Biomedical subjects
Publications and source records attributed to H S Tharp.
A nonlinear, time-delay differential equation is postulated as a possible structure to describe the temperature dynamics at a point inside living tissue. The presented analysis explains how this differential equation can lead to four different temperature response types that have been previously observed in vivo.
Improved hyperthermia applicator technology is allowing finer spatial power resolution within the heated tissue volume. Effective utilization of these planar applicator arrays requires an understanding of the interrelationships between the lateral dimensions of the tumor and the applicators, the power field produced by the applicators, the amount of surface cooling, the tumor tissue blood perfusion, and the normal tissue blood perfusion. These interrelationships are investigated using three-dimensional power patterns and temperature fields produced by optimizing the power amplitudes of the individual applicators located within an array of small, but finite, planar applicators. Five major conclusions are obtained. First, optimization works and is effective in determining optimal power fields. Second, for optimal treatments the lateral dimensions of a single superficial applicator need to extend beyond the tumor boundary. Third, surface cooling is needed to reduce the high normal tissue temperatures at shallow depths. Fourth, finer power resolution becomes more important as the tumor size decreases, but, little improvement in the temperature field is achieved beyond a 3 x 3 array configuration. Fifth, increasing the normal blood perfusion rate can decrease the temperature on the tumor boundary if direct power deposition on that boundary is unavailable.
This paper analyzes the feasibility of using reduced-order modeling techniques in the design of multiple-input, multiple-output (MIMO) hyperthermia temperature controllers. State space thermal models are created based upon a finite difference expansion of the bioheat transfer equation model of a scanned focused ultrasound system (SFUS). These thermal state space models are reduced using the balanced realization technique, and an order reduction criterion is tabulated. Results show that a drastic reduction in model dimension can be achieved using the balanced realization. The reduced-order model is then used to design a reduced-order optimal servomechanism controller for a two-scan input, two thermocouple output tissue model. In addition, a full-order optimal servomechanism controller is designed for comparison and validation purposes. These two controllers are applied to a variety of perturbed tissue thermal models to test the robust nature of the reduced-order controller. A comparison of the two controllers validates the use of open-loop balanced reduced-order models in the design of MIMO hyperthermia controllers.
Multiple model estimation is a viable technique for dealing with the spatial perfusion model mismatch associated with hyperthermia dosimetry. Using multiple models, spatial discrimination can be obtained without increasing the number of unknown perfusion zones. Two multiple model estimators based on the extended Kalman filter (EKF) are designed and compared with two EKFs based on single models having greater perfusion zone segmentation. Results given here indicate that multiple modelling is advantageous when the number of thermal sensors is insufficient for convergence of single model estimators having greater perfusion zone segmentation. In situations where sufficient measured outputs exist for greater unknown perfusion parameter estimation, the multiple model estimators and the single model estimators yield equivalent results.
The success of treating cancerous tissue with heat depends on the temperature elevation, the amount of tissue elevated to that temperature, and the length of time that the tissue temperature is elevated. In clinical situations the temperature of most of the treated tissue volume is unknown, because only a small number of temperature sensors can be inserted into the tissue. A state space model based on a finite difference approximation of the bioheat transfer equation (BHTE) is developed for identification purposes. A full-order extended Kalman filter (EKF) is designed to estimate both the unknown blood perfusion parameters and the temperature at unmeasured locations. Two reduced-order estimators are designed as computationally less intensive alternatives to the full-order EKF. Simulation results show that the success of the estimation scheme depends strongly on the number and location of the temperature sensors. Superior results occur when a temperature sensor exists in each unknown blood perfusion zone, and the number of sensors is at least as large as the number of unknown perfusion zones. Unacceptable results occur when there are more unknown perfusion parameters than temperature sensors, or when the sensors are placed in locations that do not sample the unknown perfusion information.
We examine the ability of neural networks to estimate the tissue perfusion values present and the minimum temperature in numerically calculated (Pennes, Bioheat Transfer Equation) steady-state hyperthermia temperature fields based on a limited number of measured temperatures within this field A hierarchical system of neural networks consisting of a first layer of pattern recognizing neural networks and a second layer of hypersurface reconstructing neural networks is shown to be capable of estimating these variables within a selected error tolerance. The results indicate that estimating the minimum tumour temperature directly with the system of neural networks may be more effective than using the indirect method of numerically recreating a temperature field with perfusion estimates and then obtaining the minimum tumour temperature from the estimated temperature field. Additional results indicate that if the locations of the measured temperatures within the temperature field are selected appropriately, the hierarchical system of neural networks can tolerate a moderate level of model mismatch. This model mismatch can come from errors in modelling the tumour boundaries, the sensor locations, or the magnitude of the power deposition. This paper is not intended to assess or demonstrate clinical applicability but to be a first step in investigating the feasibility of neural networks for parameter estimation related to hyperthermia studies.