Title page for ETD etd-09172004-113428

Type of Document Master's Thesis
Author Gayzik, Francis Scott
Author's Email Address sgayzik@wfubmc.edu
URN etd-09172004-113428
Title Optimal Control of Thermal Damage to Biological Materials
Degree Master of Science
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Scott, Elaine P. Committee Chair
Diller, Thomas E. Committee Member
Loulou, Tahar Committee Member
  • conjugate gradient method
  • arrhenius damage model
  • thermal dose
  • finite difference
  • optimal control
Date of Defense 2004-09-03
Availability unrestricted
Hyperthermia is a cancer treatment modality that raises cancerous tissue to cytotoxic temperature levels for roughly 30 to 45 minutes. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol to be used in a hyperthermia treatment. This thesis presents a method to optimize a hyperthermia treatment heating protocol. An algorithm is developed which recovers a heating protocol that will cause a desired amount of thermal damage within a region of tissue. The optimization algorithm is validated experimentally on an albumen tissue phantom.

The transient temperature distribution within the region is simulated using a two- dimensional, finite-difference model of the Pennes bioheat equation. The relationship between temperature and time is integrated to produce a damage field according to two different models; Henriques'' model and the thermal dose model (Moritz and Henriques (1947)), (Sapareto and Dewey (1984)). A minimization algorithm is developed which re duces the value of an objective function based on the squared difference between an optimal and calculated damage field. Either damage model can be used in the minimization algorithm. The adjoint problem in conjunction with the conjugate gradient method is used to minimize the objective function of the control problem.

The flexibility of the minimization algorithm is proven experimentally and through a variety of simulations. With regards to the validation experiment, the optimal and recovered regions of permanent thermal damage are in good agreement for each test performed. A sensitivity analysis of the finite difference and damage models shows that the experimentally-obtained extent of damage is consistently within a tolerable error range.

Excellent agreement between the optimal and recovered damage fields is also found in simulations of hyperthermia treatments on perfused tissue. A simplified and complex model of the human skin were created for use within the algorithm. Minimizations using both the Henriques'' model and the thermal dose model in the objective function are performed. The Henriques'' damage model was found to be more desirable for use in the minimization algorithm than the thermal dose model because it is less computationally intensive and includes a mechanism to predict the threshold of permanent thermal damage. The performance of the minimization algorithm was not hindered by adding complexity to the skin model. The method presented here for optimizing hyperthermia treatments is shown to be robust and merits further investigation using more complicated patient models.

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