This paper is the expanded version of a previously presented conference paper .
Optimal control of one-dimensional cellular uptake in tissue engineering†
Article first published online: 22 AUG 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Optimal Control Applications and Methods
Volume 34, Issue 6, pages 680–695, November/December 2013
How to Cite
Kishida, M., Ford Versypt, A. N., Pack, D. W. and Braatz, R. D. (2013), Optimal control of one-dimensional cellular uptake in tissue engineering. Optim. Control Appl. Meth., 34: 680–695. doi: 10.1002/oca.2047
- Issue published online: 25 OCT 2013
- Article first published online: 22 AUG 2012
- Manuscript Accepted: 3 JUL 2012
- Manuscript Received: 28 MAR 2012
- stem cell tissue engineering;
- tissue engineering;
- systems biology;
- distributed parameter systems;
- partial differential equations;
- boundary control
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 one-dimensional 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, and (iv) model predictive control (MPC). The proposed method of moments approach is computationally efficient while enforcing a nonnegativity constraint on the control input. Although more computationally expensive than methods (i)–(iii), the MPC formulation significantly reduced the computational cost compared with 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. Copyright © 2012 John Wiley & Sons, Ltd.