Mechanobiological adaptation of subchondral bone as a function of joint incongruity and loading

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Abstract

Computed tomography (CT) has been employed to determine non-invasively the distribution of subchondral bone density in joints and to evaluate their dominant loading pattern. The objective of this study was to investigate the relationship between subchondral bone adaptation, joint incongruity and loading, in order to determine to what extent the loading conditions and/or geometric configuration can be inferred from the distribution of subchondral density. Finite element models of joints with various degrees of incongruity were designed and a current remodeling theory implemented using the node-based approach. Appropriate combinations of joint incongruity and loading yielded subchondral bone density patterns consistent with experimental findings, specifically a bicentric distribution in the humero-ulnar joint and a monocentric distribution in the humero-radial joint. However, other combinations of incongruity and loading produced similar subchondral density patterns. Both the geometric joint configuration and the loading conditions influence the distribution of subchondral density in such a way that one of these factors must be known a priori to estimate the other. Since subchondral density can be assessed by CT and joint geometry by magnetic resonance imaging, the dominant loading pattern of joints may be potentially derived in the living using these non-invasive imaging methods.

Introduction

Based on the hypotheses of Bourgery[1], Roux[2], Wolff[3], Pauwels4, 5and Kummer6, 7, significant advances have been made over the last two decades in the development of a mathematical theory of mechanobiological adaptation of bone tissue 8, 9, 10, 11. The advent of finite element modeling in bone biomechanics has made it possible to relate the biological processes of bone apposition and resorption to the mechanical stresses and strains in the tissue 10, 11, 12, 13, 14, 15, 16, 17, 18. Although the precise cellular mechanism by which the “loading history” of the bone is related to a biological response remains unknown, it has become feasible to phenomenologically mimic these processes with sufficient precision to accurately predict changes in bone density, which are not only consistent with many clinical observations10, 13, but also with very specific animal experiments12, 17.

These computer simulations have so far been focused on the adaptation of normal cancellous bone14, 16, 18, cortical bone12, 19, and also on bone remodeling around orthopedic implants10, 17. However, the subchondral bone plate, a thin layer of bone tissue which is covered by a layer of calcified articular cartilage and supported by epiphyseal trabeculae, has so far received much less attention. This zone plays a unique role insofar as the stresses and strains within it are more or less directly related to the loading pattern and stress distribution within the articular surfaces.

Pauwels5, 20stated that the subchondral bone density can be interpreted as an “embodiment of the stress diagram of the joint”. Later, Tillmann[21]and Oberländer et al.[22]related subchondral mineralization to contact stress, surface morphology and cartilage degeneration in the human trochlear notch and acetabulum. CT osteoabsorptiometry23, 24has made it possible to determine the distribution of subchondral bone density non-invasively, and repeatedly. Characteristic subchondral mineralization patterns have been reported for the human hip[25], ankle[26]and elbow joint27, 28. It has also been shown that in the adult, after skeletal maturation, these mineralization patterns may still undergo important changes when the mechanical conditions are altered, for instance after a correction osteotomy[29]. It is, therefore, tempting to use CT osteoabsorptiometry for the determination of the dominant loading pattern of joints and to evaluate joint function or dysfunction in vivo. Individuals may be followed up longitudinally with this technique, in a clinical or a research context.

However, some of the larger articulations of the human body such as the hip30, 31, ankle[32], and elbow 27, 33, 34, 35, 36, 37have been observed to be physiologically incongruous, and in the hip and ankle this incongruity has been reported to decrease as a function of age30, 32. It has been assumed that the subchondral mineralization patterns of these joints are (at least partly) determined by their particular geometric configuration24, 25, 26, 27, 28and that therefore changes in joint incongruity can also be monitored using CT osteoabsorptiometry24, 25, 26.

Since it is impractical to test the distinctive influences of variations in joint incongruity and loading on the distribution of contact stress and subchondral bone adaptation experimentally, we have employed the finite element method to solve the non-linear contact problem arising with the loading of incongruous joints, and to iteratively adapt the apparent bone density to a given mechanical signal, as described by current bone-remodeling theory.

In the current study we hypothesized that a given geometric joint configuration and a certain type of loading would lead to a characteristic distribution of subchondral bone density, specifically a bicentric pattern in articulations with deeper sockets (such as the hip, ankle and humero-ulnar joint) and a monocentric pattern in joints with congruous or wider sockets (such as the humero-radial joint). It is proposed that subchondral bone is a mechanically efficient structure, yielding an optimal distribution of density, and that density patterns should in turn provide information about the dominant loading pattern and/or the incongruity of this articulation. We will show that the geometric configuration of a joint and its loading conditions interact in a complex manner, so that at least one of these factors must be known a priori if clear conclusions are to be drawn about either of the two from the pattern of subchondral mineralization.

Section snippets

Materials and methods

Five two-dimensional plain-stress finite element models were designed (Fig. 1) with different joint sockets and a uniform head (2017 bilinear elements, thickness=20 mm). In order to provide a realistic framework, the data on joint incongruity and loading were taken from the human elbow, since this articulation has been extensively studied in terms of joint space width and contact27, 33, 34, 35, 36, 37, loading38, 39, and subchondral mineralization5, 20, 21, 27, 28. However, because the objective

Results

In the standard model (model 4, 10% deeper socket, wide-spread loading with 70 N) a dense subchondral bone plate was observed after 300 days of bone remodeling (Fig. 2). The density was not distributed homogeneously in this layer, but a bicentric pattern emerged with two maxima located approximately 6 mm (30°) on either side of the center of the socket (Fig. 3). The subchondral density ranged from 0.2 to 1.4 g/cm3. Changing the cartilage modulus had very little effect on the density distribution.

Discussion

In this study we have investigated the relationship between the mechanobiological adaptation of the subchondral bone, joint incongruity, and joint loading, using the finite element method and current bone remodeling theory11, 14, 16. We aimed to demonstrate that subchondral is a mechanically efficient structure, which yields an optimal distribution of density and is determined by the shape of the joint, as well as by its dominant loading pattern. We asked whether variations in the geometric

Conclusions

In this computer simulation of mechanobiological bone remodeling we have shown that given combinations of joint incongruity and loading, based on experimental results in the human elbow, yield mineralization patterns consistent with radiological findings in this joint. Specifically, a bicentric pattern was obtained in the humero-ulnar joint (deeper joint socket) and a monocentric pattern in the humero-radial articulation (wider or congruous joint socket). The current study thus demonstrates

Acknowledgements

We would like to thank the Deutsche Forschungsgemeinschaft for supporting this study.

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