The conditions on the value of m and n for stability of the process are expected. For a stable process, the stimulus S(Φ) is a decreasing function of the density Φ (e.g., as in Eq. 5 when m > n), and the rate of change in density (partial derivΦ)/(partial deriv t) is an increasing function of the stimulus (i.e., (partial deriv Φ)/(partial deriv S) > 0). Therefore, the process is able to reach an adaptation equilibrium. In Part II, the process will be simulated and the influence of themagnitude of m and n on the computed density will be shown. It is worth noting here that only the particular geometry of a long bone diaphysis has been considered in the present study, so that the conditions for stability should be viewed as necessary but not sufficient.The similarity of the change in density and geometry independent of the stimulus is not unexpected as the different stimuli are all dependent quantities. Therefore, simulation of the BRP demands greater attention on its stability characteristics than thechoice of the stimulus.
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