A mathematical model for neuron reorientation and axonal outgrowth on a cyclically stretched substrate

Throughout their lifetime, neurons are constantly exposed to a large variety of mechanical stimuli in many physiological circumstances. In this regard, experimental evidence demonstrated how mechanical cues play a central role in determining the direction and velocity of axonal outgrowth. In particular, neurons seeded on planar substrates undergoing periodic stretches have been shown to reorient almost perpendicularly to the main stretching direction, reaching a stable equilibrium orientation in correspondence with angles within the interval [60°, 90°]. The entire reorientation and outgrowth process is guided by a highly motile structure at the axon tip: the growth cone. In this Thesis, we present a new model for the reorientation and growth of neurons in response to cyclic stretching. A linear viscoelastic model for the growth cone reorientation with the addition of a stochastic term is merged with a moving-boundary model for tubulin-driven neurite growth to simulate the axonal pathfinding process. Various combinations of stretching frequencies and strain amplitudes have been tested, using the proposed model's numerical simulation. Specifically, simulations show that neurons tend to reorient almost perpendicularly to the stretching direction in great agreement with biological evidence. Moreover, the model captures the relation between the stretching condition and the velocity of reorientation. Indeed, numerical results show that as the frequency and amplitude of oscillation increase, neurons tend to reorient themselves more rapidly.