An analytical solution countercurrent heat transfer between parallel vessels with a linear axial temperature gradient

Presented in this paper is a solution for countercurrent heat exchange between two parallel vessels embedded in an infinite medium with a linear temperature gradient along the axes of the vessels. The velocity profile within the vessel is assumed to be parabolic. This solution describes the temperature field within the vessels, as well as in the tissue, and establishes that the intravessel temperature is not uniform, as is generally assumed to be the case. An explicit expression for the intervessel thermal resistance based on the difference between cup-mixed mean temperatures is derived.     

Readdressing the issue of thermally significant blood vessels using a countercurrent vessel network

A physiologically realistic arterio-venous countercurrent vessel network model consisting of ten branching vessel generations, where the diameter of each generation of vessels is smaller than the previous ones, has been created and used to determine the thermal significance of different vessel generations by investigating their ability to exchange thermal energy with the tissue. The temperature distribution in the 3D network (8178 vessels; diameters from 10 to 1000 microm) is obtained by solving the conduction equation in the tissue and the convective energy equation with a specified Nusselt number in the vessels. The sensitivity of the exchange of energy between the vessels and the tissue to changes in the network parameters is studied for two cases; a high temperature thermal therapy case when tissue is heated by a uniformly distributed source term and the network cools the tissue, and a hypothermia related case, when tissue is cooled from the surface and the blood heats the tissue. Results show that first, the relative roles of vessels of different diameters are strongly determined by the inlet temperatures to those vessels (e.g., as affected by changing mass flow rates), and the surrounding tissue temperature, but not by their diameter. Second, changes in the following do not significantly affect the heat transfer rates between tissue and vessels; (a) the ratio of arterial to venous vessel diameter, (b) the diameter reduction coefficient (the ratio of diameters of successive vessel generations), and (c) the Nusselt number. Third, both arteries and veins play significant roles in the exchange of energy between tissue and vessels, with arteries playing a more significant role. These results suggest that the determination of which diameter vessels are thermally important should be performed on a case-by-case, problem dependent basis. And, that in the development of site-specific vessel network models, reasonable predictions of the relative roles of different vessel diameters can be obtained by using any physiologically realistic values of Nusselt number and the diameter reduction coefficient.     

Plasma membrane electron transport in frog blood vessels

In an attempt to see if frog blood vessels possess a plasma membrane electron transport system, the postcaval vein and aorta isolated from Rana tigrina were tested for their ability to reduce ferricyanide, methylene blue, and 2,6-dichloroindophenol. While the dyes remained unchanged, ferricyanide was reduced to ferrocyanide. This reduction was resistant to inhibition by cyanide and azide. Heptane extraction or formalin fixation of the tissues markedly reduced the capability to reduce ferricyanide. Denuded aortas retained only 30% of the activity of intact tissue. Our results indicate that the amphibian postcaval vein and aorta exhibit plasma membrane electron transport.     

Evidence for the transport of manganous ion against an activity gradient by mitochondria

Mn²⁺ taken up by mitochondria through the often discussed energy dependent process has been previously shown to be separable by EPR spectroscopy into two spectral fractions (T. E. Gunter and J. S. Puskin, Biophys. J., 12 (1972) 625). One of these spectral fractions shows the characteristics of spin exchange. The other fraction, comprising roughly 10 % of the spectrally observed Mn²⁺, shows a hyperfine sextet.

Evidence is presented supporting the view that under conditions of maximum uptake of Mn²⁺ by the mitochondria in the absence of exogenous phosphate, the bulk of the hyperfine sextet fraction is in the Mn²⁺(H₂O)₆ form.

Spectral data is then used to show that if this view is correct, this fraction is found within mitochondria under conditions where it can be shown to have been accumulated against an activity gradient.

Spectral line width data for this fraction is interpreted in such a way as to provide an upper limit to intramitochondrial local viscosity where this hexahydrate form of manganese is present. This upper limit is approximately 1.5 cP at 37 °C and 0.25 M external osmolarity for example.     

Glutamate transport driven by an electrochemical gradient of sodium ions in Escherichia coli.

The role of Na+ in glutamate transport was studied in Escherichia coli B, strain 29-78, which possesses a very high activity of glutamate transport (L. Frank and I. Hopkins, J. Bacteriol., 1969). Energy-depleted cells were exposed to radioactive glutamate in the presence of a sodium gradient, a membrane potential, or both. One hundred- to 200-fold accumulation of the amino acid was attained in the presence of both electrical and chemical driving forces for the sodium ion. Somewhat lower accumulation values were obtained when either chemical or electrical driving forces were applied separately. A chemical driving force was produced by the addition of external Na+ to Na+-free cells. A membrane potential was established by a diffusion potential either of H+ in the presence of carbonyl cyanide p-trifluoromethoxyphenylhydrazone or of SCN-. These results support the hypothesis of a Na+-glutamate cotransport. Na+-driven glutamate transport was also observed in wild-type E. coli B but not in a strain of K-12.     

3D-reconstruction of blood vessels by ultramicroscopy

As recently shown, ultramicroscopy (UM) allows 3D-visualization of even large microscopic structures with µm resolution. Thus, it can be applied to anatomical studies of numerous biological and medical specimens. We reconstructed the three-dimensional architecture of tomato-lectin (Lycopersicon esculentum) stained vascular networks by UM in whole mouse organs. The topology of filigree branches of the microvasculature was visualized. Since tumors require an extensive growth of blood vessels to survive, this novel approach may open up new vistas in neurobiology and histology, particularly in cancer research.Key words: 3D-reconstruction, blood vessels, cancer, LEA, lectin, microvasculature, morphology, ultramicroscopy, whole mount     

Amino acid transport in the thermophilic anaerobe Clostridium fervidus is driven by an electrochemical sodium gradient.

Amino acid transport was studied in membranes of the peptidolytic, thermophilic, anaerobic bacterium Clostridium fervidus. Uptake of the negatively charged amino acid L-glutamate, the neutral amino acid L-serine, and the positively charged amino acid L-arginine was examined in membrane vesicles fused with cytochrome c-containing liposomes. Artificial ion diffusion gradients were also applied to establish the specific driving forces for the individual amino acid transport systems. Each amino acid was driven by the delta psi and delta mu Na+/F and not by the Z delta pH. The Na+ stoichiometry was estimated from the amino acid-dependent 22Na+ efflux and Na(+)-dependent 3H-amino acid efflux. Serine and arginine were symported with 1 Na+ and glutamate with 2 Na+. C. fervidus membranes contain Na+/Na+ exchange activity, but Na+/H+ exchange activity could not be demonstrated.     

3D-reconstruction of blood vessels by ultramicroscopy

As recently shown, ultramicroscopy (UM) allows 3D-visualization of even large microscopic structures with µm resolution. Thus, it can be applied to anatomical studies of numerous biological and medical specimens. We reconstructed the three-dimensional architecture of tomato-lectin (lycopersicon esculentum) stained vascular networks by UM in whole mouse organs. The topology of filigree branches of the microvasculature was visualized. Since tumors require an extensive growth of blood vessels to survive, this novel approach may open up new vistas in neurobiology and histology, particularly in cancer research.     

A compartmental model for oxygen transport in brain microcirculation in the presence of blood substitutes

A compartmental model is developed for oxygen (O(2)) transport in brain microcirculation in the presence of blood substitutes (hemoglobin-based oxygen carriers). The cerebrovascular bed is represented as a series of vascular compartments, on the basis of diameters, surrounded by a tissue compartment. A mixture of red blood cells (RBC) and plasma/extracellular hemoglobin solution flows through the vascular bed from the arterioles through the capillaries to the venules. Oxygen is transported by convection in the vascular compartments and by diffusion in the surrounding tissue where it is utilized. Intravascular resistance and the diffusive loss of oxygen from the arterioles to the tissue are incorporated in the model. The model predicts that most of the O(2) transport occurs at the level of capillaries. Results computed from the present model in the presence of hemoglobin-based oxygen carriers are consistent with those obtained from the earlier validated model (Sharan et al., 1989, 1998a) on oxygen transport in brain circulation in the absence of extracellular hemoglobin. We have found that: (a) precapillary PO(2) gradients increase as PO(2) in the arterial blood increases, P(50 p) (oxygen tension at 50% saturation of hemoglobin with O(2) in plasma) decreases, i.e. O(2) affinity of the extracellular hemoglobin is increased, the flow rate of the mixture decreases, hematocrit decreases at constant flow, metabolic rate increases, and intravascular transport resistance in the arterioles is neglected; (b) precapillary PO(2) gradients are not sensitive to (i) intracapillary transport resistance, (ii) cooperativity (n(p)) of hemoglobin with oxygen in plasma, (iii) hemoglobin concentration in the plasma and (iv) hematocrit when accounting for viscosity variation in the flow; (c) tissue PO(2) is not sensitive to the variation of intravascular transport resistance in the arterioles. We also found that tissue PO(2) is a non-monotonic function of the Hill coefficient n(p) for the extracellular hemoglobin with a maximum occurring when n(p) equals the blood Hill coefficient. The results of the computations give estimates of the magnitudes of the increases in tissue PO(2) as arterial PO(2) increases,P(50 p) increases, flow rate increases, hematocrit increases, hemoglobin concentration in the plasma increases, metabolic rate decreases, the capillary mass transfer coefficient increases or the intracapillary transport resistance decreases.     

Kelvin-Helmholtz instability of a cylindrical plasma flow with an arbitrary temperature

The dispersion relation for Kelvin-Helmholtz magnetohydrodynamic instability of a cylindrical plasma flow in a longitudinal magnetic field is studied with allowance for plasma compressibility. Stability of the system in a wide range of plasma parameters is thoroughly analyzed in the incompressible plasma approximation. Using the results obtained, a diagram of the system stability is constructed in terms of the magnetic field and the ratio between the plasma densities in the flow and the ambient space. It is shown by numerically solving the dispersion relation for the case of a compressible plasma that perturbations with scale lengths on the order of the flow diameter and larger can develop even at a zero temperature. For low ion-sound velocities, c _S ²/U ₀² < 0.25, the growth rate of the axisymmetric mode with m = 0 is much smaller than that of non-axisymmetric modes. It is shown that, in an incompressible plasma, the eigenmodes are damped monotonically with distance from the flow. In plasma with a finite temperature, the character of damping is oscillatory; in this case, the lower the plasma temperature, the larger the distance at which the ambient plasma is perturbed.     

Quantification of the effects of vasomotion on mass transport to tissue from axisymmetric blood vessels

The process known as vasomotion, rhythmic oscillations in vessel diameter, has been proposed to act as a protective mechanism for tissue under conditions of reduced perfusion, since it is frequently only observed experimentally when perfusion levels are reduced. This could be due to a resultant increase in oxygen transport from the vasculature to the surrounding tissue, either directly or indirectly. It is thus potentially of significant clinical interest as a warning signal for ischemia. However, there has been little analysis performed to quantify the effects of vessel wall movement on time-averaged mass transport. We thus present a detailed analysis of such mass transport for an axisymmetric vessel with a periodically oscillating wall, by solving the non-linear mass transport equation, and quantify the differences between the time-averaged mass transport under conditions of no oscillation (i.e. the steady-state) and varying wall oscillation amplitude. The results show that if the vessel wall alone is oscillated, with an invariant wall concentration, the time-averaged mass transport is reduced relative to the steady-state, but if the vessel wall concentration is also oscillated, then mass transport is increased, although this is generally only true when these oscillate in phase with each other. The influence of Péclet number and the non-dimensional rate of consumption of oxygen in tissue, as well as the amplitude of oscillations, are fully characterised. We conclude by considering the likely implications of these results in the context of oxygen transport to tissue.     

Altered DNA sedimentation by the presence of erythrocytes in alkaline sucrose gradient centrifugation

The presence of a relatively small number of red cells was found to affect DNA sedimentation profile of normal lymphocytes and acute leukemia cells, as observed by the alkaline sucrose gradient centrifugation technique coupled with the fluorometric measurement of DNA. Significant alteration was observed at a nucleated cell/erythrocyte ratio of $\text{20}\text{1}$ to $\text{0.2}\text{1}$, resulting in retardation of the $\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ value and the entire sedimentation profile. This effect seemed to be rather specific to erythrocyte lysate, since corresponding amounts of erythrocyte ghost, IgM, bovine serum albumin, and an increased number of nucleated cells did not influence the profile to an appreciable degree.     

Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels

The effect of blood velocity pulsations on bioheat transfer is studied. A simple model of a straight rigid blood vessel with unsteady periodic flow is considered. A numerical solution that considers the fully coupled Navier-Stokes and energy equations is used for the simulations. The influence of the pulsation rate on the temperature distribution and energy transport is studied for four typical vessel sizes: aorta, large arteries, terminal arterial branches, and arterioles. The results show that: the pulsating axial velocity produces a pulsating temperature distribution; reversal of flow occurs in the aorta and in large vessels, which produces significant time variation in the temperature profile. Change of the pulsation rate yields a change of the energy transport between the vessel wall and fluid for the large vessels. For the thermally important terminal arteries (0.04-1 mm), velocity pulsations have a small influence on temperature distribution and on the energy transport out of the vessels (8 percent for the Womersley number corresponding to a normal heart rate). Given that there is a small difference between the time-averaged unsteady heat flux due to a pulsating blood velocity and an assumed nonpulsating blood velocity, it is reasonable to assume a nonpulsating blood velocity for the purposes of estimating bioheat transfer.     

The effects of large blood vessels on temperature distributions during simulated hyperthermia.

Several three-dimensional vascular models have been developed to study the effects of adding equations for large blood vessels to the traditional bioheat transfer equation of Pennes when simulating tissue temperature distributions. These vascular models include "transiting" vessels, "supplying" arteries, and "draining" veins, for all of which the mean temperature of the blood in the vessels is calculated along their lengths. For the supplying arteries this spatially variable temperature is then used as the arterial temperature in the bioheat transfer equation. The different vascular models produce significantly different locations for both the maximum tumor and the maximum normal tissue temperatures for a given power deposition pattern. However, all of the vascular models predict essentially the same cold regions in the same locations in tumors: one set at the tumors' corners and another around the inlets of the large blood vessels to the tumor. Several different power deposition patterns have been simulated in an attempt to eliminate these cold regions; uniform power in the tumor, annular power in the tumor, preheating of the blood in the vessels while they are traversing the normal tissue, and an "optimal" power pattern which combines the best features of the above approaches. Although the calculations indicate that optimal power deposition patterns (which improve the temperature distributions) exist for all of the vascular models, none of the heating patterns studied eliminated all of the cold regions. Vasodilation in the normal tissue is also simulated to see its effects on the temperature fields.(ABSTRACT TRUNCATED AT 250 WORDS)