Multiscale computational and experimental approaches to elucidate bone and ligament mechanobiology using the ulna-radius-interosseous membrane construct as a model system

Abstract

An in vivo axial loading model of the rat ulna was developed almost two decades ago. As a minimally invasive model, it lends itself particularly well for the study of functional adaptation in bone and the interosseous membrane, a ligament spanning between the radius and ulna. The objective of this paper is to review computational and experimental approaches to elucidate its applicability for the study of multiscale bone and ligament mechanobiology. Specifically, this review describes approaches, including i) measurement of strains on bone tissue surfaces, ii) development of a three-dimensional finite element (FE) mesh of a skeletally mature rat ulna, iii) parametric study of the relative influence of mechanical constants and materials properties on computational model predictions, iv) comparison of experimental and computational strain distribution data, and analysis of the radius and interosseous membrane (IOM) ligament's effect on axial load distribution through the ulna of the rat, and v) the effect of mechanical loading on transport through the IOM using different molecular weight fluorescent tagged dextrans. In the first stage of the study a computational stress analysis was performed after applying a 20 N single static load at the ulnar extremities, corresponding to values of experimental strain gauge measurements. To account for the anisotropy of the bone matrix, transverse isotraopic, elastic material properties were applied. In a parametric study, we analyzed the qualitative effect of different material properties on the global load and displacement behavior of the computational model. In a second stage, the same ulnar model used in the parametric study was extended to account for the interaction between the ulna, radius and IOM. The three-dimensional FE model of the rat forelimb confirms the influence of ulnar curvature on its deformation and underscores the influence of the radius and IOM on strain distribution through the ulna. The mode of strain, {i.e.} compression or tension, and strain distribution along the bone diaphysis correspond to those measured experimentally in vivo. When the radius and, indirectly, the IOM were loaded, the bone deformation shifted distally with respect to the diaphysis. In a final stage, the aforementioned ulnar model was used to study the permeability of fluorescent tagged dextrans with different molecular weights in the presence and absence of ulnar compression. Small molecular weight dextrans (3,000 Da) were distributed throughout the IOM in the absence of as well as after mechanical loading. Interestingly, no gradient in distribution was observed in either case. In contrast, very high molecular weight dextrans (1,000,000 Da) were observed only within vascular and lymphatic spaces in the bone (as well as periosteum) and IOM, both in the absence of and after the application of mechanical loading via end load compression. Between the two extremes, both 10 and 70 kDa tracers were distributed throughout the IOM after application of compressive loading. Loading appears to dissipate the steep gradient of fluorescent 70 kDa tracer observed along the lateral surface of the unloaded IOM and its insertion into the radius and ulna. Hence, this combined computational and experimental analysis of the ulna compression model provides new insight into multiscale mechanobiology of the ulna-radius-interosseous membrane construct and may provide new avenues for elucidation of ligament's remarkable structure-function relationships.