A Mathematical Model for Postimplant Collagen Remodeling in an Autologous Engineered Pulmonary Arterial Conduit.

This study was undertaken to develop a mathematical model of the long-term in vivo remodeling processes in postimplanted pulmonary artery (PA) conduits. Experimental results from two extant ovine in vivo studies, wherein polyglycolic-acid (PGA)/poly-L-lactic acid tubular conduits were constructed, cell seeded, incubated for 4 weeks, and then implanted in mature sheep to obtain the remodeling data for up to two years. Explanted conduit analysis included detailed novel structural and mechanical studies. Results in both studies indicated that the in vivo conduits remained dimensionally stable up to 80 weeks, so that the conduits maintained a constant in vivo stress and deformation state. In contrast, continued remodeling of the constituent collagen fiber network as evidenced by an increase in effective tissue uniaxial tangent modulus, which then stabilized by one year postimplant. A mesostructural constitute model was then applied to extant planar biaxial mechanical data and revealed several interesting features, including an initial pronounced increase in effective collagen fiber modulus, paralleled by a simultaneous shift toward longer, more uniformly length-distributed collagen fibers. Thus, while the conduit remained dimensionally stable, its internal collagen fibrous structure and resultant mechanical behaviors underwent continued remodeling that stabilized by one year. A time-evolving structural mixture-based mathematical model specialized for this unique form of tissue remodeling was developed, with a focus on time-evolving collagen fiber stiffness as the driver for tissue-level remodeling. The remodeling model was able to fully reproduce (1) the observed tissue-level increases in stiffness by time-evolving simultaneous increases in collagen fiber modulus and lengths, (2) maintenance of the constant collagen fiber angular dispersion, and (3) stabilization of the remodeling processes at one year. Collagen fiber remodeling geometry was directly verified experimentally by histological analysis of the time-evolving collagen fiber crimp, which matches model predictions very closely. Interestingly, the remodeling model indicated that the basis for tissue homeostasis was maintenance of the collagen fiber ensemble stress for all orientations, and not individual collagen fiber stresses. Unlike other growth and remodeling models that traditionally treat changes in the external boundary conditions (e.g., changes in blood pressure) as the primary input stimuli, the driver herein is changes to the internal constituent collagen fiber themselves due to cellular mediated cross-linking.

Simulated Effects of Acute Left Ventricular Myocardial Infarction on Mitral Regurgitation in an Ovine Model.

Ischemic mitral regurgitation (IMR) occurs from incomplete coaptation of the mitral valve (MV) after myocardial infarction (MI), typically worsened by continued remodeling of the left ventricular (LV). The importance of LV remodeling is clear as IMR is induced by the post-MI dual mechanisms of mitral annular dilation and leaflet tethering from papillary muscle (PM) distension via the MV chordae tendineae (MVCT). However, the detailed etiology of IMR remains poorly understood, in large part due to the complex interactions of the MV and the post-MI LV remodeling processes. Given the patient-specific anatomical complexities of the IMR disease processes, simulation-based approaches represent an ideal approach to improve our understanding of this deadly disease. However, development of patient-specific models of left ventricle-mitral valve (LV-MV) interactions in IMR are complicated by the substantial variability and complexity of the MR etiology itself, making it difficult to extract underlying mechanisms from clinical data alone. To address these shortcomings, we developed a detailed ovine LV-MV finite element (FE) model based on extant comprehensive ovine experimental data. First, an extant ovine LV FE model (Sci. Rep. 2021 Jun 29;11(1):13466) was extended to incorporate the MV using a high fidelity ovine in vivo derived MV leaflet geometry. As it is not currently possible to image the MVCT in vivo, a functionally equivalent MVCT network was developed to create the final LV-MV model. Interestingly, in pilot studies, the MV leaflet strains did not agree well with known in vivo MV leaflet strain fields. We then incorporated previously reported MV leaflet prestrains (J. Biomech. Eng. 2023 Nov 1;145(11):111002) in the simulations. The resulting LV-MV model produced excellent agreement with the known in vivo ovine MV leaflet strains and deformed shapes in the normal state. We then simulated the effects of regional acute infarctions of varying sizes and anatomical locations by shutting down the local myocardial contractility. The remaining healthy (noninfarcted) myocardium mechanical behaviors were maintained, but allowed to adjust their active contractile patterns to maintain the prescribed pressure-volume loop behaviors in the acute post-MI state. For all cases studied, the LV-MV simulation demonstrated excellent agreement with known LV and MV in vivo strains and MV regurgitation orifice areas. Infarct location was shown to play a critical role in resultant MV leaflet strain fields. Specifically, extensional deformations of the posterior leaflets occurred in the posterobasal and laterobasal infarcts, while compressive deformations of the anterior leaflet were observed in the anterobasal infarct. Moreover, the simulated posterobasal infarct induced the largest MV regurgitation orifice area, consistent with experimental observations. The present study is the first detailed LV-MV simulation that reveals the important role of MV leaflet prestrain and functionally equivalent MVCT for accurate predictions of LV-MV interactions. Importantly, the current study further underscored simulation-based methods in understanding MV function as an integral part of the LV.

An Inverse Modeling Approach to Estimate Three-Dimensional Aortic Valve Interstitial Cell Stress Fiber Force Levels.

Within the aortic valve (AV) leaflet exists a population of interstitial cells (AVICs) that maintain the constituent tissues by extracellular matrix (ECM) secretion, degradation, and remodeling. AVICs can transition from a quiescent, fibroblast-like phenotype to an activated, myofibroblast phenotype in response to growth or disease. AVIC dysfunction has been implicated in AV disease processes, yet our understanding of AVIC function remains quite limited. A major characteristic of the AVIC phenotype is its contractile state, driven by contractile forces generated by the underlying stress fibers (SF). However, direct assessment of the AVIC SF contractile state and structure within physiologically mimicking three-dimensional environments remains technically challenging, as the size of single SFs are below the resolution of light microscopy. Therefore, in the present study, we developed a three-dimensional (3D) computational approach of AVICs embedded in 3D hydrogels to estimate their SF local orientations and contractile forces. One challenge with this approach is that AVICs will remodel the hydrogel, so that the gel moduli will vary spatially. We thus utilized our previous approach (Khang et al. 2023, "Estimation of Aortic Valve Interstitial Cell-Induced 3D Remodeling of Poly (Ethylene Glycol) Hydrogel Environments Using an Inverse Finite Element Approach," Acta Biomater., 160, pp. 123-133) to define local hydrogel mechanical properties. The AVIC SF model incorporated known cytosol and nucleus mechanical behaviors, with the cell membrane assumed to be perfectly bonded to the surrounding hydrogel. The AVIC SFs were first modeled as locally unidirectional hyperelastic fibers with a contractile force component. An adjoint-based inverse modeling approach was developed to estimate local SF orientation and contractile force. Substantial heterogeneity in SF force and orientations were observed, with the greatest levels of SF alignment and contractile forces occurring in AVIC protrusions. The addition of a dispersed SF orientation to the modeling approach did not substantially alter these findings. To the best of our knowledge, we report the first fully 3D computational contractile cell models which can predict locally varying stress fiber orientation and contractile force levels.

The Accelerated Transcatheter Heart Valve Testing Environment: Loading, Motion, and Fluid Dynamics.

Transcatheter aortic valve replacements (TAVRs) are an increasingly common treatment for aortic valve disease due to their minimally invasive delivery. As TAVR designs require thinner leaflets to facilitate catheter-based delivery, they experience greater leaflet operational stresses and potentially greater durability issues than conventional surgical valves. Yet, our understanding of TAVR durability remains largely unexplored. Currently, preclinical TAVR durability is evaluated within an ISO:5840 compliant accelerated wear tester (AWT) up to a required 200 × 106 cycles, corresponding to approximately five years in vivo. While AWTs use high cycle frequencies (10-20 Hz) to achieve realistic timeframes, the resulting valve loading behaviors and fluid dynamics are not representative of the in vivo environment and thus may not accurately predict failure mechanisms. Despite the importance of fatigue and failure predictions for replacement heart valves, surprisingly, little quantitative information exists on the dynamic AWT environment. To better understand this environment, we examined frequency and diastolic period effects for the first time using high-speed enface imaging and particle image velocimetry to quantify valve motion and flow, respectively, using a Durapulse™ AWT at frequencies of 10, 15, and 20 Hz. Regardless of operating condition, no waveform achieved a physiologically relevant transvalvular loading pressure, despite having an ISO compliant geometric orifice area (GOA) and waveform. General fluid mechanics were consistent with in vivo but the AWT geometry developed secondary flow structures, which could impact mechanical loading. Therefore, the nonphysiologic loading and variability induced by changes in operating condition must be carefully regulated to ensure physiologically relevant fatigue.

A Computational Pipeline for Patient-Specific Prediction of the Postoperative Mitral Valve Functional State.

While mitral valve (MV) repair remains the preferred clinical option for mitral regurgitation (MR) treatment, long-term outcomes remain suboptimal and difficult to predict. Furthermore, pre-operative optimization is complicated by the heterogeneity of MR presentations and the multiplicity of potential repair configurations. In the present work, we established a patient-specific MV computational pipeline based strictly on standard-of-care pre-operative imaging data to quantitatively predict the post-repair MV functional state. First, we established human mitral valve chordae tendinae (MVCT) geometric characteristics obtained from five CT-imaged excised human hearts. From these data, we developed a finite-element model of the full patient-specific MV apparatus that included MVCT papillary muscle origins obtained from both the in vitro study and the pre-operative three-dimensional echocardiography images. To functionally tune the patient-specific MV mechanical behavior, we simulated pre-operative MV closure and iteratively updated the leaflet and MVCT prestrains to minimize the mismatch between the simulated and target end-systolic geometries. Using the resultant fully calibrated MV model, we simulated undersized ring annuloplasty (URA) by defining the annular geometry directly from the ring geometry. In three human cases, the postoperative geometries were predicted to 1 mm of the target, and the MV leaflet strain fields demonstrated close agreement with noninvasive strain estimation technique targets. Interestingly, our model predicted increased posterior leaflet tethering after URA in two recurrent patients, which is the likely driver of long-term MV repair failure. In summary, the present pipeline was able to predict postoperative outcomes from pre-operative clinical data alone. This approach can thus lay the foundation for optimal tailored surgical planning for more durable repair, as well as development of mitral valve digital twins.

Thinner biological tissues induce leaflet flutter in aortic heart valve replacements.

Valvular heart disease has recently become an increasing public health concern due to the high prevalence of valve degeneration in aging populations. For patients with severely impacted aortic valves that require replacement, catheter-based bioprosthetic valve deployment offers a minimally invasive treatment option that eliminates many of the risks associated with surgical valve replacement. Although recent percutaneous device advancements have incorporated thinner, more flexible biological tissues to streamline safer deployment through catheters, the impact of such tissues in the complex, mechanically demanding, and highly dynamic valvular system remains poorly understood. The present work utilized a validated computational fluid-structure interaction approach to isolate the behavior of thinner, more compliant aortic valve tissues in a physiologically realistic system. This computational study identified and quantified significant leaflet flutter induced by the use of thinner tissues that initiated blood flow disturbances and oscillatory leaflet strains. The aortic flow and valvular dynamics associated with these thinner valvular tissues have not been previously identified and provide essential information that can significantly advance fundamental knowledge about the cardiac system and support future medical device innovation. Considering the risks associated with such observed flutter phenomena, including blood damage and accelerated leaflet deterioration, this study demonstrates the potentially serious impact of introducing thinner, more flexible tissues into the cardiac system.

Altered Responsiveness to TGFß and BMP and Increased CD45+ Cell Presence in Mitral Valves Are Unique Features of Ischemic Mitral Regurgitation.

[Figure: see text].

Neural Network Approaches for Soft Biological Tissue and Organ Simulations.

Given the functional complexities of soft tissues and organs, it is clear that computational simulations are critical in their understanding and for the rational basis for the development of therapies and replacements. A key aspect of such simulations is accounting for their complex, nonlinear, anisotropic mechanical behaviors. While soft tissue material models have developed to the point of high fidelity, in-silico implementation is typically done using the finite element (FE) method, which remains impractically slow for translational clinical time frames. As a potential path toward addressing the development of high fidelity simulations capable of performing in clinically relevant time frames, we review the use of neural networks (NN) for soft tissue and organ simulation using two approaches. In the first approach, we show how a NN can learn the responses for a detailed meso-structural soft tissue material model. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. In the second approach, we go a step further with the use of a physics-based surrogate model to directly learn the displacement field solution without the need for raw training data or FE simulation datasets. In this approach we utilize a finite element mesh to define the domain and perform the necessary integrations, but not the finite element method (FEM) itself. We demonstrate with this approach, termed neural network finite element (NNFE), results in a trained NNFE model with excellent agreement with the corresponding "ground truth" FE solutions over the entire physiological deformation range on a cuboidal myocardium specimen. More importantly, the NNFE approach provided a significantly decreased computational time for a range of finite element mesh sizes. Specifically, as the FE mesh size increased from 2744 to 175,615 elements, the NNFE computational time increased from 0.1108 s to 0.1393 s, while the "ground truth" FE model increased from 4.541 s to 719.9 s, with the same effective accuracy. These results suggest that NNFE run times are significantly reduced compared with the traditional large-deformation-based finite element solution methods. We then show how a nonuniform rational B-splines (NURBS)-based approach can be directly integrated into the NNFE approach as a means to handle real organ geometries. While these and related approaches are in their early stages, they offer a method to perform complex organ-level simulations in clinically relevant time frames without compromising accuracy.

Simulation of the 3D Hyperelastic Behavior of Ventricular Myocardium using a Finite-Element Based Neural-Network Approach.

High-fidelity cardiac models using attribute-rich finite element based models have been developed to a very mature stage. However, such finite-element based approaches remain time consuming, which have limited their clinical use. There remains a need for alternative methods for novel cardiac simulation methods of capable of high fidelity simulations in clinically relevant time frames. Surrogate models are one approach, which traditionally use a data-driven approach for training, requiring the generation of a sufficiently large number of simulation results as the training dataset. Alternatively, a physics-informed neural network can be trained by minimizing the PDE residuals or energy potentials. However, this approach does not provide for a general method to easily using existing finite element models. To address these challenges, we developed a hybrid approach that seamlessly bridged a neural network surrogate model with a differentiable finite element domain representation (NNFE). Given its importance in cardiac simulations, we applied this approach to simulations of the hyperelastic mechanical behavior of ventricular myocardium from recent 3D kinematic constitutive model (J Mech Behav Biomed Mater, 2020 doi: 10.1016/j.jmbbm.2019.103508). We utilized cuboidal domain and conducted numerical studies of individual myocardium specimens discretized by a finite element mesh and assigned with experimentally obtained myofiber architectures. Both parameterized Dirichlet and Neumann boundary conditions were studied. We developed a second-order Newton optimization method, instead of using stochastic gradient descent method, to train the neural network efficiently. The resulting trained neural network surrogate model demonstrated excellent agreement with the corresponding 'ground truth' finite element solutions over the entire physiological deformation range. More importantly, the NNFE approach provided a significantly decreased computational time for a range of finite element mesh sizes for online predictions. For example, as the finite element mesh sized increased from 2744 to 175615 elements the NNFE computational time increased from 0.1108 s to 0.1393 s, while the 'ground truth' FE model increased from 4.541 s to 719.9 s. These results suggests that NNFE run times can be significantly reduced compared with the traditional large-deformation based finite element solution methods. The trade off is to train the NNFE off-line within a range of anticipated physiological responses. However, training time would only have to be performed once before any number of application uses. Moreover, since the NNFE is an analytical function its computational performance will be amplified when the corresponding problem becomes more complex.

On the Three-Dimensional Correlation Between Myofibroblast Shape and Contraction.

Myofibroblasts are responsible for wound healing and tissue repair across all organ systems. In periods of growth and disease, myofibroblasts can undergo a phenotypic transition characterized by an increase in extracellular matrix (ECM) deposition rate, changes in various protein expression (e.g., alpha-smooth muscle actin (αSMA)), and elevated contractility. Cell shape is known to correlate closely with stress-fiber geometry and function and is thus a critical feature of cell biophysical state. However, the relationship between myofibroblast shape and contraction is complex, even as well in regards to steady-state contractile level (basal tonus). At present, the relationship between myofibroblast shape and basal tonus in three-dimensional (3D) environments is poorly understood. Herein, we utilize the aortic valve interstitial cell (AVIC) as a representative myofibroblast to investigate the relationship between basal tonus and overall cell shape. AVICs were embedded within 3D poly(ethylene glycol) (PEG) hydrogels containing degradable peptide crosslinkers, adhesive peptide sequences, and submicron fluorescent microspheres to track the local displacement field. We then developed a methodology to evaluate the correlation between overall AVIC shape and basal tonus induced contraction. We computed a volume averaged stretch tensor ⟨U⟩ for the volume occupied by the AVIC, which had three distinct eigenvalues (λ1,2,3=1.08,0.99, and 0.89), suggesting that AVIC shape is a result of anisotropic contraction. Furthermore, the direction of maximum contraction correlated closely with the longest axis of a bounding ellipsoid enclosing the AVIC. As gel-imbedded AVICs are known to be in a stable state by 3 days of incubation used herein, this finding suggests that the overall quiescent AVIC shape is driven by the underlying stress-fiber directional structure and potentially contraction level.

Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement.

The left ventricle of the heart is a fundamental structure in the human cardiac system that pumps oxygenated blood into the systemic circulation. Several valvular conditions can cause the aortic and mitral valves associated with the left ventricle to become severely diseased and require replacement. However, the clinical outcomes of such operations, specifically the postoperative ventricular hemodynamics of replacing both valves, are not well understood. This work uses computational fluid-structure interaction (FSI) to develop an improved understanding of this effect by modeling a left ventricle with the aortic and mitral valves replaced with bioprostheses. We use a hybrid Arbitrary Lagrangian-Eulerian/immersogeometric framework to accommodate the analysis of cardiac hemodynamics and heart valve structural mechanics in a moving fluid domain. The motion of the endocardium is obtained from a cardiac biomechanics simulation and provided as an input to the proposed numerical framework. The results from the simulations in this work indicate that the replacement of the native mitral valve with a tri-radially symmetric bioprosthesis dramatically changes the ventricular hemodynamics. Most significantly, the vortical motion in the left ventricle is found to reverse direction after mitral valve replacement. This study demonstrates that the proposed computational FSI framework is capable of simulating complex multiphysics problems and can provide an in-depth understanding of the cardiac mechanics.

A Contemporary Look at Biomechanical Models of Myocardium.

Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.

Interactions Between Structural Remodeling and Hypertrophy in the Right Ventricle in Response to Pulmonary Arterial Hypertension.

Pulmonary arterial hypertension (PAH) exerts substantial pressure overload on the right ventricle (RV), inducing RV remodeling and myocardial tissue adaptation often leading to right heart failure. The associated RV free wall (RVFW) adaptation involves myocardial hypertrophy, augmented intrinsic contractility, collagen fibrosis, and structural remodeling in an attempt to cope with pressure overload. If RVFW adaptation cannot maintain the RV stroke volume (SV), RV dilation will prevail as an exit mechanism, which usually decompensates RV function, leading to RV failure. Our knowledge of the factors determining the transition from the upper limit of RVFW adaptation to RV decompensation and the role of fiber remodeling events such as extracellular fibrosis and fiber reorientation in this transition remains very limited. Computational heart models that connect the growth and remodeling (G&R) events at the fiber and tissue levels with alterations in the organ-level function are essential to predict the temporal order and the compensatory level of the underlying mechanisms. In this work, building upon our recently developed rodent heart models (RHM) of PAH, we integrated mathematical models that describe volumetric growth of the RV and structural remodeling of the RVFW. The time-evolution of RV remodeling from control and post-PAH time points was simulated. The results suggest that the augmentation of the intrinsic contractility of myofibers, accompanied by an increase in passive stiffness of RVFW, is among the first remodeling events through which the RV strives to maintain the cardiac output. Interestingly, we found that the observed reorientation of the myofibers toward the longitudinal (apex-to-base) direction was a maladaptive mechanism that impaired the RVFW contractile pattern and advanced along with RV dilation at later stages of PAH. In fact, although individual fibers were more contractile post-PAH, the disruption in the optimal transmural fiber architecture compromised the effective contractile function of the RVFW, contributing to the depressed ejection fraction (EF) of the RV. Our findings clearly demonstrate the critical need for developing multiscale approaches that can model and delineate relationships between pathological alterations in cardiac function and underlying remodeling events across fiber, cellular, and molecular levels.

Serotonin receptor 2B signaling with interstitial cell activation and leaflet remodeling in degenerative mitral regurgitation.

AIMS: Mitral valve interstitial cells (MVIC) play an important role in the pathogenesis of degenerative mitral regurgitation (MR) due to mitral valve prolapse (MVP). Numerous clinical studies have observed serotonin (5HT) dysregulation in cardiac valvulopathies; however, the impact of 5HT-mediated signaling on MVIC activation and leaflet remodeling in MVP have been investigated to a limited extent. Here we test the hypothesis that 5HT receptors (5HTRs) signaling contributes to MVP pathophysiology. METHODS AND RESULTS: Diseased human MV leaflets were obtained during cardiac surgery for MVP; normal MV leaflets were obtained from heart transplants. MV RNA was used for microarray analysis of MVP patients versus control, highlighting genes that indicate the involvement of 5HTR pathways and extracellular matrix remodeling in MVP. Human MV leaflets were also studied in vitro and ex vivo with biomechanical testing to assess remodeling in the presence of a 5HTR2B antagonist (LY272015). MVP leaflets from Cavalier King Charles Spaniels were used as a naturally acquired in vivo model of MVP. These canine MVP leaflets (N=5/group) showed 5HTR2B upregulation. This study also utilized CB57.1ML/6 mice in order to determine the effect of Angiotensin II infusion on MV remodeling. Histological analysis showed that MV thickening due to chronic Angiotensin II remodeling is mitigated by a 5HTR2B antagonist (LY272015) but not by 5HTR2A inhibitors. CONCLUSION: In humans, MVP is associated with an upregulation in 5HTR2B expression and increased 5HT receptor signaling in the leaflets. Antagonism of 5HTR2B mitigates MVIC activation in vitro and MV remodeling in vivo. These observations support the view that 5HTR signaling is involved not only in previously reported 5HT-related valvulopathies, but it is also involved in the pathological remodeling of MVP.

A Novel Small-Specimen Planar Biaxial Testing System With Full In-Plane Deformation Control.

Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × âˆ¼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.

Optical-Based Analysis of Soft Tissue Structures.

Fibrous structures are an integral and dynamic feature of soft biological tissues that are directly related to the tissues' condition and function. A greater understanding of mechanical tissue behavior can be gained through quantitative analyses of structure alone, as well as its integration into computational models of soft tissue function. Histology and other nonoptical techniques have traditionally dominated the field of tissue imaging, but they are limited by their invasiveness, inability to provide resolution on the micrometer scale, and dynamic information. Recent advances in optical modalities can provide higher resolution, less invasive imaging capabilities, and more quantitative measurements. Here we describe contemporary optical imaging techniques with respect to their suitability in the imaging of tissue structure, with a focus on characterization and implementation into subsequent modeling efforts. We outline the applications and limitations of each modality and discuss the overall shortcomings and future directions for optical imaging of soft tissue structure.

On the Functional Role of Valve Interstitial Cell Stress Fibers: A Continuum Modeling Approach.

The function of the heart valve interstitial cells (VICs) is intimately connected to heart valve tissue remodeling and repair, as well as the onset and progression of valvular pathological processes. There is yet only very limited knowledge and extant models for the complex three-dimensional VIC internal stress-bearing structures, the associated cell-level biomechanical behaviors, and how they change under varying activation levels. Importantly, VICs are known to exist and function within the highly dynamic valve tissue environment, including very high physiological loading rates. Yet we have no knowledge on how these factors affect VIC function. To this end, we extended our previous VIC computational continuum mechanics model (Sakamoto, et al., 2016, "On Intrinsic Stress Fiber Contractile Forces in Semilunar Heart Valve Interstitial Cells Using a Continuum Mixture Model," J. Mech. Behav. Biomed. Mater., 54(244-258)). to incorporate realistic stress-fiber geometries, force-length relations (Hill model for active contraction), explicit α-smooth muscle actin (α-SMA) and F-actin expression levels, and strain rate. Novel micro-indentation measurements were then performed using cytochalasin D (CytoD), variable KCl molar concentrations, both alone and with transforming growth factor ß1 (TGF-ß1) (which emulates certain valvular pathological processes) to explore how α-SMA and F-actin expression levels influenced stress fiber responses under quasi-static and physiological loading rates. Simulation results indicated that both F-actin and α-SMA contributed substantially to stress fiber force generation, with the highest activation state (90 mM KCL + TGF-ß1) inducing the largest α-SMA levels and associated force generation. Validation was performed by comparisons to traction force microscopy studies, which showed very good agreement. Interestingly, only in the highest activation state was strain rate sensitivity observed, which was captured successfully in the simulations. These unique findings demonstrated that only VICs with high levels of αSMA expression exhibited significant viscoelastic effects. Implications of this study include greater insight into the functional role of α-SMA and F-actin in VIC stress fiber function, and the potential for strain rate-dependent effects in pathological states where high levels of α-SMA occur, which appear to be unique to the valvular cellular in vivo microenvironment.

Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines.

This paper uses a divergence-conforming B-spline fluid discretization to address the long-standing issue of poor mass conservation in immersed methods for computational fluid-structure interaction (FSI) that represent the influence of the structure as a forcing term in the fluid subproblem. We focus, in particular, on the immersogeometric method developed in our earlier work, analyze its convergence for linear model problems, then apply it to FSI analysis of heart valves, using divergence-conforming B-splines to discretize the fluid subproblem. Poor mass conservation can manifest as effective leakage of fluid through thin solid barriers. This leakage disrupts the qualitative behavior of FSI systems such as heart valves, which exist specifically to block flow. Divergence-conforming discretizations can enforce mass conservation exactly, avoiding this problem. To demonstrate the practical utility of immersogeometric FSI analysis with divergence-conforming B-splines, we use the methods described in this paper to construct and evaluate a computational model of an in vitro experiment that pumps water through an artificial valve.

On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet.

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) = 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.

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 layer's 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.