Quasi-Linear Viscoelastic theory applied to internal shearing of porcine aortic valve leaflets

Mechanical considerations for polymeric heart valve development: Biomechanics, materials, design and manufacturing

The native human heart valve leaflet contains a layered microstructure comprising a hierarchical arrangement of collagen, elastin, proteoglycans and various cell types. Here, we review the various experimental methods that have been employed to probe this intricate microstructure and which attempt to elucidate the mechanisms that govern the leaflet's mechanical properties. These methods include uniaxial, biaxial, and flexural tests, coupled with microstructural characterization techniques such as small angle X-ray scattering (SAXS), small angle light scattering (SALS), and polarized light microscopy. These experiments have revealed complex elastic and viscoelastic mechanisms that are highly directional and dependent upon loading conditions and biochemistry. Of all engineering materials, polymers and polymer-based composites are best able to mimic the tissue-level mechanical behavior of the native leaflet. This similarity to native tissue permits the fabrication of polymeric valves with physiological flow patterns, reducing the risk of thrombosis compared to mechanical valves and in some cases surpassing the in vivo durability of bioprosthetic valves. Earlier work on polymeric valves simply assumed the mechanical properties of the polymer material to be linear elastic, while more recent studies have considered the full hyperelastic stress-strain response. These material models have been incorporated into computational models for the optimization of valve geometry, with the goal of minimizing internal stresses and improving durability. The latter portion of this review recounts these developments in polymeric heart valves, with a focus on mechanical testing of polymers, valve geometry, and manufacturing methods.

Degenerative aortic valve disease and diabetes: Implications for a link between proteoglycans and diabetic disorders in the aortic valve

Degenerative aortic valve disease in combination with diabetes is an increasing burden worldwide. There is growing evidence that particularly small leucine-rich proteoglycans are involved in the development of degenerative aortic valve disease. Nevertheless, the role of these molecules in this disease in the course of diabetes has not been elucidated in detail and previous studies remain controversial. Therefore, the aim of this study is to broaden the knowledge about small leucine-rich proteoglycans in degenerative aortic valve disease and the influence of diabetes and hyperglycaemia on aortic valves and valvular interstitial cells is examined. Analyses were performed using reverse-transcription polymerase chain reaction, Western blot, enzyme-linked immunosorbent assay, (immuno)histology and colorimetric assays. We could show that biglycan, but not decorin and lumican, is upregulated in degenerated human aortic valve cusps. Subgroup analysis reveals that upregulation of biglycan is stage-dependent. In vivo, loss of biglycan leads to stage-dependent calcification and also to migratory effects on interstitial cells within the extracellular matrix. In late stages of degenerative aortic valve disease, diabetes increases the expression of biglycan in aortic valves. In vitro, the combinations of hyperglycaemic with pro-degenerative conditions lead to an upregulation of biglycan. In conclusion, biglycan represents a potential link between degenerative aortic valve disease and diabetes.

Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix

Characterizing how a tissue's constituents give rise to its viscoelasticity is important for uncovering how hidden timescales underlie multiscale biomechanics. These constituents are viscoelastic in nature, and their mechanics must typically be assessed from the uniaxial behavior of a tissue. Confounding the challenge is that tissue viscoelasticity is typically associated with nonlinear elastic responses. Here, we experimentally assessed how fibroblasts and extracellular matrix (ECM) within engineered tissue constructs give rise to the nonlinear viscoelastic responses of a tissue. We applied a constant strain rate, "triangular-wave" loading and interpreted responses using the Fung quasi-linear viscoelastic (QLV) material model. Although the Fung QLV model has several well-known weaknesses, it was well suited to the behaviors of the tissue constructs, cells, and ECM tested. Cells showed relatively high damping over certain loading frequency ranges. Analysis revealed that, even in cases where the Fung QLV model provided an excellent fit to data, the the time constant derived from the model was not in general a material parameter. Results have implications for design of protocols for the mechanical characterization of biological materials, and for the mechanobiology of cells within viscoelastic tissues.

Quasi-linear viscoelastic properties of the human medial patello-femoral ligament

The evaluation of viscoelastic properties of human medial patello-femoral ligament is fundamental to understand its physiological function and contribution as stabilizer for the selection of the methods of repair and reconstruction and for the development of scaffolds with adequate mechanical properties. In this work, 12 human specimens were tested to evaluate the time- and history-dependent non linear viscoelastic properties of human medial patello-femoral ligament using the quasi-linear viscoelastic (QLV) theory formulated by Fung et al. (1972) and modified by Abramowitch and Woo (2004). The five constant of the QLV theory, used to describe the instantaneous elastic response and the reduced relaxation function on stress relaxation experiments, were successfully evaluated. It was found that the constant A was 1.21±0.96MPa and the dimensionless constant B was 26.03±4.16. The magnitude of viscous response, the constant C, was 0.11±0.02 and the initial and late relaxation time constants τ1 and τ2 were 6.32±1.76s and 903.47±504.73s respectively. The total stress relaxation was 32.7±4.7%. To validate our results, the obtained constants were used to evaluate peak stresses from a cyclic stress relaxation test on three different specimens. The theoretically predicted values fit the experimental ones demonstrating that the QLV theory could be used to evaluate the viscoelastic properties of the human medial patello-femoral ligament.

Effect of non-uniform thickness of samples in stress relaxation tests under unconfined compression of samples of articular discs

A precise information of the biomechanical properties of soft tissues is required to develop a suitable simulation model, with which the distribution of stress and strain in the complex structures can be estimated. Many soft tissues have been mechanically characterized by stress relaxation tests under unconfined or confined compression. In general, full-thickness samples are extracted to reduce the damage in the tissue as much as possible. However, it is not guaranteed that these samples have a uniform thickness or, in other words, planar parallel faces. In particular, in the articular disc of the temporomandibular joint, many studies can be found testing full-thickness samples for which that thickness is known to be non-uniform, while making the assumption of uniaxial stress state to extract the mechanical properties from those tests. That inaccuracy may have a strong influence in some cases and needs a profound revision. The main goal of this work is to quantify the error committed in that assumption and the influence of the variation of thickness on that error in a particular test: stress relaxation tests under unconfined compression. Based on this error and defining an allowable tolerance, a criterion is established to reject samples depending on their aspect ratio.

A study of the temporomandibular joint during bruxism

A finite element model of the temporomandibular joint (TMJ) and the human mandible was fabricated to study the effect of abnormal loading, such as awake and asleep bruxism, on the articular disc. A quasilinear viscoelastic model was used to simulate the behaviour of the disc. The viscoelastic nature of this tissue is shown to be an important factor when sustained (awake bruxism) or cyclic loading (sleep bruxism) is simulated. From the comparison of the two types of bruxism, it was seen that sustained clenching is the most detrimental activity for the TMJ disc, producing an overload that could lead to severe damage of this tissue.

How preconditioning affects the measurement of poro-viscoelastic mechanical properties in biological tissues

It is known that initial loading curves of soft biological tissues are substantially different from subsequent loadings. The later loading curves are generally used for assessing the mechanical properties of a tissue, and the first loading cycles, referred to as preconditioning, are omitted. However, slow viscoelastic phenomena related to fluid flow or collagen viscoelasticity are initiated during these first preconditioning loading cycles and may persist during the actual data collection. When these data are subsequently used for fitting of material properties, the viscoelastic phenomena that occurred during the initial cycles are not accounted for. The aim of the present study is to explore whether the above phenomena are significant for articular cartilage, by evaluating the effect of such time-dependent phenomena by means of computational modeling. Results show that under indentation, collagen viscoelasticity dominates the time-dependent behavior. Under UC, fluid-dependent effects are more important. Interestingly, viscoelastic and poroelastic effects may act in opposite directions and may cancel each other out in a stress-strain curve. Therefore, equilibrium may be apparent in a stress-strain relationship, even though internally the tissue is not in equilibrium. Also, the time-dependent effects of viscoelasticity and poroelasticity may reinforce each other, resulting in a sustained effect that lasts longer than suggested by their individual effects. Finally, the results illustrate that data collected from a mechanical test may depend on the preconditioning protocol. In conclusion, preconditioning influences the mechanical response of articular cartilage significantly and therefore cannot be neglected when determining the mechanical properties. To determine the full viscoelastic and poroelastic properties of articular cartilage requires fitting to both preconditioning and post-preconditioned loading cycles.

Numerical simulation of a relaxation test designed to fit a quasi-linear viscoelastic model for temporomandibular joint discs

The main objectives of this work are: (a) to introduce an algorithm for adjusting the quasi-linear viscoelastic model to fit a material using a stress relaxation test and (b) to validate a protocol for performing such tests in temporomandibular joint discs. This algorithm is intended for fitting the Prony series coefficients and the hyperelastic constants of the quasi-linear viscoelastic model by considering that the relaxation test is performed with an initial ramp loading at a certain rate. This algorithm was validated before being applied to achieve the second objective. Generally, the complete three-dimensional formulation of the quasi-linear viscoelastic model is very complex. Therefore, it is necessary to design an experimental test to ensure a simple stress state, such as uniaxial compression to facilitate obtaining the viscoelastic properties. This work provides some recommendations about the experimental setup, which are important to follow, as an inadequate setup could produce a stress state far from uniaxial, thus, distorting the material constants determined from the experiment. The test considered is a stress relaxation test using unconfined compression performed in cylindrical specimens extracted from temporomandibular joint discs. To validate the experimental protocol, the test was numerically simulated using finite-element modelling. The disc was arbitrarily assigned a set of quasi-linear viscoelastic constants (c1) in the finite-element model. Another set of constants (c2) was obtained by fitting the results of the simulated test with the proposed algorithm. The deviation of constants c2 from constants c1 measures how far the stresses are from the uniaxial state. The effects of the following features of the experimental setup on this deviation have been analysed: (a) the friction coefficient between the compression plates and the specimen (which should be as low as possible); (b) the portion of the specimen glued to the compression plates (smaller areas glued are better); and (c) the variation in the thickness of the specimen. The specimen’s faces should be parallel to ensure a uniaxial stress state. However, this is not possible in real specimens, and a criterion must be defined to accept the specimen in terms of the specimen’s thickness variation and the deviation of the fitted constants arising from such a variation.

Strain Transfer Through the Aortic Valve

The complex structural organization of the aortic valve (AV) extracellular matrix (ECM) enables large and highly nonlinear tissue level deformations. The collagen and elastin (elastic) fibers within the ECM form an interconnected fibrous network (FN) and are known to be the main load-bearing elements of the AV matrix. The role of the FN in enabling deformation has been investigated and documented. However, there is little data on the correlation between tissue level and FN-level strains. Investigating this correlation will help establish the mode of strain transfer (affine or nonaffine) through the AV tissue as a key feature in microstructural modeling and will also help characterize the local FN deformation across the AV sample in response to applied tissue level strains. In this study, the correlation between applied strains at tissue level, macrostrains across the tissue surface, and local FN strains were investigated. Results showed that the FN strain distribution across AV samples was inhomogeneous and nonuniform, as well as anisotropic. There was no direct transfer of the deformation applied at tissue level to the fibrous network. Loading modes induced in the FN are different than those applied at the tissue as a result of different local strains in the valve layers. This nonuniformity of local strains induced internal shearing within the FN of the AV, possibly exposing the aortic valve interstitial cells (AVICs) to shear strains and stresses.

The shear mechanical properties of diabetic and non-diabetic plantar soft tissue

Changes in the plantar soft tissue shear properties may contribute to ulceration in diabetic patients, however, little is known about these shear parameters. This study examines the elastic and viscoelastic shear behavior of both diabetic and non-diabetic plantar tissue. Previously compression tested plantar tissue specimens (n=54) at six relevant plantar locations (hallux, first, third, and fifth metatarsal heads, lateral midfoot, and calcaneus) from four cadaveric diabetic feet and five non-diabetic feet were utilized. Per in vivo data (i.e., combined deformation patterns of compression followed by shear), an initial static compressive strain (36-38%) was applied to the tissue followed by target shear strains of 50% and 85% of initial thickness. Triangle waves were used to quantify elastic parameters at both strain levels and a stress relaxation test (0.25 s ramp and 300 s hold) was used to quantify the viscoelastic parameters at the upper strain level. Several differences were found between test groups including a 52-62% increase in peak shear stress, a 63% increase in toe shear modulus, a 47% increase in final shear modulus, and a 67% increase in middle slope magnitude (sharper drop in relaxation) in the diabetic tissue. Beyond a 54% greater peak compressive stress in the third metatarsal compared to the lateral midfoot, there were no differences in shear properties between plantar locations. Notably, this study demonstrates that plantar soft tissue with diabetes is stiffer than healthy tissue, thereby compromising its ability to dissipate shear stresses borne by the foot that may increase ulceration risk.

Viscoelastic effects during loading play an integral role in soft tissue mechanics

Viscoelastic relaxation during tensioning is an intrinsic protective mechanism of biological soft tissues. However, current viscoelastic characterization methodologies for these tissues either negate this important behavior or provide correction methods that are severely restricted to a specific viscoelastic formulation and/or assume an a priori (linear) strain ramp history. In order to address these shortcomings, we present a novel finite ramp time correction method for stress relaxation experiments (to incorporate relaxation manifested during loading) that is independent of a specific viscoelastic formulation and can accommodate an arbitrary strain ramp history. We demonstrate transferability of our correction method between viscoelastic formulations by applying it to quasi-linear viscoelastic (QLV) and fully nonlinear viscoelastic constitutive equations. The errors associated with currently accepted methodologies for QLV and fully nonlinear viscoelastic formulations are elucidated. Our correction method is validated by demonstrating the ability of its fitted parameters to predict an independent cyclic experiment across multiple strain amplitudes and frequencies. The results presented herein: (i) indicate that our correction method significantly reduces the errors associated with previous methodologies; and (ii) demonstrate the necessity for the use of a fully nonlinear viscoelastic formulation, which incorporates relaxation manifested during loading, to model the viscoelastic behavior of biological soft tissues.

Age-related changes in material behavior of porcine mitral and aortic valves and correlation to matrix composition

Recent studies showing significant changes in valvular matrix composition with age offer design criteria for age-specific tissue-engineered heart valves. However, knowledge regarding aging-related changes in valvular material properties is limited. Therefore, 6-week, 6-month, and 6-year-old porcine aortic valves (AV) and mitral valves (MV) were subjected to uniaxial tensile testing. In addition to standard material parameters, the radius of transition curvature (RTC) was measured to assess the acuteness of the transition region of the tension-strain curve. Radially, the MV had greater stiffness and a smaller RTC compared with the AV. Circumferentially, the center of the MV anterior leaflet (MVAC) had the highest stiffness (MVAC > AV > MV free edge [MVF]), greater stress relaxation (MVAC > MVF/AV), lowest extensibility (MVAC < AV < MVF), and smaller RTC compared with MVF (AV < MVAC < MVF). AV and MV radial strips had a larger RTC compared with circumferential strips. Aging elevated stiffness for MV and AV radial and circumferential strips, elevated stress relaxation in AV and MVF circumferential strips, and increased RTC for MV radial and MVF circumferential strips. In conclusion, there are significant age-related differences in the material properties of heart valves, which parallel differences in tissue composition and structure, likely impact valve function, and highlight the need for age-specific design goals for tissue-engineered heart valves.

The viscoelastic properties of passive eye muscle in primates. II: testing the quasi-linear theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung's quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung's theory.We found that the basic properties assumed under the QLV theory (separability and superposition) are not typical of passive eye muscles. We show that some recent extensions of Fung's model can deal successfully with the lack of separability, but fail to reproduce the deviation from superposition.While appealing for their elegance, the QLV model and its descendants are not able to capture the complex mechanical properties of passive eye muscles. In particular, our measurements suggest that in a passive extraocular muscle the force does not depend on the entire length history, but to a great extent is only a function of the last elongation to which it has been subjected. It is currently unknown whether other passive biological tissues behave similarly.

On the biomechanics of heart valve function

Heart valves (HVs) are fluidic control components of the heart that ensure unidirectional blood flow during the cardiac cycle. However, this description does not adequately describe the biomechanical ramifications of their function in that their mechanics are multi-modal. Moreover, they must replicate their cyclic function over an entire lifetime, with an estimated total functional demand of least 3x10(9) cycles. The focus of the present review is on the functional biomechanics of heart valves. Thus, the focus of the present review is on functional biomechanics, referring primarily to biosolid as well as several key biofluid mechanical aspects underlying heart valve physiological function. Specifically, we refer to the mechanical behaviors of the extracellular matrix structural proteins, underlying cellular function, and their integrated relation to the major aspects of valvular hemodynamic function. While we focus on the work from the author's laboratories, relevant works of other investigators have been included whenever appropriate. We conclude with a summary of important future trends.

Role of biomechanics in the understanding of normal, injured, and healing ligaments and tendons

Ligaments and tendons are soft connective tissues which serve essential roles for biomechanical function of the musculoskeletal system by stabilizing and guiding the motion of diarthrodial joints. Nevertheless, these tissues are frequently injured due to repetition and overuse as well as quick cutting motions that involve acceleration and deceleration. These injuries often upset this balance between mobility and stability of the joint which causes damage to other soft tissues manifested as pain and other morbidity, such as osteoarthritis.

The healing of ligament and tendon injuries varies from tissue to tissue. Tendinopathies are ubiquitous and can take up to 12 months for the pain to subside before one could return to normal activity. A ruptured medial collateral ligament (MCL) can generally heal spontaneously; however, its remodeling process takes years and its biomechanical properties remain inferior when compared to the normal MCL. It is also known that a midsubstance anterior cruciate ligament (ACL) tear has limited healing capability, and reconstruction by soft tissue grafts has been regularly performed to regain knee function. However, long term follow-up studies have revealed that 20–25% of patients experience unsatisfactory results. Thus, a better understanding of the function of ligaments and tendons, together with knowledge on their healing potential, may help investigators to develop novel strategies to accelerate and improve the healing process of ligaments and tendons.

With thousands of new papers published in the last ten years that involve biomechanics of ligaments and tendons, there is an increasing appreciation of this subject area. Such attention has positively impacted clinical practice. On the other hand, biomechanical data are complex in nature, and there is a danger of misinterpreting them. Thus, in these review, we will provide the readers with a brief overview of ligaments and tendons and refer them to appropriate methodologies used to obtain their biomechanical properties. Specifically, we hope the reader will pay attention to how the properties of these tissues can be altered due to various experimental and biologic factors. Following this background material, we will present how biomechanics can be applied to gain an understanding of the mechanisms as well as clinical management of various ligament and tendon ailments. To conclude, new technology, including imaging and robotics as well as functional tissue engineering, that could form novel treatment strategies to enhance healing of ligament and tendon are presented.

In situ measurement and modeling of biomechanical response of human cadaveric soft tissues for physics-based surgical simulation

BACKGROUND

Development of a laparoscopic surgery simulator that delivers high-fidelity visual and haptic (force) feedback, based on the physical models of soft tissues, requires the use of empirical data on the mechanical behavior of intra-abdominal organs under the action of external forces. As experiments on live human patients present significant risks, the use of cadavers presents an alternative. We present techniques of measuring and modeling the mechanical response of human cadaveric tissue for the purpose of developing a realistic model. The major contribution of this paper is the development of physics-based models of soft tissues that range from linear elastic models to nonlinear viscoelastic models which are efficient for application within the framework of a real-time surgery simulator.

METHODS

To investigate the in situ mechanical, static, and dynamic properties of intra-abdominal organs, we have developed a high-precision instrument by retrofitting a robotic device from Sensable Technologies (position resolution of 0.03 mm) with a six-axis Nano 17 force-torque sensor from ATI Industrial Automation (force resolution of 1/1,280 N along each axis), and used it to apply precise displacement stimuli and record the force response of liver and stomach of ten fresh human cadavers.

RESULTS

The mean elastic modulus of liver and stomach is estimated as 5.9359 kPa and 1.9119 kPa, respectively over the range of indentation depths tested. We have also obtained the parameters of a quasilinear viscoelastic (QLV) model to represent the nonlinear viscoelastic behavior of the cadaver stomach and liver over a range of indentation depths and speeds. The models are found to have an excellent goodness of fit (with R (2) > 0.99).

CONCLUSIONS

The data and models presented in this paper together with additional ones based on the principles presented in this paper would result in realistic physics-based surgical simulators.

Mechanical Characterization of Electrospun Polycaprolactone (PCL): A Potential Scaffold for Tissue Engineering

This paper investigates the mechanical behavior of electrospun polycaprolactone (PCL) under tensile loading. PCL in bulk form degrades slowly and is biocompatible, two properties that make it a viable option for tissue engineering applications in biomedicine. Of particular interest is the use of electrospun PCL tubes as scaffolds for tissue engineered blood vessel implants. Stress relaxation and tensile tests have been conducted with specimens at room temperature (21°C) and 37°C. Additionally, to probe the effects of moisture on mechanical behavior, specimens were tested either dry (in air) or submerged in water. In general, the electrospun PCL was found to exhibit rate dependence, as well as some dependence on the test temperature and on whether the sample was wet or dry. Two different models were investigated to describe the experimentally observed material behavior. The models used were Fung’s theory of quasilinear viscoelasticity (QLV) and the eight-chain model developed for rubber elastomers by Arruda and Boyce (1993, “A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials,” J. Mech. Phys. Solids, 41(2), pp. 389–412). The implementation and fitting results, as well as the advantages and disadvantages of each model, are presented. In general, it was found that the QLV theory provided a better fit.

Reduced Parameter Formulation for Incorporating Fiber Level Viscoelasticity into Tissue Level Biomechanical Models

Collagen is known to be a viscoelastic material and therefore is an important source of time dependent behavior in soft tissue. Though there are material models for soft tissue that rely on properties and structure of constituent collagen fibers, such models generally utilize only the elastic properties of collagen, and thus the resulting tissue level response does not possess any viscoelastic features. Here, the time dependent properties of collagen are directly incorporated into a fiber based hyperelastic model using the one dimensional theory of quasi-linear viscoelasticity within the context of a locally defined, anisotropic representation of extracellular matrix structure. The resulting model possesses seven material parameters and, using numerical and computational analysis, is shown to successfully predict many key features of soft tissue response including anisotropy, strain hardening, preconditioning, and rate independent hysteresis. A formulation is also introduced for incorporating fiber level viscoelasticity into structural models derived from a continuous representation of fiber structure.

Mechanical testing of human cardiac tissue: some implications for MRI safety

PURPOSE

The effects of aging on tissue strength and its ability to withstand forces associated with MRI have not been investigated. This study aimed to determine the forces required to cause partial or total detachment of a heart valve prosthesis in patients with age-related degenerative diseases exposed to MRI.

METHODS

Eighteen tissue samples excised during routine heart valve replacement surgery were subjected to a suture pull-out test using a tensile materials testing machine. Five preconditioning cycles were applied before commencing the final destructive test. The test was complete when the sample ruptured and the suture was pulled completely free from the tissue. Results were compared with previously calculated magnetically induced forces at 4.7 T.

RESULTS

All tissue samples displayed a basic failure pattern. Mean forces required to cause initial yield and total rupture were 4.0 N (+/- 3.3 N) and 4.9 N (+/- 3.6 N), respectively. Significant factors determining initial yield were stenosed calcific tissue (p < .01), calcific degeneration (single pathology) (p < .04) and tissue stiffness (p < .01). Calcific degeneration (p < .03) and tissue stiffness (p < .03) were also significant in determining maximum force required to cause total rupture.

CONCLUSION

Specific age-related degenerative cardiac diseases stiffen and strengthen tissue resulting in significant forces being required to pull a suture through valve annulus tissue. These forces are significantly greater than magnetically induced < 4.7 T. Therefore, patients with degenerative valvular diseases are unlikely to be at risk of valve dehiscence during exposure to static magnetic field < or = 4.7 T.

Heart Valve Tissue Engineering

Tissue-engineered heart valves have been proposed by physicians and scientists alike to be the ultimate solution for treating valvular heart disease. Rather than replacing a diseased or defective native valve with a mechanical or animal tissue-derived artificial valve, a tissue-engineered valve would be a living organ, able to respond to growth and physiological forces in the same way that the native aortic valve does. Two main approaches have been attempted over the past 10 to 15 years: regeneration and repopulation. Regeneration involves the implantation of a resorbable matrix that is expected to remodel in vivo and yield a functional valve composed of the cells and connective tissue proteins of the patient. Repopulation involves implanting a whole porcine aortic valve that has been previously cleaned of all pig cells, leaving an intact, mechanically sound connective tissue matrix. The cells of the patients are expected to repopulate and revitalize the acellular matrix, creating living tissue that already has the complex microstructure necessary for proper function and durability. Regrettably, neither of the 2 approaches has fared well in animal experiments, and the only clinical experience with tissue-engineered valves resulted in a number of early failures and patient death. This article reviews the technological details of the 2 main approaches, their rationale, their strengths and weaknesses, and the likely mechanisms for their failure. Alternative approaches to valvular tissue engineering, as well as the role of industry in shaping this field in the future, are also reviewed.

Fractional Order Viscoelasticity of the Aortic Valve Cusp: An Alternative to Quasilinear Viscoelasticity

Background: Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however, particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a fractional order integral to describe the relaxation response. FOV implies a fractal-like tissue structure, reflecting the hierarchical arrangement of collagenous tissues. Method of Approach: A one-dimensional (1-D) FOV reduced relaxation function was developed, replacing the QLV “box-spectrum” function with a fractional relaxation function. A direct-fit, global optimization method was used to estimate material parameters from stress relaxation tests on aortic valve tissue. Results: We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV, particularly for the long time constant (τ2). The mean (n=5) fractional order was 0.29, indicating that the viscoelastic response of the tissue was strongly fractal-like. Results summary: mean QLV parameters were C=0.079, τ1=0.004, τ2=76, and mean FOV parameters were β=0.29, τ=0.076, and ρ=1.84. Conclusions: FOV can provide valuable new insights into tissue viscoelastic behavior. Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison.

Biomechanics of knee ligaments: injury, healing, and repair

Knee ligament injuries are common, particularly in sports and sports related activities. Rupture of these ligaments upsets the balance between knee mobility and stability, resulting in abnormal knee kinematics and damage to other tissues in and around the joint that lead to morbidity and pain. During the past three decades, significant advances have been made in characterizing the biomechanical and biochemical properties of knee ligaments as an individual component as well as their contribution to joint function. Further, significant knowledge on the healing process and replacement of ligaments after rupture have helped to evaluate the effectiveness of various treatment procedures. This review paper provides an overview of the current biological and biomechanical knowledge on normal knee ligaments, as well as ligament healing and reconstruction following injury. Further, it deals with new and exciting functional tissue engineering approaches (ex. growth factors, gene transfer and gene therapy, cell therapy, mechanical factors, and the use of scaffolding materials) aimed at improving the healing of ligaments as well as the interface between a replacement graft and bone. In addition, it explores the anatomical, biological and functional perspectives of current reconstruction procedures. Through the utilization of robotics technology and computational modeling, there is a better understanding of the kinematics of the knee and the in situ forces in knee ligaments and replacement grafts. The research summarized here is multidisciplinary and cutting edge that will ultimately help improve the treatment of ligament injuries. The material presented should serve as an inspiration to future investigators.

An Improved Method to Analyze the Stress Relaxation of Ligaments Following a Finite Ramp Time Based on the Quasi-Linear Viscoelastic Theory

The quasi-linear viscoelastic (QLV) theory proposed by Fung (1972) has been frequently used to model the nonlinear time- and history-dependent viscoelastic behavior of many soft tissues. It is common to use five constants to describe the instantaneous elastic response (constants A and B) and reduced relaxation function (constants C, τ1, and τ2) on experiments with finite ramp times followed by stress relaxation to equilibrium. However, a limitation is that the theory is based on a step change in strain which is not possible to perform experimentally. Accounting for this limitation may result in regression algorithms that converge poorly and yield nonunique solutions with highly variable constants, especially for long ramp times (Kwan et al. 1993). The goal of the present study was to introduce an improved approach to obtain the constants for QLV theory that converges to a unique solution with minimal variability. Six goat femur-medial collateral ligament-tibia complexes were subjected to a uniaxial tension test (ramp time of 18.4 s) followed by one hour of stress relaxation. The convoluted QLV constitutive equation was simultaneously curve-fit to the ramping and relaxation portions of the data r2>0.99. Confidence intervals of the constants were generated from a bootstrapping analysis and revealed that constants were distributed within 1% of their median values. For validation, the determined constants were used to predict peak stresses from a separate cyclic stress relaxation test with averaged errors across all specimens measuring less than 6.3±6.0% of the experimental values. For comparison, an analysis that assumed an instantaneous ramp time was also performed and the constants obtained for the two approaches were compared. Significant differences were observed for constants B, C, τ1, and τ2, with τ1 differing by an order of magnitude. By taking into account the ramping phase of the experiment, the approach allows for viscoelastic properties to be determined independent of the strain rate applied. Thus, the results obtained from different laboratories and from different tissues may be compared.