van Cc René Donkelaar

A Comparison Between Mechano-Electrochemical and Biphasic Swelling Theories for Soft Hydrated Tissues

Biological tissues like intervertebral discs and articular cartilage primarily consist of interstitial fluid, collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans, the total ion concentration inside the tissue is higher than in the surrounding synovial fluid (cation concentration is higher and the anion concentration is lower). This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. In the last decade several mechano-electrochemical models, which include this mechanism, have been developed. As these models are complex and computationally expensive, it is only possible to analyze geometrically relatively small problems. Furthermore, there is still no commercial finite element tool that includes such a mechano-electrochemical theory. Lanir (Biorheology, 24, pp. 173-187, 1987) hypothesized that electrolyte flux in articular cartilage can be neglected in mechanical studies. Lanirs hypothesis implies that the swelling behavior of cartilage is only determined by deformation of the solid and by fluid flow. Hence, the response could be described by adding a deformation-dependent pressure term to the standard biphasic equations. Based on this theory we developed a biphasic swelling model. The goal of the study was to test Lanirs hypothesis for a range of material properties. We compared the deformation behavior predicted by the biphasic swelling model and a full mechano-electrochemical model for confined compression and 1D swelling. It was shown that, depending on the material properties, the biphasic swelling model behaves largely the same as the mechano-electrochemical model, with regard to stresses and strains in the tissue following either mechanical or chemical perturbations. Hence, the biphasic swelling model could be an alternative for the more complex mechano-electrochemical model, in those cases where the ion flux itself is not the subject of the study. We propose thumbrules to estimate the correlation between the two models for specific problems.

An in vitro organ culturing system for intervertebral disc explants with vertebral endplates : a feasibility study with ovine caudal discs

Study Design. Whole ovine caudal intervertebral discs with vertebral endplates were cultured under uniaxial diurnal loading for 7 days. Objectives. To establish and characterize an organ culture system for intervertebral discs, in which disc cells may be “maintained” in their native three-dimensional environment under load. Summary of Background Data. In vitro culturing of entire discs with preserved biologic and structural integrity would be a useful model to study the effects of nutrition and mechanical loading. Methods. To maintain endplate permeability, sheep were systemically anticoagulated before death and their caudal vasculature was evacuated with saline postmortem. The first 4 caudal discs were explanted with their adjacent endplates and cultured in bioreactors under uniaxial diurnal loading (0.2 MPa for 8 hours and 0.8 MPa for 16 hours) for 4 or 7 days. Solute transport into the center of the disc was measured after 4 days of culture using a low molecular weight fluorescent marker. Cell viability, glycosaminoglycan synthesis rate, and gene expression profile were measured after 7 days of culture and compared with fresh tissue. Results. Fluorescent images showed that solutes could diffuse into the disc under both static and diurnal loading, but penetration through the endplate increased with diurnal loading. Cell viability and glycosaminoglycan synthesis rates remained unchanged after 7 days of culture. Expression of catabolic genes was significantly up-regulated, whereas anabolic genes tended to be down-regulated after 7 days. Conclusions. With this novel preparation and culturing technique, endplate permeability could be maintained, which allowed culturing of intact disc explants with endplates for up to 7 days.

Computational study of culture conditions and nutrient supply in cartilage tissue engineering.

Different culture conditions for cartilage tissue engineering were evaluated with respect to the supply of oxygen and glucose and the accumulation of lactate. A computational approach was adopted in which the culture configurations were modeled as a batch process and transport was considered within constructs seeded at high cell concentrations and of clinically relevant dimensions. To assess the extent to which mass transfer can be influenced theoretically, extreme cases were distinguished in which the culture medium surrounding the construct was assumed either completely static or well mixed and fully oxygenated. It can be concluded that severe oxygen depletion and lactate accumulation can occur within constructs for cartilage tissue engineering. However, the results also indicate that transport restrictions are not insurmountable, providing that the medium is well homogenized and oxygenated and the constructapos;s surfaces are sufficiently exposed to the medium. The large variation in uptake rates of chondrocytes indicates that for any specific application the quantification of cellular utilization rates, depending on the cell source and culture conditions, is an essential starting point for optimizing culture protocols.

Skeletal muscle transverse strain during isometric contraction at different lengths.

An important assumption in 2D numerical models of skeletal muscle contraction involves deformation in the third dimension of the included muscle section. The present paper studies the often used plane strain description. Therefore, 3D muscle surface deformation is measured from marker displacements during isometric contractions at various muscle lengths. Longitudinal strains at superficial muscle fibers ( - 14 +/- 2.6% at L0, n = 57) and aponeurosis (0.8 +/- 0.9% at L0) decrease with increasing muscle length. The same holds for transverse muscle surface strains in superficial muscle fibers and aponeurosis, which are comparable at intermediate muscle length, but differ at long and short muscle length. Because transverse strains during isometric contraction change with initial muscle length, it is concluded that the effect of muscle length on muscle deformation cannot be studied in plane strain models. These results do not counteract the use of these models to study deformation in contractions with approximately - 9 % longitudinal muscle fiber strain, as transverse strain in superficial muscle fibers and in aponeurosis tissue is minimal in that case. Aponeurosis surface area change decreases with increasing initial muscle length, but muscle fiber surface area change is - 11%, independent of muscle length. Assuming incompressible muscle material, this means that strain perpendicular to the muscle surface equals 11%. Taking the relationship between transverse and longitudinal muscle fiber strain into account, it is hypothesized that superficial muscle fibers flatten during isometric contractions.

The local matrix distribution and the functional development of tissue engineered cartilage, a finite element study

Assessment of the functionality of tissue engineered cartilage constructs is hampered by the lack of correlation between global measurements of extra cellular matrix constituents and the global mechanical properties. Based on patterns of matrix deposition around individual cells, it has been hypothesized previously, that mechanical functionality arises when contact occurs between zones of matrix associated with individual cells. The objective of this study is to determine whether the local distribution of newly synthesized extracellular matrix components contributes to the evolution of the mechanical properties of tissue engineered cartilage constructs. A computational homogenization approach was adopted, based on the concept of a periodic representative volume element. Local transport and immobilization of newly synthesized matrix components were described. Mechanical properties were taken dependent on the local matrix concentration and subsequently the global aggregate modulus and hydraulic permeability were derived. The transport parameters were varied to assess the effect of the evolving matrix distribution during culture. The results indicate that the overall stiffness and permeability are to a large extent insensitive to differences in local matrix distribution. This emphasizes the need for caution in the visual interpretation of tissue functionality from histology and underlines the importance of complementary measurements of the matrix’s intrinsic molecular organization.

Tuning the differentiation of periosteum-derived cartilage using biochemical and mechanical stimulations

OBJECTIVE In this study, we aim at tuning the differentiation of periosteum in an organ culture model towards cartilage, rich in collagen type II, using combinations of biochemical and mechanical stimuli. We hypothesize that addition of TGF-β will stimulate chondrogenesis, whereas sliding indentation will enhance collagen synthesis. DESIGN Periosteum was dissected from the tibiotarsus of 15-day-old chick embryos. Explants were embedded in between two agarose layers, and cultured without stimulation (control), with biochemical stimulation (10 ng/ml TGF-β1), with mechanical stimulation (sliding indentation), or both biochemical and mechanical stimulations. Sliding indentation was introduced as a method to induce tensile tissue strain. Analysis included quantification of DNA, collagen and GAG content, conventional histology, and immunohistochemistry for collagen type I and II at 1 or 2 weeks of culture. RESULTS Embedding the periosteal explants in between agarose layers induced cartilage formation, confirmed by synthesis of sGAG and collagen type II. Addition of TGF-β1 to the culture medium did not further enhance this chondrogenic response. Applying sliding indentation only to the periosteum in between agarose layers enhanced the production of collagen type I, leading to the formation of fibrous tissue without any evidence of cartilage formation. However, when stimulated by both TGF-β1 and sliding indentation, collagen production was still enhanced, but now collagen type II, while sGAG was found to be similar to TGF-β1 or unloaded samples. CONCLUSIONS The type of tissue produced by periosteal explants can be tuned by combining mechanical stimulation and soluble factors. TGF-β1 stimulated a chondrocyte phenotype and sliding indentation stimulated collagen synthesis. Such a combination may be valuable for improvement of the quality of tissue-engineered cartilage.

Mechanics of chondrocyte hypertrophy

Chondrocyte hypertrophy is a characteristic of osteoarthritis and dominates bone growth. Intra- and extracellular changes that are known to be induced by metabolically active hypertrophic chondrocytes are known to contribute to hypertrophy. However, it is unknown to which extent these mechanical conditions together can be held responsible for the total magnitude of hypertrophy. The present paper aims to provide a quantitative, mechanically sound answer to that question. To address this aim requires a quantitative tool that captures the mechanical effects of collagen and proteoglycans, allows temporal changes in tissue composition, and can compute cell and tissue deformations. These requirements are met in our numerical model that is validated for articular cartilage mechanics, which we apply to quantitatively explain a range of experimental observations related to hypertrophy. After validating the numerical approach for studying hypertrophy, the model is applied to evaluate the direct mechanical effects of axial tension and compression on hypertrophy (Hueter-Volkmann principle) and to explore why hypertrophy is reduced in case of partially or fully compromised proteoglycan expression. Finally, a mechanical explanation is provided for the observation that chondrocytes do not hypertrophy when enzymatical collagen degradation is prohibited (S1Pcko knock-out mouse model). This paper shows that matrix turnover by metabolically active chondrocytes, together with externally applied mechanical conditions, can explain quantitatively the volumetric change of chondrocytes during hypertrophy. It provides a mechanistic explanation for the observation that collagen degradation results in chondrocyte hypertrophy, both under physiological and pathological conditions.

The role of pressurized fluid in subchondral bone cyst growth

Pressurized fluid has been proposed to play an important role in subchondral bone cyst development. However, the exact mechanism remains speculative. We used an established computational mechanoregulated bone adaptation model to investigate two hypotheses: 1) pressurized fluid causes cyst growth through altered bone tissue loading conditions, 2) pressurized fluid causes cyst growth through osteocyte death. In a 2D finite element model of bone microarchitecture, a marrow cavity was filled with fluid to resemble a cyst. Subsequently, the fluid was pressurized, or osteocyte death was simulated, or both. Rather than increasing the load, which was the prevailing hypothesis, pressurized fluid decreased the load on the surrounding bone, thereby leading to net bone resorption and growth of the cavity. In this scenario an irregularly shaped cavity developed which became rounded and obtained a rim of sclerotic bone after removal of the pressurized fluid. This indicates that cyst development may occur in a step-wise manner. In the simulations of osteocyte death, cavity growth also occurred, and the cavity immediately obtained a rounded shape and a sclerotic rim. Combining both mechanisms increased the growth rate of the cavity. In conclusion, both stress-shielding by pressurized fluid, and osteocyte death may cause cyst growth. In vivo observations of pressurized cyst fluid, dead osteocytes, and different appearances of cysts similar to our simulation results support the idea that both mechanisms can simultaneously play a role in the development and growth of subchondral bone cysts.

Analysis of bone architecture sensitivity for changes in mechanical loading, cellular activity, mechanotransduction, and tissue properties

Bone has an architecture which is optimized for its mechanical environment. In various conditions, this architecture is altered, and the underlying cause for this change is not always known. In the present paper, we investigated the sensitivity of the bone microarchitecture for four factors: changes in bone cellular activity, changes in mechanical loading, changes in mechanotransduction, and changes in mechanical tissue properties. The goal was to evaluate whether these factors can be the cause of typical bone structural changes seen in various pathologies. For this purpose, we used an established computational model for the simulation of bone adaptation. We performed two sensitivity analyses to evaluate the effect of the four factors on the trabecular structure, in both developing and adult bone. According to our simulations, alterations in mechanical load, bone cellular activities, mechanotransduction, and mechanical tissue properties may all result in bone structural changes similar to those observed in various pathologies. For example, our simulations confirmed that decreases in loading and increases in osteoclast number and activity may lead to osteoporotic changes. In addition, they showed that both increased loading and decreased bone matrix stiffness may lead to bone structural changes similar to those seen in osteoarthritis. Finally, we found that the model may help in gaining a better understanding of the contribution of individual disturbances to a complicated multi-factorial disease process, such as osteogenesis imperfecta.

Bone structural changes in osteoarthritis as a result of mechanoregulated bone adaptation: a modeling approach

OBJECTIVE There are strong indications that subchondral bone may play an important role in osteoarthritis (OA), making it an interesting target for medical therapies. The subchondral bone structure changes markedly during OA, and it has long been assumed that this occurs secondary to cartilage degeneration. However, for various conditions that are associated with OA, it is known that they may also induce bone structural changes in the absence of cartilage degeneration. We therefore aimed to investigate if OA bone structural changes can result from mechanoregulated bone adaptation, independent of cartilage degeneration. METHOD With a bone adaptation model, we simulated various conditions associated with OA -without altering the articular cartilage- and we evaluated if mechanoregulated bone remodeling by itself could lead to OA-like bone structural changes. RESULTS For each of the conditions, the predicted changes in bone structural parameters (bone fraction, trabecular thickness, trabecular number, and trabecular separation) were similar to those observed in OA. CONCLUSION This indicates that bone adaptation in OA can be mechanoregulated with structural changes occurring independent of cartilage degeneration.