An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment

Lee, Chung‐Hao; Amini, Rouzbeh; Gorman, Robert C.; Gorman, Joseph H.; Sacks, Michael S.

doi:10.1016/j.jbiomech.2013.10.058

Cited by 77 publications

(60 citation statements)

References 40 publications

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“…More recent studies have directly incorporated measures such as fiber crimp and orientation (5)(6)(7)(8). Structural constitutive modeling approaches have been extended to computational simulations of soft tissue function (9)(10)(11)(12)(13).…”

Section: Introductionmentioning

confidence: 99%

On the Presence of Affine Fibril and Fiber Kinematics in the Mitral Valve Anterior Leaflet

Lee

Zhang

Liao

et al. 2015

Biophysical Journal

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In this study, we evaluated the hypothesis that the constituent fibers follow an affine deformation kinematic model for planar collagenous tissues. Results from two experimental datasets were utilized, taken at two scales (nanometer and micrometer), using mitral valve anterior leaflet (MVAL) tissues as the representative tissue. We simulated MVAL collagen fiber network as an ensemble of undulated fibers under a generalized two-dimensional deformation state, by representing the collagen fibrils based on a planar sinusoidally shaped geometric model. The proposed approach accounted for collagen fibril amplitude, crimp period, and rotation with applied macroscopic tissue-level deformation. When compared to the small angle x-ray scattering measurements, the model fit the data well, with an r 2 ¼ 0.976. This important finding suggests that, at the homogenized tissue-level scale of~1 mm, the collagen fiber network in the MVAL deforms according to an affine kinematics model. Moreover, with respect to understanding its function, affine kinematics suggests that the constituent fibers are largely noninteracting and deform in accordance with the bulk tissue. It also suggests that the collagen fibrils are tightly bounded and deform as a single fiber-level unit. This greatly simplifies the modeling efforts at the tissue and organ levels, because affine kinematics allows a straightforward connection between the macroscopic and local fiber strains. It also suggests that the collagen and elastin fiber networks act independently of each other, with the collagen and elastin forming long fiber networks that allow for free rotations. Such freedom of rotation can greatly facilitate the observed high degree of mechanical anisotropy in the MVAL and other heart valves, which is essential to heart valve function. These apparently novel findings support modeling efforts directed toward improving our fundamental understanding of tissue biomechanics in healthy and diseased conditions.

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Section: Introductionmentioning

confidence: 99%

On the Presence of Affine Fibril and Fiber Kinematics in the Mitral Valve Anterior Leaflet

Lee

Zhang

Liao

et al. 2015

Biophysical Journal

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“…The fiber distribution parameters were chosen in a similar way as presented by Lee et al [24]. The mean value of preferred fiber direction (l) was chosen to be either 0 or 45 deg with respect to the X 1 axis.…”

Section: Biaxial Test Simulationsmentioning

confidence: 99%

“…For this purpose, we chose two material models based on typical aortic valve [25,26] and pericardium [27] tissue (Table 4), and introduced heterogeneities based on Lee et al [24] to evaluate the associated error and validity of the homogeneous assumption. We noticed no difference in our ability to estimate the stresses based on the material model, and the estimated stress is comparable to the mean stress of the ROI for the FE simulation (Figs.…”

Section: Effect Of Materials Model and Heterogeneitiesmentioning

confidence: 99%

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

Zhang

Feng

Lee

et al. 2015

Journal of Biomechanical Engineering

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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.

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“…The resulting stress-strain behavior was described through the constitutive model recently proposed in Ref. 45 , and implemented in a VUMAT subroutine:…”

Section: Tissues Mechanical Propertiesmentioning

confidence: 99%

“…65 In the present work, we adopted a passive, nonlinear elastic and transversely isotropic model to describe both leaflets; however, we switched from the widely adopted constitutive model originally proposed by MayNewman 54 to the one recently adopted by Lee and colleagues. 45 Both models are based on the interpretation of leaflets microstructure as an elastic matrix reinforced by crimped preferentially oriented collagen fibers, are invariantbased, and use exponential functions of the 1st and 4th invariants of the right Cauchy-Green strain tensor. However, the model by MayNewman assumes that collagen fibers are perfectly aligned, whereas the model by Lee accounts for fiber dispersion through the parameter δ.…”

Section: On the Modeling Strategymentioning

confidence: 99%

Functional and Biomechanical Effects of the Edge-to-Edge Repair in the Setting of Mitral Regurgitation: Consolidated Knowledge and Novel Tools to Gain Insight into Its Percutaneous Implementation

Sturla

Redaelli

Puppini

et al. 2014

Cardiovasc Eng Tech

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Mitral regurgitation is the most prevalent heart valve disease in the western population. When severe, it requires surgical treatment, repair being the preferred option. The edgetoedge repair technique treats mitral regurgitation by suturing the leaflets together and creating a doubleorifice valve. Due to its relative simplicity and versatility, it has become progressively more widespread. Recently, its percutaneous version has become feasible, and has raised interest thanks to the positive results of the Mitraclip device. Edgetoedge features and evolution have stimulated debate and multidisciplinary research by both clinicians and engineers. After providing an overview of representative studies in the field, here we propose a novel computational approach to the most recent percutaneous evolution of the edgetoedge technique. Imagebased structural finite element models of three mitral valves affected by posterior prolapse were derived from cinecardiac magnetic resonance imaging. The models accounted for the patientspecific 3D geometry of the valve, including leaflet compound curvature pattern, patientspecific motion of annulus and papillary muscles, and hyperelastic and anisotropic mechanical properties of tissues. The biomechanics of the three valves throughout the entire cardiac cycle was simulated before and after Mitraclip implantation, assessing the biomechanical impact of the procedure. For all three simulated MVs, Mitraclip implantation significantly improved systolic leaflets coaptation, without inducing major alterations in systolic peak stresses. Diastolic orifice area was decreased, by up to 58.9%, and leaflets diastolic stresses became comparable, although lower, to systolic ones. Despite established knowledge on the edgetoedge surgical repair, latest technological advances make its percutanoues implementation a challenging field of research. The modeling approach herein proposed may be expanded to analyze clinical scenarios that are currently critical for Mitraclip implantation, helping the search for possible solutions.

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An inverse modeling approach for stress estimation in mitral valve anterior leaflet valvuloplasty for in-vivo valvular biomaterial assessment

Cited by 77 publications

References 40 publications

On the Presence of Affine Fibril and Fiber Kinematics in the Mitral Valve Anterior Leaflet

On the Presence of Affine Fibril and Fiber Kinematics in the Mitral Valve Anterior Leaflet

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

Functional and Biomechanical Effects of the Edge-to-Edge Repair in the Setting of Mitral Regurgitation: Consolidated Knowledge and Novel Tools to Gain Insight into Its Percutaneous Implementation

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