Thermal Effects of Laser-osteotomy on Bone: Mathematical Computation Using Maple

In recent years, interest in medical application of lasers especially as a surgical alternative is considerably increasing due to their distinct advantages such as non-contact intervention, bacteriostasis, less traumatization, minimal invasiveness, decreased bleeding and less heat damage. The present study aimed to evaluate the temperature changes and the consequent released thermal stress in cortical bone caused by an Erbium:yttrium aluminum garnet (Er:YAG) laser (Fideliss 320A, Fotona Inc., Deggingen, Germany) during osteotomy, using mathematical computation by means of Maple software, version 9.5 (Maplesoft, a division of Waterloo Maple Inc., Canada). The results obtained here were compared with the experimental measurements using Er:YAG laser in the osteotomy clinics. A bone slab with thickness of 1 mm was simulated in Maple software. Then, an Er:YAG laser emitting 100 μs pulses at a wavelength of 2940 nm were modeled. Two different clinical settings of the Er:YAG laser with 200 mJ and 400 mJ energies, both with 100 μs exposure and 500 μs silence were studied. To investigate the temperature distribution in the cortical bone, the time-dependent heat conduction equations were defined and solved in the Maple software. Finally, by defining the heat distribution function in the Maple, thermal stress in the bone was investigated. Results of the computations showed that, on the bone irradiated area (center of the bone surface) the maximum temperature rise was 0.8°C and 1.6°C, for 200 mJ and 400 mJ Er:YAG laser exposure, respectively. The temperature rise reached to its minimum at radial distances of 1.2 cm from the point of irradiated area for 200 mJ laser while it was 1.5 cm for 400 mJ laser. For 200 mJ laser the maximum derived radial (σ(rr)), axial (σ(zz)) and azimuthally (σ(θθ)) stress components were 0.20, 0.16 and 0.08 MPa, respectively. While, for 400 mJ laser the maximum derived σ(rr), σ(zz) and σ(θθ) stress components were 0.39, 0.31 and 0.16 MPa, respectively. These results confirm that use of 100 μs Er:YAG laser pulses with 500 μs silence at 200 and 400 mJ energies minimizes thermal tissue damage for the laser osteotomies, without continued water cooling (irrigation) on the exposed area.