Optimal control of one-dimensional cellular uptake in tissue engineering

Masako Kishida, Ashlee N. Ford Versypt, Daniel W. Pack, Richard D. Braatz

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Pages (from-to)680-695
Number of pages16
JournalOptimal Control Applications and Methods
Issue number6
StatePublished - Nov 2013


  • boundary control
  • distributed parameter systems
  • partial differential equations
  • stem cell tissue engineering
  • systems biology
  • tissue engineering

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Control and Optimization
  • Applied Mathematics


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