Optimal Control of One-dimensional Cellular Uptake in Tissue Engineering

A control problem motivated by tissue engineering is formulated and solved in which control of the uptake of growth factors (signaling molecules) is necessary to spatially and temporally regulate cellular processes for the desired growth or regeneration of a tissue. Four approaches are compared for determining 1D optimal boundary control trajectories for a distributed parameter model with reaction, diffusion, and convection: (i) basis function expansion, (ii) method of moments, (iii) internal model control (IMC), and (iv) model predictive control (MPC). The proposed method-of-moments approach is computationally efficient while enforcing a non-negativity constraint on the control input. While more computationally expensive than methods (i)-(iii), the MPC formulation significantly reduced the computational cost compared to simultaneous optimization of the entire control trajectory. A comparison of the pros and cons of each of the four approaches suggests that an algorithm that combines multiple approaches is most promising for solving the optimal control problem for multiple spatial dimensions.