Mathematical modeling of guided neurite extension in an engineered conduit with multiple concentration gradients of nerve growth factor (NGF).

Neurotrophic factors such as nerve growth factor (NGF) provide essential cues to navigate growing axon toward their targets. Concentration and concentration gradient of NGF are key parameters affecting the growth rate and direction of neurites and axons. However, the maximum distance for guided nerve growth under stimulation of a single concentration gradient is limited and is thus unfavorable in nerve regeneration. Since the sensitivity of PC12 cells to NGF signals is restorable even after brief removal of the factors, exposure to multiple concentration gradients of the factor can achieve longer distances and greater rates of guided growth. In this study, a mathematical model simulating nerve growth in a virtually constructed nerve conduit incorporating multiple NGF concentration gradients is established. Using a genetic algorithm, optimized initial profiles of NGF able to achieve 4.5 cm of guided growth with a significantly improved growth rate has been obtained. The model also predicts an inverse relationship between the diffusion coefficient of the factor and the neurite growth rate. This model provides a useful tool for evaluating various conduit designs before fabrication and evaluation.