Extension of Murray's law using a non-Newtonian model of blood flow

Background  

So far, none of the existing methods on Murray's law deal with the non-Newtonian behavior of blood flow although the non-Newtonian approach for blood flow modelling looks more accurate.     

The evaluation of Murray's law in Psilotum nudum (Psilotaceae), an analogue of ancestral vascular plants

Previous work has shown that the xylem of seed plants follows Murray's law when conduits do not provide structural support to the plant. Here, compliance with Murray's law was tested in the stem photosynthesizer Psilotum nudum, a seedless vascular plant. Psilotum nudum was chosen because the central stele does not provide structural support, which means that Murray's law is applicable, and because its simple shoot structure resembles the earliest vascular plants. Murray's law predicts that the sum of the conduit radii cubed (Σr(3)) should decrease in direct proportion with the volume flow rate (Q) to maximize the hydraulic conductance per unit vascular investment. Agreement with Murray's law was assessed by estimating the transpiration rate distal to a cross-section, which should determine Q under steady state conditions, and comparing that with the Σr(3) of that cross-section. As predicted, regressions between the Σr(3) of the cross-section and Q resulted in a linear relationship with a y-intercept that was not different from zero. Two more rigorous statistical tests were also unable to reject Murray's law. Psilotum nudum plants also increased their conductance per investment by having more conduits distally than proximally, which is more efficient hydraulically than equal or declining conduit numbers distally.     

The meaning of the Weber-Fechner law: IV. The psychometric curve and interhemispheric and intrahemispheric interactions

A subject was presented two horizontal lines. One of them was an objective reference line (Ro), whose length was unchanged. There were a total of five Ro lines. The other line was a test line (T), whose length varied. The subject had to say whether the longer line was above or below the shorter one. The results were treated using a model of neuronal constructions consisting of a number of similar constructions fulfilling different functions along the route from inputting information to obtaining Weber’s ΔL/L ratio. Psychometric curves and the reference stimulus (Rs) as their derivative were determined at the initial stage. In this case, Rs≠Ro. At the final stage of simulation, Rs = Ro. The Weber-Fechner fraction was calculated using the standard formula (T - Ro)/Ro. The same initial data introduced to the model yielded a curve entirely coinciding with the curve calculated experimentally. At the final stage of stimulation, Rs and Ro were equal to each other. Their inequality at the initial stages was necessary for calculating the mutual positions of the elements of a scene. It was concluded that the model constructions are similar to real neuronal constructions of the visual brain.     

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)     

A steady-state filtration model for transluminal water movement in small and large blood vessels

It is now generally accepted that the intercellular cleft between adjacent endothelial cells is the primary pathway for the transluminal movement of water and small ions in the vasculature. A steady-state theoretical model has been developed to show quantitatively how the geometry of the intercellular cleft between adjacent endothelial cells is related to both the water movement and pressure distribution in the subendothelial space and to examine how the existence of a subendothelial interaction layer affects the hydraulic resistance of the media of vessels of varying wall thickness. The velocity and pressure fields in the media are described using porous matrix theory based on Darcy's law and a lubrication-type analysis is used to describe the flow in a variable geometry intercellular cleft. These two equations are solved simultaneously to determine the unknown pressure distribution beneath the endothelium and the flow in the arterial media. Application of this model shows that, when the tight junction in the cleft is 26 A or less, more than half of the total hydraulic resistance of the wall occurs across the endothelial cell monolayer, for a vessel whose wall thickness is less than 0.02 cm. This finding is in good agreement with the experimental findings of Vargas, et al. (1978) for rabbit aorta. Contrary to previous belief, the model shows that the filtration resistance of an arterial wall with intact endothelium does not scale linearly with wall thickness due to the highly nonlinear resistance of the endothelial interaction layer.     

Blunt trauma to large vessels: a mathematical study

Background  

Blunt trauma causes short-term compression of some or all parts of the chest, abdomen or pelvis and changes hemodynamics of the blood. Short-term compression caused by trauma also results in a short-term decrease in the diameter of blood vessels. It has been shown that with a sudden change in the diameter of a tube or in the direction of the flow, the slower-moving fluid near the wall stops or reverses direction, which is known as boundary layer separation (BLS). We hypothesized that a sudden change in the diameter of elastic vessel that results from compression may lead not only to BLS but also to other hemodynamic changes that can damage endothelium.     

From large networks to small molecules

Large-scale analysis of genetic and physical interaction networks has begun to reveal the global organization of the cell. Cellular phenotypes observed at the macroscopic level depend on the collective characteristics of protein and genetic interaction networks, which exhibit scale-free properties and are highly resistant to perturbation of a single node. The nascent field of chemical genetics promises a host of small-molecule probes to explore these emerging networks. Although the robust nature of cellular networks usually resists the action of single agents, they may be susceptible to rationally designed combinations of small molecules able to collectively shift network behavior.     

Assessment of endothelial function of large, medium, and small vessels: a unified myograph

Endothelial dysfunction precedes the development of morphological atherosclerotic changes and can also contribute to lesion development in cardiovascular diseases. Currently, there is a lack of a single method to determine endothelial function of the entire range of vessel dimensions from aorta to arterioles. Here we assessed endothelial function of a large range of size arteries using a unified isovolumic myograph method. The method maintains a constant volume of fluid in the lumen of the vessel during contraction and relaxation, which are characterized by an increase and a decrease of pressure, respectively. Segments of six aortas, six common femoral arteries, and six mesenteric arteries from rats; six carotid arteries from mice; and six coronary and carotid arteries from pigs were used. The endothelium-dependent dose-response vasorelaxation was determined with endothelium-dependent vasodilators while arterial preconstriction was induced with vasoconstrictors at a submaximal dose. The circumferential midtension during vascular reactivity varied from 43.1 ± 7.9 to 2.59 ± 0.46 mN/mm (from large to small arteries), whereas the circumferential midstress showed a much smaller variation from 217 ± 23.5 to 123 ± 15.3 kPa (in the same range of vessels). We also found that overinflation and axial overelongation compromised endothelium-dependent vasorelaxation to underscore the significance of vessel preload. In conclusion, an isovolumic myograph was used to unify arterial vasoreactivity from large to small arteries and shows the uniformity of wall stress and %tension throughout the range of vessel sizes.     

Relationship of blood vessels to small intensely fluorescent cells in the autonomic ganglion.

In our experiments we observed the relationship of the blood vessels to the small, intensely fluorescent cells (SIF cells) in the lower mesenteric ganglion of the cat. We injected the solution of Evan's blue into the ganglia and processed them with the fluorescent histochemical method by Falck and Hillarp. We observed that the SIF cells are placed in the ganglia closely to the blood vessels or closely round them. When observing lager groups of SIF cells placed at the edge of the ganglia a dense network of the blood vessels was observed among these cells.     

Anatomical variants of the lymphatic vessels connecting the inguinal lymph nodes]

The study of anatomical variants of lymphatic vessels connecting inguinal lymph nodes was carried out on 56 corpses of adult persons of both sex whose deaths were not connected with lesions in the lymphatic system of the pelvis and lower extremities. The inguinal lymph nodes and their afferent and efferent lymphatic vessels were detected by the method of intradermal injection and by the method of direct injection into the lymphatic vessels. It was stated that groups of the inguinal lymph nodes, as well as the nodes in every group determined, can serve as nodes of different stages for afferent lymphatic vessels running from different parts of the body and organs.     

The meaning of the Weber-Fechner law and description of scenes: III. Description of the visual space

The Weber-Fechner fraction was measured in experiments where a subject was presented with a pair of lines, the length of one (reference) line being constant and the length of the other (test) one varying. The subject had to say whether the longer line was above or below the shorter one. The subject was trained to distinguish the positions of lines in areas limited in the number of reference lines located at different degrees of eccentricity. The fraction curve for each area proved to be of the same shape as the curve obtained for the entire range and reflecting the Weber-Fechner law. The fraction was originally maximum and only slightly decreased afterwards. On the basis of these data, a neural construction is suggested that serves for describing the visual space and explains the shape of the curve reflecting the Weber-Fechner law.