Gerard A. Ateshian

Functional tissue engineering of articular cartilage through dynamic loading of chondrocyte-seeded agarose gels

Due to its avascular nature, articular cartilage exhibits a very limited capacity to regenerate and to repair. Although much of the tissue-engineered cartilage in existence has been successful in mimicking the morphological and biochemical appearance of hyaline cartilage, it is generally mechanically inferior to the natural tissue. In this study, we tested the hypothesis that the application of dynamic deformational loading at physiological strain levels enhances chondrocyte matrix elaboration in cell-seeded agarose scaffolds to produce a more functional engineered tissue construct than in free swelling controls. A custom-designed bioreactor was used to load cell-seeded agarose disks dynamically in unconfined compression with a peak-to-peak compressive strain amplitude of 10 percent, at a frequency of 1 Hz, 3 x (1 hour on, 1 hour off)/day, 5 days/week for 4 weeks. Results demonstrated that dynamically loaded disks yielded a sixfold increase in the equilibrium aggregate modulus over free swelling controls after 28 days of loading (100 +/- 16 kPa versus 15 +/- 8 kPa, p < 0.0001). This represented a 21-fold increase over the equilibrium modulus of day 0 (4.8 +/- 2.3 kPa). Sulfated glycosaminoglycan content and hydroxyproline content was also found to be greater in dynamically loaded disks compared to free swelling controls at day 21 (p < 0.0001 and p = 0.002, respectively).

Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression

Interstitial fluid pressurization has long been hypothesized to play a fundamental role in the load support mechanism and frictional response of articular cartilage. However, to date, few experimental studies have been performed to verify this hypothesis from direct measurements. The first objective of this study was to investigate experimentally the hypothesis that cartilage interstitial fluid pressurization does support the great majority of the applied load, in the testing configurations of confined compression creep and stress relaxation. The second objective was to investigate the hypothesis that the experimentally observed interstitial fluid pressurization could also be predicted using the linear biphasic theory of Mow et al. (J. Biomech. Engng ASME, 102, 73-84, 1980). Fourteen bovine cartilage samples were tested in a confined compression chamber fitted with a microchip piezoresistive transducer to measure interstitial fluid pressure, while simultaneously measuring (during stress relaxation) or prescribing (during creep) the total stress. It was found that interstitial fluid pressure supported more than 90% of the total stress for durations as long as 725 +/- 248 s during stress relaxation (mean +/- S.D., n = 7), and 404 +/- 229 s during creep (n = 7). When comparing experimental measurements of the time-varying interstitial fluid pressure against predictions from the linear biphasic theory, nonlinear coefficients of determination r2 = 0.871 +/- 0.086 (stress relaxation) and r2 = 0.941 +/- 0.061 (creep) were found. The results of this study provide some of the most direct evidence to date that interstitial fluid pressurization plays a fundamental role in cartilage mechanics; they also indicate that the mechanism of fluid load support in cartilage can be properly predicted from theory.

FEBio: finite elements for biomechanics.

In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://mrl.sci.utah.edu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics.

An asymptotic solution for the contact of two biphasic cartilage layers

The purpose of this study was to present a solution for the contact of two biphasic cartilage layers which can be used for dynamic loading, is not restricted to predictions over small time periods, and predicts biologically meaningful changes in contact areas over time. The proposed solution was based on the work of Ateshian et al. (1994, J. Biomechanics 27, 1347-1360) who retained the first term of an asymptotic expansion and used an approximate integration which is valid for short time periods. The solution proposed here uses an exact integration, is valid over long time periods, and can be used for increasing loading. The new solution corrects a limitation of the work by Ateshian et al., which manifests itself immediately (i.e. at time t = 0+ s): the rate of change in the contact radius (and therefore, the contact area) is increasing in Ateshian et al.s solution for a constant force, whereas it is decreasing in the new solution. An increasing rate of change in the contact radius suggests that the contact radius (area) is unbounded, and a steady-state solution cannot be reached, which is physically not correct for the contact of two joint surfaces. In the new solution, the contact radius reaches a steady-state value given sufficient time.

Synergistic action of growth factors and dynamic loading for articular cartilage tissue engineering.

It has previously been demonstrated that dynamic deformational loading of chondrocyte-seeded agarose hydrogels over the course of 1 month can increase construct mechanical and biochemical properties relative to free-swelling controls. The present study examines the manner in which two mediators of matrix biosynthesis, the growth factors TGF-beta1 and IGF-I, interact with applied dynamic deformational loading. Under free-swelling conditions in control medium (C), the [proteoglycan content][collagen content][equilibrium aggregate modulus] of cell-laden (10 x 10(6) cells/mL) 2% agarose constructs reached a peak of [0.54% wet weight (ww)][0.16% ww][13.4 kPa]c, whereas the addition of TGF-beta1 or IGF-I to the control medium led to significantly higher peaks of [1.18% ww][0.97% ww][23.6 kPa](C-TGF) and [1.00% ww][0.63% ww][19.3 kPa](C-IGF), respectively, by day 28 or 35 (p<0.01). Under dynamic loading in control medium (L), the measured parameters were [1.10% ww][0.52% ww][24.5 kPa]L, and with the addition of TGF-beta1 or IGF-I to the control medium these further increased to [1.49% ww][1.07% ww][50.5 kPa](L-TGF) and [1.48% ww][0.81% ww][46.2 kPa](L-IGF), respectively (p<0.05). Immunohistochemical staining revealed that type II collagen accumulated primarily in the pericellular area under free-swelling conditions, but spanned the entire tissue in dynamically loaded constructs. Applied in concert, dynamic deformational loading and TGF-beta1 or IGF-I increased the aggregate modulus of engineered constructs by 277 or 245%, respectively, an increase greater than the sum of either stimulus applied alone. These results support the hypothesis that the combination of chemical and mechanical promoters of matrix biosynthesis can optimize the growth of tissue-engineered cartilage constructs.

Influence of seeding density and dynamic deformational loading on the developing structure/function relationships of chondrocyte-seeded agarose hydrogels.

AbstractChondrocytes cultured in agarose hydrogels develop a functional extracellular matrix. Application of dynamic strain at physiologic levels to these constructs over time can increase their mechanical properties. In this study, the effect of seeding density (20 and 60×106 cells/ml) on tissue elaboration was investigated. Higher seeding densities increased tissue properties in free-swelling culture, with constructs seeded at 20 and 60×106 cells/ml reaching maximum values over the 63 day culture period of aggregate modulus HA: 43±15 kPa, Young’s modulus EY: 39±3 kPa, and glycosaminglycan content [GAG]: 0.96%±0.13% wet weight; and HA: 58±12 kPa, EY: 60±5 kPa, and [GAG]: 1.49% ± 0.26% wet weight, respectively. It was further observed that the application of daily dynamic deformational loading to constructs seeded at 20×106 cells/ml enhanced biochemical content (∼150%) and mechanical properties (∼threefold) compared to free-swelling controls by day 28. However, at a concentration of 60×106 cells/ml, no difference in mechanical properties was found in loaded samples versus their free-swelling controls. Multiple regression analysis showed that the mechanical properties of the tissue constructs depend more strongly on collagen content than GAG content; a finding that is more pronounced with the application of daily dynamic deformational loading. Our findings provide evidence for initial cell seeding density and nutrient accessibility as important parameters in modulating tissue development of engineered constructs, and their ability to respond to a defined mechanical stimulus.

Finite deformation biphasic material properties of bovine articular cartilage from confined compression experiments

In 1990, Holmes and Mow [Journal of Biomechanics 23, 1145-1156] developed a hyperelastic biphasic theory to describe finite deformation behaviors of articular cartilage. To date, however, no experimental finite deformation studies have been made to assess the ability of this constitutive model to describe its finite deformation behaviors (e.g. kinetic creep and stress-relaxation, and equilibrium responses). The objectives of this study are: (1) to investigate whether this hyperelastic biphasic theory can be used to curve-fit the finite deformation compressive stress-relaxation behavior of the tissue, and from this procedure, to calculate its material coefficients; and (2) to investigate whether the theory, together with the calculated material coefficients, can accurately predict the outcome of an independent creep experiment followed by cyclical loading of the tissue. To achieve these objectives, circular cylindrical cartilage plugs were tested in confined compression in both stress-relaxation and creep experiments. Results demonstrated that curve-fits of the stress-relaxation experiments produced nonlinear generalized correlation coefficients of r2 = 0.99 +/- 0.02 (mean +/- standard deviation); theoretical predictions of the creep test differed on average by 10.0% +/- 2.0% relative to experimental results. When curve-fitting the creep experiments as well, it was found that the permeability coefficients differed from those obtained from the stress-relaxation experiments (k0,cr = 2.2 +/- 0.8 x 10(-15) m4 N-1 s-1 and Mcr = 0.4 +/- 0.8 vs k0,sr = 2.7 +/- 1.5 x 10(-15) m4 N-1 s-1, and Msr = 2.2 +/- 1.0); these differences may be attributed to imprecisions in the curve-fitting procedure stemming from the low sensitivity of the stress-relaxation and creep behaviors to large variations of M in the permeability function. Advantages and limitations of this theoretical model are presented in the text.

A CONEWISE LINEAR ELASTICITY MIXTURE MODEL FOR THE ANALYSIS OF TENSION-COMPRESSION NONLINEARITY IN ARTICULAR CARTILAGE

A biphasic mixture model is developed that can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J. Elasticity, 37, 1-38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H-A = 0.64 +/- 0.22 MPa, k2 = 3.62 +/- 0.97 x 10(-16) m4/N.s, r2 = 0.95 +/- 0.03), the tensile modulus, compressive Poisson ratio, and radial permeability were obtained from unconfined compression (E+Y = 12.75 +/- 1.56 MPa, v- = 0.03 +/- 0.01, kr = 6.06 +/- 2.10 x 10(-16) m4/N.s, r2 = 0.99 +/- 0.00), and the shear modulus was obtained from torsional shear (mu = 0.17 +/- 0.06 MPa). The model was also employed to predict the interstitial fluid pressure successfully at the center of the cartilage plug in unconfined compression (r2 = 0.98 +/- 0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage that can successfully curve-fit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.

Quantitation of articular surface topography and cartilage thickness in knee joints using stereophotogrammetry

An analytical stereophotogrammetry (SPG) technique has been developed based upon some of the pioneering work of Selvik [Ph.D. thesis, University of Lund, Sweden (1974)] and Huiskes and coworkers [J. Biomechanics 18, 559-570 (1985)], and represents a fundamental step in the construction of biomechanical models of diarthrodial joints. Using this technique, the precise three-dimensional topography of the cartilage surfaces of various diarthrodial joints has been obtained. The system presented in this paper delivers an accuracy of 90 microns in the least favorable conditions with 95% coverage using the same calibration method as Huiskes et al. (1985). In addition, a method has been developed, using SPG, to quantitatively map the cartilage thickness over the entire articular surface of a joint with a precision of 134 microns (95% coverage). In the present study, our SPG system has been used to quantify the topography, including surface area, of the articular surfaces of the patella, distal femur, tibial plateau, and menisci of the human knee. Furthermore, examples of cartilage thickness maps and corresponding thickness data including coefficient of variation, minimum, maximum, and mean cartilage thickness are also provided for the cartilage surfaces of the knee. These maps illustrate significant variations over the joint surfaces which are important in the determination of the stresses and strains within the cartilage during diarthrodial joint function. In addition, these cartilage surface topographies and thickness data are essential for the development of anatomically accurate finite element models of diarthrodial joints.(ABSTRACT TRUNCATED AT 250 WORDS)

A Paradigm for Functional Tissue Engineering of Articular Cartilage via Applied Physiologic Deformational Loading

Deformational loading represents a primary component of the chondrocyte physical environment in vivo. This review summarizes our experience with physiologic deformational loading of chondrocyte-seeded agarose hydrogels to promote development of cartilage constructs having mechanical properties matching that of the parent calf tissue, which has a Youngs modulus EY = 277 kPa and unconfined dynamic modulus at 1 Hz G*=7 MPa. Over an 8-week culture period, cartilage-like properties have been achieved for 60 × 106 cells/ml seeding density agarose constructs, with EY = 186 kPa, G*=1.64 MPa. For these constructs, the GAG content reached 1.74% ww and collagen content 2.64% ww compared to 2.4% ww and 21.5% ww for the parent tissue, respectively. Issues regarding the deformational loading protocol, cell-seeding density, nutrient supply, growth factor addition, and construct mechanical characterization are discussed. In anticipation of cartilage repair studies, we also describe early efforts to engineer cylindrical and anatomically shaped bilayered constructs of agarose hydrogel and bone (i.e., osteochondral constructs). The presence of a bony substrate may facilitate integration upon implantation. These efforts will provide an underlying framework from which a functional tissue-engineering approach, as described by Butler and coworkers (2000), may be applied to general cell-scaffold systems adopted for cartilage tissue engineering.