Integration of polarized spatial frequency domain imaging (pSFDI) with a biaxial mechanical testing system for quantification of load-dependent collagen architecture in soft collagenous tissues

Quantified planar collagen distribution in healthy and degenerative mitral valve: biomechanical and clinical implications

Degenerative mitral valve disease is a common valvular disease with two arguably distinct phenotypes: fibroelastic deficiency and Barlow's disease. These phenotypes significantly alter the microstructures of the leaflets, particularly the collagen fibers, which are the main mechanical load carriers. The predominant method of investigation is histological sections. However, the sections are cut transmurally and provide a lateral view of the microstructure of the leaflet, while the mechanics and function are determined by the planar arrangement of the collagen fibers. This study, for the first time, quantitatively examined planar collagen distribution quantitatively in health and disease using second harmonic generation microscopy throughout the thickness of the mitral valve leaflets. Twenty diseased samples from eighteen patients and six control samples were included in this study. Healthy tissue had highly aligned collagen fibers. In fibroelastic deficiency they are less aligned and in Barlow's disease they are completely dispersed. In both diseases, collagen fibers have two preferred orientations, which, in contrast to the almost constant one orientation in healthy tissues, also vary across the thickness. The results indicate altered in vivo mechanical stresses and strains on the mitral valve leaflets as a result of disease-related collagen remodeling, which in turn triggers further remodeling.

Biaxial stretch can overcome discrepancy between global and local orientations of wavy collagen fibres

Most frequently used structure-based constitutive models of arterial wall apply assumptions on two symmetric helical (and dispersed) fibre families which, however, are not well supported with histological findings where two collagen fibre families are seldom found. Moreover, bimodal distributions of fibre directions may originate also from their waviness combined with ignoring differences between local and global fibre orientations. In contrast, if the model parameters are identified without histological information on collagen fibre directions, the resulting mean angles of both fibre families are close to ±45°, which contradicts nearly all histologic findings. The presented study exploited automated polarized light microscopy for detection of collagen fibre directions in porcine aorta under different biaxial extensions and approximated the resulting histograms with unimodal and bimodal von Mises distributions. Their comparison showed dominantly circumferential orientation of collagen fibres. Their concentration parameter for unimodal distributions increased with circumferential load, no matter if acting uniaxially or equibiaxially. For bimodal distributions, the angle between both dominant fibre directions (chosen as measure of fibre alignment) decreased similarly for both uniaxial and equibiaxial loads. These results indicate the existence of a single family of wavy circumferential collagen fibres in all layers of the aortic wall. Bimodal distributions of fibre directions presented sometimes in literature may come rather from waviness of circumferentially arranged fibres than from two symmetric families of helical fibres. To obtain a final evidence, the fibre orientation should be analysed together with their waviness.

An inverse fitting strategy to determine the constrained mixture model parameters: application in patient-specific aorta

The Constrained Mixture Model (CMM) is a novel approach to describe arterial wall mechanics, whose formulation is based on a referential physiological state. The CMM considers the arterial wall as a mixture of load-bearing constituents, each of them with characteristic mass fraction, material properties, and deposition stretch levels from its stress-free state to the in-vivo configuration. Although some reports of this model successfully assess its capabilities, they barely explore experimental approaches to model patient-specific scenarios. In this sense, we propose an iterative fitting procedure of numerical-experimental nature to determine material parameters and deposition stretch values. To this end, the model has been implemented in a finite element framework, and it is calibrated using reported experimental data of descending thoracic aorta. The main results obtained from the proposed procedure consist of a set of material parameters for each constituent. Moreover, a relationship between deposition stretches and residual strain measurements (opening angle and axial stretch) has been numerically proved, establishing a strong consistency between the model and experimental data.

An investigation of how specimen dimensions affect biaxial mechanical characterizations with CellScale BioTester and constitutive modeling of porcine tricuspid valve leaflets

Biaxial mechanical characterizations are the accepted approach to determine the mechanical response of many biological soft tissues. Although several computational and experimental studies have examined how experimental factors (e.g., clamped vs. suture mounting) affect the acquired tissue mechanical behavior, little is known about the role of specimen dimensions in data acquisition and the subsequent modeling. In this study, we combined our established mechanical characterization framework with an iterative size-reduction protocol to test the hypothesis that specimen dimensions affect the observed mechanical behavior of biaxial characterizations. Our findings indicated that there were non-significant differences in the peak equibiaxial stretches of tricuspid valve leaflets across four specimen dimensions ranging from 4.5×4.5mm to 9 × 9mm. Further analyses revealed that there were significant differences in the low-tensile modulus of the circumferential tissue direction. These differences resulted in significantly different constitutive model parameters for the Tong-Fung model between different specimen dimensions of the posterior and septal leaflets. Overall, our findings demonstrate that specimen dimensions play an important role in experimental characterizations, but not necessarily in constitutive modeling of soft tissue mechanical behavior during biaxial testing with the commercial CellScale BioTester.

Local Characterization of Collagen Architecture and Mechanical Failure Properties of Fibrous Plaque Tissue of Atherosclerotic Human Carotid Arteries

Atherosclerotic plaque rupture in carotid arteries is a major cause of cerebrovascular events. Plaque rupture is the mechanical failure of the heterogeneous fibrous plaque tissue. Local characterization of the tissue's failure properties and the collagen architecture are of great importance to have insights in plaque rupture for clinical event prevention. Previous studies were limited to average rupture properties and global structural characterization, and did not provide the necessary local information. In this study, we assessed the local collagen architecture and failure properties of fibrous plaque tissue, by analyzing 30 tissue strips from 18 carotid plaques. Our study framework entailed second harmonic generation imaging for local collagen orientation and dispersion, and uniaxial tensile testing and digital image correlation for local tissue mechanics. The results showed that 87% of the imaged locations had collagen orientation close to the circumferential direction (0°) of the artery, and substantial dispersion locally. All regions combined, median [Q1:Q3] of the predominant angle measurements was -2° [-16°:16°]. The stretch ratio measurements clearly demonstrated a nonuniform stretch ratio distribution in the tissue under uniaxial loading. The rupture initiation regions had significantly higher stretch ratios (1.26 [1.15-1.40]) than the tissue average stretch ratio (1.11 [1.10-1.16]). No significant difference in collagen direction and dispersion was identified between the rupture regions and the rest of the tissue. The presented study forms an initial step towards gaining better insights into the characterization of local structural and mechanical fingerprints of fibrous plaque tissue in order to aid improved assessment of plaque rupture risk. STATEMENT OF SIGNIFICANCE: Plaque rupture risk assessment, critical to prevent cardiovascular events, requires knowledge on local failure properties and structure of collagenous plaque tissue. Our current knowledge is unfortunately limited to tissue's overall ultimate failure properties with scarce information on collagen architecture. In this study, local failure properties and collagen architecture of fibrous plaque tissue were obtained. We found predominant circumferential alignment of collagen fibers with substantial local dispersion. The tissue showed nonuniform stretch distribution under uniaxial tensile loading, with high stretches at rupture spots. This study highlights the significance of local mechanical and structural assessment for better insights into plaque rupture and the potential use of local stretches as risk marker for plaque rupture for patient-specific clinical applications.

Mechanical Behavior and Collagen Structure of Degenerative Mitral Valve Leaflets and a Finite Element Model of Primary Mitral Regurgitation

Degenerative mitral valve disease is the main cause of primary mitral regurgitation with two phenotypes: fibroelastic deficiency (FED) often with localized myxomatous degeneration and diffuse myxomatous degeneration or Barlow's disease. Myxomatous degeneration disrupts the microstructure of the mitral valve leaflets, particularly the collagen fibers, which affects the mechanical behavior of the leaflets. The present study uses biaxial mechanical tests and second harmonic generation microscopy to examine the mechanical behavior of Barlow and FED tissue. Three tissue samples were harvested from a FED patient and one sample is from a Barlow patient. Then we use an appropriate constitutive model by excluding the collagen fibers under compression. Finally, we built an FE model based on the echocardiography of patients diagnosed with FED and Barlow and the characterized material model and collagen fiber orientation. The Barlow sample and the FED sample from the most affected segment showed different mechanical behavior and collagen structure compared to the other two FED samples. The FE model showed very good agreement with echocardiography with 2.02±1.8 mm and 1.05±0.79 mm point-to-mesh distance errors for Barlow and FED patients, respectively. It has also been shown that the exclusion of collagen fibers under compression provides versatility for the material model; it behaves stiff in the belly region, preventing excessive bulging, while it behaves very softly in the commissures to facilitate folding. STATEMENT OF SIGNIFICANCE: None.

Characterization and modeling of the in-plane collagen fiber distribution in the porcine dermis

The structural arrangement of collagen fibers in the plane of the dermis layer plays a critical role in accurately predicting the mechanical behavior of skin tissues. This paper combines a histological analysis with statistical modeling to characterize and model the in-plane collagen fiber distribution in the porcine dermis. The histology data reveals that the fiber distribution in the plane of the porcine dermis is non-symmetric. The histology data forms the basis of our model, which employs a combination of two π-periodic von-Mises distribution density functions to create a non-symmetric distribution. We demonstrate that a non-symmetric in-plane fiber distribution is a significant improvement over a symmetric distribution.

Spatial frequency domain Mueller matrix imaging

SIGNIFICANCE

Mueller matrix polarimetry (MMP) and spatial frequency domain imaging (SFDI) are wide-field optical imaging modalities that differentiate tissue primarily by structure alignment and photon transport coefficient, respectively. Because these effects can be related, combining MMP and SFDI may enhance tissue differentiation beyond the capability of each modality alone.

AIM

An instrument was developed to combine MMP and SFDI with the goal of testing whether it enhances contrast of features in reflection mode.

APPROACH

The instrument was constructed using liquid crystal elements for polarization control, a digital light processing projector for generating sinusoidal illumination patterns, and a digital camera for imaging. A theoretical analysis shows that the SFD Mueller matrix is complex-valued and does not follow the same behavior as a regular Mueller matrix. Images were acquired from an anisotropic tissue phantom, an optical fiber bundle, and cerebellum, thalamus, and cerebrum tissues.

RESULTS

The measurement results suggest that singly scattered, few scattered, and diffusely scattered photon paths can be distinguished in some of the samples investigated. The combined imaging modality yields additional spatial frequency phase information, which highlights paths having only a few scattering events.

CONCLUSIONS

The combination of MMP and SFDI offers contrast mechanisms inaccessible by each modality used alone.

Force Profiles of Single Ventricle Atrioventricular Leaflets in Response to Annular Dilation and Leaflet Tethering

We sought to understand how leaflet forces change in response to annular dilation and leaflet tethering (LT) in single ventricle physiology. Explanted fetal bovine tricuspid valves were sutured onto image-derived annuli and ventricular mounts. Control valves (CON) were secured to a size-matched hypoplastic left heart syndrome (HLHS)-type annulus and compared to: (1) normal tricuspid valves secured to a size-matched saddle-shaped annulus, (2) HLHS-type annulus with LT, (3) HLHS-type annulus with annular dilation (dilation valves), or (4) a combined disease model with both dilation and tethering (disease valves). The specimens were tested in a systemic heart simulator at various single ventricle physiologies. Leaflet forces were measured using optical strain sensors sutured to each leaflet edge. Average force in the anterior leaflet was 43.2% lower in CON compared to normal tricuspid valves (P < 0.001). LT resulted in a 6.6% increase in average forces on the anterior leaflet (P = 0.04), 10.7% increase on the posterior leaflet (P = 0.03), and 14.1% increase on the septal leaflet (P < 0.001). In dilation valves, average septal leaflet forces increased relative to the CON by 42.2% (P = 0.01). In disease valves, average leaflet forces increased by 54.8% in the anterior leaflet (P < 0.001), 37.6% in the posterior leaflet (P = 0.03), and 79.9% in the septal leaflet (P < 0.001). The anterior leaflet experiences the highest forces in the normal tricuspid annulus under single ventricle physiology conditions. Annular dilation resulted in an increase in forces on the septal leaflet and LT resulted in an increase in forces across all 3 leaflets. Annular dilation and LT combined resulted in the largest increase in leaflet forces across all 3 leaflets.

Linking the region-specific tissue microstructure to the biaxial mechanical properties of the porcine left anterior descending artery

Coronary atherosclerosis is the main cause of death worldwide. Advancing the understanding of coronary microstructure-based mechanics is fundamental for the development of therapeutic tools and surgical procedures. Although the passive biaxial properties of the coronary arteries have been extensively explored, their regional differences and the relationship between tissue microstructure and mechanics have not been fully characterized. In this study, we characterized the passive biaxial mechanical properties and microstructural properties of the proximal, medial, and distal regions of the porcine left anterior descending artery (LADA). We also attempted to relate the biaxial stress-stretch response of the LADA and its respective birefringent responses to the polarized light for obtaining information about the load-dependent microstructural variations. We found that the LADA extensibility is reduced in the proximal-to-distal direction and that the medial region exhibits more heterogeneous mechanical behavior than the other two regions. We have also observed highly dynamic microstructural behavior where fiber families realign themselves depending on loading. In addition, we found that the microstructure of the distal region exhibited highly aligned fibers along the longitudinal axis of the artery. To verify this microstructural feature, we imaged the LADA specimens with multi-photon microscopy and observed that the adventitia microstructure transitioned from a random fiber network in the proximal region to highly aligned fibers in the distal region. Our findings could offer new perspectives for understanding coronary mechanics and aid in the development of tissue-engineered vascular grafts, which are currently limited due to their mismatch with native tissue in terms of mechanical properties and microstructural features. STATEMENT OF SIGNIFICANCE: The tissue biomechanics of coronary arteries is fundamental for the development of revascularization techniques such as coronary artery bypass. These therapeutics require a deep understanding of arterial mechanics, microstructure, and mechanobiology to prevent graft failure and reoperation. The present study characterizes the unique regional mechanical and microstructural properties of the porcine left anterior descending artery using biaxial testing, polarized-light imaging, and confocal microscopy. This comprehensive characterization provides an improved understanding of the collagen/elastin architecture in response to mechanical loads using a region-specific approach. The unique tissue properties obtained from this study will provide guidance for the selection of anastomotic sites in coronary artery bypass grafting and for the design of tissue-engineered vascular grafts.

Benchtop characterization of the tricuspid valve leaflet pre-strains

The pre-strains of biological soft tissues are important when relating their in vitro and in vivo mechanical behaviors. In this study, we present the first-of-its-kind experimental characterization of the tricuspid valve leaflet pre-strains. We use 3D photogrammetry and the reproducing kernel method to calculate the pre-strains within the central 10×10 mm region of the tricuspid valve leaflets from n=8 porcine hearts. In agreement with previous pre-strain studies for heart valve leaflets, our results show that all the three tricuspid valve leaflets shrink after explant from the ex vivo heart. These calculated strains are leaflet-specific and the septal leaflet experiences the most compressive changes. Furthermore, the strains observed after dissection of the central 10×10 mm region of the leaflet are smaller than when the valve is explanted, suggesting that our computed pre-strains are mainly due to the release of in situ annulus and chordae connections. The leaflets are then mounted on a biaxial testing device and preconditioned using force-controlled equibiaxial loading. We show that the employed preconditioning protocol does not 100% restore the leaflet pre-strains as removed during tissue dissection, and future studies are warranted to explore alternative preconditioning methods. Finally, we compare the calculated biomechanically oriented metrics considering five stress-free reference configurations. Interestingly, the radial tissue stretches and material anisotropies are significantly smaller compared to the post-preconditioning configuration. Extensions of this work can further explore the role of this unique leaflet-specific leaflet pre-strains on in vivo valve behavior via high-fidelity in-silico models.

Biomechanics of mitral valve leaflets: Second harmonic generation microscopy, biaxial mechanical tests and tissue modeling

Collagen fibers are the main load carrier in the mitral valve (MV) leaflets. Their orientation and dispersion are an important factor for the mechanical behavior. Most recent studies of collagen fibers in MVs lack either entire thickness study or high transmural resolution. The present study uses second harmonic generation (SHG) microscopy in combination with planar biaxial mechanical tests to better model and examine collagen fibers and mechanical properties of MV leaflets. SHG in combination with tissue clearing enables the collagen fibers to be examined through the entire thickness of the MV leaflets. Planar biaxial mechanical tests, on the other hand, enable the characterization of the mechanical tissue behavior, which is represented by a structural tissue model. Twelve porcine MV leaflets are examined. The SHG recording shows that the mean fiber angle for all samples varies on average by ±12° over the entire thickness and the collagen fiber dispersion changes strongly over the thickness. A constitutive model based on the generalized structure tensor approach is used for the associated tissue characterization. The model represents the tissue with three mechanical parameters plus the mean fiber direction and the dispersion, and predicts the biomechanical response of the leaflets with a good agreement (average r²=0.94). It is found that the collagen structure can be represented by a mean direction and a dispersion with a single family of fibers despite the variation in the collagen fiber direction and the dispersion over the entire thickness of MV leaflets. STATEMENT OF SIGNIFICANCE: Despite its prominent role in the mechanical behavior of mitral valve (MV) leaflets, the collagen structure has not yet been investigated over the entire thickness with high transmural resolution. The present study quantifies the detailed through thickness collagen fiber structure and examines the effects of its variation on MV tissue modeling. This is important because the study evaluates the assumption that the collagen fibers can be modeled with a representative single fiber family despite the variation across the thickness. In addition, the current comprehensive data set paves the way for quantifying the disruption of collagen fibers in myxomatous MV leaflets associated with disrupted collagen fibers.

Simultaneous Wide-Field Planar Strain-Fiber Orientation Distribution Measurement Using Polarized Spatial Domain Imaging

In the present study, we demonstrate that soft tissue fiber architectural maps captured using polarized spatial frequency domain imaging (pSFDI) can be utilized as an effective texture source for DIC-based planar surface strain analyses. Experimental planar biaxial mechanical studies were conducted using pericardium as the exemplar tissue, with simultaneous pSFDI measurements taken. From these measurements, the collagen fiber preferred direction [Formula: see text] was determined at the pixel level over the entire strain range using established methods ( https://doi.org/10.1007/s10439-019-02233-0 ). We then utilized these pixel-level [Formula: see text] maps as a texture source to quantify the deformation gradient tensor [Formula: see text] as a function of spatial position [Formula: see text] within the specimen at time t. Results indicted that that the pSFDI approach produced accurate deformation maps, as validated using both physical markers and conventional particle based method derived from the DIC analysis of the same specimens. We then extended the pSFDI technique to extract the fiber orientation distribution [Formula: see text] as a function of [Formula: see text] from the pSFDI intensity signal. This was accomplished by developing a calibration procedure to account for the optical behavior of the constituent fibers for the soft tissue being studied. We then demonstrated that the extracted [Formula: see text] was accurately computed in both the referential (i.e. unloaded) and deformed states. Moreover, we noted that the measured [Formula: see text] agreed well with affine kinematic deformation predictions. We also demonstrated this calibration approach could also be effectively used on electrospun biomaterials, underscoring the general utility of the approach. In a final step, using the ability to simultaneously quantify [Formula: see text] and [Formula: see text], we examined the effect of deformation and collagen structural measurements on the measurement region size. For pericardial tissues, we determined a critical length of [Formula: see text] 8 mm wherein the regional variations sufficiently dissipated. This result has immediate potential in the identification of optimal length scales for meso-scale strain measurement in soft tissues and fibrous biomaterials.

An in-silico benchmark for the tricuspid heart valve - Geometry, finite element mesh, Abaqus simulation, and result data set

This article provides Abaqus input files and user subroutines for performing finite element simulations of the tricuspid heart valve with an idealized geometry. Additional post-processing steps to obtain a ParaView visualization file (*.vtk) of the deformed geometry are also provided to allow the readers to use the included ParaView state file (*.pvsm) for customizable visualization and evaluation of the simulation results. We expect this first-of-its-kind in-silico benchmark dataset will facilitate user-friendly simulations considering material nonlinearity, leaflet-to-leaflet contact, and large deformations. Additionally, the information included herein can be used to rapidly evaluate other novel in-silico approaches developed for simulating cardiac valve function. The benchmark can be expanded to consider more complex features of the tricuspid valve function, such as the dynamic annulus motion or the time-varying transvalvular pressure. Interested readers are referred to the companion article (Johnson et al., 2021) for an example application of this in-silico tool for isogeometric analysis of tricuspid valves.

Determination of a Strain Energy Density Function for the Tricuspid Valve Leaflets Using Constant Invariant-Based Mechanical Characterizations

The tricuspid valve (TV) regulates the blood flow within the right side of the heart. Despite recent improvements in understanding TV mechanical and microstructural properties, limited attention has been devoted to the development of TV-specific constitutive models. The objective of this work is to use the first-of-its-kind experimental data from constant invariant-based mechanical characterizations to determine a suitable invariant-based strain energy density function (SEDF). Six specimens for each TV leaflet are characterized using constant invariant mechanical testing. The data is then fit with three candidate SEDF forms: (i) a polynomial model-the transversely isotropic version of the Mooney-Rivlin model, (ii) an exponential model, and (iii) a combined polynomial-exponential model. Similar fitting capabilities were found for the exponential and the polynomial forms (R2=0.92-0.99 versus 0.91-0.97) compared to the combined polynomial-exponential SEDF (R2=0.65-0.95). Furthermore, the polynomial form had larger Pearson's correlation coefficients than the exponential form (0.51 versus 0.30), indicating a more well-defined search space. Finally, the exponential and the combined polynomial-exponential forms had notably smaller but more eccentric model parameter's confidence regions than the polynomial form. Further evaluations of invariant decoupling revealed that the decoupling of the invariant terms within the exponential form leads to a less satisfactory performance. From these results, we conclude that the exponential form is better suited for the TV leaflets owing to its superb fitting capabilities and smaller parameter's confidence regions.

Uniaxial properties of ascending aortic aneurysms in light of effective stretch

A constitutive model that explicitly considers the gradual recruitment of collagen fibers is applied to investigate the uniaxial properties of human ascending aortic aneurysms. The model uses an effective stretch, which is a continuum scale kinematic variable measuring the true stretch of the tissue, to formulate the fiber stress. The constitutive equation contains two shape parameters characterizing the stochastic distribution of fiber waviness, and two elastic parameters accounting for, respectively, the elastic properties of ground substance and the straightened collagen fibers. The model is applied to 156 sets of uniaxial stress-stretch data obtained from 52 aneurysm samples. Major findings include (1) the uniaxial response can be well described by a quadratic strain energy function of the effective strain; (2) the ultimate stretches, when measured in terms of the effective stretch, are closely clustered around 1.1, in contrast to a much wider range in the original stretch; and (3) the ultimate stress correlates positively with the fiber stiffness. The age dependence and directional differences of constitutive parameters are also investigated. Results indicate that only the waviness depends strongly on age; no clear alterations occur in elastic parameters. Further, the fibers are wavier and stiffer in the circumferential direction than in the longitudinal direction. No other parameters exhibit significant direction difference. STATEMENT OF SIGNIFICANCE: We introduced a constitutive model which explicitly accounts for collagen fiber recruitment to investigate the uniaxial properties of human ascending aortic aneurysm tissues. Uniaxial response data from 156 specimens were considered in the study. It was found that the seemingly dissimilar response curves are, in fact, similar if we measure the deformation using an effective stretch which factors out the uncrimping deformation. The rupture stretches in terms of the effective stretch are closely packed around 1.1. And the stress-stretch curves collapse to a canonical curve after a transformation.

Full-Range Optical Imaging of Planar Collagen Fiber Orientation Using Polarized Light Microscopy

A novel method for semiautomated assessment of directions of collagen fibers in soft tissues using histological image analysis is presented. It is based on multiple rotated images obtained via polarized light microscopy without any additional components, i.e., with just two polarizers being either perpendicular or nonperpendicular (rotated). This arrangement breaks the limitation of 90° periodicity of polarized light intensity and evaluates the in-plane fiber orientation over the whole 180° range accurately and quickly. After having verified the method, we used histological specimens of porcine Achilles tendon and aorta to validate the proposed algorithm and to lower the number of rotated images needed for evaluation. Our algorithm is capable to analyze 5·105 pixels in one micrograph in a few seconds and is thus a powerful and cheap tool promising a broad application in detection of collagen fiber distribution in soft tissues.

Linking collagen fiber architecture to tissue-level biaxial mechanical behaviors of porcine semilunar heart valve cusps

The semilunar heart valves regulate the blood flow from the ventricles to the major arteries through the opening and closing of the scallop shaped cusps. These cusps are composed of collagen fibers that act as the primary loading-bearing component. The load-dependent collagen fiber architecture has been previously examined in the existing literature; however, these studies relied on chemical clearing and tissue modifications to observe the underlying changes in response to mechanical loads. In the present study, we address this gap in knowledge by quantifying the collagen fiber orientations and alignments of the aortic and pulmonary cusps through a multi-scale, non-destructive experimental approach. This opto-mechanical approach, which combines polarized spatial frequency domain imaging and biaxial mechanical testing, provides a greater field of view (10-25mm) and faster imaging time (45-50s) than other traditional collagen imaging techniques. The birefringent response of the collagen fibers was fit with a von Mises distribution, while the biaxial mechanical testing data was implemented into a modified full structural model for further analysis. Our results showed that the semilunar heart valve cusps are more extensible in the tissue's radial direction than the circumferential direction under all the varied biaxial testing protocols, together with greater material anisotropy among the pulmonary valve cusps compared to the aortic valve cusps. The collagen fibers were shown to reorient towards the direction of the greatest applied loading and incrementally realign with the increased applied stress. The collagen fiber architecture within the aortic valve cusps were found to be more homogeneous than the pulmonary valve counterparts, reflecting the differences in the physiological environments experienced by these two semilunar heart valves. Further, the von Mises distribution fitting highlighted the presence and contribution of two distinct fiber families for each of the two semilunar heart valves. The results from this work would provide valuable insight into connecting tissue-level mechanics to the underlying collagen fiber architecture-an essential information for the future development of high-fidelity aortic/pulmonary valve computational models.

Effects of enzyme-based removal of collagen and elastin constituents on the biaxial mechanical responses of porcine atrioventricular heart valve anterior leaflets

The leaflets of the atrioventricular heart valves (AHVs) regulate the one-directional flow of blood through a coordination of the extracellular matrix components, including the collagen fibers, elastin, and glycosaminoglycans. Dysfunction of the AHVs, such as those caused by unfavorable microstructural remodeling, lead to valvular heart diseases and improper blood flow, which can ultimately cause heart failure. In order to better understand the mechanics and remodeling of the AHV leaflets and how therapeutics can inadvertently cause adverse microstructural changes, a systematic characterization of the role of each constituent in the biomechanical properties is appropriate. Previous studies have quantified the contributions of the individual microstructural components to tissue-level behavior for the semilunar valve cusps, but not for the AHV leaflets. In this study, for the first time, we quantify the relationships between microstructure and mechanics of the AHV leaflet using a three-step experimental procedure: (i) biaxial tension and stress relaxation testing of control (untreated) porcine AHV anterior leaflet specimens; (ii) enzyme treatment to remove a portion of either the collagen or elastin constituent; and (iii) biaxial tensile and stress relaxation testing of the constituent-removed (treated) specimens. We have observed that the removal of ∼100% elastin resulted in a ∼10% decrease in the tissue extensibility with biaxial tension and a ∼10% increase in the overall stress reduction with stress relaxation. In contrast, removal of 46% of the collagen content insignificantly affected tissue extensibility with biaxial tension and significantly increased stress decay (10%) with stress relaxation. These findings provide an insight into the microstructure-mechanics relationship of the AHVs and will be beneficial for future developments and refinements of microstructurally informed constitutive models for the simulation of diseased and surgically intervened AHV function. STATEMENT OF SIGNIFICANCE: This study presents, for the first time, a thorough mechanical characterization of the atrioventricular heart valve leaflets before and after enzymatic removal of elastin and collagen. We found that the biaxial tensile properties of elastin-deficient tissues and collagen-deficient are stiffer. The fact of elastin supporting low-stress valve function and collagen as the main load-bearing component was evident in a decrease in the low-tension modulus for elastin-deficient tissues and in the high-tension modulus for collagen-deficient tissues. Our quantification and experimental technique could be useful in predicting the disease-related changes in heart valve mechanics. The information obtained from this work is valuable for refining the constitutive models that describe the essential microstructure-mechanics relationship.

Parameterization, geometric modeling, and isogeometric analysis of tricuspid valves

Approximately 1.6 million patients in the United States are affected by tricuspid valve regurgitation, which occurs when the tricuspid valve does not close properly to prevent backward blood flow into the right atrium. Despite its critical role in proper cardiac function, the tricuspid valve has received limited research attention compared to the mitral and aortic valves on the left side of the heart. As a result, proper valvular function and the pathologies that may cause dysfunction remain poorly understood. To promote further investigations of the biomechanical behavior and response of the tricuspid valve, this work establishes a parameter-based approach that provides a template for tricuspid valve modeling and simulation. The proposed tricuspid valve parameterization presents a comprehensive description of the leaflets and the complex chordae tendineae for capturing the typical three-cusp structural deformation observed from medical data. This simulation framework develops a practical procedure for modeling tricuspid valves and offers a robust, flexible approach to analyze the performance and effectiveness of various valve configurations using isogeometric analysis. The proposed methods also establish a baseline to examine the tricuspid valve's structural deformation, perform future investigations of native valve configurations under healthy and disease conditions, and optimize prosthetic valve designs.

An Information-Theoretic Framework for Optimal Design: Analysis of Protocols for Estimating Soft Tissue Parameters in Biaxial Experiments

A new framework for optimal design based on the information-theoretic measures of mutual information, conditional mutual information and their combination is proposed. The framework is tested on the analysis of protocols—a combination of angles along which strain measurements can be acquired—in a biaxial experiment of soft tissues for the estimation of hyperelastic constitutive model parameters. The proposed framework considers the information gain about the parameters from the experiment as the key criterion to be maximised, which can be directly used for optimal design. Information gain is computed through k-nearest neighbour algorithms applied to the joint samples of the parameters and measurements produced by the forward and observation models. For biaxial experiments, the results show that low angles have a relatively low information content compared to high angles. The results also show that a smaller number of angles with suitably chosen combinations can result in higher information gains when compared to a larger number of angles which are poorly combined. Finally, it is shown that the proposed framework is consistent with classical approaches, particularly D-optimal design.

Evaluation of affine fiber kinematics in porcine tricuspid valve leaflets using polarized spatial frequency domain imaging and planar biaxial testing

Collagen fibers are the primary load-bearing microstructural constituent of bodily soft tissues, and, when subjected to external loading, the collagen fibers reorient, uncrimp, and elongate. Specific to the atrioventricular heart valve leaflets, the collagen fiber kinematics form the basis of many constitutive models; however, some researchers claim that modeling the affine fiber kinematics (AFK) are sufficient for accurately predicting the macroscopic tissue deformations, while others state that modeling the non-affine kinematics (i.e., fiber uncrimping together with elastic elongation) is required. Experimental verification of the AFK theory has been previously performed for the mitral valve leaflets in the left-side heart; however, this same evaluation has yet to be performed for the morphologically distinct tricuspid valve (TV) leaflets in the right-side heart. In this work, we, for the first time, evaluated the AFK theory for the TV leaflets using an integrated biaxial testing-polarized spatial frequency domain imaging device to experimentally quantify the load-dependent collagen fiber reorientations for comparison to the AFK theory predictions. We found that the AFK theory generally underpredicted the fiber reorientations by 3.1°, on average, under the applied equibiaxial loading with greater disparity when the tissue was subjected to the applied non-equibiaxial loading. Furthermore, increased AFK errors were observed with increasing collagen fiber reorientations (Pearson coefficient r = -0.36, equibiaxial loading), suggesting the AFK theory is better suited for relatively smaller reorientations. Our findings suggest the AFK theory may require modification for more accurate predictions of the collagen fiber kinematics in the TV leaflets, which will be useful in refining modeling efforts for more accurate TV simulations.

A pilot study on biaxial mechanical, collagen microstructural, and morphological characterizations of a resected human intracranial aneurysm tissue

Intracranial aneurysms (ICAs) are focal dilatations that imply a weakening of the brain artery. Incidental rupture of an ICA is increasingly responsible for significant mortality and morbidity in the American’s aging population. Previous studies have quantified the pressure-volume characteristics, uniaxial mechanical properties, and morphological features of human aneurysms. In this pilot study, for the first time, we comprehensively quantified the mechanical, collagen fiber microstructural, and morphological properties of one resected human posterior inferior cerebellar artery aneurysm. The tissue from the dome of a right posterior inferior cerebral aneurysm was first mechanically characterized using biaxial tension and stress relaxation tests. Then, the load-dependent collagen fiber architecture of the aneurysm tissue was quantified using an in-house polarized spatial frequency domain imaging system. Finally, optical coherence tomography and histological procedures were used to quantify the tissue’s microstructural morphology. Mechanically, the tissue was shown to exhibit hysteresis, a nonlinear stress-strain response, and material anisotropy. Moreover, the unloaded collagen fiber architecture of the tissue was predominantly aligned with the testing Y-direction and rotated towards the X-direction under increasing equibiaxial loading. Furthermore, our histological analysis showed a considerable damage to the morphological integrity of the tissue, including lack of elastin, intimal thickening, and calcium deposition. This new unified characterization framework can be extended to better understand the mechanics-microstructure interrelationship of aneurysm tissues at different time points of the formation or growth. Such specimen-specific information is anticipated to provide valuable insight that may improve our current understanding of aneurysm growth and rupture potential.

Instant polarized light microscopy for imaging collagen microarchitecture and dynamics

Collagen fibers are a primary load-bearing component of connective tissues and are therefore central to tissue biomechanics and pathophysiology. Understanding collagen architecture and behavior under dynamic loading requires a quantitative imaging technique with simultaneously high spatial and temporal resolutions. Suitable techniques are thus rare and often inaccessible. In this study, we present instant polarized light microscopy (IPOL), in which a single snapshot image encodes information on fiber orientation and retardance, thus fulfilling the requirement. We utilized both simulation and experimental data from collagenous tissues of chicken tendon, sheep eye, and porcine heart to evaluate the effectiveness of IPOL as a quantitative imaging technique. We demonstrate that IPOL allows quantitative characterization of micron-scale collagen fiber architecture at full camera frame rates (156 frames/second herein).

Quantification of load-dependent changes in the collagen fiber architecture for the strut chordae tendineae-leaflet insertion of porcine atrioventricular heart valves

Atrioventricular heart valves (AHVs) regulate the unidirectional flow of blood through the heart by opening and closing of the leaflets, which are supported in their functions by the chordae tendineae (CT). The leaflets and CT are primarily composed of collagen fibers that act as the load-bearing component of the tissue microstructures. At the CT-leaflet insertion, the collagen fiber architecture is complex, and has been of increasing focus in the previous literature. However, these previous studies have not been able to quantify the load-dependent changes in the tissue's collagen fiber orientations and alignments. In the present study, we address this gap in knowledge by quantifying the changes in the collagen fiber architecture of the mitral and tricuspid valve's strut CT-leaflet insertions in response to the applied loads by using a unique approach, which combines polarized spatial frequency domain imaging with uniaxial mechanical testing. Additionally, we characterized these microstructural changes across the same specimen without the need for tissue fixatives. We observed increases in the collagen fiber alignments in the CT-leaflet insertion with increased loading, as described through the degree of optical anisotropy. Furthermore, we used a leaflet-CT-papillary muscle entity method during uniaxial testing to quantify the chordae tendineae mechanics, including the derivation of the Ogden-type constitutive modeling parameters. The results from this study provide a valuable insight into the load-dependent behaviors of the strut CT-leaflet insertion, offering a research avenue to better understand the relationship between tissue mechanics and the microstructure, which will contribute to a deeper understanding of AHV biomechanics.

A pilot in silico modeling-based study of the pathological effects on the biomechanical function of tricuspid valves

Current clinical assessment of functional tricuspid valve regurgitation relies on metrics quantified from medical imaging modalities. Although these clinical methodologies are generally successful, the lack of detailed information about the mechanical environment of the valve presents inherent challenges for assessing tricuspid valve regurgitation. In the present study, we have developed a finite element-based in silico model of one porcine tricuspid valve (TV) geometry to investigate how various pathological conditions affect the overall biomechanical function of the TV. There were three primary observations from our results. Firstly, the results of the papillary muscle (PM) displacement study scenario indicated more pronounced changes in the TV biomechanical function. Secondly, compared to uniform annulus dilation, nonuniform dilation scenario induced more evident changes in the von Mises stresses (83.8-125.3 kPa vs 65.1-84.0 kPa) and the Green-Lagrange strains (0.52-0.58 vs 0.47-0.53) for the three TV leaflets. Finally, results from the pulmonary hypertension study scenario showed opposite trends compared to the PM displacement and annulus dilation scenarios. Furthermore, various chordae rupture scenarios were simulated, and the results showed that the chordae tendineae attached to the TV anterior and septal leaflets may be more critical to proper TV function. This in silico modeling-based study has provided a deeper insight into the tricuspid valve pathologies that may be useful, with moderate extensions, for guiding clinical decisions. NOVELTY STATEMENT: The novelties of the research are summarized below: A comprehensive in silico pilot study of how isolated functional tricuspid regurgitation pathologies and ruptured chordae tendineae would alter the tricuspid valve function; An extensive analysis of the tricuspid valve function, including mechanical quantities (eg, the von Mises stress and the Green-Lagrange strain) and clinically-relevant geometry metrics (eg, the tenting area and the coaptation height); and A developed computational modeling pipeline that can be extended to evaluate patient-specific tricuspid valve geometries and enhance the current clinical diagnosis and treatment of tricuspid regurgitation.

A Pilot Study on Linking Tissue Mechanics with Load-Dependent Collagen Microstructures in Porcine Tricuspid Valve Leaflets

The tricuspid valve (TV) is composed of three leaflets that coapt during systole to prevent deoxygenated blood from re-entering the right atrium. The connection between the TV leaflets’ microstructure and the tissue-level mechanical responses has yet to be fully understood in the TV biomechanics society. This pilot study sought to examine the load-dependent collagen fiber architecture of the three TV leaflets, by employing a multiscale, combined experimental approach that utilizes tissue-level biaxial mechanical characterizations, micro-level collagen fiber quantification, and histological analysis. Our results showed that the three TV leaflets displayed greater extensibility in the tissues’ radial direction than in the circumferential direction, consistently under different applied biaxial tensions. Additionally, collagen fibers reoriented towards the direction of the larger applied load, with the largest changes in the alignment of the collagen fibers under radially-dominant loading. Moreover, collagen fibers in the belly region of the TV leaflets were found to experience greater reorientations compared to the tissue region closer to the TV annulus. Furthermore, histological examinations of the TV leaflets displayed significant regional variation in constituent mass fraction, highlighting the heterogeneous collagen microstructure. The combined experimental approach presented in this work enables the connection of tissue mechanics, collagen fiber microstructure, and morphology for the TV leaflets. This experimental methodology also provides a new research platform for future developments, such as multiscale models for the TVs, and the design of bioprosthetic heart valves that could better mimic the mechanical, microstructural, and morphological characteristics of the native tricuspid valve leaflets.

Mechanics and Microstructure of the Atrioventricular Heart Valve Chordae Tendineae: A Review

The atrioventricular heart valves (AHVs) are responsible for directing unidirectional blood flow through the heart by properly opening and closing the valve leaflets, which are supported in their function by the chordae tendineae and the papillary muscles. Specifically, the chordae tendineae are critical to distributing forces during systolic closure from the leaflets to the papillary muscles, preventing leaflet prolapse and consequent regurgitation. Current therapies for chordae failure have issues of disease recurrence or suboptimal treatment outcomes. To improve those therapies, researchers have sought to better understand the mechanics and microstructure of the chordae tendineae of the AHVs. The intricate structures of the chordae tendineae have become of increasing interest in recent literature, and there are several key findings that have not been comprehensively summarized in one review. Therefore, in this review paper, we will provide a summary of the current state of biomechanical and microstructural characterizations of the chordae tendineae, and also discuss perspectives for future studies that will aid in a better understanding of the tissue mechanics-microstructure linking of the AHVs' chordae tendineae, and thereby improve the therapeutics for heart valve diseases caused by chordae failures.

Mechanics of Porcine Heart Valves' Strut Chordae Tendineae Investigated as a Leaflet-Chordae-Papillary Muscle Entity

Proper blood flow through the atrioventricular heart valves (AHVs) relies on the holistic function of the valve and subvalvular structures, and a failure of any component can lead to life-threatening heart disease. A comprehension of the mechanical characteristics of healthy valvular components is necessary for the refinement of heart valve computational models. In previous studies, the chordae tendineae have been mechanically characterized as individual structures, usually in a clamping-based approach, which may not accurately reflect the in vivo chordal interactions with the leaflet insertion and papillary muscles. In this study, we performed uniaxial mechanical testing of strut chordae tendineae of the AHVs under a unique tine-based leaflet-chordae-papillary muscle testing to observe the chordae mechanics while preserving the subvalvular component interactions. Results of this study provided insight to the disparity of chordae tissue stress-stretch responses between the mitral valve (MV) and the tricuspid valve (TV) under their respective emulated physiological loading. Specifically, strut chordae tendineae of the MV anterior leaflet had peak stretches of 1.09-1.16, while peak stretches of 1.08-1.11 were found for the TV anterior leaflet strut chordae. Constitutive parameters were also derived for the chordae tissue specimens using an Ogden model, which is useful for AHV computational model refinement. Results of this study are beneficial to the eventual improvement of treatment methods for valvular disease.

Load-dependent collagen fiber architecture data of representative bovine tendon and mitral valve anterior leaflet tissues as quantified by an integrated opto-mechanical system

The data presented in this article provide load-dependent collagen fiber architecture (CFA) of one representative bovine tendon tissue sample and two representative porcine mitral valve anterior leaflet tissues, and they are stored in a MATLAB MAT-file format. Each dataset contains: (i) the number of pixel points, (ii) the array of pixel's x- and y-coordinates, (iii) the three acquired pixel intensity arrays, and (iv) the Delaunay triangulation for visualization purpose. This dataset is associated with a companion journal article, which can be consulted for further information about the methodology, results, and discussion of the opto-mechanical characterization of the tissue's CFA's (Jett etal. [1]).