Several three-dimensional vascular models have been developed to study the effects of adding equations for large blood vessels to the traditional bioheat transfer equation of Pennes when simulating tissue temperature distributions. These vascular models include “transiting” vessels, “supplying” arteries, and “draining” veins, for all of which the mean temperature of the blood in the vessels is calculated along their lengths. For the supplying arteries this spatially variable temperature is then used as the arterial temperature in the bioheat transfer equation. The different vascular models produce significantly different locations for both the maximum tumor and the maximum normal tissue temperatures for a given power deposition pattern. However, all of the vascular models predict essentially the same cold regions in the same locations in tumors: one set at the tumors’ corners and another around the inlets of the large blood vessels to the tumor. Several different power deposition patterns have been simulated in an attempt to eliminate these cold regions; uniform power in the tumor, annular power in the tumor, preheating of the blood in the vessels while they are traversing the normal tissue, and an “optimal” power pattern which combines the best features of the above approaches. Although the calculations indicate that optimal power deposition patterns (which improve the temperature distributions) exist for all of the vascular models, none of the heating patterns studied eliminated all of the cold regions. Vasodilation in the normal tissue is also simulated to see its effects on the temperature fields. This technique can raise the temperatures around the inlet of the large blood vessles to the tumor (due to the higher power deposition rates possible), but on the other hand, normal tissue vasodilation makes the temperatures at the tumor corners slightly colder.
The Effects of Large Blood Vessels on Temperature Distributions During Simulated Hyperthermia
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Chen, Z., and Roemer, R. B. (November 1, 1992). "The Effects of Large Blood Vessels on Temperature Distributions During Simulated Hyperthermia." ASME. J Biomech Eng. November 1992; 114(4): 473–481. https://doi.org/10.1115/1.2894097
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