On the generalization of the Weinbaum-Jiji bioheat equation to microvessels of unequal size; the relation between the near field and local average tissue temperatures

The extensive series of experiments reported in Lemons et al. [1] show that measureable local tissue temperature fluctuations are observed primarily in the vicinity of the 100-500 micron countercurrent vessels of the microcirculation and thus strongly support the basic hypothesis in the new bioheat equation of Weinbaum and Jiji [2] that these countercurrent microvessels are the principal determinants of local blood-tissue heat transfer. However, the detailed temperature profiles in the vicinity of these vessels indicate that large asymmetries in the local temperature field can result from the significant differences in size between the countercurrent artery and vein. Using the superposition techniques of Baish et al. [9], the paper first presents a solution to the classic problem of an unequal countercurrent heat exchanger with heat loss to the far field. This solution is then used to generalize the Weinbaum-Jiji bioheat equation and the conductivity tensor that appears in this equation to vessels of unequal size. An asymptotic analysis has also been developed to elucidate the relationship between the near field temperature of the artery-vein pair and the local average tissue temperature. This analysis is used to rigorously prove the closure approximation relating the local arterial-venous temperature difference and the mean tissue temperature gradient which had been derived in [2] using a more heuristic approach.     

Enzyme-induced Formation of Spheres from Cells and Envelopes of Escherichia coli

Normal and filamentous whole cells and isolated envelopes of Escherichia coli B were exposed to various enzymatic treatments to remove surface layers and to characterize the component(s) conferring rigidity in this organism. Modification of cell rigidity was determined by sphere formation in both whole cells and isolated envelopes. Enzymes capable of converting trypsinized normal or untreated filamentous whole cells and untreated envelopes to spheres included: lysozyme plus ethylenediaminetetraacetic acid, clostridial phospholipase C, and phospholipase D from cabbage. These data suggest that there are at least two components essential for maintenance of cell rigidity in E. coli B. The first is the peptidoglycan (mucopeptide), which is susceptible to lysozyme. The second is a phospholipid which is either covalently linked to the mucopeptide or in close association with it. This phospholipase C-sensitive component is protected more completely in normal than in filamentous whole cells by a protein layer which is easily modified by trypsin treatment to allow enzymatically induced sphere formation to occur.     

Alternate bearing influences annual nutrient consumption and the total nutrient content of mature pistachio trees

The influence of alternate bearing on nutrient utilization and total tree nutrient content was investigated in mature pistachio (Pistacia vera L. cv Kerman trees). Removal of N, P and Zn in fruit and abscised leaves of cropping (‘on’) trees averaged 5, 6, and 2 times, respectively, the removal in abscised leaflets of the non-fruiting, ‘off’ year trees. One hundred and thirty-five kg N, 131 kg K, 86 kg Ca, 39 kg Mg and 18 kg P per hectare were removed in fruits and abscised leaves in ‘on’ year trees. Tree nutrient contents and, presumably, the size of nutrient storage pools in dormant trees varied between ‘on’ and ‘off’ years. There was 22% and 14% more N and P, respectively, in dormant trees following ‘off’ than ‘on’ years. The greater N and P accumulation in ‘off’ year trees is depleted in support of the large fruit demand for N and P during ‘on’ years. In contrast to N and P, there was greater K and Ca accumulation in perennial tree parts during ‘on’ years than during ‘off’ years. The greater K accumulation in perennial tree parts and approximately 30% greater removal of K in annual organs during ‘on’ than ‘off’ years suggests that K uptake could be 4 times higher in ‘on’ year trees than in (non-cropping), ‘off’ year trees.     

Immunity to sporozoite-induced malaria infeciton in mice. I. The effect of immunization of T and B cell-deficient mice.

The cellular basis of immunity to sporozoites was investigated by examing the effect of immunization of T and B cell-deficient C57BL/6N X BALB/c AnN F1 (BLCF1) mice compared to immunocompetent controls. Immunization of T cell-deficient (ATX-BM-ATS) BLCF1 mice with x-irradiated sporozoites did not result in the generation of protective immunity. The same immunization protocols protected all immunocompetent controls. In contrast, B cell-deficient (micron-suppressed) BLCF1 mice were protected by immunization in the majority of cases. The absence of detectable serum circumsporozoite precipitins or sporozoite neutralizing activity in the micron-suppressed mice that resisted a sporozoite challenge suggests a minor role for these humoral factors in protection. These data demonstrate a preeminent role for T cells in the induction of protective immunity in BLCF 1 mice against a P. berghei sporozoite infection.     

Immunity to Plasmodium berghei yoelii in mice. II. Specific and nonspecific cellular and humoral responses during the course of infection.

The kinetics of various specific and nonspecific immunologic responses were examined in BALB/c mice infected with 17X nonlethal Plasmodium berghei yoelii (a self-limiting infection). The sequence of events after infection was characterized by rapid sensitization of splenic T cells to malaria antigen and polyclonal B cell activation, followed by a period of depressed splenic proliferative responses in vitro to mitogens (PHA and LPS) and malaria (specific) antigen. At the same time, suppressed primary in vitro splenic PFC responses to trinitrophenyl-aminoethylcarbamylmethyl-Ficoll (TNP-F) were seen. This suppression was an active process requiring adherent cells. During this period, levels of antimalarial antibody also increased exponentially. As the infection was cleared, splenic malaria antigen-specific proliferative responses were again observed and splenic PFC and in vitro mitogen responses returned to preinfection levels after variable periods of time. Both splenic proliferative responses to malaria antigen and antimalarial antibody responses remained persistently elevated. In addition, some responses were examined in mice infected with 17X lethal P.b. yoelii (a fatal infection); in comparison to the early responses of mice infected with the nonlethal substrain, there was a decrease and delay in the development of a splenic T cell response to malaria antigen and a blunted antimalarial antibody response.     

The bleed off perfusion term in the Weinbaum-Jiji bioheat equation.

The microvascular organization and thermal equilibration of the primary and secondary arteries and veins that comprise the bleed off circulation to the muscle fibers from the parent countercurrent supply artery and veins are analyzed. The blood perfusion heat source term in the tissue energy equation is shown to be related to this vascular organization and to undergo a fundamental change in behavior as one proceeds from the more peripheral tissue, where the perfusion term is proportional to the Ta--Tv difference in the parent supply vessels, to the deeper tissue layers where the bleed off vessels themselves form a branching countercurrent system for each muscle tissue cylinder and the venous return temperature can vary between the local tissue temperature and Ta. The consequences of this change in behavior are examined for the Weinbaum-Jiji bioheat equation and a modified expression for the effective conductivity of perfused tissue is derived for countercurrent bleed off exchange.     

A new fundamental bioheat equation for muscle tissue--part II: Temperature of SAV vessels

In this study, a new theoretical framework was developed to investigate temperature variations along countercurrent SAV blood vessels from 300 to 1000 microm diameter in skeletal muscle. Vessels of this size lie outside the range of validity of the Weinbaum-Jiji bioheat equation and, heretofore, have been treated using discrete numerical methods. A new tissue cylinder surrounding these vessel pairs is defined based on vascular anatomy, Murray's law, and the assumption of uniform perfusion. The thermal interaction between the blood vessel pair and surrounding tissue is investigated for two vascular branching patterns, pure branching and pure perfusion. It is shown that temperature variations along these large vessel pairs strongly depend on the branching pattern and the local blood perfusion rate. The arterial supply temperature in different vessel generations was evaluated to estimate the arterial inlet temperature in the modified perfusion source term for the s vessels in Part I of this study. In addition, results from the current research enable one to explore the relative contribution of the SAV vessels and the s vessels to the overall thermal equilibration between blood and tissue.     

Structural changes in rat aortic intima due to transmural pressure.

Huang et al. (1997) propose a new hypothesis and develop a mathematical model to explain rationally the in vitro and in situ measured changes (Tedgui and Lever, 1984; Baldwin and Wilson, 1993) in the hydraulic conductivity of the artery wall of rabbit aorta with transmural pressure. The model leads to the intriguing prediction that this hydraulic conductivity would decrease by one half if the thin intimal layer between the endothelium and the internal elastic lamina volume-compresses approximately fivefold. This paper presents the first measurements of the effect of transmural pressure on intimal layer thickness and shows that the intimal matrix is, indeed, surprisingly compressible. We perfusion-fixed rat thoracic aortas in situ with 2 percent glutaraldehyde solution at 0, 50, 100, or 150 mm Hg lumen pressure and sectioned for light and electron microscopic observations. Electron micrographs show a dramatic, nonlinear decrease in average intimal thickness, i.e., 0.62 +/- 0.26, 0.27 +/- 0.14, 0.15 +/- 0.10, and 0.12 +/- 0.07 (SD) micron for 0, 50, 100, and 150 mm Hg lumen pressure, respectively. The volume strain of the intima is more than 20 times greater than the radial strain of the artery wall due to hoop tension and two orders of magnitude greater than the consolidation of the artery wall as a whole assuming constant medial density (Chuong and Fung, 1984). Moreover, in both light and electron microscopic observations, it is easy to find numerous sites where the endothelium puckers into the fenestral pores at high lumen pressure, as predicted by the theory in Huang et al. (1997). In contrast, the average diameter of a fenestral pore increases only 10 percent as the lumen pressure is increased from 0 to 150 mm Hg. These results indicate that the thin intimal layer comprising less than 1 percent of the wall thickness can have a profound effect on the filtration properties of the wall due to the large change in Darcy permeability of the layer and the large reduction in the entrance area of the flow entering the fenestral pores, though the pores themselves experience only a minor enlargement due to hoop tension.     

A 1-D model to explore the effects of tissue loading and tissue concentration gradients in the revised Starling principle

The recent experiments in Hu et al. (Am J Physiol Heart Circ Physiol 279: H1724-H1736, 2000) and Adamson et al. (J Physiol 557: 889-907, 2004) in frog and rat mesentery microvessels have provided strong evidence supporting the Michel-Weinbaum hypothesis for a revised asymmetric Starling principle in which the Starling force balance is applied locally across the endothelial glycocalyx layer rather than between lumen and tissue. These experiments were interpreted by a three-dimensional (3-D) mathematical model (Hu et al.; Microvasc Res 58: 281-304, 1999) to describe the coupled water and albumin fluxes in the glycocalyx layer, the cleft with its tight junction strand, and the surrounding tissue. This numerical 3-D model converges if the tissue is at uniform concentration or has significant tissue gradients due to tissue loading. However, for most physiological conditions, tissue gradients are two to three orders of magnitude smaller than the albumin gradients in the cleft, and the numerical model does not converge. A simpler multilayer one-dimensional (1-D) analytical model has been developed to describe these conditions. This model is used to extend Michel and Phillips's original 1-D analysis of the matrix layer (J Physiol 388: 421-435, 1987) to include a cleft with a tight junction strand, to explain the observation of Levick (Exp Physiol 76: 825-857, 1991) that most tissues have an equilibrium tissue concentration that is close to 0.4 lumen concentration, and to explore the role of vesicular transport in achieving this equilibrium. The model predicts the surprising finding that one can have steady-state reabsorption at low pressures, in contrast to the experiments in Michel and Phillips, if a backward-standing gradient is established in the cleft that prevents the concentration from rising behind the glycocalyx.     

Deficiency in microfibril-associated glycoprotein-1 leads to complex phenotypes in multiple organ systems

Microfibril-associated glycoprotein-1 (MAGP-1) is a small molecular weight component of the fibrillin-rich microfibril. Gene-targeted inactivation of MAGP-1 reveals a complex phenotype that includes increased body weight and size due to excess body fat, an altered wound healing response in bone and skin, and a bleeding diathesis. Elastic tissues rich in MAGP-1-containing microfibrils develop normally and show normal function. The penetrance of MAGP-1-null phenotypes is highly variable and mouse strain-dependent, suggesting the influence of modifier genes. MAGP-1 was found to bind active transforming growth factor-beta (TGF-beta) and BMP-7 with high affinity, suggesting that it may be an important modulator of microfibril-mediated growth factor signaling. Many of the phenotypic traits observed in MAGP-1-deficient mice are consistent with loss of TGF-beta function and are generally opposite those associated with mutations in fibrillin-1 that result in enhanced TGF-beta signaling. Increased body size and fat deposition in MAGP-1-mutant animals are particularly intriguing given the localization of obesity traits in humans to the region on chromosome 1 containing the MAGP-1 gene.