Computer simulation of heat and mass transfer in tissue during high-intensity long-range laser irradiation

Modeling and ex vivo experimental validation of liver tissue carbonization with laser ablation

OBJECTIVE

The purpose of this study was to model the process of liver tissue carbonization with laser ablation (LA).

METHODS

A dynamic heat source model was proposed and combined with the light distribution model as well as bioheat transfer model to predict the development of tissue carbonization with laser ablation (LA) using an ex vivo porcine liver tissue model. An ex vivo laser ablation experiment with porcine liver tissues using a custom-made 1064 nm bare fiber was then used to verify the simulation results at 3, 5, and 7 W laser administrations for 5 min. The spatiotemporal temperature distribution was monitored by measuring the temperature changes at three points close the fiber during LA. Both the experiment and simulation of the temperature, tissue carbonization zone, and ablation zone were then compared.

RESULTS

Four stages were recognized in the development of liver tissue carbonization during LA. The growth of the carbonization zone along the fiber axial and radial directions were different in the four stages. The carbonization zone along the fiber axial direction (L2) grew in the four stages with a sharp increase in the initial period and a minor increase in Stage 4. However, the change in the carbonization zone along the fiber radial direction (D2) increased dramatically (Stage 1) to a long-time plateau (Stages 2 and 3) followed by a slow growth in Stage 4. An acceptable agreement between the computer simulation and ex vivo experiment in the temperature changes at the three points was found at all three testing laser administrations. A similar result was also obtained for the dimensions of coagulation zone and ablation zone between the computer simulation and ex vivo experiment (carbonization zone: 2.99± 0.10 vs. 2.78 mm², 67.39± 0.09 vs. 63.53 mm², and 90.53± 0.11 vs. 85.15 mm²; ablation zone: 68.95± 0.28 vs. 65.29 mm², 182.11± 0.24 vs. 213.81 mm², and 244.80± 0.06 vs. 251.79 mm² at 3, 5, and 7 W, respectively).

CONCLUSION

This study demonstrates that the proposed dynamic heat source model combined with the light distribution model as well as bioheat transfer model can predict the development of liver tissue carbonization with an acceptable accuracy. This study contributes to an improved understanding of the LA process in the treatment of liver tumors.

Simulation of laser-induced thermotherapy using a dual-reciprocity boundary element model with dynamic tissue properties

This paper presents a nonlinear dual-reciprocity boundary element method (DRBEM) for bioheat transfer in laser-induced thermotherapy. The nonlinearity stems from the dynamic changes of tissue thermophysical and optical properties and the blood perfusion rate during laser heating. The proposed DRBEM is coupled with a modified Monte Carlo method and the Arrhenius rate equation to investigate laser light propagation, bioheat transfer, and irreversible thermal damage in tumors. The computer code is justified by comparing the DRBEM results with the finite-difference results. The photothermal processes in interstitial laser thermotherapy with single or double laser fiber scattering applicators are chosen as the demonstrative examples. The dynamic nature, together with the unique advantages of "boundary-only" and excellent adaptability to complex anatomical geometries that the DRBEM method offers, makes the present nonlinear DRBEM a powerful tool for analysis and optimization of the parameters in laser surgical procedure.

Modelling of experimentally created partial-thickness human skin burns and subsequent therapeutic cooling: a new measure for cooling effectiveness

Rapid post-injury cooling of a skin burn has been shown to have both symptomatic and therapeutic benefits. However, the latter cannot be explained by temperature reduction alone, and must thus be secondary to an altered biological response. In this study, we construct a computational model to calculate the heat transfer and damage accumulation in human skin during and after a burn. This enables us to assess the effectiveness of various cooling protocols (involving both free and forced convection to air and water respectively) in terms of their reduction in Arrhenius tissue damage. In this process, we propose an extension of the Arrhenius damage model in the form of a new measure xi, which estimates the relevance of post-burn accrued damage. It was found that the reduction in Arrhenius damage integrals near the skin surface was too small to be physiologically relevant. Hence our results confirm that while the reduction in tissue temperatures is indeed quicker, the therapeutic benefit of cooling cannot be explained by thermal arguments (i.e. based on Arrhenius damage models) alone. We plan to validate this hypothesis by conducting future microarray analyses of differential gene expression in cooled and non-cooled burn lesions. Our computational model will support such experiments by calculating the necessary conditions to produce a burn of specified severity for a given experimental setup.

Numerical study on the thawing process of biological tissue induced by laser irradiation

Most of the laser applications in medicine and biology involve thermal effects. The laser-tissue thermal interaction has therefore received more and more attentions in recent years. However, previous works were mainly focused on the case of laser heating on normal tissues (37 degrees C or above). To date, little is known on the mechanisms of laser heating on the frozen biological tissues. Several latest experimental investigations have demonstrated that lasers have great potentials in tissue cryopreservation. But the lack of theoretical interpretation limits its further application in this area. The present paper proposes a numerical model for the thawing of biological tissues caused by laser irradiation. The Monte Carlo approach and the effective heat capacity method are, respectively, employed to simulate the light propagation and solid-liquid phase change heat transfer. The proposed model has four important features: (1) the tissue is considered as a nonideal material, in which phase transition occurs over a wide temperature range; (2) the solid phase, transition phase, and the liquid phase have different thermophysical properties; (3) the variations in optical properties due to phase-change are also taken into consideration; and (4) the light distribution is changing continually with the advancement of the thawing fronts. To this end, 15 thawing-front geometric configurations are presented for the Monte Carlo simulation. The least-squares parabola fitting technique is applied to approximate the shape of the thawing front. And then, a detailed algorithm of calculating the photon reflection/refraction behaviors at the thawing front is described. Finally, we develop a coupled light/heat transport solution procedure for the laser-induced thawing of frozen tissues. The proposed model is compared with three test problems and good agreement is obtained. The calculated results show that the light reflectance/transmittance at the tissue surface are continually changing with the progression of the thawing fronts and that lasers provide a new heating method superior to conventional heating through surface conduction because it can achieve a uniform volumetric heating. Parametric studies are performed to test the influences of the optical properties of tissue on the thawing process. The proposed model is rather general in nature and therefore can be applied to other nonbiological problems as long as the materials are absorbing and scattering media.

Three-dimensional model on thermal response of skin subject to laser heating

A three-dimensional (3D) multilayer model based on the skin physical structure is developed to investigate the transient thermal response of human skin subject to laser heating. The temperature distribution of the skin is modeled by the bioheat transfer equation, and the influence of laser heating is expressed as a source term where the strength of the source is a product of a Gaussian shaped incident irradiance, an exponentially shaped axial attenuation, and a time function. The water evaporation and diffusion is included in the model by adding two terms regarding the heat loss due to the evaporation and diffusion, where the rate of water evaporation is determined based on the theory of laminar boundary layer. Cryogen spray cooling (CSC) in laser therapy is studied, as well as its effect on the skin thermal response. The time-dependent equation is discretized using the finite difference method with the Crank-Nicholson scheme and the stability of the numerical method is analyzed. The large sparse linear system resulted from discretizing the governing partial differential equation is solved by a GMRES solver and the expected simulation results are obtained.