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

Abstract

a b s t r a c tDeveloping 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, a, 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.

Balancing the Rates of New Bone Formation and Polymer Degradation Enhances Healing of Weight-Bearing Allograft/Polyurethane Composites in Rabbit Femoral Defects

“…Hydrolytically degradable polymers undergo autocatalytic degradation, resulting in poor healing in the interior of the graft due to transport limitations associated with ingrowth of new bone. 57 Closely balancing the rates of new bone formation and polymer degradation, accomplished by local delivery of rhBMP-2 in this study, allowed healing to progress to later stages (up to f H = 70%). A limitation of this study is that none of the areas healed > 70% over the 12-week duration.…”

“…However, r B = d(%B)/dt in the inner regions decreased with time, suggesting that masstransfer limitations associated with infiltration of cells from the host bone into the interior of the scaffold slowed bone formation. A diffusion model for bone formation in scaffolds has been proposed 57 :…”

Translation of Biomechanical Concepts in Bone Tissue Engineering: From Animal Study to Revision Knee Arthroplasty

“…We have previously developed and validated a mathematical model of bone formation in the scaffold by considering that this process follows a diffusion phenomenon (Roshan-Ghias, Vogel, et al 2011). The model with identified parameters successfully predicted the results of two different animal experiments.…”

“…In addition, micro-CT imaging provides spatial information on the bone formation in the scaffold. Spatial and temporal experimental data for loaded and non-loaded scaffolds are then inputted into the bone formation model developed previously (Roshan-Ghias, Vogel, et al 2011), and the corresponding sets of parameters (one for loaded and another for non-loaded scaffolds) of the model are identified accordingly (Box 3). The bone formation model with the two sets of identified parameters allows comparing bone formation in RKA scaffold with or without mechanical stimulation.…”

“…The magnitude and frequency of loading were determined such that the mechanical stimulus, S (Equation (1)), in the implanted scaffold is close to the calculated mechanical stimulus in RKA scaffold obtained from Box 1 (RoshanGhias et al 2010). The BVF in the animal study was measured using micro-CT imaging at different time points and into 16 donut-shaped concentric regions in the scaffold (Roshan-Ghias, Vogel, et al 2011). Spatial and temporal BVF data were then obtained for loaded and control scaffolds.…”