the presence of the microcalcifications significantly influences the distribution of stress by shifting the maximum circumferential stress away from the cap shoulders, where failure is most common when the effective region of microcalcification is located at the center of the cap. This is a possible explanation of why 40% of plaque ruptures occur away from the shoulder region of the cap.

First Evidence of Depressed Contractility in the Border Zone of a Human Myocardial Infarction

BACKGROUND The temporal progression in extent and severity of regional myofiber contractile dysfunction in normally perfused border zone (BZ) myocardium adjacent to a myocardial infarction (MI) has been shown to be an important pathophysiologic feature of the adverse remodeling process in large animal models. We sought, for the first time, to document the presence of impaired contractility of the myofibers in the human BZ myocardium. METHODS A 62-year-old man who experienced an MI in 1985 and had recently had complete revascularization was studied. Myofiber systolic contractile stress developed in the normally perfused BZ adjacent to the MI (T(max_B)) and that developed in regions remote from the MI (T(max_R)) were quantified using cardiac catheterization, magnetic resonance imaging, and mathematical modeling. RESULTS The resulting finite element model of the patients beating left ventricle was able to simulate the reduced systolic strains measured using magnetic resonance imaging at matching left ventricular pressures and volumes. The T(max_B) (73.1 kPa) was found to be greatly reduced relative to T(max_R) (109.5 kPa). These results were found to be independent of assumptions relating to BZ myofiber orientation. CONCLUSIONS The results of this study document the presence of impaired contractility of the myofibers in the BZ myocardium and support its role in the post-MI remodeling process in patients. To fully establish this important conclusion serial evaluations beginning at the time of the index MI will need to be performed in a cohort of patients. The current study supports the importance and demonstrates the feasibility of larger and longer-term studies.

Experimental and Computational Investigation of Altered Mechanical Properties in Myocardium after Hydrogel Injection

The material properties of myocardium are an important determinant of global left ventricular function. Myocardial infarction results in a series of maladaptive geometric alterations which lead to increased stress and risk of heart failure. In vivo studies have demonstrated that material injection can mitigate these changes. More importantly, the material properties of these injectates can be tuned to minimize wall thinning and ventricular dilation. The current investigation combines experimental data and finite element modeling to correlate how injectate mechanics and volume influence myocardial wall stress. Experimentally, mechanics were characterized with biaxial testing and injected hydrogel volumes were measured with magnetic resonance imaging. Injection of hyaluronic acid hydrogel increased the stiffness of the myocardium/hydrogel composite region in an anisotropic manner, significantly increasing the modulus in the longitudinal direction compared to control myocardium. Increased stiffness, in combination with increased volume from hydrogel injection, reduced the global average fiber stress by ~14% and the transmural average by ~26% in the simulations. Additionally, stiffening in an anisotropic manner enhanced the influence of hydrogel treatment in decreasing stress. Overall, this work provides insight on how injectable biomaterials can be used to attenuate wall stress and provides tools to further optimize material properties for therapeutic applications.

Human Cardiac Function Simulator for the Optimal Design of a Novel Annuloplasty Ring with a Sub-valvular Element for Correction of Ischemic Mitral Regurgitation

AbstractIschemic mitral regurgitation is associated with substantial risk of death. We sought to: (1) detail significant recent improvements to the Dassault Systèmes human cardiac function simulator (HCFS); (2) use the HCFS to simulate normal cardiac function as well as pathologic function in the setting of posterior left ventricular (LV) papillary muscle infarction; and (3) debut our novel device for correction of ischemic mitral regurgitation. We synthesized two recent studies of human myocardial mechanics. The first study presented the robust and integrative finite element HCFS. Its primary limitation was its poor diastolic performance with an LV ejection fraction below 20% caused by overly stiff ex vivo porcine tissue parameters. The second study derived improved diastolic myocardial material parameters using in vivo MRI data from five normal human subjects. We combined these models to simulate ischemic mitral regurgitation by computationally infarcting an LV region including the posterior papillary muscle. Contact between our novel device and the mitral valve apparatus was simulated using Dassault Systèmes SIMULIA software. Incorporating improved cardiac geometry and diastolic myocardial material properties in the HCFS resulted in a realistic LV ejection fraction of 55%. Simulating infarction of posterior papillary muscle caused regurgitant mitral valve mechanics. Implementation of our novel device corrected valve dysfunction. Improvements in the current study to the HCFS permit increasingly accurate study of myocardial mechanics. The first application of this simulator to abnormal human cardiac function suggests that our novel annuloplasty ring with a sub-valvular element will correct ischemic mitral regurgitation.

Injectable Shear-Thinning Hydrogels for Minimally Invasive Delivery to Infarcted Myocardium to Limit Left Ventricular Remodeling

Background—Injectable, acellular biomaterials hold promise to limit left ventricular remodeling and heart failure precipitated by infarction through bulking or stiffening the infarct region. A material with tunable properties (eg, mechanics, degradation) that can be delivered percutaneously has not yet been demonstrated. Catheter-deliverable soft hydrogels with in vivo stiffening to enhance therapeutic efficacy achieve these requirements. Methods and Results—We developed a hyaluronic acid hydrogel that uses a tandem crosslinking approach, where the first crosslinking (guest–host) enabled injection and localized retention of a soft (<1 kPa) hydrogel. A second crosslinking reaction (dual-crosslinking) stiffened the hydrogel (41.4±4.3 kPa) after injection. Posterolateral infarcts were investigated in an ovine model (n≥6 per group), with injection of saline (myocardial infarction control), guest–host hydrogels, or dual-crosslinking hydrogels. Computational (day 1), histological (1 day, 8 weeks), morphological, and functional (0, 2, and 8 weeks) outcomes were evaluated. Finite-element modeling projected myofiber stress reduction (>50%; P<0.001) with dual-crosslinking but not guest–host injection. Remodeling, assessed by infarct thickness and left ventricular volume, was mitigated by hydrogel treatment. Ejection fraction was improved, relative to myocardial infarction at 8 weeks, with dual-crosslinking (37% improvement; P=0.014) and guest–host (15% improvement; P=0.058) treatments. Percutaneous delivery via endocardial injection was investigated with fluoroscopic and echocardiographic guidance, with delivery visualized by magnetic resonance imaging. Conclusions—A percutaneous delivered hydrogel system was developed, and hydrogels with increased stiffness were found to be most effective in ameliorating left ventricular remodeling and preserving function. Ultimately, engineered systems such as these have the potential to provide effective clinical options to limit remodeling in patients after infarction.

An integrated electromechanical-growth heart model for simulating cardiac therapies

An emerging class of models has been developed in recent years to predict cardiac growth and remodeling (G&R). We recently developed a cardiac G&R constitutive model that predicts remodeling in response to elevated hemodynamics loading, and a subsequent reversal of the remodeling process when the loading is reduced. Here, we describe the integration of this G&R model to an existing strongly coupled electromechanical model of the heart. A separation of timescale between growth deformation and elastic deformation was invoked in this integrated electromechanical-growth heart model. To test our model, we applied the G&R scheme to simulate the effects of myocardial infarction in a realistic left ventricular (LV) geometry using the finite element method. We also simulate the effects of a novel therapy that is based on alteration of the infarct mechanical properties. We show that our proposed model is able to predict key features that are consistent with experiments. Specifically, we show that the presence of a non-contractile infarct leads to a dilation of the left ventricle that results in a rightward shift of the pressure volume loop. Our model also predicts that G&R is attenuated by a reduction in LV dilation when the infarct stiffness is increased.

Biventricular Finite Element Modeling of the Acorn CorCap Cardiac Support Device on a Failing Heart

BACKGROUND The Acorn CorCap Cardiac Support Device (CSD; Acorn Cardiovascular Inc, St. Paul, MN) is a woven polyester jacket that is placed around the heart and designed to reverse the progressive remodeling associated with dilated cardiomyopathy. However, the effects of the Acorn CSD on myofiber stress and ventricular function remain unknown. We tested the hypothesis that the Acorn CSD reduces end-diastolic (ED) myofiber stress. METHODS A previously described weakly coupled biventricular finite element (FE) model and circulatory model based on magnetic resonance images of a dog with dilated cardiomyopathy was used. Virtual applications of the CSD alone (Acorn), CSD with rotated fabric fiber orientation (rotated), CSD with 5% prestretch (tight), and CSD wrapped only around the left ventricle (LV; LV-only) were performed, and the effect on myofiber stress at ED and pump function was calculated. RESULTS The Acorn CSD has a large effect on ED myofiber stress in the LV free wall, with reductions of 55%, 79%, 92%, and 40% in the Acorn, rotated, tight, and LV-only cases, respectively. However, there is a tradeoff in which the Acorn CSD reduces stroke volume at LV end-diastolic pressure of 8 mm Hg by 23%, 25%, 30%, and 7%, respectively, in the Acorn, rotated, tight, and LV-only cases. CONCLUSIONS The Acorn CSD significantly reduces ED myofiber stress. However, CSD wrapped only around the LV was the only case with minimal negative effect on pump function. Findings suggest that LV-only CSD and Acorn fabric orientation should be optimized to allow maximal myofiber stress reduction with minimal reduction in pump function.

Left Ventricular Myocardial Contractility Is Depressed in the Borderzone After Posterolateral Myocardial Infarction

BACKGROUND Contractility in the borderzone (BZ) after anteroapical myocardial infarction (MI) is depressed. We tested the hypothesis that BZ contractility is also decreased after posterolateral MI. METHODS Five sheep underwent posterolateral MI. Magnetic resonance imaging (MRI) was performed 2 weeks before and 16 weeks after MI, and left ventricular (LV) volume and regional strain were measured. Finite element (FE) models were constructed, and the systolic material parameter, Tmax, was calculated in the BZ and remote myocardium by minimizing the difference between experimentally measured and calculated LV strain and volume. Sheep were sacrificed 17 weeks after MI, and myocardial muscle fibers were taken from the BZ and remote myocardium. Fibers were chemically demembranated, and isometric developed force, Fmax, was measured at supramaximal [Ca(2+)]. Routine light microscopy was also performed. RESULTS There was no difference in Tmax in the remote myocardium before and 16 weeks after MI. However, there was a large decrease (63.3%, p = 0.005) in Tmax in the BZ when compared with the remote myocardium 16 weeks after MI. In addition, there was a significant reduction of BZ Fmax for all samples (18.9%, p = 0.0067). Myocyte cross-sectional area increased by 61% (p = 0.021) in the BZ, but there was no increase in fibrosis. CONCLUSIONS Contractility in the BZ is significantly depressed relative to the remote myocardium after posterolateral MI. The reduction in contractility is due at least in part to a decrease in contractile protein function.

Numerical Evaluation of Myofiber Orientation and Transmural Contractile Strength on Left Ventricular Function

The left ventricle (LV) of the heart is composed of a complex organization of cardiac muscle fibers, which contract to generate force and pump blood into the body. It has been shown that both the orientation and contractile strength of these myofibers vary across the ventricular wall. The hypothesis of the current study is that the transmural distributions of myofiber orientation and contractile strength interdependently impact LV pump function. In order to quantify these interactions a finite element (FE) model of the LV was generated, which incorporated transmural variations. The influences of myofiber orientation and contractile strength on the Starling relationship and the end-systolic (ES) apex twist of the LV were assessed. The results suggest that reductions in contractile strength within a specific transmural layer amplified the effects of altered myofiber orientation in the same layer, causing greater changes in stroke volume (SV). Furthermore, when the epicardial myofibers contracted the strongest, the twist of the LV apex was greatest, regardless of myofiber orientation. These results demonstrate the important role of transmural distribution of myocardial contractile strength and its interplay with myofiber orientation. The coupling between these two physiologic parameters could play a critical role in the progression of heart failure.

Computational Modeling of Healthy Myocardium in Diastole

In order to better understand the mechanics of the heart and its disorders, engineers increasingly make use of the finite element method (FEM) to investigate healthy and diseased cardiac tissue. However, FEM is only as good as the underlying constitutive model, which remains a major challenge to the biomechanics community. In this study, a recently developed structurally based constitutive model was implemented to model healthy left ventricular myocardium during passive diastolic filling. This model takes into account the orthotropic response of the heart under loading. In-vivo strains were measured from magnetic resonance images (MRI) of porcine hearts, along with synchronous catheterization pressure data, and used for parameter identification of the passive constitutive model. Optimization was performed by minimizing the difference between MRI measured and FE predicted strains and cavity volumes. A similar approach was followed for the parameter identification of a widely used phenomenological constitutive law, which is based on a transversely isotropic material response. Results indicate that the parameter identification with the structurally based constitutive law is more sensitive to the assigned fiber architecture and the fit between the measured and predicted strains is improved with more realistic sheet angles. In addition, the structurally based model is capable of generating a more physiological end-diastolic pressure–volume relationship in the ventricle.