Optimal control of cellular uptake in tissue engineering

The optimal control of a distributed parameter system with reaction, diffusion, and convection is investigated. The problem is motivated by tissue engineering where the control of the uptake of growth factors (signaling molecules) is required to spatially and temporally regulate cellular processes for the growth or regeneration of a tissue. Four approaches for solving the optimal control problem are compared: (i) basis function expansion, (ii) method of moments, (iii) internal model control, and (iv) model predictive control. This comparison suggests that these approaches should be combined to solve the optimal control problem for multiple spatial dimensions.