A theoretical model of gas transport between arterioles and tissue

Informational dynamics of vasomotion in microvascular networks: a review

Vasomotion refers to spontaneous oscillation of small vessels observed in many microvascular beds. It is an intrinsic phenomenon unrelated to cardiac rhythm or neural and hormonal regulation. Vasomotion is found to be particularly prominent under conditions of metabolic stress. In spite of a significant existent literature on vasomotion, its physiological and pathophysiological roles are not clear. It is thought that modulation of vasomotion by vasoactive substances released by metabolizing tissue plays a role in ensuring optimal delivery of nutrients to the tissue. Vasomotion rhythms exhibit a great variety of temporal patterns from regular oscillations to chaos. The nature of vasomotion rhythm is believed to be significant to its function, with chaotic vasomotion offering several physiological advantages over regular, periodic vasomotion. In this article, we emphasize that vasomotion is best understood as a network phenomenon. When there is a local metabolic demand in tissue, an ideal vascular response should extend beyond local microvasculature, with coordinated changes over multiple vascular segments. Mechanisms of information transfer over a vessel network have been discussed in the literature. The microvascular system may be regarded as a network of dynamic elements, interacting, either over the vascular anatomical network via gap junctions, or physiologically by exchange of vasoactive substances. Drawing analogies with spatiotemporal patterns in neuronal networks of central nervous system, we ask if properties like synchronization/desynchronization of vasomotors have special significance to microcirculation. Thus the contemporary literature throws up a novel view of microcirculation as a network that exhibits complex, spatiotemporal and informational dynamics.

Theoretical models of microvascular oxygen transport to tissue

To improve understanding of microvascular O(2) transport, theoretical modeling has been pursued for many years. The large number of studies in this area attests to the complexities (i.e., biochemical, structural, and hemodynamic) involved. This article focuses on theoretical studies from the last two decades and, in particular, on models of O(2) transport to tissue by discrete microvessels. A brief discussion of intravascular O(2) transport is first given, highlighting the physiological importance of intravascular resistance to blood-tissue O(2) transfer. This is followed by a description of the Krogh tissue cylinder model of O(2) transport by a single capillary, which is shown to remain relevant in modified forms that relax many of the original biophysical assumptions. However, there are many geometric and hemodynamic complexities that require the consideration of microvascular arrays and networks. Multivessel models are discussed that have shown the physiological importance of heterogeneities in vessel spacing, O(2) supply, red blood cell flow path, as well as interactions between capillaries and arterioles. These realistic models require sophisticated methods for solving the governing partial differential equations, and a range of solution techniques are described. Finally, the issue of experimental validation of microvascular O(2) delivery models is discussed, and new directions in O(2) transport modeling are outlined.

Effect of crystalloid administration on oxygen extraction in endotoxemic pigs

We asked whether crystalloid administration improves tissue oxygen extraction in endotoxicosis. Four groups of anesthetized pigs (n = 8/group) received either normal saline infusion or no saline and either endotoxin or no endotoxin. We measured whole body (WB) and gut oxygen delivery and consumption during hemorrhage to determine the critical oxygen extraction ratio (ERO2 crit). Just after onset of ischemia (critical oxygen delivery rate), gut was removed for determination of area fraction of interstitial edema and capillary hematocrit. Radiolabeled microspheres were used to determine erythrocyte transit time for the gut. Endotoxin decreased WB ERO2 crit (0.82 +/- 0.06 to 0.55 +/- 0.08, P < 0.05) and gut ERO2 crit (0.77 +/- 0.07 to 0.52 +/- 0.06, P < 0.05). Unexpectedly, saline administration also decreased WB ERO2 crit (0.82 +/- 0.06 to 0.62 +/- 0.08, P < 0.05) and gut ERO2 crit (0.77 +/- 0.07 to 0.67 +/- 0.06, P < 0.05) in nonendotoxin pigs. Saline administration increased the area fraction of interstitial space (P < 0.05) and resulted in arterial hemodilution (P < 0.05) but not capillary hemodilution (P > 0.05). Saline increased the relative dispersion of erythrocyte transit times from 0.33 +/- 0.08 to 0.72 +/- 0.53 (P < 0.05). Thus saline administration impairs tissue oxygen extraction possibly by increasing interstitial edema or increasing heterogeneity of microvascular erythrocyte transit times.

Incorporating O2-Hb reaction kinetics and the Fåhraeus effect into a microcirculatory O2-CO2 transport model

The influence of O2-Hb reaction kinetics and the Fåhraeus effect on steady state O2 and CO2 transport in cat brain microcirculation was investigated using our refined multicompartmental model. The most important model predictions include: 1) capillaries are the sites in the microcirculation where the effect of O2-Hb kinetics is most pronounced; 2) while there is only a small difference between equilibrium and actual oxygen saturation, this effect is not negligible; 3) O2-Hb kinetics tends to make the PO2 level at the venous entrance higher than in venules; 4) the influence of the Fåhraeus effect leads to a lower tissue PO2 level than in venules and the outlet vein. The resultant decline in tissue PO2 may lead to a decrease in O2 consumption rate and extraction ratio; 5) although the Fåhraeus effect changes the ratio between arteriolar flux and capillary flux, incorporating the Fåhraeus effect and O2-Hb kinetics into the simulation does not change our previous conclusion, that most of the O2 and CO2 exchange takes place at the capillary level; 6) in general, influences of O2-Hb kinetics and Fåhraeus effect are synergistic; 7) a model that excludes these two mechanisms might overestimate the tissue oxygenation level especially during severe hypoxia.

A compartmental model for oxygen-carbon dioxide coupled transport in the microcirculation

We present a multicompartmental model for an oxygen-carbon dioxide transport system. The compartmental equations and their lumped parameters are derived through space averaging of the corresponding distributed model. The model can predict compartmental distributions of oxygen and carbon dioxide partial pressures, oxygen-hemoglobin saturation, and pH. Other unique features include the effects of the radial distribution of partial pressures and the difference in metabolic rates between vessel wall and tissue. A model for the cat brain, based on this formulation, is compared with results of experiments and with two types of earlier models: one without space averaging and one without carbon dioxide transport. The results suggest that space averaging the convective terms significantly affects the behavior of the model. This is consistent with conclusions from our earlier oxygen-only model. Our observations also demonstrate, however, significant differences between the results from the oxygen-carbon dioxide model and the oxygen-only model. For instance, at low blood flow rates or at low level of oxygen input, predicted oxygen partial pressures can differ by as much as 30% between the two models. Results obtained from the present model are supported by available experimental findings.

A model of brain arteriolar oxygen and carbon dioxide transport during anemia

Existing experimental and theoretical evidence suggests that precapillary diffusion of O2 and CO2 occurs between arterioles and tissue under normal physiologic conditions. However, limited information is available on arteriolar gas transport during anemia. With use of a mathematical model of an arteriolar network in brain tissue, anemic hematocrits of 35, 25, and 15% were modeled to determine the effect of anemia on the exchange, the change in the equilibrium tissue O2 and CO2 tensions, and the increase in blood flow needed to restore tissue oxygenation. We found that the blood PO2 exiting the network fell from 66 mm Hg normally to 48 mm Hg during the severest anemia. Concurrently, the equilibrium tissue O2 tensions dropped from 44 to 23 mm Hg. For CO2 the exit blood PCO2 was 58 mm Hg for a 15% hematocrit, an increase of 4 mm Hg from the normal value, and equilibrium tissue PCO2 increased from 56 to 61 mm Hg. Blood flow increases from normal values necessary to offset the effects of the decreased O2 delivery to the tissue were 26, 86, and 222%, respectively, for hematocrits of 35, 25, and 15%. We compared our model results with recent experimental studies that have suggested that the amount of O2 diffusion is much higher than predicted values. We found that these experimental O2 gradients are three to four times larger than theoretical.

A method for measuring the rate of oxygen release from single microvessels

A system determining the rate of oxygen release from erythrocytes flowing in single microvessels was constructed with an inverted microscope by connecting 1) a scanning/grating spectrophotometer equipped with a photon-counting detector through a thin light guide, to obtain the visible absorption spectrum of a spot (5 microns in diameter) focused on a microvessel, 2) two photomultipliers (connected to a microcomputer via an analog-to-digital converter) through two light guides, to determine the flow velocity of erythrocytes by calculating the cross correlation between the light-intensity changes of two spots (3 microns in diameter, 5 microns apart from each other) focused on the microvessel, and 3) an image processor through a video camera, to estimate the diameter of microvessel from the digitized video images. The rate of oxygen release from single microvessels 7-25 microns in diameter in rat mesentery was measured under the superfusion of deoxygenated solution: 1) The maximal rate was obtained in capillaries, and the rate in arterial microvessels was larger than that in venous microvessels, when similar diameters were compared. 2) The rate was maximum at pH 7.0-7.2, and it decreased in more acidic and alkaline pH values. 3) The rate decreased with a decrease in temperature. The reliability of the measurement using the present apparatus was tested in detail.