Heat Transfer In Biological Tissues Research Articles

Solution of the heat transfer problem in tissues during hyperthermia by finite difference–decomposition method

In this article, a mathematical model describing the process of heat transfer in biological tissues with blood perfusion having different values under different temperature range for various coordinate system and different boundary conditions during thermal therapy by electromagnetic radiation is studied. Using the method of finite differences, the boundary value problem governing this process has been converted to an initial value problem of ordinary differential equations, which is solved by the Adomian decomposition method. The effects of blood perfusion rate intended for a different temperature range of temperature at target point during thermal therapy for different boundary conditions are discussed in detail. And we have also checked our results with the result of exact solutions for one case and it shows a good agreement.

Analytical Solution of Thermal Wave Models on Skin Tissue Under Arbitrary Periodic Boundary Conditions

Modeling and understanding the heat transfer in biological tissues is important in medical thermal therapeutic applications. The biothermomechanics of skin involves interdisciplinary features, such as bioheat transfer, biomechanics, and burn damage. The hyperbolic thermal wave model of bioheat transfer and the parabolic Pennes bioheat transfer equations with blood perfusion and metabolic heat generation are applied for the skin tissue as a finite and semi-infinite domain when the skin surface temperature is suddenly exposed to a source of an arbitrary periodic temperature. These equations are solved analytically by Laplace transform methods. The thermal wave model results indicate that a non-Fourier model has predicted the thermal behavior correctly, compared to that of previous experiments. The results of the thermal wave model show that when the first thermal wave moves from the first boundary, the temperature profiles for finite and semi-infinite domains of skin become separated for these phenomena; the discrepancy between these profiles is negligible. The accuracy of the obtained results is validated through comparisons with existing numerical results. The results demonstrate that the non-Fourier model is significant in describing the thermal behavior of skin tissue.

Thermal wave model of bioheat transfer with modified Riemann–Liouville fractional derivative

In this paper a new fractional thermal wave model of the bioheat transfer (FTWMBT) caused by spatial heating is built using Taylor’s series expansion of modified Riemann–Liouville fractional derivatives. A one-dimensional analytical solution of the FTWMBT in a finite medium is obtained. The FTWMBT in the case (α = 1) interpolates the standard thermal wave model of bioheat transfer and the well-known Pennes’ bioheat equation (τ = 0). Finally, numerical results are presented graphically for various values of different parameters. This study demonstrates that fractional models can provide a unified approach to examine the heat transfer in biological tissue.

Non-Fourier phase change heat transfer in biological tissues during solidification

The phase change in biological tissues during a freezing process is simulated by hyperbolic and parabolic heat equations with temperature-dependent enthalpy. It is observed that the experimental results are in a good agreement with that the calculated results by the enthalpy method. The results shown that the Fourier model predicts tissues temperature lower than of the non-Fourier model. Further decrease in freezing rate and freezing velocity is noticed with an increase in relaxation time value.

Three-Dimensional Numerical Study on Freezing Phase Change Heat Transfer in Biological Tissue Embedded With Two Cryoprobes

Biological tissues undergo complex phase change heat transfer processes during cryosurgery, and a theoretical model is preferable to forecast this heat experience. A mathematical model for phase change heat transfer in cryosurgery was established. In this model, a fractal treelike branched network was used to describe the complicated geometrical frame of blood vessels. The temperature distribution and ice crystal growth process in biological tissue including normal tissue and tumor embedded with two cryoprobes were numerically simulated. The effects of cooling rate, initial temperature, and distance of two cryoprobes on freezing process of tissue were also studied. The results show that the ice crystal grows more rapidly in the initial freezing stage (<600 s) and then slows down in the following process, and the precooling of cryoprobes has no obvious effect on freezing rate of tissue. It also can be seen that the distance of 10 mm between two cryoprobes produces an optimal freezing effect for the tumor size (20 mm × 10 mm) in the present study compared with the distances of 6 mm and 14 mm. The numerical results are significant in providing technical reference for application of cryosurgery in clinical medicine.

Numerical simulation on freezing phase change heat transfer in cryosurgery with two cryoprobes

AbstractA mathematical model for phase change heat transfer in biological tissue (including tumor and normal tissue) embedded with two cryoprobes was established. In this model, the vascular architecture was described as a tree‐like branched fractal network, and the effective thermal conductivity and flow rate of blood were presented based on this fractal structure. Occurrence of three regions including frozen, phase‐changing, and unfrozen regions in biological tissue during the freezing process was also considered. The numerical studies on temperature distribution and ice crystal growth process in biological tissue embedded with two cryoprobes were performed. The results showed that the growth rate of ice crystal is more rapid in the initial freezing stage and becomes slower later. So it is unreasonable to prolong freezing time merely without other assisting measures for enlarging the freezing region in the late freezing stage. Furthermore, the placement distance of the two cryoprobes plays a significant role in the growth of ice crystal in the initial freezing stage, and the influence of different distances between two probes on ice crystal growth becomes less profound with an increasing of freezing time. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/htj.20332

Numerical simulation for heat transfer in tissues during thermal therapy

In this paper, a mathematical model describing the process of heat transfer in biological tissues for different coordinate system during thermal therapy by electromagnetic radiation is studied. The boundary value problem governing this process has been solved using Galerkin’s method taking B-polynomial as basis function. The system of ordinary differential equation in unknown time variable, thus obtained, is solved by homotopy perturbation method. The effect of thermal conductivity, antenna power constant, surface temperature, and blood perfusion rate on temperature for different coordinates are discussed. It has been observed that the process is faster in spherical symmetric coordinates in comparison to axisymmetric coordinate and faster in axisymmetric in comparison to Cartesian coordinate.

On vortices heating biological excitable media

An extension of the Hodgkin–Huxley mathematical model for the propagation of nerve signal which takes into account dynamical heat transfer in biological tissue is derived and fine tuned with existing experimental data. The medium is heated by Joule’s effect associated with action potential propagation, leading to characteristic thermal patterns in association with spiral and scroll waves. The introduction of heat transfer—necessary on physical grounds—provides a novel way to directly observe the movement, regular or chaotic, of the tip of spiral waves in numerical simulations and possibly in experiments regarding different biological excitable media.

Numerical study on freezing-thawing phase change heat transfer in biological tissue embedded with two cryoprobes

A two-dimensional model for freezing and thawing phase change heat transfer in biological tissue embedded with two cryoprobes was established. In this model, the blood vessels were considered as tree-like branched fractal network, and the effective flow rate and effective thermal conductivity of blood were obtained by fractal method. The temperature distribution and ice crystal growth process in biological tissue embedded with two cryoprobes during freezing-thawing process were numerically simulated. The results show that the growth velocity of ice crystal in freezing process from 200 to 400 s is more rapid than that from 400 to 600 s. Thawing process of frozen tissue occurs in the regions around cryoprobes tips and tissue boundary simultaneously, and the phase interfaces are close to each other until ice crystal melts completely. The distance of two cryoprobes has a more profound effect on the temperature distribution in freezing process at 400 s than at 800 s.

Parameter identification problems and analysis of the impact of porous media in biofluid heat transfer in biological tissues during thermal therapy

This paper considers time-dependent identification problems governed by some generalized transient bioheat transfer type models in biological systems with porous structures and directional blood flow. The analysis and the real applications of the porous media models and biofluid heat transfer in living tissues are relatively recent, however the blood perfusion rate and the porosity parameter affect considerably the effects of thermal physical properties on the transient temperature of biological tissues. The control considered in this work estimates simultaneously these two parameters. The result can be very beneficial for thermal diagnostics in medical practices, for example for laser surgery, photo and thermotherapy for regional hyperthermia, often used in the treatment of cancer. First, the mathematical models are introduced and the existence, the uniqueness and the regularity of the solution of the state equation are proved as well as stability and maximum principle under extra assumptions. Afterwards the identification problems with Tichonov regularization are formulated, in different situations, in order to control the online temperature given by radiometric measurement. An optimal solution is proven to exist and finally necessary optimality conditions are given. Some strategies for numerical realization based on the adjoint variables are provided.

Simulation of heat transfer of biological tissue during cryosurgery based on vascular trees

During the freezing process in cryosurgery, the blood flow and blood perfusion have great influence on the heat transfer of the biological tissue. The effect of blood vessels on the temperature distribution of biological tissue is studied in this paper. The blood vessels are assumed as vascular trees using fractal methods. The method is based on the calculation of the ‘fractal dimension’ of blood vessels, considering the parameters of blood vessels and blood flows. The biological tissue is assumed as porous media and a numerical model of phase change heat transfer in biological tissue is established. The temperature distribution in biological tissue considering the effect of blood flow is simulated. The effect of the geometry of the vascular tree on the phase change heat transfer in biological tissue during cryosurgery is also analyzed.

Pilot study on cryogenic heat transfer in biological tissues embedded with large blood vessels

Blood flow through large vessel plays an important role in affecting the temperature profiles of the living tissues under cryosurgery. Besides, arresting of blood vessels due to freezing may possibly cause danger to the patient, which needs to be considered when operating the cryoprobe. However, such important issues received few attentions in the bioheat field even up to date. In this paper, pilot studies were performed to investigate the cryogenic heat transfer behaviors in biological tissues embedded with large blood vessels. First, a simple however intuitive theoretical model was established and then analytically solved. Parametric studies were performed to test the influences of the blood vessel entrance temperature, the vessel diameter, the blood flow velocity and the vessel length etc. to the whole region's temperature distribution. The critical tissue surface temperature to freeze the blood vessel was theoretically predicted. Second, to reveal the role of the countercurrent artery-vein blood flows to the transient phase change in living tissues subject to freezing, qualitative simulating experiments on phantom gel were performed. A 3 cm-diameter, 14 cm-length cylindrical copper block pre-frozen by liquid nitrogen was applied to freeze the gel embedded with two parallel countercurrent 1.1 mm OD/0.8 mm ID Teflon tubes with 30 °C warm water flowing through at the velocity of 0.1 m/s. Temperatures were measured at the selected positions on the tube wall in a step of 2 cm. As a comparison, experiments were also conducted on the same gel without running warm water. It was demonstrated that the countercurrent water flow has significant effect on the freezing progress of the phantom gel in comparison with that of non-flow gel. This study raised an important issue to study the phase change heat transfer of blood vessels to the living tissues subject to cryosurgery, which may have significant clinical applications. The present method can also possibly be extended to wider fields such as heat transfer in buried pipes and collectors.

Study on the heat transfer aspect of thermal burns caused by mats with warm water circulation.

In order to prevent an anesthetized patient's body temperature from decreasing in the operating room, a mat with warm water circulation is often used. However, burn injuries sometimes occur on a patient's body in spite of the correct use of the mat. The cause of this injury has not yet been clarified. In this study, heat transfer between the bio1ogical tissue and the mat was calculated numerically under the condition of heat transfer by blood flow. The effects of the thickness of biological tissue, water temperature, heat transfer coefficient of the water flow in the mat, metabolic heat production rate, and blood perfusion rate distribution on heat transfer in biological tissues were clarified. From the standpoint of these effects, the conditions of occurrence of burn injury were examined. Results indicated that the model in this study was capable of simulating the mechanism by which burn injuries in the operating room are caused.