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Comparison of the adjoint and influence coefficient methods for solving the inverse hyperthermia problem
C T Liauh1, R G Hills, R B Roemer
1Aerospace and Mechanical Engineering Department, University of Arizona, Tucson 85721.
Journal of Biomechanical Engineering
|February 1, 1993
Summary
The adjoint method offers a faster way to estimate Jacobian matrices for hyperthermia treatments when sensor numbers are limited. However, its computational efficiency depends on the sensor-to-parameter ratio, posing challenges for clinical applications.
Area of Science:
- Biomedical Engineering
- Computational Physics
- Medical Imaging
Background:
- Hyperthermia cancer treatments require accurate estimation of blood perfusion and temperature.
- Inverse problems are crucial for determining these parameters from sensor data.
- Existing methods for Jacobian matrix calculation have limitations.
Purpose of the Study:
- To derive and evaluate an adjoint formulation for Jacobian matrix estimation in hyperthermia.
- To compare the adjoint method with the influence coefficient method.
- To assess the computational efficiency and applicability of the adjoint method.
Main Methods:
- Derivation of an adjoint formulation for Jacobian matrix calculation.
- Numerical simulation of inverse hyperthermia problems.
- Comparative analysis of adjoint and influence coefficient methods based on CPU time and accuracy.
Main Results:
- The adjoint method requires fewer bioheat transfer equation solutions when sensor count is less than parameter count.
- A critical ratio exists where both methods have similar CPU time per iteration.
- The adjoint method is faster only when this ratio is below the critical value, often with limited sensors.
Conclusions:
- The adjoint method is advantageous for hyperthermia with limited sensors but requires computationally intensive convolutions.
- Its speed advantage is realized only at low sensor-to-parameter ratios.
- Clinical application may be limited by the trade-off between sensor number and data quality for accurate inverse problem solutions.