The aim of this study is to evaluate the effect of pulsatile blood flow in thermally significant blood vessels on the thermal lesion region during thermal therapy of tumor. A sinusoidally pulsatile velocity profile for blood flow was employed to simulate the cyclic effect of the heart beat on the blood flow. The evolution of temperature field was governed by the energy transport equation for blood flow together with Pennes' bioheat equation for perfused tissue encircling the blood vessel. The governing equations were numerically solved by a novel multi-block Chebyshev pseudospectral method and the accumulated thermal dose in tissue was computed. Numerical results show that pulsatile velocity profile, with various combinations of pulsatile amplitude and frequency, has little difference in effect on the thermal lesion region of tissue compared with uniform or parabolic velocity profile. However, some minor differences on the thermal lesion region of blood vessel is observed for middle-sized blood vessel. This consequence suggests that, in this kind of problem, we may as well do the simulation simply by a steady uniform velocity profile for blood flow.
The aim of this study was to investigate the effects of the propagation speed of a thermal wave in terms of the thermal relaxation time on the temperature/thermal dose distributions in living tissue during thermal therapies. The temperature field in tissue was solved by the finite difference method, and the thermal dose was calculated from the formulation proposed by Sapareto and Dewey [Int. J. Radiat. Oncol. Biol. Phys. 10, 787-800 (1984)]. Under the same total deposited energy, for a rapid heating process the time lagging behavior of the peak temperature became pronounced and the level of the peak temperature was decreased with increasing the thermal relaxation time. When the heating duration was longer than the thermal relaxation time of tissues, there was no significant difference between the thermal dose distributions with/without considering the effect of the thermal relaxation time. In other words, when the heating duration is comparable to or shorter than the thermal relaxation time of tissue, the results of the wave bioheat transfer equation (WBHTE) are fully different from that of the Pennes' bioheat transfer equation (PBHTE). Besides, for a rapid heating process the dimension of thermal lesion was still significantly affected by perfusion, because this is what is predicted by the WBHTE but not by the PBHTE, i.e., the wave feature of the temperature field cannot fully be predicted by the PBHTE.
This paper examines the distributions of the SAR (specific absorption rate) ratio and temperature elevation when an ultrasound beam propagates through the interface of muscle and bone. This interface is regarded as a flat boundary to partition the energy of the ultrasound beam, and the analytical solution of temperature distribution is based on the steady-state bio-heat transfer equation. The parameters considered are the incident angle of ultrasound beam, the ultrasound frequency, the acoustic attenuation coefficients of refracted longitudinal and shear waves in bone, and the blood perfusion in muscle. The results show that the peak of the SAR ratio is always at the interface of muscle and bone, while the peak of temperature is located in the bone region beyond the interface. A muscle with lower perfusion or a bone with higher acoustic attenuation results in the shifting of the temperature peak closer to the interface. It is more difficult to heat a higher perfused muscle in front of a bone using a lower frequency ultrasound since the temperature elevation for bone relative to muscle is greater.
BackgroundPennes Bio Heat Transfer Equation (PBHTE) has been widely used to approximate the overall temperature distribution in tissue using a perfusion parameter term in the equation during hyperthermia treatment. In the similar modeling, effective thermal conductivity (Keff) model uses thermal conductivity as a parameter to predict temperatures. However the equations do not describe the thermal contribution of blood vessels. A countercurrent vascular network model which represents a more fundamental approach to modeling temperatures in tissue than do the generally used approximate equations such as the Pennes BHTE or effective thermal conductivity equations was presented in 1996. This type of model is capable of calculating the blood temperature in vessels and describing a vasculature in the tissue regions.MethodsIn this paper, a countercurrent blood vessel network (CBVN) model for calculating tissue temperatures has been developed for studying hyperthermia cancer treatment. We use a systematic approach to reveal the impact of a vasculature of blood vessels against a single vessel which most studies have presented. A vasculature illustrates branching vessels at the periphery of the tumor volume. The general trends present in this vascular model are similar to those shown for physiological systems in Green and Whitmore. The 3-D temperature distributions are obtained by solving the conduction equation in the tissue and the convective energy equation with specified Nusselt number in the vessels.ResultsThis paper investigates effects of size of blood vessels in the CBVN model on total absorbed power in the treated region and blood flow rates (or perfusion rate) in the CBVN on temperature distributions during hyperthermia cancer treatment. Also, the same optimized power distribution during hyperthermia treatment is used to illustrate the differences between PBHTE and CBVN models. Keff (effective thermal conductivity model) delivers the same difference as compared to the CBVN model. The optimization used here is adjusting power based on the local temperature in the treated region in an attempt to reach the ideal therapeutic temperature of 43°C. The scheme can be used (or adapted) in a non-invasive power supply application such as high-intensity focused ultrasound (HIFU). Results show that, for low perfusion rates in CBVN model vessels, impacts on tissue temperature becomes insignificant. Uniform temperature in the treated region is obtained.ConclusionTherefore, any method that could decrease or prevent blood flow rates into the tumorous region is recommended as a pre-process to hyperthermia cancer treatment. Second, the size of vessels in vasculatures does not significantly affect on total power consumption during hyperthermia therapy when the total blood flow rate is constant. It is about 0.8% decreasing in total optimized absorbed power in the heated region as γ (the ratio of diameters of successive vessel generations) increases from 0.6 to 0.7, or from 0.7 to 0.8, or from 0.8 to 0.9. Last, in hyperthermia treatmen...
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