Analytical solution of heat-transfer in central part of tibia bone tissue using non-Fourier heat equation with a laser heat source

Hyperbolic heat transfer equation considering a laser heat source is analytically investigated using Laplace transform method to study the temperature distribution in the central part of the tibia bone tissue. The target zone is the compact layer of tibia, and the laser irradiation in four near-surface points during 2 s is taken into account. Holmium-Yttrium-Aluminum-Garnet (Ho-YAG) laser is utilized in the simulations. Results indicate that there is a trilateral relationship among the temperature changes of various points in the tissue, the power used and the wavelength. While neglecting the effects of blood circulation upon laser interaction with the bone surface, the results reveal that the temperature of the points adjacent to the bone surface dramatically increases up to 85 degrees C. Meanwhile, the heat source is provided based on the Beer-Lambert law, and finally it demonstrates that the penetration depth exponentially reduces the intensity and causing considerable decrease in temperature. For the first time, the non-Fourier heat transfer equation was solved using the Laplace transform method for the tibia bone, and its results were compared with the numerical solution results using the Leap- Frog method. Knowing the temperature changes caused by laser inside the tissue is very crucial in Laser tissue welding, tissue ablation, photocoagulation and photo-thermal denaturation, angioplasty, treatment of granulation tissues, change and deformation of cartilage.