Oxygen Dynamics in Brain

MKROVASCULARESEARCH 13, 337-344 (1977) Oxygen Dynamics in Brain DANIEL D. RENEAU, ERIC J. GUILBEAU, AND RANDAL E. NULLS Department of Biomedical Engineering, Louisiana Tech University, Ruston, Louisiana 71270 Received October 22, 1976 Following cardiac arrest, measurements with microelectrodes indicate that extracellular brain PO2 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 PO2 is attained. INTRODUCTION In attempting to conduct a comprehensive analysis of oxygen transport in the microcirculation of the cortex during arterial hypoxia or ischemia, one finds several conflicting viewpoints in the literature. For instance, using oxygen microelectrodes Dorson and Bogue (1975) measured the response of brain PO, to transient changes in arterial PO,. According to their results, brain POZ in healthy animals decreased only a few millimetres of Hg when arterial blood PO, was continuously changed from 75 to 30 to 75 mm Hg. Combined theoretical analyses indicated that a mathematical model featuring a changing metabolic rate during hypoxia more closely predicted the experimental results than a model featuring a constant metabolic rate. In addition, Bicher et al. (1973) reported that brain PO, stabilized at a value several millimeters of Hg above zero following nitrogen inhalation. Theoretical analyses indicated that this condition could be explained by a decreasing metabolic rate during hypoxia. Finally, Duffey et al. (1972) postulated that hypoxia is accompanied by a reduction in cerebral energy requirements. In contrast Leniger-Follert et a/. (1975), Metzger et al. (1971), and Nair et al. (1975), among others, have reported a rapidly disappearing brain POZ following initiation of arterial blood hypoxia. These results are an indication of the maintenance of a high metabolic rate. Leniger-Follert et al. (1975) also reported studies that simultaneously measured brain PO, and microflow changes during induced hypoxia. These results demonstrate that microflow changes play a very important role in the regulation of brain POZ. Hence, prior theoretical and experimental studies analyzing PO, changes in the brain during hypoxia have been influenced by an unknown change in microflow. To the best of our knowledge, analyses heretofore have failed to achieve a separation of metabolic effects from microflow effects. The purpose of this paper is to present the 1 This paper was presented at the Anaheim Symposium, International Society on Oxygen Transport to Tissue, April 11-16, 1976. Z Present address: Department of Biomedical Engineering, University of Virginia, Charlottesville, VA. 22901. Copyright ~33 1977 by Academic Press, Inc. 337 All rights of reproduction in any form reserved. Printed in Great Britain ISSN 00264862

338 RENEAU, GUILBEAU, AND NULL results of an experimental and theoretical attempt to separate and study these effects by eliminating flow completely-total &hernia. MATERIALS AND METHODS A. Experimental Locally obtained New Zealand white rabbits (both male and female) were chosen as experimental animals for the project. Exact experimental techniques for using these animals and oxygen microelectrodes to record PO, values in the brain have been reported elsewhere by Smith et al. (1975). In general the rabbits were anesthetized with urethane (1 g/kg) and placed in a stereotaxic device. Following surgery, an oxygen microelectrode having a tip diameter of l-3 pm was inserted into the extracellular space of brain cortex near the junction of the medial and bregma sutures. Microelectrodes were constructed in our laboratory according to instructions reported by Silver (1965) with the modifications outlined in Smith et al. (1975). All physiological factors were allowed to stabilize following preparation, and measurements included ECG, blood pressure, carotid blood flow, and brain PO,. The heart was stopped by a bolus injection into the femoral vein of 3-4 ml of saturated KCl. The results presented herein are examples of results obtained from over 15 successful experiments and are representative of measurements at various depths in the cortex. B. Theoretical In conjunction with the experimental measurements a theoretical analysis was conducted by simulating the capillary-tissue system in the microcirculation with mathematical models based on distributed and lumped parameter geometry. The models were standardized with data to represent normal conditions and then solved for the situation of total ischemia. (I) Distributedparameter model. Based on the Krogh geometry, known phenomena, and certain assumptions which are outlined by Reneau et al. (1967, 1969, 1970) a mathematical model has been developed which describes the change in oxygen partial pressure in capillary blood and tissue as a function of time, position, flow rate, ph, oxygen capacity, metabolic rate, and various constants such as diffusion coefficients and solubility. The model consists of four equations, one each for the capillary and tissue and two for the interface between tissue and blood. As shown below, the equations are coupled, nonlinear, partial differential equations with one dependent and three independent variables. Additional details concerning the model and its development are given in previous publications. Capillary Nknp - )P=D~ ( I+ c,(l + kp )Z at (!?&T+~!)+DIE!$- ~x&-c~~y~t22 (1) Interface pi I blood = Pi I tissue (2)

OXYGEN DYNAMICS IN BRAIN 339 Note that the two interface equations indicate that the oxygen partial pressure profile is continuous across the blood-tissue interface, and oxygen is transported across the interface according to Fick s first law. Numerical solution techniques have been developed to soive this model for various conditions and are available in the literature quoted above. Simulations for cardiac arrest may be found in Reneau et al. (1970). (2) Lumped parameter model. In order to facilitate the calculation time and mass transfer coefficients, a lumped parameter model consisting of differential equations was developed to simulate the diffusion problem described by Eqs. (l)-(4). The equations describe the interaction between erythrocyte, plasma, extracellular space, and intracellular space. Mass transfer coefficients and other constants were estimated from a knowledge of system behavior. Details of this approach are given in Null (1976) and solution was obtained by means of the CSMP simulation language. (4) DISCUSSION OF RESULTS Following injection of KCI, simultaneous recordings of brain tissue POz, ECG, pulsatile carotid flood flow, mean carotid blood flow, and femoral artery blood pressure are presented in Figs. l-3. These results are representative of all 15 experiments and show responses from various initial steady states and from various depths in the cortex. General results indicated that a failure occurred first in the ECG and was followed by a failure in blood pressure, blood flow, and brain POz, respectively. The PO, responses in Figs. 1-3 were redrawn and are presented in Fig. 4. Inspection of Fig. 4 reveals that the following three factors are characteristic responses. 1, Brain PO, decreases to values equal to or very near 0 mm Hg. 2. Brain POz response to circulatory arrest is very rapid. In less than 1 set tissue PO, begins to decrease and in all cases has decreased to approximately 0 mm Hg in less than 5 sec. The three curves show a decrease to 0 mm Hg in 4, 3, and 1.5 set, respectively. 3. The rate of change of brain PO, with respect to time is constant until a very low extracellularp0, of approximately 1.O mm Hg is attained. This constancy in the rate of change is shown by the straight-line decrease in all three curves. Figure 5 compares one of the experimental responses (top curve) with a theoretical simulation of circulatory arrest. No attempt was made to quantitatively match the experimental data but shapes and trends were compared. With the distributed parameter model (bottom curve) capillary blood flow ceased instantly, and the metabolic consumption rate of oxygen was maintained constant. Note that the simulation takes into

340 RENEAU, GUILBEAU, AND NULL consideration the release of O2 from hemoglobin, the supply of O2 to tissue by diffusion, and the consumption of O2 by a constant metabolic rate. In comparison with the experimental curve the same constant rate of change of PO, with respect to time is found except that the change in shape at a low POz is not present in the theoretical simulation. Similar simulations have been shown by Reneau et al. (1970) and Bruley et al. (1971). BRAIN OXYGEN TENSION RESPONSE Ok 200-0 1 2 3 4 5 6 7 TIME, SECONDS FIG. 1. Parameter responses following cardiac arrest. The middle curve in Fig. 5 is the result of the same theoretical simulation using the lumped parameter mathematical model and the following changes : 1. After extracellular tissue PO, decreases below a critical PO, of 1.O mm Hg, the metabolic rate of consumption of oxygen is allowed to change according to first-order kinetics. 2. Capillary blood flow is allowed to decrease linearly to zero during the initial phase of the response instead of ceasing instantly. The shape of the middle curve of Fig. 5 is the same as the bottom curve except that it more closely fits the shape of the experimental curve at initial, intermediate, and low POz values. The transient cessation of flow affects the initial slope, and the changing metabolic rate at the critical POz significantly changes the final slope. However, only

OXYGENDYNAMICSINBRAIN 341 when metabolism changed from a constant value did the straight-line appearance of the PO2 versus time curve change. CONCLUSIONS When autoregulation by means of adjustments in microflow is removed by stopping all flow in the brain, the extracellular PO, response is very rapid and decreases to values near zero in a few seconds. Theoretical analyses combined with experimental measurements indicate that the metabolic rate remains essentially constant as PO2 decreases BRAIN OXYGEN TENSION RESPONSE RAIN OXYGEN TENSION ECG ILEAD ni PULSATILE Y CAROTID FLOW BLOOD PRESSURE (FEMORAL ARTERY) 0 1 2 3 4 5 6 7 TIME, SECONDS FIG. 2. Parameter responses following cardiac arrest. to values very near 0 mm Hg; or, at the very least, the degree of any metabolic change is not sufficient to be detected by our methods. These resuits are not applicable to conditions of(i) changing demands for energy or (ii) biochemical contamination resulting from a slow approach to hypoxia. The results do demonstrate that under the conditions outlined the metabolic rate is not a function of decreasing POZ, and the cerebral demand for energy is approximately constant during this transient approach to anoxia.

342 RENEAU, GUILBEAU, AND NULL BRAIN OXYGEN TENSION RESPONSE nmiw 0 k lm 50 /) i : ; 1 / 0 1 2 3 4 5 6 7 TIME, SECONDS FIG. 3. Parameter responses following cardiac arrest. TIME, SECONDS FIG. 4. Brain PO2 response following circulatory arrest.

OXYGEN DYNAMICS IN BRAIN 343 TIME. SECONDS Fig. 5. Comparison of theoretical simulations with experimental measurement. ACKNOWLEDGMENT This research was supported in part by NIH Grant NS-08802. REFERENCES BICHER, H. I., RENEAU, D. D., BRULEY, D. F., AND KNISELY, M. H. (1973). Brain oxygen supply and neuronal activity under normal and hypoglycemic conditions. Amer. J. Physiol. 224,275-282. BRULEY, D. F., BICHER, H. O., RENEAU, D. D., AND KNISELY, M. H. (1971). Effect of intravascular red cell aggregation and its counter-action by anti-adhesive drugs on brain tissue oxygenation. Zrz 6th European Conference on Microcirculation, Aalborg (J. Ditsel and D. H. Lewis, eds), pp. 193-196. DORSON, W., AND BOGUE, A. (1975). In Oxygen Transport to Tissue (J. Grote, D. Reneau, and G. Thews, eds.). Plenum Press, in press. DUFFY, T. E., NELSON, S. R., AND LOWRY, 0. H., (1972). Cerebral carbohydrate metabolism during acute hypoxia and recovery. J. Neurochem. 19,959-977. LENIGER-FOLLERT, E., WRABETZ, W., AND LUBBERS, D. W. (1975). Local tissue PO2 and microflow of the brain cortex under varying arterial oxygen pressure. In Oxygen Transport to Tissue (J. Grote, D. Reneau, and G. Thews, eds.), Plenum Press, in press. METZGER, H., ERDMANN, W., AND THEWS, G. (1971). Effect of short periods of hypoxia, hyperoxia, and hypercapnia on brain 0, supply. J. Appl. Physiol. 31, 751-759. NAIR, P., WHALEN, W. J., AND BUERK, D. (1975). PO, of cat cortex: Response to breathing N, and 100% Oz. Microuasc. Res. 9, 158-165. NULL, R. E. (1976). A Transient Analysis of Multicomponent Transport and Reaction in the Microcirculation of Brain. Ph.D. Dissertation, Louisiana Tech University, Ruston, Lou. RENEAU, D. D., BRULEY, D. F., AND KNISELY, M. H. (1967). A mathematical simulation of oxygen release, diffusion, and consumption in the capillaries and tissue of the human brain. In Chemical Engineering in Medicine and Biology (D. Hershey, ed.), pp. 135-241. Plenum Press, New York. RENEAU, D. D., BRULEY, D. F., AND KNISELY, M. H. (1969). A digital simulation of transient oxygen transport in capillary-tissue systems (cerebral gray matter). J. Amer. Inst. Chem. Eng. 15,916-925.

344 RENEAU, GUILBEAU, AND NULL RENEAU, D. D., BRULEY, D. F., AND KNISELY, M. H. (1970). A computer simulation for prediction of oxygen limitations in cerebra1 gray matter. JAAMZ4,211-223. RENEAU, D. D., HUNG, D., AND KNISELY, M. H. (1970). Simultaneous diffusion of oxygen and glucose in the human brain after cardiac arrest. In Proceedings. 23rd Annual Conference on Engineering in Medicine and Biology, Vol. 12, p. 90. SILVER, I. A. (1965). Some observations on the cerebra1 cortex with an ultramicro, membrane-covered, oxygen electrode. Med. Electron. Biol. Biol. Eng. 3, 377-387. SMITH, R. H., GUILBEAU, E. J., AND RENEAU, D. D. The oxygen tension field with a discrete volume of cerebral cortex. Submitted for publication.