Biomedical subjects

C T Liauh

Publications and source records attributed to C T Liauh.

4 recordsLinked to original sources

PubMed1993

Comparison of the adjoint and influence coefficient methods for solving the inverse hyperthermia problem.

An adjoint formulation is derived and used to determine the elements in the Jacobian matrix associated with the inverse problem of estimating the blood perfusion and temperature fields during hyperthermia cancer treatments. This method and a previously developed influence coefficient method for obtaining that matrix are comparatively evaluated by solving a set of numerically simulated inverse hyperthermia problems. The adjoint method has the advantage of requiring fewer solutions of the bioheat transfer equation to estimate the Jacobian than does the influence coefficient method when the number of measurement sensors is significantly smaller than the number of unknown parameters. Thus, it could be a preferable method to use in hyperthermia applications where the number of sensors is strictly limited by patient considerations. However, the adjoint method requires that CPU time intensive convolutions be numerically evaluated. Comparisons of the performance of the adjoint formulation and the influence coefficient method show that, first, there is a critical ratio of the number of measurement sensors to the number of unknown parameters at which the CPU time per iteration required to calculate the Jacobian matrix is the same for both methods. The adjoint method is faster than the influence coefficient method only when the value of the ratio is less than that critical value. For the hyperthermia problems investigated in the present study, this only occurs for cases with a very small number of measurement sensors. This presents a potential problem for clinical applications because the fewer measurement sensors used, the less information that can be gathered to correctly solve the inverse problem.(ABSTRACT TRUNCATED AT 250 WORDS)

Blood Flow Velocity↗

PubMed1993

Multiple minima in inverse hyperthermia temperature estimation problems.

Using one-, two-, and three-dimensional numerical simulation models it is shown that multiple minima solutions exist for some inverse hyperthermia temperature estimation problems. This is a new observation that has important implications for all potential applications of these inverse techniques. The general conditions under which these multiple minima occur are shown to be solely due to the existence of symmetries in the bio-heat transfer model used to solve the inverse problem. General rules for determining the number of these global minimum points in the unknown parameter (perfusion) space are obtained for several geometrically symmetric (with respect to the sensor placement and the inverse case blood perfusion model) one-, two-, and three-dimensional problem formulations with multiple perfusion regions when no model mismatch is present. As the amount of this symmetry is successively reduced, all but one of these global minima caused by symmetry become local minima. A general approach for (a) detecting when the inverse algorithm has converged to a local minimum, and (b) for using that knowledge to direct the search algorithm toward the global minimum is presented. A three-dimensional, random perfusion distribution example is given which illustrates the effects of the multiple minima on the performance of a state and parameter estimation algorithm. This algorithm attempts to reconstruct the entire temperature field during simulated hyperthermia treatments based on knowledge of measured temperatures from a limited number of locations.

Algorithms↗

PubMed1993

A semilinear state and parameter estimation algorithm for inverse hyperthermia problems.

An improved state and parameter estimation algorithm has been developed which decreases the total computational time required to accurately reconstruct complete hyperthermia temperature fields. Within this improved iterative estimation algorithm, if the change in the unknown perfusion parameters is small a linear approximation scheme is implemented in which the old Jacobian matrix (the sensitivity matrix) is used, instead of recalculating the new Jacobian matrix for the next iteration. In the hyperthermia temperature estimation problem the relationship between the temperature and the blood perfusion based on the bioheat transfer equation is generally nonlinear. However, the temperature can be approximated as a linear function of the blood perfusion over a certain range thus allowing this improved approach to work. Results show that if the temperature is approximated as a linear (or quasi-linear) function of the blood perfusion, the linearizing approach considerably reduces the CPU time required to accurately reconstruct the temperature field. The limiting case of implementing this approach is to calculate the Jacobian matrix for each iteration, which is identical to the approach used in the original nonlinear algorithm. Critical values of determining whether or not there is a need to recalculate the new Jacobian matrix during the iterations are presented for several inverse hyperthermia temperature estimation problems.

Algorithms↗

PubMed1991

Estimating three-dimensional temperature fields during hyperthermia: studies of the optimal regularization parameter and time sampling period.

During hyperthermia therapy it is desirable to know the entire temperature field in the treatment region. However, accurately inferring this field from the limited number of temperature measurements available is very difficult, and thus state and parameter estimation methods have been used to attempt to solve this inherently ill-posed problem. To compensate for this ill-posedness and to improve the accuracy of this method, Tikhonov regularization of order zero has been used to significantly improve the results of the estimation procedure. It is also shown that the accuracies of the temperature estimates depend upon the value of the regularization parameter, which has an optimal value that is dependent on the perfusion pattern and magnitude. In addition, the transient power-off time sampling period (i.e., the length of time over which transient data is collected and used) influences the accuracy of the estimates, and an optimal sampling period is shown to exist. The effects of additive measurement noise are also investigated, as are the effects of the initial guess of the perfusion values, and the effects of both symmetric and asymmetric blood perfusion patterns. Random perfusion patterns with noisy data are the most difficult cases to evaluate. The cases studied are not a comprehensive set, but continue to show the feasibility of using state and parameter estimation methods to reconstruct the entire temperature field.

Algorithms↗