Tissue cylinder

Krogh used this solution to express the concentration difference from the capillary (r = R ) to the outside of the tissue cylinder ... 

Divisions of Analysis. The preceding model describes conditions within a single fetal capillary surrounded by a thin tissue cylinder and supplied by a cylindrical annulus of maternal blood, as shown in Figure 3. Since the numerical techniques required for the solution of such equations were not well defined, the determination of a steady-state concurrent solution was first obtained. Based upon the results of this work, an unsteady-state concurrent solution was assumed possible and feasible. 

Partial pressure of oxygen calculated from the space average fractional saturation of blood, torr Radius of fetal capillary, cm Radius of maternal channel, cm Radius of tissue cylinder, cm Dimensionless radial distance Variable radius, cm Time, sec... 

A vast amount of work is being done to describe quantitatively the - transport of anabolites and metabolites in the microcirculation of the brain. The classical geometry for the capillaries and tissue has been the Krogh capillary-tissue cylinder. Recent investigations have considered other geometrical configurations to determine if other models derived for multicapillary systems are more descriptive than the single capillary structure used here. 

Table I. Normal Values of Parameters and Variables for the Krogh Capillary—Tissue Cylinder...

Figure 2. Lumped capillary-tissue cylinder with autoregulation...

The basic assumption for all theoretical oxygen tension calculations was introduced by August Krogh. The organs, especially the muscles, are assumed to be composed of numerous, equal tissue cylinders with concentric capillaries. This rough assumption does not cover blood flow differences within the branches of the capillary bed which can be microscopically observed. 

Figure 1.11 Geometry of the Krogh cylinder-type model. The inner cylinder represents the capillary the outer cylinder corresponds to the tissue cylinder. Shaded area example of hypoxic region under conditions of high demand. Rt, tissue cylinder radius Rc, capillary radius z, distance along the capillary. (From McGuire and Secomb, 2001.)...

It is assumed that no oxygen is exchanged across the outer boundary of the tissue cylinder, so that... 

Equation (1-120) can be used to predict whether under a given set of parameters, there are hypoxic regions—where the partial pressure of oxygen is less than 1 torr—in the tissue cylinder. Table 1.3 summarizes parameter values used in the Krogh model. 

Krogh tissue cylinder model A cylindrical volume of tissue supplied by a central cylindrical capillary. Myogenic response Vasoconstriction in response to elevated transmural pressure and vasodilation in response to reduced transmural pressure. 

Figure 3.5 Schematic representation of tissue microarray (TMA) fabrication. The tissue cylinders are taken by a sampling needle and embedded into the acceptor block, followed by immunostaining and evaluation of staining intensity.

In an anatomic study performed on rabbit limbs, Weinbaum et al. (1984) identified three vascular layers (deep, intermediate, and cutaneous) in the outer 1-cm tissue layer. Subsequently, three fundamental vascular structures were derived from the anatomic observation (1) an isolated vessel embedded in a tissue cylinder, as shown by the intermediate tissue layer, (2) a large artery and its countercurrent vein oriented obliquely to the skin surface, as shown in the deep tissue layer, and (3) a vessel or vessel pair running parallel to the skin surface in the cutaneous plexus. These three vascular structures served as the basic heat transfer units in the thermal equilibration analysis in Weinbaum et al. (1984). 

As shown in Weinbaum et al. (1984), 99 percent thermal equilibration length of a single blood vessel embedded in a tissue cylinder was derived as... 

TABLE 2.1 Thermal Equilibration Length in a Single Vessel Embedded in a Tissue Cylinder... 

FIGURE 2.2 Macro- and microvascular arrangement in skeletal mnscle. The blood supply for the muscle tissue cylinder comes from a branching countercurrent network of supply vessels. The primary (F) vessels, originatirrg limn the SAV vessels, rrm obliquely across the muscle tissue cylirtders and then brartch into the long secondary (s) vessels. IFrom Myrhage a Eriksson (1984), with pennission.]... 

FIGURE 6.1 Representative tissue cylinder surrounding a blood vessel showing the radial and axial position coordinates. 

Fig. 6.59 View inside a ribbed tissue cylinder with soda straw siphons for condensate removai (source Andritz).

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