Theoretical analysis on thermal treatment of skin with repetitive pulses

Thermal ablation is an efficient method of medical treatment, such as cancer therapy, wound closure, laser cutting, freckle removal and other treatments. In order to guarantee the curative effect and the safety of the patients, the thermal response of the tissue which is subjected to the heat source need to be carefully monitored. However, it is too difficult to achieve real-time monitoring on the full-field temperature. In the present study, efforts were made to build up a theoretical model for the prediction of the thermal response in the human skin. The Dual-Phase-Lag (DPL) bio-heat transfer model and the Henrique’s burn assessment model were employed to describe the interaction of multi-pulse heat source and the skin. The repeated multi-pulse laser is a common heat source in the thermal treatment and the thermal responses of the skin would be complicated under the common effects of the non-Fourier effects and the multi-pulse source. The Green’s function approach was used to solve the governing equations analytically. The closed-form solution for the temperature distribution of the skin was obtained and the thermal damage was estimated based on the temperature results. The influences of the biological parameters (the phase lags of the heat flux and the temperature gradient) and the heat source parameters (the pulse number and the duty ratio) on the temperature distribution, the burn degree and the irreversible burn depth of the irradiated region were discussed.

SEMI-ANALYTICAL SOLUTION OF BIO-HEAT CONDUCTION FOR MULTI-LAYERS SKIN SUBJECTED TO LASER HEATING AND FLUID COOLING

A semi-analytical solution of bio-heat conduction on the three-layer skin is presented. The performance of the typical heat treatment (heating by laser and cooling by fluid at skin surface) is studied. The transient temperature field and thermal damage of skin are investigated. Effects of several parameters on temperature variation and thermal damage are discussed. The results of the paper will be useful for heat therapy in clinics. In addition, the presented result is very consistent to that by the finite element method. The semi-analytical method can be easily applied for solving the general problem of heat conduction in any multilayer structure.

FRACTIONAL MODELING OF HYPERBOLIC BIOHEAT TRANSFER EQUATION DURING THERMAL THERAPY

In this paper, we have developed a fractional hyperbolic bioheat transfer (FHBHT) model by applying fractional Taylor series formula to the single-phase-lag constitutive relation. A new hybrid numerical scheme that combines the multi-resolution and multi-scale computational property of Legendre wavelets based on fractional operational matrix has been used to find the numerical solution of the present problem. This study demonstrates that FHBHT model can provide a unified approach for analyzing heat transfer within living biological tissues, as standard hyperbolic bioheat transfer (SHBHT) and Pennes models are particular cases of FHBHT model. The effect of phase lag time and order of fractional derivative on temperature distribution within living biological tissues for both SHBHT and FHBHT models have been studied and shown graphically. It has been observed that thermal signal propagates more easily with larger values of order of fractional derivative within living biological tissues. The time interval for achieving temperature range of thermal treatment for different models have been studied and compared. It is least for Pennes model, highest for FHBHT model and in between them for SHBHT model. The whole analysis is presented in dimensionless form.

NEW COMPUTATIONAL APPROACHES FOR BIOPHYSICAL HEAT TRANSFER IN TISSUE UNDER ULTRASONIC WAVES: THE VARIATIONAL ITERATION AND CHEBYSCHEV SPECTRAL SIMULATIONS

A mathematical and numerical study is presented for simulating temperature distribution in a two-dimensional tissue medium using Pennes bioheat transfer equation, when the tissue is subjected to ultrasonic waves. Following nondimensionalization of the governing partial differential equation, a novel variational iteration method (VIM) solution is developed. This excellent technique introduced by He [Variational iteration method — a kind of non-linear analytical technique: Some examples, Int J Non-Linear Mech.34:699–708, 1999] employs Lagrange multipliers which can be identified optimally via variational theory. The space and time distributions of temperature are studied and solutions visualized via Mathematica. The influence of thermal conductivity and relaxation time are also examined. Excellent stability and convergence characteristics of VIM are demonstrated. Validation is achieved with a Chebyschev spectral collocation method (CSCM). The present work demonstrates the excellent potential of this powerful semi-numerical method in nonlinear biological heat transfer and furthermore provides an alternative strategy to conventional finite element and finite difference computational simulations. The model finds applications in minimally-invasive spinal laser treatments, glaucoma therapy in ophthalmology and thermoradiotherapy for malignant tumors.