Wavelets approach for optimal boundary control of cellular uptake in tissue engineering

^†This paper is dedicated to the memory of Prof. Ibrahim Sadek.

Abstract

The control of the uptake of growth factors in tissue engineering is mathematically modelled by a partial differential equation subject to boundary and initial conditions. The main objective is to regulate cellular processes for the growth or regeneration of a tissue within an assigned terminal time. The techniques of basis function expansion and direct state parameterization were employed to yield efficient computational methods for this problem. Using Legendre and Chebyshev wavelets, the optimal control of the lumped-parameter system was transformed into a system of algebraic equations. The computational efficiency and effectiveness of the proposed method are illustrated by numerical examples.

Keywords:

• optimal control
• tissue engineering
• wavelets

2010 AMS Subject Classifications::

• 49J20
• 49N90

Notes

^† This paper is dedicated to the memory of Prof. Ibrahim Sadek.