Bioheat transfer problem for one-dimensional spherical biological tissues

Commentary on the clinical and preclinical dosage limits of interstitially administered magnetic fluids for therapeutic hyperthermia based on current practice and efficacy models

“…Given these parameters, various theoretical models exist that describe the expected biophysical heat flows in different conditions, which we can use to predict in silico the temperature increase DT at and around the injection site. Surveying a selection of recent publications on such models in the field of magnetic hyperthermia [65][66][67][68][69][70][71][72], two things are apparent: (i) that the methods that different authors adopt to address the problem are many and varied, and can be mathematically very complex; and (ii) they all take as their starting point the "Pennes equation":…”

“…In this paper, it is not our intention to critique the various available bioheat models for magnetic heating, nor do we wish to introduce a comprehensive but complex model that covers multiple scenarios such as time-dependent effects, thermally-varying perfusion or variations in metabolic rate between tumour tissue and healthy tissue. Such considerations have been covered in other works, including those already cited [65][66][67][68][69][70][71][72]. Instead, we present here a simple analytical model that enables a "first approximation" predictive step to be taken in the translation of magnetic hyperthermia, directed towards treatment planning.…”

Numerical simulation of dual-phase-lag bioheat transfer model during thermal therapy

“…Radio-frequency ablation uses a heating probe and can be approximated by axisymmetric or spherical symmetric coordinates as the study by Haugk et al [20] suggests. Cheng and Liu [21] , Kengne and Lakhssasi [22] numerically studied heat transport phenomenon in biological tissues using spherical coordinates. Akbarzadeh and Chen [23] has derived heat conduction equations based on DPL theory and different coordinate system.…”

Validating the relationship between burn temperature, duration of exposure and tissue injury severity for scald burns

“…Mathematical models of heat transfer in skin are traditionally based on the Pennes bioheat equation (75,200,201). This model is an extension of the standard linear heat equation (202,203) with an additional source term that accounts for thermal energy loss (200,201).…”

“…Often the source term is used to represent loss to the blood supply, which is known as perfusion (75,200,201). Studies that directly combine mathematical modelling with comprehensive in vivo experimental data sets are scarce.…”