Prediction of spatio-temporal bone formation in scaffold by diffusion equation.

Developing a successful bone tissue engineering strategy entails translation of experimental findings to clinical needs. A major leap forward toward this goal is developing a quantitative tool to predict spatial and temporal bone formation in scaffold. We hypothesized that bone formation in scaffold follows diffusion phenomenon. Subsequently, we developed an analytical formulation for bone formation, which had only three unknown parameters: C, the final bone volume fraction, α, the so-called scaffold osteoconduction coefficient, and h, the so-called peri-scaffold osteoinduction coefficient. The three parameters were estimated by identifying the model within vivo data of polymeric scaffolds implanted in the femoral condyle of rats. In vivo data were obtained by longitudinal micro-CT scanning of the animals. Having identified the three parameters, we used the model to predict the course of bone formation in two previously published in vivo studies. We found the predicted values to be consistent with the experimental ones. Bone formation into a scaffold can then adequately be described through diffusion phenomenon. This model allowed us to spatially and temporally predict the outcome of tissue engineering scaffolds with only 3 physically relevant parameters.