Daniel D. Reneau

Oxygen Transport to Tissue — II

Material balances around a small, but finite volume element have formed the basis for previous mathematical models describing the transport of oxygen in the brain microcirculation. Seeking a model which would be both simple and versatile, a stochastic model was proposed based on the assumption that oxygenation of the brain can be described quantitatively by simulating the activity of only one erythrocyte and the oxygen molecules surrounding it. Compared with existing deterministic models, the capillary space-average oxygen partial pressure profiles were in close agreement. Tissue tensions were decidedly different.

The Oxygen Tension Field within a Discrete Volume of Cerebral Cortex

Abstract The purpose of this investigation was to experimentally determine with oxygen microelectrodes the characteristics of the oxygen tension field in a discrete volume of rabbit cortex. Over 20,000 measurements were made in 40 New Zealand white rabbits. These measurements were analyzed: (a) graphically, by plotting oxygen tension versus cortex depth; (b) statistically, by constructing oxygen tension histograms; and (c) mathematically, by calculating the arithmetic mean and standard deviation. The majority of values were between 0 and 40 mm Hg. Often sharp changes occurred within small distances. The measured oxygen tension values ranged from near 0 to 90 mm Hg, but 50% of the values occurred between 5 and 20 mm Hg and 70% of all values were below 35 mm Hg. The arithmetic mean was calculated to be 24.54 mm Hg with a standard deviation of 17.98. The oxygen tension histogram was characterized by a concentration of values between 10 and 20 mm Hg and was skewed toward the higher oxygen tension values.

Interpretation of Oxygen Disappearance Rates in Brain Cortex Following Total Ischaemia

The purpose of this project was to attempt to obtain a more precise interpretation of the meaning of the rates of disappearance curves of PO2 in brain cortex following complete ischaemia as measured with microelectrodes. The following three specific studies are discussed: (1) Analysis of individual PO2 disappearance as a function of time. (2) Analysis of the rate of disappearance as a function of the initial tissue PO2. (3) Analysis of the rates of disappearance curves with respect to the possibility of prediction of local metabolic rates.

A Critical Evaluation of Oxygen Disappearance during Stop Flow in the Gerbil Brain

The rate of oxygen disappearance from the gerbil cerebral cortex was measured during bilateral carotid artery occlusion with an oxygen microelectrode at normal tissue PO2 and under hyperbaric oxygenation. The oxygen disappearance rate (ODR) was found to be heavily dependent on the PO2 at occlusion due to the desaturation of hemoglobin-bound oxygen. When the tissue PO2 was elevated to a level high enough to saturate hemoglobin, the ODR reflected the oxygen consumption rate which was calculated to range from 1.6-7.4 cc O2/100 cc tissue-min. for ten barbiturate-anesthetized animals. The fall in PO2 was found not to be totally linear to zero in many cases, but instead consisted of a linear phase followed by a period of decreasing slope. We believe this phase of changing slope represents a diminishing oxygen consumption rate. The exact nature of this decrease is not known but perhaps is an inhibitory response to the accumulation of metabolites as a result of the circulation arrest.

Oxygen Dynamics in Brain

Abstract Following cardiac arrest, measurements with microelectrodes indicate that extracellular brain P O 2 decreases to approximately 0 mm Hg within a few seconds. Theoretical simulations compared with the experimental measurements indicate that the metabolic demand for oxygen, under these conditions, is constant until a very low extracellular P O 2 is attained.

A theoretical analysis of the dynamics of oxygen transport and exchange in the placental-fetal system

This paper presents a systematic mathematical analysis of the transient response of oxygen in the placental and fetal system when disturbances create changes in normal conditions. Particular emphasis is given to changes resulting from upsets in placental maternal flow such as may occur during the contractions of labor. Response in the placenta was found to be rapid, but when interconnected with the fetal system both the quality and quantity of response was altered. Oxygen response in the fetal system to changes in maternal placental flow was considerably damped at the organ level and relatively slow. Following a total cessation of maternal flow, several minutes were required theoretically to obtain anoxia in brain provided all other factors remained constant.

An analytical model for axial diffusion in the Krogh cylinder.

The tissue level distribution of oxygen (O2) in the hemoglobinless perfused heart has been measured under controlled conditions with Whalen PO2 microelectrodes (Schubert, Whalen, and Nair, 19 78). In an attempt to understand tissue level details of O2 transport we compared that PO2 distribution to those predicted by mathmatical models. Models incorporating only radial transport in the tissue compared poorly with the measured histograms. Blum’s (1960) model with radial and axial diffusion was found to be in error (Schubert, 1976), and a correct solution had not been published. A unique analytic model was derived by modifying the radial transport phenomena so that the axial diffusional transport could be included. This model displays trends seen in the experimental data. Unfortunately the best match was obtained by increasing the value of the axial diffusion coefficient, D, considerably beyond the value accepted in the literature. This led to questions about the appropriateness of the radial transport assumptions which could be answered only be seeking the correct solution to the problem originally posed by Blum.

Mathematical Analysis of Combined Placental-Fetal Oxygen Transport

During contractions of labor, uterine blood flow varies directly with the strength and duration of the contraction (3,5,6). in addition to observations in sheep and dogs, radioangiographic studies have shown that in both monkeys and humans, placental intervillous blood flow is reianded in bySynchrony Will the atenine contractions of labor (2,13). Prolonged partial asphyxia resulting from strong oxytoxin induced contractions have been shown to produce varying degrees of brain damage in term monkey fetuses (11,12).

Fetal brain PO2 transient response during hypoxia and hyperoxia

Abstract The purpose of this investigation was to experimentally determine the response of fetal brain PO2 to dynamic changes in the oxygen tension of maternal arterial blood using oxygen microelectrodes. Both hyperoxia and hypoxia were investigated. Recordings of the variation in fetal cortical oxygen tension during the transition from maternal hyperoxia to maternal normoxia and the return to maternal hyperoxia were obtained. Also recordings showing the variations in fetal cortical oxygen tension during the transition from maternal hyperoxia to maternal hypoxia and the subsequent return to hyperoxia were obtained. It was observed that fetal brain oxygen tensions are considerably lower than those measured in the adult. In many instances administration of 100% oxygen to the mother improved fetal brain oxygenation. The response of fetal brain PO2 to changes in the oxygen tension of maternal arterial blood was delayed by a finite quantity of time. The average value obtained for this delay was 38 sec. An overshoot phenomena was observed during hypoxia recovery, which indicates a fetal control mechanism which acts to compensate for brief periods of hypoxia in the microenvironment.

An Analysis of Ion Distribution in Brain Following Anoxia

Experimental measurements of changes in the extracellular ion concentrations of rat brain cortex have been made with ultrami croelectrodes (1). During extended anoxia of several minutes duration, the changes in ionic concentrations may be characterized by the following statements: (1) Changes occurred in two phases: A preanoxic depolarization phase and an anoxic depolarization phase. (2) The preanoxic depolarization phase was characterized by small increases in extracellular Na+, K+, Cl- concentrations and usually a slight decrease in brain DC potential. (3) The anoxic depolarization phase was characterized by wery rapid increases in extracellular K+, simultaneous decreases in Na+ and Cl-, and rapid decreases in DC potential.