Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended g...Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues.展开更多
We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method w...We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method with symbolic computation, we obtain the exact analytical thermal traveling wave solution, which describes the non-uniform temperature distribution inside the bodies. The found exact solution is used to investigate the temperature distribution in the tissues. It is found that the surrounding medium with higher temperature does not necessarily imply that the tissue will quickly (after a short duration of heating process) reach the desired temperature. It is also found that increased perfusion causes a decline in local temperature.展开更多
In most previous models,simulation of the temperature generation in tissue is based on the Pennes bio-heat transfer equation,which implies an instantaneous thermal energy deposition in the medium.Due to the long therm...In most previous models,simulation of the temperature generation in tissue is based on the Pennes bio-heat transfer equation,which implies an instantaneous thermal energy deposition in the medium.Due to the long thermal relaxation time τ（20 s-30 s） in biological tissues,the actual temperature elevation during clinical treatments could be different from the value predicted by the Pennes bioheat equation.The thermal wave model of bio-heat transfer（TWMBT） defines a thermal relaxation time to describe the tissue heating from ultrasound exposure.In this paper,COMSOL Multiphysics 3.5a,a finite element method software package,is used to simulate the temperature response in tissues based on Pennes and TWMBT equations.We further discuss different factors in the bio-heat transfer model on the influence of the temperature rising and it is found that the temperature response in tissue under ultrasound exposure is a rising process with a declining rate.The thermal relaxation time inhibits the temperature elevation at the beginning of ultrasonic heating.Besides,thermal relaxation in TWMBT leads to lower temperature estimation than that based on Pennes equation during the same period of time.The blood flow carrying heat dominates most to the decline of temperature rising rate and the influence increases with temperature rising.On the contrary,heat diffusion,which can be described by thermal conductivity,has little effect on the temperature rising.展开更多
文摘Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues.
文摘We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method with symbolic computation, we obtain the exact analytical thermal traveling wave solution, which describes the non-uniform temperature distribution inside the bodies. The found exact solution is used to investigate the temperature distribution in the tissues. It is found that the surrounding medium with higher temperature does not necessarily imply that the tissue will quickly (after a short duration of heating process) reach the desired temperature. It is also found that increased perfusion causes a decline in local temperature.
基金Project supported by the National Basic Research Program of China (Grant Nos. 2011CB707902 and 2012CB921504)the National Natural Science Foundation of China (Grant No. 11274166)the State Key Laboratory of Acoustics,Chinese Academy of Sciences (Grant No. SKLA201207)
文摘In most previous models,simulation of the temperature generation in tissue is based on the Pennes bio-heat transfer equation,which implies an instantaneous thermal energy deposition in the medium.Due to the long thermal relaxation time τ（20 s-30 s） in biological tissues,the actual temperature elevation during clinical treatments could be different from the value predicted by the Pennes bioheat equation.The thermal wave model of bio-heat transfer（TWMBT） defines a thermal relaxation time to describe the tissue heating from ultrasound exposure.In this paper,COMSOL Multiphysics 3.5a,a finite element method software package,is used to simulate the temperature response in tissues based on Pennes and TWMBT equations.We further discuss different factors in the bio-heat transfer model on the influence of the temperature rising and it is found that the temperature response in tissue under ultrasound exposure is a rising process with a declining rate.The thermal relaxation time inhibits the temperature elevation at the beginning of ultrasonic heating.Besides,thermal relaxation in TWMBT leads to lower temperature estimation than that based on Pennes equation during the same period of time.The blood flow carrying heat dominates most to the decline of temperature rising rate and the influence increases with temperature rising.On the contrary,heat diffusion,which can be described by thermal conductivity,has little effect on the temperature rising.
