Mathematical Modeling of Laser Ablation

ABSTRACT: In new surgery, there are various surgical methods for heating human tissue which are applied in an accurate and secure way. All these methods are based on particular applicator such as laser, radiofrequency device and microwave. In the past, Pennes defined bio-heat (BE) equation by considering Fourier’s law of heat conduction to model heat transfer in biological tissues. With the progression of modern operational methods, medical therapies involve shorter time steps and higher heat fluxes, thus the classical model has been become inappropriate. The fact is that, the heat flux does not have enough time to propagate after imposing thermal energy. Therefore, this thesis introduces a more precise and pragmatic model by using of hyperbolic bio-heat equation (HBE) which uses thermal relaxation time that is necessary for heat propagation after radiation. There are different types of numerical methods which are applied to analysis temperature distribution during laser heating. One of the frequently applied numerical methods is Finite Difference Method (FDM). In this study, FDM method is used for analyzing temperature profile for both standard and hyperbolic bio-heat equations in 7 different penetration depths. This analysis has been performed for two various initial temperatures 35°C and 40°C, the differences between two models for both initial temperatures have been reported and the effect of increasing initial temperature on the behaviors of two model has been investigated. To prove some specifications and benefits of the modified model, the results received from tissue heating with great energy fluxes are applied to correct Hyperopia (far-sightedness). Keyword: Laser, heat transfer, biological tissues, bio-heat equation, cornea, modeling, Finite Difference Method. …………………………………………………………………………………………………………………………