A continuous method to compute model parameters for soft biological materials

An Apparatus for Measuring Combined Shear-Tensile Loading in Fibrous Tissues Ex Vivo

Soft tissues such as tendon and ligament undergo a combination of shear and tensile loading in vivo due to their boundary conditions at muscle and/or bone. Current experimental protocols are limited to pure tensile loading, biaxial loading, or simple shear, and thus may not fully characterize the mechanics of these tissues under physiological loading scenarios. Our objective was to create an experimental protocol to determine the shear modulus of fibrous tissues at different tensile loads. We assembled a four-actuator experimental system that facilitated shear deformation to be superimposed on a tissue subjected to an axial preload. We measured shear modulus in axially loaded electrospun nanofiber scaffolds with either randomly oriented or aligned fibers. We found that shear modulus in the nanofiber phantoms was shear-strain stiffening and dependent on both the axial load (p < 0.001) and fiber alignment (p < 0.001) of the scaffold. The proposed system can enhance our understanding of microstructure and functional mechanics in soft tissues, while also providing a platform to investigate the behavior of electrospun scaffolds for tissue regeneration. Our experimental protocol for determining loaded shear modulus would be further useful as a method to gauge tissue mechanics under loading conditions that are more representative of physiological loads applied to tendon and ligament.

Dots-on-Plots: A Web Application to Analyze Stress-Strain Curves From Tensile Tests of Soft Tissue

The calculation of tensile mechanical properties from stress-strain curves is a fundamental step in characterizing material behavior, yet no standardized method exists to perform these calculations for soft tissue. To address this deficiency, we developed a free web application called Dots-on-Plots2 that fully automates the calculation of tensile mechanical properties from stress-strain curves. The analyzed mechanical properties include the strength, strain, and energy at four points of interest (transition, yield, ultimate, and rupture), and the linear modulus. Users of Dots-on-Plots can upload multiple files, view and download results, and adjust threshold settings. This study determined a threshold setting that minimized error when calculating the transition point, where the stress-strain curve "transitions" from a nonlinear "toe" region to a linear region. Using the optimal threshold (2% stress deviation from a linear region fit), Dots-on-Plots calculated the transition strains from twenty tensile experiments of human meniscus to be 0.049 ± 0.007, which nearly matched the known transition strain values of 0.050 ± 0.006 (determined using finite element parameter optimization). The sensitivity of the calculated transition strain to the shape of various stress-strain curves was analyzed using sets of model-generated synthetic data. This free web application offers a convenient and reliable tool to systematically enhance the speed, transparency, and consistency of mechanical analysis across biomedical research groups.

Biomechanical consequences of cement discoplasty: An in vitro study on thoraco-lumbar human spines

With the ageing of the population, there is an increasing need for minimally invasive spine surgeries to relieve pain and improve quality of life. Percutaneous Cement Discoplasty is a minimally invasive technique to treat advanced disc degeneration, including vacuum phenomenon. The present study aimed to develop an in vitro model of percutaneous cement discoplasty to investigate its consequences on the spine biomechanics in comparison with the degenerated condition. Human spinal segments (n = 27) were tested at 50% body weight in flexion and extension. Posterior disc height, range of motion, segment stiffness, and strains were measured using Digital Image Correlation. The cement distribution was also studied on CT scans. As main result, percutaneous cement discoplasty restored the posterior disc height by 41% for flexion and 35% for extension. Range of motion was significantly reduced only in flexion by 27%, and stiffness increased accordingly. The injected cement volume was 4.56 ± 1.78 ml (mean ± SD). Some specimens (n = 7) exhibited cement perforation of one endplate. The thickness of the cement mass moderately correlated with the posterior disc height and range of motion with different trends for flexions vs. extension. Finally, extreme strains on the discs were reduced by percutaneous cement discoplasty, with modified patterns of the distribution. To conclude, this study supported clinical observations in term of recovered disc height close to the foramen, while percutaneous cement discoplasty helped stabilize the spine in flexion and did not increase the risk of tissue damage in the annulus.

Development and evaluation of ligament phantoms targeted for shear wave tensiometry

Developing a shear wave tensiometer capable of non-invasively measuring ligament tension holds promise for enhancing research and clinical assessments of ligament function. Such development would benefit from tunable test specimens fabricated from well-characterized and consistent materials. Although previous work found that yarn can replicate the mechanical behavior of collateral ligaments, it is not obvious whether yarn-based phantoms would be suitable for development of a shear wave tensiometer for measuring ligament tension. Accordingly, the primary objective of this study was to characterize the mechanical properties and shear wave speed - stress relationships of ligament phantoms fabricated from yarn and silicone, and compare these results to published data from biological ligaments. We measured the mechanical properties and shear wave speeds during axial loading in nine phantoms with systematically varied material properties. We performed a simple linear regression between shear wave speed squared and axial stress to determine the shear wave speed - stress relationship for each phantom. We found comparable elastic moduli, hysteresis, and shear wave speed squared - stress regression parameters between the phantoms and collateral ligaments. For example, the ranges of the coefficients of determination (R²) and slopes across the nine phantoms were 0.84-0.95, and 0.78-1.27 kPa/m²/s², respectively, which overlapped with the ranges found in a prior study in porcine collateral ligaments (0.84-0.996 and 0.34-1.18 kPa/m²/s², respectively). Additionally, the shear wave speed squared - stress regression parameters varied predictably with the density of the phantom and the shear modulus of the silicone. In summary, we found that yarn-based phantoms serve as mechanical analogs for ligaments (i.e., are ligament mimicking), and thus, should prove beneficial for investigations into ligament structure-function relationships and in the development of a shear wave tensiometer for measuring ligament tension.

Six-Month Outcomes of Clinically Relevant Meniscal Injury in a Large-Animal Model

BACKGROUND

The corrective procedures for meniscal injury are dependent on tear type, severity, and location. Vertical longitudinal tears are common in young and active individuals, but their natural progression and impact on osteoarthritis (OA) development are not known. Root tears are challenging and they often indicate poor outcomes, although the timing and mechanisms of initiation of joint dysfunction are poorly understood, particularly in large-animal and human models.

PURPOSE/HYPOTHESIS

In this study, vertical longitudinal and root tears were made in a large-animal model to determine the progression of joint-wide dysfunction. We hypothesized that OA onset and progression would depend on the extent of injury-based load disruption in the tissue, such that root tears would cause earlier and more severe changes to the joint.

STUDY DESIGN

Controlled laboratory study.

METHODS

Sham surgeries and procedures to create either vertical longitudinal or root tears were performed in juvenile Yucatan mini pigs through randomized and bilateral arthroscopic procedures. Animals were sacrificed at 1, 3, or 6 months after injury and assessed at the joint and tissue level for evidence of OA. Functional measures of joint load transfer, cartilage indentation mechanics, and meniscal tensile properties were performed, as well as histological evaluation of the cartilage, meniscus, and synovium.

RESULTS

Outcomes suggested a progressive and sustained degeneration of the knee joint and meniscus after root tear, as evidenced by histological analysis of the cartilage and meniscus. This occurred in spite of spontaneous reattachment of the root, suggesting that this reattachment did not fully restore the function of the native attachment. In contrast, the vertical longitudinal tear did not cause significant changes to the joint, with only mild differences compared with sham surgery at the 6-month time point.

CONCLUSION

Given that the root tear, which severs circumferential connectivity and load transfer, caused more intense OA compared with the circumferentially stable vertical longitudinal tear, our findings suggest that without timely and mechanically competent fixation, root tears may cause irreversible joint damage.

CLINICAL RELEVANCE

More generally, this new model can serve as a test bed for experimental surgical, scaffold-based, and small molecule-driven interventions after injury to prevent OA progression.

Tuning the Structure of Nylon 6,6 Electrospun Bundles to Mimic the Mechanical Performance of Tendon Fascicles

Tendon and ligament injuries are triggered by mechanical loading, but the specific mechanisms are not yet clearly identified. It is well established however, that the inflection and transition points in tendon stress-strain curves represent thresholds that may signal the onset of irreversible fibrillar sliding. This phenomenon often results in a progressive macroscopic failure of these tissues. With the aim to simulate and replace tendons, electrospinning has been demonstrated to be a suitable technology to produce nanofibers similar to the collagen fibrils in a mat form. These nanofibrous mats can be easily assembled in higher hierarchical levels to reproduce the whole tissue structure. Despite the fact that several groups have developed electrospun tendon-inspired structures, an investigation of the inflection and transition point mechanics is missing. Comparing their behavior with that of the natural counterpart is important to adequately replicate their behavior at physiological strain levels. To fill this gap, in this work fascicle-inspired electrospun nylon 6,6 bundles were produced with different collector peripheral speeds (i.e., 19.7 m s^–1; 13.7 m s^–1; 7.9 m s^–1), obtaining different patterns of nanofibers alignment. The scanning electron microcopy revealed a fibril-inspired structure of the nanofibers with an orientation at the higher speed similar to those in tendons and ligaments (T/L). A tensile mechanical characterization was carried out showing an elastic-brittle biomimetic behavior for the higher speed bundles with a progressively more ductile behavior at slower speeds. Moreover, for each sample category the transition and the inflection points were defined to study how these points can shift with the nanofiber arrangement and to compare their values with those of tendons. The results of this study will be of extreme interest for the material scientists working in the field, to model and improve the design of their electrospun structures and scaffolds and enable building a new generation of artificial tendons and ligaments.

Identifiability of tissue material parameters from uniaxial tests using multi-start optimization

Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the "identifiability" or "uniqueness" of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.

Structure, function, and defect tolerance with maturation of the radial tie fiber network in the knee meniscus

The knee menisci are comprised of two orthogonal collagenous networks-circumferential and radial-that combine to enable efficient load bearing by the tissue in adults. Here, we assessed how the structural and functional characteristics of these networks developed over the course of skeletal maturation and determined the role of these fiber networks in defect tolerance with tissue injury. Imaging of the radial tie fiber (RTF) collagen structure in medial bovine menisci from fetal, juvenile, and adult specimens showed increasing heterogeneity, anisotropy, thickness, and density with skeletal development. The mechanical analysis showed that the tensile modulus in the radial direction did not change with skeletal development, though the resilience (in the radial direction) increased and the tolerance to defects in the circumferential direction decreased, in adult compared to fetal tissues. This loss of defect tolerance correlated with increased order in the RTF network in adult tissue. These data provide new insights into the role of the radial fiber network in meniscus function, will lead to improved clinical decision-making in the presence of a tear and may improve engineering efforts to reproduce this critical load-bearing structure in the knee.

Biomimetic Hierarchically Arranged Nanofibrous Structures Resembling the Architecture and the Passive Mechanical Properties of Skeletal Muscles: A Step Forward Toward Artificial Muscle

Skeletal muscles are considered to date the best existing actuator in nature thanks to their hierarchical multiscale fibrous structure capable to enhance their strength and contractile performances. In recent years, driven by the growing of the soft robotics and tissue-engineering research field, many biomimetic soft actuators and scaffolds were designed by taking inspiration from the biological skeletal muscle. In this work we used the electrospinning technique to develop a hierarchically arranged nanofibrous structure resembling the morphology and passive biomechanical properties of skeletal muscles. To mimic the passive properties of muscle, a low-modulus polyurethane was used. Several electrospun structures (mats, bundles, and a muscle-like assembly) were produced with different internal 3D arrangements of the nanofibers. A thermal characterization through thermogravimetric and differential scanning calorimetry analysis investigated the physico-chemical properties of the material. The multiscale morphological similarities with the biological counterpart were verified by means of scanning electron microscopy investigation. The tensile tests on the different electrospun samples revealed that the muscle-like assembly presented slightly higher strength and stiffness compared to the skeletal muscle ones. Moreover, mathematical models of the mechanical behavior of the nanofibrous structures were successfully developed, allowing to better investigate the relationships between structure and mechanics of the samples. The promising results suggest the suitability of this hierarchical electrospun nanofibrous structure for applications in regenerative medicine and, if combined with active materials, in soft actuators for robotic.

Correlation of Force to Deformation of the Anterior Bundle of the Medial Collateral Ligament Through Consideration of Band Laxity

The anterior bundle of the medial collateral ligament (AMCL) resists the loads that arise at the elbow during overhand throwing and has commonly been divided into posterior and anterior bands. While these anterior and posterior bands have been thought to bear the load at different flexion angles, any transition of the load distribution between the two bands is poorly understood and has not considered laxity (slack). This study considers the AMCL as three bands and quantifies the mechanical response to vertical distraction, simulating valgus-load joint opening, through the sequential superposition of the band responses after the elimination of inherent laxity. Eight cadaveric elbow specimens were used for the study. The intact AMCL of each specimen was tested under vertical distraction in a specialized load frame at four elbow flexion angles and then subsequently retested after two longitudinal transections. The greatest laxity at full extension and full flexion belonged to the posterior (1.9 mm) and anterior (2.4 mm) band, respectively. At the lesser and higher flexion angles, the greatest structural stiffness belonged to the anterior and middle band. The overall AMCL was the most structurally stiff at 60°, with approximately 150 N of force required for 2% elongation. This study shows that the different bands of the AMCL may have different load bearing properties at different flexion angles, causing each band to support different proportions of an imposed load. The presence of the laxity may impose a load-bearing delay, causing load-bearing in each band to begin asynchronously. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:2027-2034, 2019.

Multi-Scale Loading and Damage Mechanisms of Plantaris and Rat Tail Tendons

Tendinopathy, degeneration of the tendon that leads to pain and dysfunction, is common in both sports and occupational settings, but multi-scale mechanisms for tendinopathy are still unknown. We recently showed that micro-scale sliding (shear) is responsible for both load transfer and damage mechanisms in the rat tail tendon; however, the rat tail tendon is a specialized non-load-bearing tendon, and thus the load transfer and damage mechanisms are still unknown for load-bearing tendons. The objective of this study was to investigate the load transfer and damage mechanisms of load-bearing tendons using the rat plantaris tendon. We demonstrated that micro-scale sliding is a key component for both mechanisms in the plantaris tendon, similar to the tail tendon. Namely, the micro-scale sliding was correlated with applied strain, demonstrating that load was transferred via micro-scale sliding in the plantaris and tail tendons. In addition, while the micro-scale strain fully recovered, the micro-scale sliding was non-recoverable and strain-dependent, and correlated with tissue-scale mechanical parameters. When the applied strain was normalized, the % magnitudes of non-recoverable sliding was similar between the plantaris and tail tendons. Statement of clinical significance: Understanding the mechanisms responsible for the pathogenesis and progression of tendinopathy can improve prevention and rehabilitation strategies and guide therapies and the design of engineered constructs. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:1827-1837, 2019.

Characterization of the Continuous Elastic Parameters of Porcine Vocal Folds

This paper presents an evaluation of the elastic properties of porcine vocal folds through uniaxial tensile tests. Inferior vocal fold tissue samples were subjected to tension in the longitudinal direction while digital image correlation techniques were employed to determine strain values throughout the tests. The stress-strain results showed a low-strain linear region, followed by both a nonlinear exponential and then a higher strain linear region. Data from 16 porcine vocal fold samples were analyzed following a similar optimization method as proposed in prior studies [1] to yield continuous model parameters which describe the elastic properties of the tissue. The average low and high strain linear modulus values were found to be 17.86 kPa and 609.27 kPa, respectively. The model also identified the location of two transition points: p₁, describing the transition from the low-strain linear region to an exponential region at 0.122 ± 0.058 mm/mm and p₂, describing the transition from the exponential to the high strain linear region at 0.308 ± 0.069 mm/mm. The exponential region of the averaged data set was found to be described by the relationship [Formula: see text] kPa. In addition to locating transition points, the optimization method maintained modulus continuity across all strain values. Averaged elastic modulus values across strain from 0 to 0.40 mm/mm were compared to representative low and high strain linear modulus which were measured at 0.05 and 0.35 mm/mm, respectively. Statistically significant differences were found among all strain intervals between the two transition points and the linear modulus values. These results indicate the need to consider the location of transition points and further highlight the nonlinearity and changes in elastic modulus which are especially important when using excised porcine vocal folds as a model for phonation. The results quantify continuous linear and nonlinear parameters describing the elastic properties which can be used as a framework for future excised larynx tests and while evaluating the dynamics of sound production, which rely heavily on the elastic properties of the tissue.

Freezing does not alter multiscale tendon mechanics and damage mechanisms in tension

It is common in biomechanics to use previously frozen tissues, where it is assumed that the freeze-thaw process does not cause consequential mechanical or structural changes. We have recently quantified multiscale tendon mechanics and damage mechanisms using previously frozen tissue, where damage was defined as an irreversible change in the microstructure that alters the macroscopic mechanical parameters. Because freezing has been shown to alter tendon microstructures, the objective of this study was to determine if freezing alters tendon multiscale mechanics and damage mechanisms. Multiscale testing using a protocol that was designed to evaluate tendon damage (tensile stress-relaxation followed by unloaded recovery) was performed on fresh and previously frozen rat tail tendon fascicles. At both the fascicle and fibril levels, there was no difference between the fresh and frozen groups for any of the parameters, suggesting that there is no effect of freezing on tendon mechanics. After unloading, the microscale fibril strain fully recovered, and interfibrillar sliding only partially recovered, suggesting that the tendon damage is localized to the interfibrillar structures and that mechanisms of damage are the same in both fresh and previously frozen tendons.

Investigating mechanisms of tendon damage by measuring multi-scale recovery following tensile loading

Tendon pathology is associated with damage. While tendon damage is likely initiated by mechanical loading, little is known about the specific etiology. Damage is defined as an irreversible change in the microstructure that alters the macroscopic mechanical parameters. In tendon, the link between mechanical loading and microstructural damage, resulting in macroscopic changes, is not fully elucidated. In addition, tendon damage at the macroscale has been proposed to initiate when tendon is loaded beyond a strain threshold, yet the metrics to define the damage threshold are not determined. We conducted multi-scale mechanical testing to investigate the mechanism of tendon damage by simultaneously quantifying macroscale mechanical and microstructural changes. At the microscale, we observe full recovery of the fibril strain and only partial recovery of the interfibrillar sliding, indicating that the damage initiates at the interfibrillar structures. We show that non-recoverable sliding is a mechanism for tendon damage and is responsible for the macroscale decreased linear modulus and elongated toe-region observed at the fascicle-level, and these macroscale properties are appropriate metrics that reflect tendon damage. We concluded that the inflection point of the stress-strain curve represents the damage threshold and, therefore, may be a useful parameter for future studies. Establishing the mechanism of damage at multiple length scales can improve prevention and rehabilitation strategies for tendon pathology.

STATEMENT OF SIGNIFICANCE

Tendon pathology is associated with mechanically induced damage. Damage, as defined in engineering, is an irreversible change in microstructure that alters the macroscopic mechanical properties. Although microstructural damage and changes to macroscale mechanics are likely, this link to microstructural change was not yet established. We conducted multiscale mechanical testing to investigate the mechanism of tendon damage by simultaneously quantifying macroscale mechanical and microstructural changes. We showed that non-recoverable sliding between collagen fibrils is a mechanism for tendon damage. Establishing the mechanism of damage at multiple length scales can improve prevention and rehabilitation strategies for tendon pathology.

Mechanical function near defects in an aligned nanofiber composite is preserved by inclusion of disorganized layers: Insight into meniscus structure and function

The meniscus is comprised of circumferentially aligned fibers that resist the tensile forces within the meniscus (i.e., hoop stress) that develop during loading of the knee. Although these circumferential fibers are severed by radial meniscal tears, tibial contact stresses do not increase until the tear reaches ∼90% of the meniscus width, suggesting that the severed circumferential fibers still bear load and maintain the mechanical functionality of the meniscus. Recent data demonstrates that the interfibrillar matrix can transfer strain energy to disconnected fibrils in tendon fascicles. In the meniscus, interdigitating radial tie fibers, which function to stabilize and bind the circumferential fibers together, are hypothesized to function in a similar manner by transmitting load to severed circumferential fibers near a radial tear. To test this hypothesis, we developed an engineered fibrous analog of the knee meniscus using poly(ε-caprolactone) to create aligned scaffolds with variable amounts of non-aligned elements embedded within the scaffold. We show that the tensile properties of these scaffolds are a function of the ratio of aligned to non-aligned elements, and change in a predictable fashion following a simple mixture model. When measuring the loss of mechanical function in scaffolds with a radial tear, compared to intact scaffolds, the decrease in apparent linear modulus was reduced in scaffolds containing non-aligned layers compared to purely aligned scaffolds. Increased strains in areas adjacent to the defect were also noted in composite scaffolds. These findings indicate that non-aligned (disorganized) elements interspersed within an aligned network can improve overall mechanical function by promoting strain transfer to nearby disconnected fibers. This finding supports the notion that radial tie fibers may similarly promote tear tolerance in the knee meniscus, and will direct changes in clinical practice and provide guidance for tissue engineering strategies.

STATEMENT OF SIGNIFICANCE

The meniscus is a complex fibrous tissue, whose architecture includes radial tie fibers that run perpendicular to and interdigitate with the predominant circumferential fibers. We hypothesized that these radial elements function to preserve mechanical function in the context of interruption of circumferential bundles, as would be the case in a meniscal tear. To test this hypothesis, we developed a biomaterial analog containing disorganized layers enmeshed regularly throughout an otherwise aligned network. Using this material formulation, we showed that strain transmission is improved in the vicinity of defects when disorganized fiber layers were present. This supports the idea that radial elements within the meniscus improve function near a tear, and will guide future clinical interventions and the development of engineered replacements.

DTAF dye concentrations commonly used to measure microscale deformations in biological tissues alter tissue mechanics

Identification of the deformation mechanisms and specific components underlying the mechanical function of biological tissues requires mechanical testing at multiple levels within the tissue hierarchical structure. Dichlorotriazinylaminofluorescein (DTAF) is a fluorescent dye that is used to visualize microscale deformations of the extracellular matrix in soft collagenous tissues. However, the DTAF concentrations commonly employed in previous multiscale experiments (≥2000 µg/ml) may alter tissue mechanics. The objective of this study was to determine whether DTAF affects tendon fascicle mechanics and if a concentration threshold exists below which any observed effects are negligible. This information is valuable for guiding the continued use of this fluorescent dye in future experiments and for interpreting the results of previous work. Incremental strain testing demonstrated that high DTAF concentrations (≥100 µg/ml) increase the quasi-static modulus and yield strength of rat tail tendon fascicles while reducing their viscoelastic behavior. Subsequent multiscale testing and modeling suggests that these effects are due to a stiffening of the collagen fibrils and strengthening of the interfibrillar matrix. Despite these changes in tissue behavior, the fundamental deformation mechanisms underlying fascicle mechanics appear to remain intact, which suggests that conclusions from previous multiscale investigations of strain transfer are still valid. The effects of lower DTAF concentrations (≤10 µg/ml) on tendon mechanics were substantially smaller and potentially negligible; nevertheless, no concentration was found that did not at least slightly alter the tissue behavior. Therefore, future studies should either reduce DTAF concentrations as much as possible or use other dyes/techniques for measuring microscale deformations.

Power type strain energy function model and prediction of the anisotropic mechanical properties of skin using uniaxial extension data

Many successful models to describe the biomechanical characteristics of planar biological soft tissues are based on strain energy function. However, the parameters in these models are determined by biaxial extension test, which might be difficult to exercise for certain types of soft tissue. This study presents a new constitutive model, the power type strain energy density function model (PTM), and a method to identify its material parameters for rabbit skin using uniaxial extension test of 4-direction strip samples. The abdominal skins from eight rabbits were taken to perform uniaxial tension tests in 7 different directions. The material parameters were identified for each subject based on any 4 out of 7 directions by applying some definite conditions of this issue. For each rabbit, the 35 groups of material parameters were consistent. The 7 material parameters in PTM were identified with root mean square errors <0.061. The results indicate that the material parameters of rabbit skin can be identified from uniaxial extension test data.

Hermitian splines for modeling biological soft tissue systems that exhibit nonlinear force-elongation curves

Numerical simulation of soft tissue mechanical properties is a critical step in developing valuable biomechanical models of live organisms. A cubic Hermitian spline optimization routine is proposed in this paper to model nonlinear experimental force-elongation curves of soft tissues, in particular when modeled as lumped elements. Boundary conditions are introduced to account for the positive definiteness and the particular curvature of the experimental curve to be fitted. The constrained least-square routine minimizes user intervention and optimizes fitting of the experimental data across the whole fitting range. The routine provides coefficients of a Hermitian spline or corresponding knots that are compatible with a number of constraints that are suitable for modeling soft tissue tensile curves. These coefficients or knots may become inputs to user-defined component properties of various modeling software. Splines are particularly advantageous over the well-known exponential model to account for the traction curve flatness at low elongations and to allow for more flexibility in the fitting process. This is desirable as soft tissue models begin to include more complex physical phenomena.