Optimal control of one-dimensional cellular uptake in tissue engineering
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Braatz_Optimal control.pdf
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Author(s)
Kishida, Masako
Ford Versypt, Ashlee N.
Pack, Daniel W.
Braatz, Richard D.
Date Issued
August 2012
Journal
Optimal Control Applications and Methods
Publisher
Wiley Blackwell
Citation
Kishida, Masako, Ashlee N. Ford Versypt, Daniel W. Pack, and Richard D. Braatz. “Optimal Control of One-Dimensional Cellular Uptake in Tissue Engineering.” Optim. Control Appl. Meth. 34, no. 6 (August 23, 2012): 680–695.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
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DOI of Published Version
https://doi.org/10.1002/oca.2047
