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.

In silico evolution of functional morphology: A test on bone tissue biomechanics.

Evolutionary algorithms (EAs) use Darwinian principles--selection among random variation and heredity--to find solutions to complex problems. Mostly used in engineering, EAs gain growing interest in ecology and genetics. Here, we assess their usefulness in functional morphology, introducing finite element modelling (FEM) as a simulated mechanical environment for evaluating the 'fitness' of randomly varying structures. We used this method to identify biomechanical adaptations in bone tissue, a long-lasting problem in skeletal morphology. The algorithm started with a bone tissue model containing randomly distributed vascular spaces. The EA randomly mutated the distribution of vascular spaces, and selected the new structure if its mechanical resistance was increased. After some thousands of generations, organized phenotypes emerged, containing vascular canals and sinuses, mimicking real bone tissue organizations. This supported the hypothesis that natural bone microstructures can result from biomechanical adaptation. Despite its limited faithfulness to reality, we discuss the ability of the EA+FEM method to assess adaptation in a dynamic evolutionary framework, which is not possible in the real world because of the generation times of macro-organisms. We also point out the interesting potential of EAs to simulate not only adaptation, but also concurrent evolutionary phenomenons such as historical contingency.