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

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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 °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 expdR σ f expgσ) for RF generator-energy dependent situations and (T = h + k expmR + n exppσ) for RF generator-current limited situations, where T is the temperature (°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.