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Optimal Control of One-dimensional Cellular Uptake in Tissue Engineering.

Masako Kishida1, Ashlee N Ford Versypt2, Daniel W Pack2

  • 1University of Illinois at Urbana-Champaign, Urbana IL ; Massachusetts Institute of Technology, Cambridge, MA.

Optimal Control Applications & Methods
|March 18, 2014
PubMed
Summary

This study compares four methods for controlling growth factor uptake in tissue engineering. The method of moments is efficient, while model predictive control reduces computational cost for optimal tissue regeneration control.

Keywords:
Boundary controlDistributed parameter systemsPartial differential equationsStem cell tissue engineeringSystems biologyTissue engineering

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Area of Science:

  • Biomedical Engineering
  • Control Theory
  • Tissue Engineering

Background:

  • Controlling cellular processes is crucial for tissue engineering and regeneration.
  • Spatially and temporally regulating growth factor uptake is key to achieving desired tissue outcomes.

Purpose of the Study:

  • To formulate and solve a control problem for optimizing growth factor uptake in tissue engineering.
  • To compare four distinct approaches for determining optimal boundary control trajectories in a 1D distributed parameter model.

Main Methods:

  • Basis function expansion
  • Method of moments
  • Internal Model Control (IMC)
  • Model Predictive Control (MPC)

Main Results:

  • The method of moments offers computational efficiency and enforces non-negativity constraints on control inputs.
  • Model Predictive Control (MPC) significantly reduces computational cost compared to simultaneous trajectory optimization.
  • All four methods were evaluated for a 1D distributed parameter model involving reaction, diffusion, and convection.

Conclusions:

  • The method of moments is computationally efficient for controlling growth factor uptake.
  • MPC offers a reduced computational cost for optimizing control trajectories.
  • Combining multiple control approaches shows promise for complex, multi-dimensional tissue engineering problems.