RF tumour ablation: Computer simulation and mathematical modelling of the effects of electrical and thermal conductivity

Abstract

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

Hepatic radiofrequency ablation at low frequencies preferentially heats tumour tissue

“…The difference between normal and cancer tissue is especially pronounced in the breast due to the high fat content of breast tissue [9] and a recent modelling study suggested taking advantage of this difference to preferentially ablate breast tumours but not surrounding tissue [10]. For RF tumour ablation, two recent modelling studies have shown that differences in electrical conductivity between tumour and surrounding normal tissue significantly affect tissue heating [11,12].…”

Computer modelling of an impedance-controlled pulsing protocol for RF tumour ablation with a cooled electrode

“…To date, computer studies on RFA have examined the effect of specific factors related to the procedure and different modeling approaches [4][5][6][7][8][9][10][11]. None have focused on a direct comparison of different experimental results in terms of coagulation zone size and the evolution of electrical variables.…”

“…In some cases, the model simply reduces the applied voltage to the maximum level at which no tissue is heated beyond 100ºC [4][5][6]. Others do not provide details of the RF power delivery protocol [7], so we cannot be sure whether an impedance-controlled pulsing protocol was really modeled.…”

“…Numerous modeling studies have been published on RFA with needle-like cooled electrodes [4][5][6][7][8][9][10][11] although they rarely provide sufficient details of the pulsing protocol used.…”

Numerical Study of the Influence of Water Evaporation on Radiofrequency Ablation

“…Models have been developed to simulate the temperature distributions of tissue during the treatment [4,[23][24][25][26]. The complexity of the tumor composition, the influence of heterogeneous electrical conductivity, thermal conductivity, blood perfusion rate, and the specific distribution of blood vessels on the results have been studied [27][28][29][30][31][32][33][34][35].…”