Krogh cylinder model

For three-dimensional (spherical) tumors, most investigators have considered tumors to be avascular and have used models developed for spheroids (e.g., McFadden and Kwok, 1988 Van Osdol et al., 1993). Theoretically, these models are analogous to the Krogh cylinder model, except for the boundary conditions and the use of spherical instead of radial coordinates. Therefore, they do not provide significant insights into the role of vasculature and transvascular flux. 

Figure 1. Tissue lump-capillary lump Krogh cylinder model...

Consider the Krogh cylinder model for oxygen transport in skeletal muscles described in Example 1.26. 

Impulse Response for the Krogh Cylinder Model with Plug Flow in the Capillary (Phase 1), Finite Diffusional Resistance Perpendicular to Flow Direction in the Tissue (Phase 2) and No Resistance at the Capillary Wall (Phase Boundary). Equivalent to Case 2. 

Figure 8.2 Cylindrical geometry of the Krogh-Erlang model of blood-tissue exchange. The upper panel, from Middleman [141], illustrates the assumed parallel arrangement of capillaries with each vessel independently supplying a surrounding cylinder of tissue. A diagram of the model geometry is provided in the lower panel. Figure in upper panel is reprinted with the permission of John Wiley Sons, Inc.

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.)...

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. 

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. 

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. 

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