# The Influence of Loading Program on the Stimulated Callus Mineralization
## 3 Results
\[\widetilde{M}=\frac{M}{\frac{b\cdot b^{2}}{6}\cdot E_{0}} \tag{11}\]  
\[\widetilde{T}=\frac{T}{b\cdot h\cdot E_{0}} \tag{12}\]  
It is unlikely that in practical treatment of a patient, the load parameters (\(M\) and \(T\)) can be changed in continuous and optimal manner. The loading program might be interrupted and for a designated time interval, the loads may diminish to zero. The aim of investigating this intermittent loading program is to assess its influence on the final distribution of the callus elasticity modulus. The optimal load values (\(M\) and \(T\)) are applied for a given time interval (\(\Delta t_{\mathrm{load}}=1\) (time unit)), hence the callus density (and elasticity modulus) increases due to Equation (2). Then the loads drop to zero for equal time intervals and the modulus decreases due to the resorption effect (\(\psi<K_{\mathrm{min}}\)). The process is repeated that way for 10 time units. Figure 3 presents the outcome of the remodeling process for the intermittent loading program in which one may observe that, in general, a satisfactory homogeneous distribution of the Young's modulus in a section is achieved (\(s=0.019\)). However, the maximal value of the elasticity modulus is almost five times lower than the value obtained for the optimal loading program after the same healing time (Table 2). This loading program can still provide a sufficient value for the elasticity modulus of the callus tissue but a longer time period is required (Table 3). The homogeneity of the \"long time\" distribution is worse than the one obtained for the continuous optimal loading program. Also, remodeling effectiveness depends on the ratio between loading (\(\Delta t_{\mathrm{load}}\)) and unloading (\(\Delta t_{\mathrm{unload}}\)) time intervals, and the bigger the ratio is, the higher the value of \(E_{\mathrm{max}}\) can be remodeled in the given time. This loading program was analyzed as physiological-like when during the healing process, the callus tissue is repeatedly stimulated and not stimulated for given time intervals. Figure 4 presents the outcome of a progressive remodeling process for the intermittent loading program with the 10% residual load. That means the load values are assumed to reduce down to 10% of ones acting before unloading, instead of total vanishing. This program was analyzed only as a possibility to happen and the 10%, 20%, or 30% values for the residual loads are chosen to test how the model of the callus remodeling would respond to this type of loading scheme. Comparison of the load paths in Figures 2-4 indicates significantly different values. It is explained that optimal load values, calculated with Equations (9) and (10), are not established once for good. In contrary, they strongly depend on healing process history, exhibited by the modulus distribution \(E(z)\), obtained after all the preceding time steps. If there is no unloading, as in the optimal program, the modulus increases continuously in time at all section points, and hence the required values of optimal \(M\) and \(T\) increase too. For the sub-optimal intermittent programs, the modulus increases during loading but decreases during each unloading period. In general, if a following loading is to start after an unloading time, the optimal values of loads are less because of smaller values of \(E(z)\). One may observe for the intermittent programs that for a given time interval (Table 2) the higher is the residual load the better are values of \(E_{\max}\), but the distribution homogeneity is worse. Similarly, Table 3 indicates that for the intermittent programs the higher is the residual load the shorter is healing time, necessary for satisfactory \(E_{\max}\) value. However, the distribution homogeneity is worse. The explanation is, that during total unloading the resorption occurs with the same rate (\(-BK_{\min}\) (g/(cm\({}^{3}\cdot\)time unit)) at each section point, since the stimulator \(\psi=0\) for each coordinate \(z\).