Análise numérica dos processos de aquecimento e resfriamento da articulação do joelho

Abstract

The heating and cooling of tissues are used since ancient times for the treatment of health disorders. In physical therapy these resources are used in order to promote the relief of pain, aid in tissue repair, control or reduce the signs and inflammatory symptoms, changing the elasticity of the tissue and thus enhance the rehabilitation plan. However, benefits from these therapies rely heavily on the temperature achieved in the tissue. Different values from the recommended optimum range for obtaining therapeutic effects may result in ineffective or harmful treatments to the tissue. Therefore, to understand the heat transfer process and to know the temperature distribution in biological tissues are essential factors for such treatments to be applied in a safe and effective manner. In vivo measurements are usually invasive and often impossible to be performed when deep tissues are studied. In this context, numerical simulation becomes an interesting tool for understanding the temperature field in different tissues that constitutes the joint and thus contribute to better implementation of thermal resources used in physical therapy. Therefore, the main objective of the present study is to evaluate the distribution of temperature at the knee joint in an animal model (two-dimensional and one- dimensional) and human (two-dimensional) models using numerical simulation. The two- dimensional geometric models of the canine and human knee were elaboratedbased on a photographic record of a cross section of an anatomical specimen and real images obtained from cross sections of a corpse, respectively. Both models were built with the help of SolidWorks 2012 ® software. The mesh was generated with the ANSYS Meshing and mesh tests are conducted in both models. ANSYS-CFX® software based on finite volume method is used to perform the simulations. In the one-dimensional model, the joint was represented by a single cylinder, composed of six tissue layers. The EES 2016 ® software (V10.104 - Engineering Equation Solver) was used to elaborate the program and equations solutions. The heat transfer phenomenon was modeled by the partial differential heat diffusion equation with the terms of blood perfusion and metabolism. To investigate the impact on tissue temperature distribution, the term of blood perfusion was changed considering the blood perfusion rate constantor as a function of temperature, different blood perfusion values and blood perfusion as function of temperature. The bidimensional simulations of the canine knee during the heating and cooling procedures were performed considering different boundary conditions. The results obtained with these simulations were used to determine the boundary conditions adopted for the one-dimensional simulations of the canine and two-dimensional knee of the human knee during the heating and cooling processes. The results of animal model simulations were compared with in vivo experimental data available in the literature. The simulations of heating and cooling that had the behavior of the temperature of the epidermis as boundary condition presented the best results. The different blood perfusion values, tested under the neutrality and heating conditions, affected the simulations results only when the blood perfusion rate was considered constant. The best results were obtained when the perfusion rate was considered as a function of temperature, representing, more faithfully, the mathematical modeling proposed by Pennes. In all simulations, the lowest percentage differences were found when blood perfusion was also considered as a function of temperature. The two-dimensional simulations presented percentage differences with the experiment close to those obtained with the one- dimensional simulation, showing that both are capable of representing the phenomenon analyzed. The numerical simulations performed in the present study were an important tool for the noninvasive evaluation of the temperature distribution in the knee joint.