A generalized method for the analysis of planar biaxial mechanical data using tethered testing configurations

Tissue formation and host remodeling of an elastomeric biodegradable scaffold in an ovine pulmonary leaflet replacement model

In pursuit of a suitable scaffold material for cardiac valve tissue engineering applications, an acellular, electrospun, biodegradable polyester carbonate urethane urea (PECUU) scaffold was evaluated as a pulmonary valve leaflet replacement in vivo. In sheep (n = 8), a single pulmonary valve leaflet was replaced with a PECUU leaflet and followed for 1, 6, and 12 weeks. Implanted leaflet function was assessed in vivo by echocardiography. Explanted samples were studied for gross pathology, microscopic changes in the extracellular matrix, host cellular re-population, and immune responses, and for biomechanical properties. PECUU leaflets showed normal leaflet motion at implant, but decreased leaflet motion and dimensions at 6 weeks. The leaflets accumulated α-SMA and CD45 positive cells, with surfaces covered with endothelial cells (CD31+). New collagen formation occurred (Picrosirius Red). Accumulated tissue thickness correlated with the decrease in leaflet motion. The PECUU scaffolds had histologic evidence of scaffold degradation and an accumulation of pro-inflammatory/M1 and anti-inflammatory/M2 macrophages over time in vivo. The extent of inflammatory cell accumulation correlated with tissue formation and polymer degradation but was also associated with leaflet thickening and decreased leaflet motion. Future studies should explore pre-implant seeding of polymer scaffolds, more advanced polymer fabrication methods able to more closely approximate native tissue structure and function, and other techniques to control and balance the degradation of biomaterials and new tissue formation by modulation of the host immune response.

A viscoelastic constitutive model for human femoropopliteal arteries

High failure rates present challenges for surgical and interventional therapies for peripheral artery disease of the femoropopliteal artery (FPA). The FPA's demanding biomechanical environment necessitates complex interactions with repair devices and materials. While a comprehensive understanding of the FPA's mechanical characteristics could improve medical treatments, the viscoelastic properties of these muscular arteries remain poorly understood, and the constitutive model describing their time-dependent behavior is absent. We introduce a new viscoelastic constitutive model for the human FPA grounded in its microstructural composition. The model is capable of detailing the contributions of each intramural component to the overall viscoelastic response. Our model was developed utilizing fractional viscoelasticity and tested using biaxial experimental data with hysteresis and relaxation collected from 10 healthy human subjects aged 57 to 65 and further optimized for high throughput and automation. The model accurately described the experimental data, capturing significant nonlinearity and hysteresis that were particularly pronounced circumferentially, and tracked the contribution of passive smooth muscle cells to viscoelasticity that was twice that of the collagen fibers. The high-throughput parameter estimation procedure we developed included a specialized objective function and modifications to enhance convergence for the common exponential-type fiber laws, facilitating computational implementation. Our new model delineates the time-dependent behavior of human FPAs, which will improve the fidelity of computational simulations investigating device-artery interactions and contribute to their greater physical accuracy. Moreover, it serves as a useful tool to investigate the contribution of arterial constituents to overall tissue viscoelasticity, thereby expanding our knowledge of arterial mechanophysiology. STATEMENT OF SIGNIFICANCE: The demanding biomechanical environment of the femoropopliteal artery (FPA) necessitates complex interactions with repair devices and materials, but the viscoelastic properties of these muscular arteries remain poorly understood with the constitutive model describing their time-dependent behavior being absent. We hereby introduce the first viscoelastic constitutive model for the human FPA grounded in its microstructures. This model was tested using biaxial mechanical data collected from 10 healthy human subjects between the ages of 57 to 65. It can detail the contributions of each intramural component to the overall viscoelastic response, showing that the contribution of passive smooth muscle cells to viscoelasticity is twice that of collagen fibers. The usefulness of this model as tool to better understand arterial mechanophysiology was demonstrated.

A Bayesian constitutive model selection framework for biaxial mechanical testing of planar soft tissues: Application to porcine aortic valves

A variety of constitutive models have been developed for soft tissue mechanics. However, there is no established criterion to select a suitable model for a specific application. Although the model that best fits the experimental data can be deemed the most suitable model, this practice often can be insufficient given the inter-sample variability of experimental observations. Herein, we present a Bayesian approach to calculate the relative probabilities of constitutive models based on biaxial mechanical testing of tissue samples. Forty-six samples of porcine aortic valve tissue were tested using a biaxial stretching setup. For each sample, seven ratios of stresses along and perpendicular to the fiber direction were applied. The probabilities of eight invariant-based constitutive models were calculated based on the experimental data using the proposed model selection framework. The calculated probabilities showed that, out of the considered models and based on the information available through the utilized experimental dataset, the May-Newman model was the most probable model for the porcine aortic valve data. When the samples were further grouped into different cusp types, the May-Newman model remained the most probable for the left- and right-coronary cusps, whereas for non-coronary cusps two models were found to be equally probable: the Lee-Sacks model and the May-Newman model. This difference between cusp types was found to be associated with the first principal component analysis (PCA) mode, where this mode's amplitudes of the non-coronary and right-coronary cusps were found to be significantly different. Our results show that a PCA-based statistical model can capture significant variations in the mechanical properties of soft tissues. The presented framework is applicable to other tissue types, and has the potential to provide a structured and rational way of making simulations population-based.

Design of a Mechanobioreactor to Apply Anisotropic, Biaxial Strain to Large Thin Biomaterials for Tissue Engineered Heart Valve Applications

Repair and replacement solutions for congenitally diseased heart valves capable of post-surgery growth and adaptation have remained elusive. Tissue engineered heart valves (TEHVs) offer a potential biological solution that addresses the drawbacks of existing valve replacements. Typically, TEHVs are made from thin, fibrous biomaterials that either become cell populated in vitro or in situ. Often, TEHV designs poorly mimic the anisotropic mechanical properties of healthy native valves leading to inadequate biomechanical function. Mechanical conditioning of engineered tissues with anisotropic strain application can induce extracellular matrix remodelling to alter the anisotropic mechanical properties of a construct, but implementation has been limited to small-scale set-ups. To address this limitation for TEHV applications, we designed and built a mechanobioreactor capable of modulating biaxial strain anisotropy applied to large, thin, biomaterial sheets in vitro. The bioreactor can independently control two orthogonal stretch axes to modulate applied strain anisotropy on biomaterial sheets from 13 × 13 mm² to 70 × 40 mm². A design of experiments was performed using experimentally validated finite element (FE) models and demonstrated that biaxial strain was applied uniformly over a larger percentage of the cell seeded area for larger sheets (13 × 13 mm²: 58% of sheet area vs. 52 × 31 mm²: 86% of sheet area). Furthermore, bioreactor prototypes demonstrated that over 70% of the cell seeding area remained uniformly strained under different prescribed protocols: equibiaxial amplitudes between 5 to 40%, cyclic frequencies between 0.1 to 2.5 Hz and anisotropic strain ratios between 0:1 (constrained uniaxial) to 2:1. Lastly, proof-of-concept experiments were conducted where we applied equibiaxial (ε_x = ε_y = 8.75%) and anisotropic (ε_x = 12.5%, ε_y = 5%) strain protocols to cell-seeded, electrospun scaffolds. Cell nuclei and F-actin aligned to the vector-sum strain direction of each prescribed protocol (nuclei alignment: equibiaxial: 43.2° ± 1.8°, anisotropic: 17.5° ± 1.7°; p < 0.001). The abilities of this bioreactor to prescribe different strain amplitude, frequency and strain anisotropy protocols to cell-seeded scaffolds will enable future studies into the effects of anisotropic loading protocols on mechanically conditioned TEHVs and other engineered planar connective tissues.

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.

The Effects of Healthy Aging on Right Ventricular Structure and Biomechanical Properties: A Pilot Study

Healthy aging has been associated with alterations in pulmonary vascular and right ventricular (RV) hemodynamics, potentially leading to RV remodeling. Despite the current evidence suggesting an association between aging and alterations in RV function and higher prevalence of pulmonary hypertension in the elderly, limited data exist on age-related differences in RV structure and biomechanics. In this work, we report our preliminary findings on the effects of healthy aging on RV structure, function, and biomechanical properties. Hemodynamic measurements, biaxial mechanical testing, constitutive modeling, and quantitative transmural histological analysis were employed to study two groups of male Sprague-Dawley rats: control (11 weeks) and aging (80 weeks). Aging was associated with increases in RV peak pressures (+17%, p = 0.017), RV contractility (+52%, p = 0.004), and RV wall thickness (+38%, p = 0.001). Longitudinal realignment of RV collagen (16.4°, p = 0.013) and myofibers (14.6°, p = 0.017) were observed with aging, accompanied by transmural cardiomyocyte loss and fibrosis. Aging led to increased RV myofiber stiffness (+141%, p = 0.003), in addition to a bimodal alteration in the biaxial biomechanical properties of the RV free wall, resulting in increased tissue-level stiffness in the low-strain region, while progressing into decreased stiffness at higher strains. Our results demonstrate that healthy aging may modulate RV remodeling via increased peak pressures, cardiomyocyte loss, fibrosis, fiber reorientation, and altered mechanical properties in male Sprague-Dawley rats. Similarities were observed between aging-induced remodeling patterns and those of RV remodeling in pressure overload. These findings may help our understanding of age-related changes in the cardiovascular fitness and response to disease.

Anisotropic elastic behavior of a hydrogel-coated electrospun polyurethane: Suitability for heart valve leaflets

Although xenograft biomaterials have been used for decades in replacement heart valves, they continue to face multiple limitations, including limited durability, mineralization, and restricted design space due to their biological origins. These issues necessitate the need for novel replacement heart valve biomaterials that are durable, non-thrombogenic, and compatible with transcatheter aortic valve replacement devices. In this study, we explored the suitability of an electrospun poly(carbonate urethane) (ES-PCU) mesh coated with a poly(ethylene glycol) diacrylate (PEGDA) hydrogel as a synthetic biomaterial for replacement heart valve leaflets. In this material design, the mesh provides the mechanical support, while the hydrogel provides the required surface hemocompatibility. We conducted a comprehensive study to characterize the structural and mechanical properties of the uncoated mesh as well as the hydrogel-coated mesh (composite biomaterial) over the estimated operational range. We found that the composite biomaterial was functionally robust with reproducible stress-strain behavior within and beyond the functional ranges for replacement heart valves, and was able to withstand the rigors of mechanical evaluation without any observable damage. In addition, the composite biomaterial displayed a wide range of mechanical anisotropic responses, which were governed by fiber orientation of the mesh, which in turn, was controlled with the fabrication process. Finally, we developed a novel constitutive modeling approach to predict the mechanical behavior of the composite biomaterial under in-plane extension and shear deformation modes. This model identified the existence of fiber-fiber mechanical interactions in the mesh that have not previously been reported. Interestingly, there was no evidence of fiber-hydrogel mechanical interactions. This important finding suggests that the hydrogel coating can be optimized for hemocompatibility independent of the structural mechanical responses required by the leaflet. This initial study indicated that the composite biomaterial has mechanical properties well-suited for replacement heart valve applications and that the electrospun mesh microarchitecture and hydrogel biological properties can be optimized independently. It also reveals that the structural mechanisms contributing to the mechanical response are more complicated than what was previously established and paves the pathway for more detailed future studies.

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.

Angiotensin Receptor-Neprilysin Inhibition Attenuates Right Ventricular Remodeling in Pulmonary Hypertension

Background

Pulmonary hypertension (PH) results in increased right ventricular (RV) afterload and ventricular remodeling. Sacubitril/valsartan (sac/val) is a dual acting drug, composed of the neprilysin inhibitor sacubitril and the angiotensin receptor blocker valsartan, that has shown promising outcomes in reducing the risk of death and hospitalization for chronic systolic left ventricular heart failure. In this study, we aimed to examine if angiotensin receptor‐neprilysin inhibition using sac/val attenuates RV remodeling in PH.

Methods and Results

RV pressure overload was induced in Sprague–Dawley rats via banding the main pulmonary artery. Three different cohorts of controls, placebo‐treated PH, and sac/val‐treated PH were studied in a 21‐day treatment window. Terminal invasive hemodynamic measurements, quantitative histological analysis, biaxial mechanical testing, and constitutive modeling were employed to conduct a multiscale analysis on the effects of sac/val on RV remodeling in PH. Sac/val treatment decreased RV maximum pressures (29% improvement, P=0.002), improved RV contractile (30%, P=0.012) and relaxation (29%, P=0.043) functions, reduced RV afterload (35% improvement, P=0.016), and prevented RV‐pulmonary artery uncoupling. Furthermore, sac/val attenuated RV hypertrophy (16% improvement, P=0.006) and prevented transmural reorientation of RV collagen and myofibers (P=0.011). The combined natriuresis and vasodilation resulting from sac/val led to improved RV biomechanical properties and prevented increased myofiber stiffness in PH (61% improvement, P=0.032).

Conclusions

Sac/val may prevent maladaptive RV remodeling in a pressure overload model via amelioration of RV pressure rise, hypertrophy, collagen, and myofiber reorientation as well as tissue stiffening both at the tissue and myofiber level.

Multiaxial Lenticular Stress-Strain Relationship of Native Myocardium is Preserved by Infarct-Induced Natural Heart Regeneration in Neonatal Mice

Neonatal mice exhibit natural heart regeneration after myocardial infarction (MI) on postnatal day 1 (P1), but this ability is lost by postnatal day 7 (P7). Cardiac biomechanics intricately affect long-term heart function, but whether regenerated cardiac muscle is biomechanically similar to native myocardium remains unknown. We hypothesized that neonatal heart regeneration preserves native left ventricular (LV) biomechanical properties after MI. C57BL/6J mice underwent sham surgery or left anterior descending coronary artery ligation at age P1 or P7. Echocardiography performed 4 weeks post-MI showed that P1 MI and sham mice (n = 22, each) had similar LV wall thickness, diameter, and ejection fraction (59.6% vs 60.7%, p = 0.6514). Compared to P7 shams (n = 20), P7 MI mice (n = 20) had significant LV wall thinning, chamber enlargement, and depressed ejection fraction (32.6% vs 61.8%, p < 0.0001). Afterward, the LV was explanted and pressurized ex vivo, and the multiaxial lenticular stress-strain relationship was tracked. While LV tissue modulus for P1 MI and sham mice were similar (341.9 kPa vs 363.4 kPa, p = 0.6140), the modulus for P7 MI mice was significantly greater than that for P7 shams (691.6 kPa vs 429.2 kPa, p = 0.0194). We conclude that, in neonatal mice, regenerated LV muscle has similar biomechanical properties as native LV myocardium.

Biomechanical Restoration Potential of Pentagalloyl Glucose after Arterial Extracellular Matrix Degeneration

The objective of this study was to quantify pentagalloyl glucose (PGG) mediated biomechanical restoration of degenerated extracellular matrix (ECM). Planar biaxial tensile testing was performed for native (N), enzyme-treated (collagenase and elastase) (E), and PGG (P) treated porcine abdominal aorta specimens (n = 6 per group). An Ogden material model was fitted to the stress-strain data and finite element computational analyses of simulated native aorta and aneurysmal abdominal aorta were performed. The maximum tensile stress of the N group was higher than that in both E and P groups for both circumferential (43.78 ± 14.18 kPa vs. 10.03 ± 2.68 kPa vs. 13.85 ± 3.02 kPa; p = 0.0226) and longitudinal directions (33.89 ± 8.98 kPa vs. 9.04 ± 2.68 kPa vs. 14.69 ± 5.88 kPa; p = 0.0441). Tensile moduli in the circumferential direction was found to be in descending order as N > P > E (195.6 ± 58.72 kPa > 81.8 ± 22.76 kPa > 46.51 ± 15.04 kPa; p = 0.0314), whereas no significant differences were found in the longitudinal direction (p = 0.1607). PGG binds to the hydrophobic core of arterial tissues and the crosslinking of ECM fibers is one of the possible explanations for the recovery of biomechanical properties observed in this study. PGG is a beneficial polyphenol that can be potentially translated to clinical practice for preventing rupture of the aneurysmal arterial wall.

How important is sample alignment in planar biaxial testing of anisotropic soft biological tissues? A finite element study

Finite element models of biomedical applications increasingly use anisotropic hyperelastic material formulations. Appropriate material parameters are essential for a reliable outcome of these simulations, which is why planar biaxial testing of soft biological tissues is gaining importance. However, much is still to be learned regarding the ideal methodology for performing this type of test and the subsequent parameter fitting procedure. This paper focuses on the effect of an unknown sample orientation or a mistake in the sample orientation in a planar biaxial test using rakes. To this end, finite element simulations were conducted with various degrees of misalignment. Variations to the test method and subsequent fitting procedures are compared and evaluated. For a perfectly aligned sample and for a slightly misaligned sample, the parameters of the Gasser-Ogden-Holzapfel model can be found to a reasonable accuracy using a planar biaxial test with rakes and a parameter fitting procedure that takes into account the boundary conditions. However, after a certain threshold of misalignment, reliable parameters can no longer be found. The level of this threshold seems to be material dependent. For a sample with unknown sample orientation, material parameters could theoretically be obtained by increasing the degrees of freedom along which test data is obtained, e.g. by adding the data of a rail shear test. However, in the situation and the material model studied here, the inhomogeneous boundary conditions of the test set-ups render it impossible to obtain the correct parameters, even when using the parameter fitting method that takes into account boundary conditions. To conclude, it is always important to carefully track the sample orientation during harvesting and preparation and to minimize the misalignment during mounting. For transversely isotropic samples with an unknown orientation, we advise against parameter fitting based on a planar biaxial test, even when combined with a rail shear test.

Location-dependent correlation between tissue structure and the mechanical behaviour of the urinary bladder

The mechanical properties of the urinary bladder wall are important to understand its filling-voiding cycle in health and disease. However, much remains unknown about its mechanical properties, especially regarding regional heterogeneities and wall microstructure. The present study aimed to assess the regional differences in the mechanical properties and microstructure of the urinary bladder wall. Ninety (n=90) samples of porcine urinary bladder wall (ten samples from nine different locations) were mechanically and histologically analysed. Half of the samples (n=45) were equibiaxially tested within physiological conditions, and the other half, matching the sample location of the mechanical tests, was frozen, cryosectioned, and stained with Picro-Sirius red to differentiate smooth muscle cells, extracellular matrix, and fat. The bladder wall shows a non-linear stress-stretch relationship with hysteresis and softening effects. Regional differences were found in the mechanical response and in the microstructure. The trigone region presents higher peak stresses and thinner muscularis layer compared to the rest of the bladder. Furthermore, the ventral side of the bladder presents anisotropic characteristics, whereas the dorsal side features perfect isotropic behaviour. This response matches the smooth muscle fibre bundle orientation within the tunica muscularis. This layer, comprising approximately 78% of the wall thickness, is composed of two fibre bundle arrangements that are cross-oriented, one with respect to the other, varying the angle between them across the organ. That is, the ventral side presents a 60°/120° cross-orientation structure, while the muscle bundles were oriented perpendicular in the dorsal side.

STATEMENT OF SIGNIFICANCE

In the present study, we demonstrate that the mechanical properties and the microstructure of the urinary bladder wall are heterogeneous across the organ. The mechanical properties and the microstructure of the urinary bladder wall within nine specific locations matching explicitly the mechanical and structural variations have been examined. On the one hand, the results of this study contribute to the understanding of bladder mechanics and thus to their functional understanding of bladder filling and voiding. On the other hand, they are relevant to the fields of constitutive formulation of bladder tissue, whole bladder mechanics, and bladder-derived scaffolds i.e., tissue-engineering grafts.

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 × ∼4 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.

Experimental characterization of the biaxial mechanical properties of porcine gastric tissue

Health problems related to the stomach are among the most important sources of morbidity in industrialized countries. There is evidence that mechanics may play an important role in various such pathologies. However, so far experimental data characterizing the mechanical properties of gastric tissue remain scarce, which significantly limits our understanding of the mechanics of the stomach. To help close this gap, we performed biaxial mechanical tests of porcine gastric tissue patches. Our experiments reveal a considerable anisotropy and different mechanical properties in the three major regions of the stomach (fundus, corpus, antrum). Moreover, they demonstrate that the mechanical properties of the gastric wall and the physiological function of the different regions of the stomach are closely related. This finding suggests that further examination of the mechanics of the gastric wall may indeed be a promising avenue of research towards a better understanding of the organic causes of frequent health problems related to the stomach.

A mathematical model for the determination of forming tissue moduli in needled-nonwoven scaffolds

Formation of engineering tissues (ET) remains an important scientific area of investigation for both clinical translational and mechanobiological studies. Needled-nonwoven (NNW) scaffolds represent one of the most ubiquitous biomaterials based on their well-documented capacity to sustain tissue formation and the unique property of substantial construct stiffness amplification, the latter allowing for very sensitive determination of forming tissue modulus. Yet, their use in more fundamental studies is hampered by the lack of: (1) substantial understanding of the mechanics of the NNW scaffold itself under finite deformations and means to model the complex mechanical interactions between scaffold fibers, cells, and de novo tissue; and (2) rational models with reliable predictive capabilities describing their evolving mechanical properties and their response to mechanical stimulation. Our objective is to quantify the mechanical properties of the forming ET phase in constructs that utilize NNW scaffolds. We present herein a novel mathematical model to quantify their stiffness based on explicit considerations of the modulation of NNW scaffold fiber-fiber interactions and effective fiber stiffness by surrounding de novo ECM. Specifically, fibers in NNW scaffolds are effectively stiffer than if acting alone due to extensive fiber-fiber cross-over points that impart changes in fiber geometry, particularly crimp wavelength and amplitude. Fiber-fiber interactions in NNW scaffolds also play significant role in the bulk anisotropy of the material, mainly due to fiber buckling and large translational out-of-plane displacements occurring to fibers undergoing contraction. To calibrate the model parameters, we mechanically tested impregnated NNW scaffolds with polyacrylamide (PAM) gels with a wide range of moduli with values chosen to mimic the effects of surrounding tissues on the scaffold fiber network. Results indicated a high degree of model fidelity over a wide range of planar strains. Lastly, we illustrated the impact of our modeling approach quantifying the stiffness of engineered ECM after in vitro incubation and early stages of in vivo implantation obtained in a concurrent study of engineered tissue pulmonary valves in an ovine model.

STATEMENT OF SIGNIFICANCE

Regenerative medicine has the potential to fully restore diseased tissues or entire organs with engineered tissues. Needled-nonwoven scaffolds can be employed to serve as the support for their growth. However, there is a lack of understanding of the mechanics of these materials and their interactions with the forming tissues. We developed a mathematical model for these scaffold-tissue composites to quantify the mechanical properties of the forming tissues. Firstly, these measurements are pivotal to achieve functional requirements for tissue engineering implants; however, the theoretical development yielded critical insight into particular mechanisms and behaviors of these scaffolds that were not possible to conjecture without the insight given by modeling, let alone describe or foresee a priori.

An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress–strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.

Fixation of Bovine Pericardium-Based Tissue Biomaterial with Irreversible Chemistry Improves Biochemical and Biomechanical Properties

Bioprosthetic heart valves (BHVs), derived from glutaraldehyde crosslinked (GLUT) porcine aortic valve leaflets or bovine pericardium (BP), are used to replace defective heart valves. However, valve failure can occur within 12-15 years due to calcification and/or progressive structural degeneration. We present a novel fabrication method that utilizes carbodiimide, neomycin trisulfate, and pentagalloyl glucose crosslinking chemistry (TRI) to better stabilize the extracellular matrix of BP. We demonstrate that TRI-treated BP is more compliant than GLUT-treated BP. GLUT-treated BP exhibited permanent geometric deformation and complete alteration of apparent mechanical properties when subjected to induced static strain. TRI BP, on the other hand, did not exhibit such permanent geometric deformations or significant alterations of apparent mechanical properties. TRI BP also exhibited better resistance to enzymatic degradation in vitro and calcification in vivo when implanted subcutaneously in juvenile rats for up to 30 days.

A functionally graded material model for the transmural stress distribution of the aortic valve leaflet

Heterogeneities in structure and stress within heart valve leaflets are of significant concern to their functional physiology, as they affect how the tissue constituents remodel in response to pathological and non-pathological (e.g. exercise, pregnancy) alterations in cardiac function. Indeed, valve interstitial cells (VICs) are known to synthesize and degrade leaflet extracellular matrix (ECM) components in a manner specific to their local micromechanical environment. Quantifying local variations in ECM structure and stress is thus necessary to understand homeostatic valve maintenance as well as to develop predictive models of disease progression and post-surgical outcomes. In the aortic valve (AV), transmural variations in stress have previously been investigated by modeling the leaflet as a composite of contiguous but mechanically distinct layers. Based on previous findings about the bonded nature of these layers (Buchanan and Sacks, BMMB, 2014), we developed a more generalized structural constitutive model by treating the leaflet as a functionally graded material (FGM), whose properties vary continuously over the thickness. We informed the FGM model using high-resolution morphological measurements, which demonstrated that the composition and fiber structure change gradually over the thickness of the AV leaflet. For validation, we fit the model against an extensive database of whole-leaflet and individual-layer mechanical responses. The FGM model predicted large stress variations both between and within the leaflet layers at end-diastole, with low-collagen regions bearing significant radial stress. These novel results suggest that the continually varying structure of the AV leaflet has an important purpose with regard to valve function and tissue homeostasis.

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

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

Large strain stimulation promotes extracellular matrix production and stiffness in an elastomeric scaffold model

Mechanical conditioning of engineered tissue constructs is widely recognized as one of the most relevant methods to enhance tissue accretion and microstructure, leading to improved mechanical behaviors. The understanding of the underlying mechanisms remains rather limited, restricting the development of in silico models of these phenomena, and the translation of engineered tissues into clinical application. In the present study, we examined the role of large strip-biaxial strains (up to 50%) on ECM synthesis by vascular smooth muscle cells (VSMCs) micro-integrated into electrospun polyester urethane urea (PEUU) constructs over the course of 3 weeks. Experimental results indicated that VSMC biosynthetic behavior was quite sensitive to tissue strain maximum level, and that collagen was the primary ECM component synthesized. Moreover, we found that while a 30% peak strain level achieved maximum ECM synthesis rate, further increases in strain level lead to a reduction in ECM biosynthesis. Subsequent mechanical analysis of the formed collagen fiber network was performed by removing the scaffold mechanical responses using a strain-energy based approach, showing that the denovo collagen also demonstrated mechanical behaviors substantially better than previously obtained with small strain training and comparable to mature collagenous tissues. We conclude that the application of large deformations can play a critical role not only in the quantity of ECM synthesis (i.e. the rate of mass production), but also on the modulation of the stiffness of the newly formed ECM constituents. The improved understanding of the process of growth and development of ECM in these mechano-sensitive cell-scaffold systems will lead to more rational design and manufacturing of engineered tissues operating under highly demanding mechanical environments.

On the Biaxial Mechanical Response of Porcine Tricuspid Valve Leaflets

Located on the right side of the heart, the tricuspid valve (TV) prevents blood backflow from the right ventricle to the right atrium. Similar to other cardiac valves, quantification of TV biaxial mechanical properties is essential in developing accurate computational models. In the current study, for the first time, the biaxial stress–strain behavior of porcine TV was measured ex vivo under different loading protocols using biaxial tensile testing equipment. The results showed a highly nonlinear response including a compliant region followed by a rapid transition to a stiff region for all of the TV leaflets both in the circumferential and in the radial directions. Based on the data analysis, all three leaflets were found to be anisotropic, and they were stiffer in the circumferential direction in comparison to the radial direction. It was also concluded that the posterior leaflet was the most anisotropic leaflet.

On the accuracy and fitting of transversely isotropic material models

Fiber reinforced structures are central to the form and function of biological tissues. Hyperelastic, transversely isotropic material models are used widely in the modeling and simulation of such tissues. Many of the most widely used models involve strain energy functions that include one or both pseudo-invariants (I4 or I5) to incorporate energy stored in the fibers. In a previous study we showed that both of these invariants must be included in the strain energy function if the material model is to reduce correctly to the well-known framework of transversely isotropic linear elasticity in the limit of small deformations. Even with such a model, fitting of parameters is a challenge. Here, by evaluating the relative roles of I4 and I5 in the responses to simple loadings, we identify loading scenarios in which previous models accounting for only one of these invariants can be expected to provide accurate estimation of material response, and identify mechanical tests that have special utility for fitting of transversely isotropic constitutive models. Results provide guidance for fitting of transversely isotropic constitutive models and for interpretation of the predictions of these models.

A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues

Exogenous cross-linking of soft collagenous tissues is a common method for biomaterial development and medical therapies. To enable improved applications through computational methods, physically realistic constitutive models are required. Yet, despite decades of research, development and clinical use, no such model exists. In this study, we develop the first rigorous full structural model (i.e. explicitly incorporating various features of the collagen fibre architecture) for exogenously cross-linked soft tissues. This was made possible, in-part, with the use of native to cross-linked matched experimental datasets and an extension to the collagenous structural constitutive model so that the uncross-linked collagen fibre responses could be mapped to the cross-linked configuration. This allowed us to separate the effects of cross-linking from kinematic changes induced in the cross-linking process, which in turn allowed the non-fibrous tissue matrix component and the interaction effects to be identified. It was determined that the matrix could be modelled as an isotropic material using a modified Yeoh model. The most novel findings of this study were that: (i) the effective collagen fibre modulus was unaffected by cross-linking and (ii) fibre-ensemble interactions played a large role in stress development, often dominating the total tissue response (depending on the stress component and loading path considered). An important utility of the present model is its ability to separate the effects of exogenous cross-linking on the fibres from changes due to the matrix. Applications of this approach include the utilization in the design of novel chemical treatments to produce specific mechanical responses and the study of fatigue damage in bioprosthetic heart valve biomaterials.

Planar biaxial testing of soft biological tissue using rakes: A critical analysis of protocol and fitting process

Mechanical characterization of soft biological tissue is becoming more and more prevalent. Despite the growing use of planar biaxial testing for soft tissue characterization, testing conditions and subsequent data analysis have not been standardized and vary widely. This also influences the quality of the result of the parameter fitting. Moreover, the testing conditions and data analysis are often not or incompletely reported, which impedes the proper comparison of parameters obtained from different studies. With a focus on planar biaxial tests using rakes, this paper investigates varying testing conditions and varying data analysis methods and their effect on the quality of the parameter fitting results. By means of a series of finite element simulations, aspects such as number of rakes, rakes׳ width, loading protocol, constitutive model, material stiffness and anisotropy are evaluated based on the degree of homogeneity of the stress field, and on the correlation between the experimentally obtained stress and the stress derived from the constitutive model. When calculating the aforementioned stresses, different definitions of the section width and deformation gradient are used in literature, each of which are looked into. Apart from this degree of homogeneity and correlation, also the effect on the quality of the parameter fitting result is evaluated. The results show that inhomogeneities can be reduced to a minimum for wise choices of testing conditions and analysis methods, but never completely eliminated. Therefore, a new parameter optimization procedure is proposed that corrects for the inhomogeneities in the stress field and induces significant improvements to the fitting results. Recommendations are made for best practice in rake-based planar biaxial testing of soft biological tissues and subsequent parameter fitting, and guidelines are formulated for reporting thereof in publications.

Methodology based on genetic heuristics for in-vivo characterizing the patient-specific biomechanical behavior of the breast tissues

This paper presents a novel methodology to in-vivo estimate the elastic constants of a constitutive model proposed to characterize the mechanical behavior of the breast tissues. An iterative search algorithm based on genetic heuristics was constructed to in-vivo estimate these parameters using only medical images, thus avoiding invasive measurements of the mechanical response of the breast tissues. For the first time, a combination of overlap and distance coefficients were used for the evaluation of the similarity between a deformed MRI of the breast and a simulation of that deformation. The methodology was validated using breast software phantoms for virtual clinical trials, compressed to mimic MRI-guided biopsies. The biomechanical model chosen to characterize the breast tissues was an anisotropic neo-Hookean hyperelastic model. Results from this analysis showed that the algorithm is able to find the elastic constants of the constitutive equations of the proposed model with a mean relative error of about 10%. Furthermore, the overlap between the reference deformation and the simulated deformation was of around 95% showing the good performance of the proposed methodology. This methodology can be easily extended to characterize the real biomechanical behavior of the breast tissues, which means a great novelty in the field of the simulation of the breast behavior for applications such as surgical planing, surgical guidance or cancer diagnosis. This reveals the impact and relevance of the presented work.