Moros, E. G., A. W. Dutton, R. B. Roemer, M. Burton and K. Hynynen. Experimental evaluation of two simple thermal models using hyperthermia in muscle in vivo. Int J Hyperthermia. 9:581-98., 1993.

The predictions from two simple field equation models for calculating temperature distributions in tissue, namely, the Pennes' bioheat transfer equation (BHTE) and an effective thermal conductivity equation (ETCE), were compared to in vivo experimental temperature measurements made under hyperthermic conditions generated by scanned focused ultrasound. The models were kept simple (i.e. homogenous isotropic properties, no separate blood vessels included) in order to concentrate attention on the predictive abilities of these field equations using a minimum number of free parameters. Simulated results were fitted to the experimental data (multiple, linear temperature profiles in the thigh muscles of greyhound dogs) by minimizing a performance index using a golden section searth. This search determined a value for the single free parameter in each model (blood perfusion in the BHTE, and effective thermal conductivity in the ETCE) which minimized the square error difference between the experimental and simulated temperatures. The results showed that (a) the simple BHTE model could qualitatively reproduce the major features of the temperature patterns seen experimentally better than the ETCE model could, and (b) the simple BHTE model produced better quantitative fits to the experimental data than did the simple ETCE model. In addition, blood perfusion predictions from the BHTE model compared well to measurements done with coloured microspheres. Finally, the experimental results showed that individual, large blood vessels appeared to have a major influence in producing asymmetries in the experimental data in 21% of the measured temperature profiles.