Recent developments in modeling heat transfer in blood perfused tissues

Abstract

Successful hyperthermia treatment of tumors requires understanding the attendant thermal processes in both diseased and healthy tissue. Accordingly, it is essential for developers and users of hyperthermia equipment to predict, measure and interpret correctly the tissue thermal and vascular response to heating. Modeling of heat transfer in living tissues is a means towards this end. Due to the complex morphology of living tissues, such modeling is a difficult task and some simplifying assumptions are needed. Some investigators have recently argued that Pennes' interpretation of the vascular contribution to heat transfer in perfused tissues fails to account for the actual thermal equilibration process between the flowing blood and the surrounding tissue and proposed new models, presumably based on a more realistic anatomy of the perfused tissue. The present review compares and contrasts several of the new bio-heat transfer models, emphasizing the problematics of their experimental validation, in the absence of measuring equipment capable of reliable evaluation of tissue properties and their variations that occur in the spatial scale of blood vessels with diameters less than about .2 mm. For the most part, the new models still lack sound experimental grounding, and in view of their inherent complexity, the best practical approach for modeling bio-heat transfer during hyperthermia may still be the Pennes model, providing its use is based on some insights gained from the studies described here. In such cases, these models should yield a more realistic description of tissue locations and/or thermal conditions for which the Pennes' model might not apply.

Tissue thermal conductivity by magnetic resonance thermometry and focused ultrasound heating

“…The assumption of nondirectionality is valid because temperature variations within the dense capillary network are small and do not create significant localized temperature gradients (2). The BHT thus offers a simple and practical solution if applied to tissue under appropriate conditions, as is required even with more sophisticated models that attempt to reflect heat transfer by perfusion more accurately (21). Without the need to model the complex geometry of larger vessels, the BHT has been successfully implemented in therapeutic hyperthermia and heat clearance methods for measuring perfusion (22).…”

Thermal Therapy, Part IV: Electromagnetic and Thermal Dosimetry

“…The Pennes model describes blood perfusion with acceptable accuracy if no large vessels are nearby. 107 …”

“…Modeling of heat transfer in living tissues is a means towards this end. Due to the complex morphology of living tissues, such modeling is diffi cult and requires some simplifi cation of assumptions 107 and, as a fi rst step, mathematical techniques for solving Maxwell's equations for reasonably accurate representations of the actual objects. Because of the mathematical diffi culties encountered in this calculation, a combination of techniques is used for the computation of the absorbed EM power distribution in the tissue.…”

Sensitivity of transient temperature field in domain of forearm insulated by protective clothing with respect to perturbations of external boundary heat flux

“…The transient temperature field in tissue subdomains is determined by a Fourier-type equation called the Pennes equation [1][2][3][4][5]. This equation contains two additional components (the source functions) connected with the blood perfusion and metabolism.…”