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The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule applied to simulate the remodeling process in each element individually is, in fact, an objective function for an optimization process, relative to the external load. Its purpose is to obtain a constant, preset value for the strain energy per unit bone mass, by adapting the density. If an element in the structure cannot achieve that, it either turns to its maximal density (cortical bone) or resorbs completely. It is found that the solution obtained in generally a discontinuous patchwork. For a two-dimensional proximal femur model this patchwork shows a good resemblance with the density distribution of a real proximal femur. It is shown that the discontinuous end configuration is dictated by the nature of the differential equations describing the remodeling process. This process can be considered as a nonlinear dynamical system with many degrees of freedom, which behaves divergent relative to the objective, leading to many possible solutions. The precise solution is dependent on the parameters in the remodeling rule, the load and the initial conditions. The feedback mechanism in the process is self-enhancing, denser bone attracts more strain energy, whereby the bone becomes even more dense. It is suggested that this positive feedback of the attractor state (the strain energy field) creates order in the end configuration. In addition, the process ensures that the discontinuous end configuration is a structure with a relatively low mass, perhaps a minimal-mass structure, although this is no explicit objective in the optimization process. It is hypothesized that trabecular bone is a chaotically ordered structure which can be considered as a fractal with characteristics of optimal mechanical resistance and minimal mass, of which the actual morphology depends on the local (internal) loading characteristics, the sensor-cell density and the degree of mineralization.

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A model is presented to study and quantify the contribution of all available sensory information to human standing based on optimal estimation theory. In the model, delayed sensory information is integrated in such a way that a best estimate of body orientation is obtained. The model approach agrees with the present theory of the goal of human balance control. The model is not based on purely inverted pendulum body dynamics, but rather on a three-link segment model of a standing human on a movable support base. In addition, the model is non-linear and explicitly addresses the problem of multisensory integration and neural time delays. A predictive element is included in the controller to compensate for time delays, necessary to maintain erect body orientation. Model results of sensory perturbations on total body sway closely resemble experimental results. Despite internal and external perturbations, the controller is able to stabilise the model of an inherently unstable standing human with neural time delays of 100 ms. It is concluded, that the model is capable of studying and quantifying multisensory integration in human stance control. We aim to apply the model in (1) the design and development of prostheses and orthoses and (2) the diagnosis of neurological balance disorders.