Velocity, local blood flow

Chen and Holmes (1980) showed that in addition to the blood perfusion term, the blood flow in the microvasculature may have at least two contributions to heat transfer a contribution proportional to the local blood flow velocity vector b, and a contribution proportional to the temperature gradient similar to the effective thermal conduction term. They also suggest that in some circumstances, these two additional contributions may be negligible compared to the perfusion term. 

Questions arise as to what extent the experimental steady-state histograms depend upon the different physiological parameters—e.g., as oxygen consumption rate, local blood flow velocity, capillary length and diameter, and capillary arrangement. 

Convection of heat via blood depends primarily on the local blood flow in the tissue and the vascular morphology of the tissue. Thermal diffusion is determined by thermal conductivity in the steady state, and thermal diffusivity in the unsteady state. In addition to these transport parameters, we need to know the volumes and geometry of normal tissues and tumor. In general, tumor volume changes as a function of time more rapidly than normal tissue volume. In special applications, such as hyperthermia induced by electromagnetic waves or radiofrequency currents, we need electromagnetic properties of tissues—the electrical conductivity and the relative dielectric constant. In the case of ultrasonic heating, we need to specify the acoustic properties of the tissue—velocity of sound and attenuation (or absorption) coefficient. 

Within the vasculature of a tissue, blood flows in all directions, and the local direction of convection depends on the vascular morphology of the tissue. The situation is even more complex in tumors where the direction and magnitude of blood flow are not fixed. In tumors, blood flow is temporally and spatially inhomogeneous. Therefore, the local description of convective heat transfer term, Qb, in tissues would include a time-dependent velocity vector — a problem which is enormously complex and has thus far proven mathematically intractable. In order to circumvent a mathematical description of the details and complexities of the microcirculation in a capillary bed, primarily two approaches have been taken by investigators in this area of research (Charny, 1992). 

McDonald DA (1979) Blood Flow in Arteries. 2nd ed. London Edward Arnold Nerem RM, Rumber JA, Gross DR, Muir WW, Geiger GL (1976) Hot-film coronary artery velocity meaurements in horses. Cardiovasc Res 3 310-313 Nerem RM, Seed WQ (1983) Coronary artery geometry and its fluid mechanical implications. In Schettler G etal. (eds) Fluid Dynamics as a Localizing Factor for Atherosclerosis. Springer-Verlag Heidelberg, FRG... 

Development of the thrombus is presented in Fig. 1. Initiation of blood clotting due to a local increase in the activator concentration is accompanied by the formation of a blood clot, which displaces the blood flow from the area adjacent to the site of injury. Formation of localized thrombus is determined by the interaction between the activator and an inhibitor and also hydrodynamic flow [14], In the case of low flow velocities, the wave of coagulation activation is damped by wave of inhibitor and thrombus growth is stopped. Thrombus covers up more one-third of the transverse dimension of the vessel as in [16]. The calculations were performed for Re = 0.01, Pe = 1 on the grid with size 81x81 and St = 0.0015,6x = 0.0125, Sy = 0.00125 at time t = 0.45 - (a), f = 1.2 - (6), t = 1.8 - (c). 

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