Chung-Hao Lee

AN INVERSE MODELING APPROACH FOR STRESS ESTIMATION IN MITRAL VALVE ANTERIOR LEAFLET VALVULOPLASTY FOR IN-VIVO VALVULAR BIOMATERIAL ASSESSMENT

Estimation of regional tissue stresses in the functioning heart valve remains an important goal in our understanding of normal valve function and in developing novel engineered tissue strategies for valvular repair and replacement. Methods to accurately estimate regional tissue stresses are thus needed for this purpose, and in particular to develop accurate, statistically informed means to validate computational models of valve function. Moreover, there exists no currently accepted method to evaluate engineered heart valve tissues and replacement heart valve biomaterials undergoing valvular stresses in blood contact. While we have utilized mitral valve anterior leaflet valvuloplasty as an experimental approach to address this limitation, robust computational techniques to estimate implant stresses are required. In the present study, we developed a novel numerical analysis approach for estimation of the in-vivo stresses of the central region of the mitral valve anterior leaflet (MVAL) delimited by a sonocrystal transducer array. The in-vivo material properties of the MVAL were simulated using an inverse FE modeling approach based on three pseudo-hyperelastic constitutive models: the neo-Hookean, exponential-type isotropic, and full collagen-fiber mapped transversely isotropic models. A series of numerical replications with varying structural configurations were developed by incorporating measured statistical variations in MVAL local preferred fiber directions and fiber splay. These model replications were then used to investigate how known variations in the valve tissue microstructure influence the estimated ROI stresses and its variation at each time point during a cardiac cycle. Simulations were also able to include estimates of the variation in tissue stresses for an individual specimen dataset over the cardiac cycle. Of the three material models, the transversely anisotropic model produced the most accurate results, with ROI averaged stresses at the fully-loaded state of 432.6±46.5 kPa and 241.4±40.5 kPa in the radial and circumferential directions, respectively. We conclude that the present approach can provide robust instantaneous mean and variation estimates of tissue stresses of the central regions of the MVAL.

Quantification and simulation of layer-specific mitral valve interstitial cells deformation under physiological loading.

Within each of the four layers of mitral valve (MV) leaflet tissues there resides a heterogeneous population of interstitial cells that maintain the structural integrity of the MV tissue via protein biosynthesis and enzymatic degradation. There is increasing evidence that tissue stress-induced MV interstitial cell (MVIC) deformations can have deleterious effects on their biosynthetic states that are potentially related to the reduction of tissue-level maintenance and to subsequent organ-level failure. To better understand the interrelationships between tissue-level loading and cellular responses, we developed the following integrated experimental-computational approach. Since in vivo cellular deformations are not directly measurable, we quantified the in-situ layer-specific MVIC deformations for each of the four layers under a controlled biaxial tension loading device coupled to multi-photon microscopy. Next, we explored the interrelationship between the MVIC stiffness and deformation to layer-specific tissue mechanical and structural properties using a macro-micro finite element computational model. Experimental results indicated that the MVICs in the fibrosa and ventricularis layers deformed significantly more than those in the atrialis and spongiosa layers, reaching a nucleus aspect ratio of 3.3 under an estimated maximum physiological tension of 150N/m. The simulated MVIC moduli for the four layers were found to be all within a narrow range of 4.71-5.35kPa, suggesting that MVIC deformation is primarily controlled by each tissue layers respective structure and mechanical behavior rather than the intrinsic MVIC stiffness. This novel result further suggests that while the MVICs may be phenotypically and biomechanically similar throughout the leaflet, they experience layer-specific mechanical stimulatory inputs due to distinct extracellular matrix architecture and mechanical behaviors of the four MV leaflet tissue layers. This also suggests that MVICs may behave in a layer-specific manner in response to mechanical stimuli in both normal and surgically modified MVs.

Characterizing white matter tissue in large strain via asymmetric indentation and inverse finite element modeling

Characterizing the mechanical properties of white matter is important to understand and model brain development and injury. With embedded aligned axonal fibers, white matter is typically modeled as a transversely isotropic material. However, most studies characterize the white matter tissue using models with a single anisotropic invariant or in a small-strain regime. In this study, we combined a single experimental procedure - asymmetric indentation - with inverse finite element (FE) modeling to estimate the nearly incompressible transversely isotropic material parameters of white matter. A minimal form comprising three parameters was employed to simulate indentation responses in the large-strain regime. The parameters were estimated using a global optimization procedure based on a genetic algorithm (GA). Experimental data from two indentation configurations of porcine white matter, parallel and perpendicular to the axonal fiber direction, were utilized to estimate model parameters. Results in this study confirmed a strong mechanical anisotropy of white matter in large strain. Further, our results suggested that both indentation configurations are needed to estimate the parameters with sufficient accuracy, and that the indenter-sample friction is important. Finally, we also showed that the estimated parameters were consistent with those previously obtained via a trial-and-error forward FE method in the small-strain regime. These findings are useful in modeling and parameterization of white matter, especially under large deformation, and demonstrate the potential of the proposed asymmetric indentation technique to characterize other soft biological tissues with transversely isotropic properties.

A Generalized Method for the Analysis of Planar Biaxial Mechanical Data Using Tethered Testing Configurations

Simulation of the mechanical behavior of soft tissues is critical for many physiological and medical device applications. Accurate mechanical test data is crucial for both obtaining the form and robust parameter determination of the constitutive model. For incompressible soft tissues that are either membranes or thin sections, planar biaxial mechanical testing configurations can provide much information about the anisotropic stress-strain behavior. However, the analysis of soft biological tissue planar biaxial mechanical test data can be complicated by in-plane shear, tissue heterogeneities, and inelastic changes in specimen geometry that commonly occur during testing. These inelastic effects, without appropriate corrections, alter the stress-traction mapping and violates equilibrium so that the stress tensor is incorrectly determined. To overcome these problems, we presented an analytical method to determine the Cauchy stress tensor from the experimentally derived tractions for tethered testing configurations. We accounted for the measured testing geometry and compensate for run-time inelastic effects by enforcing equilibrium using small rigid body rotations. To evaluate the effectiveness of our method, we simulated complete planar biaxial test configurations that incorporated actual device mechanisms, specimen geometry, and heterogeneous tissue fibrous structure using a finite element (FE) model. We determined that our method corrected the errors in the equilibrium of momentum and correctly estimated the Cauchy stress tensor. We also noted that since stress is applied primarily over a subregion bounded by the tethers, an adjustment to the effective specimen dimensions is required to correct the magnitude of the stresses. Simulations of various tether placements demonstrated that typical tether placements used in the current experimental setups will produce accurate stress tensor estimates. Overall, our method provides an improved and relatively straightforward method of calculating the resulting stresses for planar biaxial experiments for tethered configurations, which is especially useful for specimens that undergo large shear and exhibit substantial inelastic effects.

Patient-specific modeling of heart valves: from image to simulation

Heart valves play a very important role in the functioning of the heart and many of the heart failures are related to the valvular dysfunctions, e.g. aortic stenosis and mitral regurgitation. As the medical field is moving towards a patient-specific diagnosis and treatment procedures, modeling of heart valves with patient-specific information is becoming a significant tool in medical field. Here we present the ingredients for valve simulation specifically the aortic valve, with a main focus on a novel spline-based mapping technique which solves many issues in generating patient-specific models - the microstructural mapping, the pre-strain calculations, prescribing dynamic boundary conditions, validation and inverse-modeling to obtain material parameters.

A high-fidelity and micro-anatomically accurate 3d finite element model for simulations of functional mitral valve

Promising mitral valve (MV) repair concepts include leaflet augmentation and saddle shaped annuloplasty, and recent long-term studies have indicated that excessive tissue stress and the resulting strain-induced tissue failure are important etiologic factors leading to the recurrence of significant MR after repair. In the present work, we are aiming at developing a high-fidelity computational framework, incorporating detailed collagen fiber architecture, accurate constitutive models for soft valve tissues, and micro-anatomically accurate valvular geometry, for simulations of functional mitral valves which allows us to investigate the organ-level mechanical responses due to physiological loadings. This computational tools also provides a means, with some extension in the future, to help the understanding of the connection between the repair-induced altered stresses/strains and valve functions, and ultimately to aid in the optimal design of MV repair procedure with better performance and durability.

A Comprehensive Framework for the Characterization of the Complete Mitral Valve Geometry for the Development of a Population-Averaged Model

Simulations of the biomechanical behavior of the Mitral Valve (MV) based on simplified geometric models are difficult to interpret due to significant intra-patient variations and pathologies in the MV geometry. Thus, it is critical to use a systematic approach to characterization and population-averaging of the patient-specific models. We introduce a multi-scale modeling framework for characterizing the entire MV apparatus geometry via a relatively small set of parameters. The leaflets and annulus are analyzed using a superquadric surface model superimposed with fine-scale filtered level-set field. Filtering of fine-scale features is performed in a spectral space to allow control of resolution, resampling and robust averaging. Chordae tendineae structure is modeled using a medial axis representation with superimposed filtered pointwise cross-sectional area field. The chordae topology is characterized using orientation and spatial distribution functions. The methodology is illustrated with the analysis of an ovine MV microtomography imaging data.

Mitral Valves: A Computational Framework

The mitral valve (MV) is one of the four heart valves which locates in between the left atrium and left ventricle and regulates the unidirectional blood flow and normal functioning of the heart during cardiac cycles. Alternation of any component of the MV apparatus will typically lead to abnormal MV function. Currently, 40,000 patients in the United States receive MV repair or replacement annually according to the American Heart Association. Clinically, this can be achieved iteratively by surgical repair that reinstates normal annular geometry (size and shape) and restores mobile leaflet tissue, resulting in reduced annular and chordae force distribution. High-fidelity computer simulations provide a means to connect the cellular function with the organ-level MV tissue mechanical responses, and to help the design of optimal MV repair strategies. As in many physiological systems, one can approach heart valve biomechanics from using multiscale modeling (MSM) methodologies, since mechanical stimuli occur and have biological impact at the organ, tissue, and cellular levels. Yet, MSM approaches of heart valves are scarce, largely due to the major difficulties in adapting conventional methods to the areas where we simply do not have requisite data. There also remains both theoretical and computational challenges to applying traditional MSM techniques to heart valves. Moreover, existing physiologically realistic computational models of heart valve function make many assumptions, such as a simplified microstructural and anatomical representation of the MV apparatus, and thorough validations with in-vitro or in-vivo data are still limited. In the following, we present the details of the state of the art of mitral valve modeling techniques, with an emphasis on what is known and investigated at various length scales.

Population-Averaged Geometric Model of Mitral Valve From Patient-Specific Imaging Data

The mitral valve (MV) is one of the atrioventricular heart valves and regulates the blood flow between the left atrium and ventricle during the cardiac cycle. Its anatomical structure is comprised of anterior and posterior leaflets, chordae tendineae, and papillary muscles. The main function of the MV is to prevent blood flow regurgitation back into the left atrium during systole. Abnormalities in geometry of MV can lead to mitral insufficiency disorder, which requires either valve replacement or surgical repair to restore proper MV coaptation. Annually, over 40,000 patients in the U.S. alone are treated for MV disorders [1]. In the past two decades, the emphasis in MV treatment has been shifting from replacement toward repair due to lower morbidity and mortality of the latter approach [2]. However, the natural anatomical variability of human MV geometry precludes the use of single or simplified geometries for the simulation of surgical repair. One of the ways to address this issue is by using patient-specific diagnosis and modeling [3], or population-averaged geometric models of MV. The existing approaches for characterization and reconstruction of the cardiovascular organ-level geometry include fitting of predefined sets of nonuniform rational B-splines (NURBS) to the imaging data [4], and using spheroidal harmonics representations [5]. Even though it is possible to construct average geometric models this way, the analysis of anatomical shape variations becomes difficult in this setting because of the confounding of dimensional and shape descriptors. At the same time, none of the existing methods allow integration of the high-fidelity in vitro data with lower-resolution in vivo imaging in a consistent manner. In this work, we formulate the framework for building the population-averaged geometric model of MV, which lends to straightforward analysis of dimensional and anatomical variations. In the sections to follow, we discuss the procedure and advantages of this method for the development of robust medical devices and treatment procedures.

Mitral valve leaflet remodelling during pregnancy: insights into cell-mediated recovery of tissue homeostasis.

Little is known about how valvular tissues grow and remodel in response to altered loading. In this work, we used the pregnancy state to represent a non-pathological cardiac volume overload that distends the mitral valve (MV), using both extant and new experimental data and a modified form of our MV structural constitutive model. We determined that there was an initial period of permanent set-like deformation where no remodelling occurs, followed by a remodelling phase that resulted in near-complete restoration of homeostatic tissue-level behaviour. In addition, we observed that changes in the underlying MV interstitial cell (MVIC) geometry closely paralleled the tissue-level remodelling events, undergoing an initial passive perturbation followed by a gradual recovery to the pre-pregnant state. Collectively, these results suggest that valvular remodelling is actively mediated by average MVIC deformations (i.e. not cycle to cycle, but over a period of weeks). Moreover, tissue-level remodelling is likely to be accomplished by serial and parallel additions of fibrillar material to restore the mean homeostatic fibre stress and MVIC geometries. This finding has significant implications in efforts to understand and predict MV growth and remodelling following such events as myocardial infarction and surgical repair, which also place the valve under altered loading conditions.