Tracer oxygen distribution is barrier-limited in the cerebral microcirculation

Nonstationary Model of Oxygen Transport in Brain Tissue

The paper addresses the mathematical study of a nonstationary continuum model describing oxygen propagation in cerebral substance. The model allows to estimate the rate of oxygen saturation and stabilization of oxygen concentration in relatively large parts of cerebral tissue. A theoretical and numerical analysis of the model is performed. The unique solvability of the underlying initial-boundary value problem for a system of coupled nonlinear parabolic equations is proved. In the numerical experiment, the tissue oxygen saturation after hypoxia is analyzed for the case when a sufficient amount of oxygen begins to flow into the capillary network. A fast stabilization of the tissue oxygen concentration is demonstrated. The reliability of the results of the numerical simulation is discussed.

Three-dimensional mapping of oxygen tension in cortical arterioles before and after occlusion

Occlusions in single cortical microvessels lead to a reduction in oxygen supply, but this decrement has not been able to be quantified in three dimensions at the level of individual vessels using a single instrument. We demonstrate a combined optical system using two-photon phosphorescence lifetime and fluorescence microscopy (2PLM) to characterize the partial pressure of oxygen (pO2) in single descending cortical arterioles in the mouse brain before and after generating a targeted photothrombotic occlusion. Integrated real-time Laser Speckle Contrast Imaging (LSCI) provides wide-field perfusion maps that are used to monitor and guide the occlusion process while 2PLM maps changes in intravascular oxygen tension. We present the technique's utility in highlighting the effects of vascular networking on the residual intravascular oxygen tensions measured after occlusion in three dimensions.

Transmembrane dynamics of water exchange in human brain

Tracking arterial spin labeled (ASL) water in the human brain with magnetic resonance imaging can provide important information on the dynamics of the trans-capillary and trans-membrane water exchange. This information however, is not only important from a basic biological standpoint, but also is essential for deciphering positron emission tomography and MRI perfusion experiments based on the movement of labeled water. While substantial information exists on water exchange through cellular membranes in vitro, the in vivo information remains limited and controversial. In this MRI study, we use a combination of pulsed ASL and recently developed quantitative blood-oxygen-level-dependent technique to address this question. Our approach is based on the measurements of the intrinsic MR transverse relaxation (T2*) properties of the ASL-labeled water. We discovered that T2* of the ASL-labeled water in the extravascular space is 87 ms ± 10 ms while T2* of the corresponding tissue water is much shorter, 50 ms ± 4 ms. This suggests that the ASL-labeled water does not reach equilibrium with the extravascular tissue and is mostly localized to the extraneuronal space. We estimated that the water transport time through the neuronal membranes is on the order of several tens of seconds; a finding consistent with older PET tracer kinetic studies using (15)O-water.

Changes in glucose uptake rather than lactate shuttle take center stage in subserving neuroenergetics: evidence from mathematical modeling

In this paper, we combined several mathematical models of cerebral metabolism and nutrient transport to investigate the energetic significance of metabolite trafficking within the brain parenchyma during a 360-secs activation. Glycolytic and oxidative cellular metabolism were homogeneously modeled between neurons and astrocytes, and the stimulation-induced neuronal versus astrocytic Na(+) inflow was set to 3:1. These assumptions resemble physiologic conditions and are supported by current literature. Simulations showed that glucose diffusion to the interstitium through basal lamina dominates the provision of the sugar to both neurons and astrocytes, whereas astrocytic endfeet transfer less than 4% of the total glucose supplied to the tissue. Neuronal access to paracellularly diffused glucose prevails even after halving (doubling) the ratio of neuronal versus astrocytic glycolytic (oxidative) metabolism, as well as after reducing the neuronal versus astrocytic Na(+) inflow to a nonphysiologic value of 1:1. Noticeably, displaced glucose equivalents as intercellularly shuttled lactate account for approximately 6% to 7% of total brain glucose uptake, an amount comparable with the concomitant drainage of the monocarboxylate by the bloodstream. Overall, our results suggest that the control of carbon recruitment for neurons and astrocytes is exerted at the level of glucose uptake rather than that of lactate shuttle.

Cerebral blood flow response to functional activation

Cerebral blood flow (CBF) and cerebral metabolic rate are normally coupled, that is an increase in metabolic demand will lead to an increase in flow. However, during functional activation, CBF and glucose metabolism remain coupled as they increase in proportion, whereas oxygen metabolism only increases to a minor degree-the so-called uncoupling of CBF and oxidative metabolism. Several studies have dealt with these issues, and theories have been forwarded regarding the underlying mechanisms. Some reports have speculated about the existence of a potentially deficient oxygen supply to the tissue most distant from the capillaries, whereas other studies point to a shift toward a higher degree of non-oxidative glucose consumption during activation. In this review, we argue that the key mechanism responsible for the regional CBF (rCBF) increase during functional activation is a tight coupling between rCBF and glucose metabolism. We assert that uncoupling of rCBF and oxidative metabolism is a consequence of a less pronounced increase in oxygen consumption. On the basis of earlier studies, we take into consideration the functional recruitment of capillaries and attempt to accommodate the cerebral tissue's increased demand for glucose supply during neural activation with recent evidence supporting a key function for astrocytes in rCBF regulation.

Oxygen transport in brain tissue

Oxygen is essential to maintaining normal brain function. A large body of evidence suggests that the partial pressure of oxygen (pO(2)) in brain tissue is physiologically maintained within a narrow range in accordance with region-specific brain activity. Since the transportation of oxygen in the brain tissue is mainly driven by a diffusion process caused by a concentration gradient of oxygen from blood to cells, the spatial organization of the vascular system, in which the oxygen content is higher than in tissue, is a key factor for maintaining effective transportation. In addition, a local mechanism that controls energy demand and blood flow supply plays a critical role in moment-to-moment adjustment of tissue pO(2) in response to dynamically varying brain activity. In this review, we discuss the spatiotemporal structures of brain tissue oxygen transport in relation to local brain activity based on recent reports of tissue pO(2) measurements with polarographic oxygen microsensors in combination with simultaneous recordings of neural activity and local cerebral blood flow in anesthetized animal models. Although a physiological mechanism of oxygen level sensing and control of oxygen transport remains largely unknown, theoretical models of oxygen transport are a powerful tool for better understanding the short-term and long-term effects of local changes in oxygen demand and supply. Finally, emerging new techniques for three-dimensional imaging of the spatiotemporal dynamics of pO(2) map may enable us to provide a whole picture of how the physiological system controls the balance between demand and supply of oxygen during both normal and pathological brain activity.

Brain tissue oxygen consumption and supply induced by neural activation: determined under suppressed hemodynamic response conditions in the anesthetized rat cerebral cortex

The dynamic changes in cerebral metabolic rate of oxygen (CMRO2) and oxygen supply during brain functions have not been well-characterized. To examine this issue, experiments with electrophysiology, oxygen microelectrode and laser-Doppler flowmetry were performed in the anesthetized rat somatosensory cortex. During neural activation, brain tissue partial pressure of oxygen (P(O2)) and local cerebral blood flow (CBF) were similarly increased. To separate the P(O2) changes originating from the increase in CMRO2 and the increase in oxygen supply, the same experiments were repeated under a vasodilator-induced hypotension condition in which evoked CBF change was minimal. In this condition, evoked P(O2) monotonically decreased, indicating an increase in CMRO2. Then, CMRO2 was determined at resting as well as activation periods using a dynamic oxygen exchange model. Our results indicated that the changes in CMRO2 were linearly related with the summation of evoked field potentials and further showed that the oxygen supply in the normal condition was about 2.5 times larger than the demand. However, this oxygen oversupply was not explainable by the change in CBF alone, but at least partly by the increase in oxygenation levels at pre-capillary arterioles (e.g., 82% to 90% O2 saturation level) when local neural activity was evoked.

Dynamics of oxygen delivery and consumption during evoked neural stimulation using a compartment model and CBF and tissue P(O2) measurements

The dynamics of blood oxygen delivery and tissue consumption produced by evoked stimulation of the rat somato-sensory cortex were investigated. Tissue oxygen tension (P(O2)) and laser Doppler flowmetry (LDF) measurements were recorded under two experimental conditions: normal, which represented both oxygen delivery and consumption, and suppressed CBF (achieved using a vasodilator), which only represented tissue oxygen consumption. Forepaw stimulation for 10 s produced increases of 27.7% and 48.8% in tissue P(O2) and LDF signal under normal conditions, respectively. The tissue P(O2) response peaked 9.8 s after stimulation onset and did not show any early transient decreases indicating that measurable oxygen deficits are not required to increase the delivery of oxygen by blood flow. Under suppressed CBF conditions, the LDF signal was mostly suppressed while the tissue P(O2) decreased by 11.7% and reached a minimum 10.8 s after stimulation onset. These data were analyzed using a dynamic model that described the transport of oxygen from blood to tissue. In order to explain the differences between the model prediction of the tissue P(O2) changes and the experimental data, several hypothetical scenarios were considered, such as changes in the vascular volume, permeability-surface area or arterial oxygenation. The increase in tissue P(O2) was found to probably require the recruitment of upstream oxygen from larger arteries as well as increases in the vascular volume at the oxygen exchange sites. The amplitude of the estimated tissue tension of oxygen delivered was about 2.7 x larger than the estimated consumption under normal conditions (45.7% vs. 17.1%, respectively).

Aging: Impact Upon Local Cerebral Oxygenation and Blood Flow With Acute Isovolemic Hemodilution

Data from the neurosurgical critical care arena demonstrate a correlation between cerebral oxygenation, survival, and cognitive function. Transfusion may increase and hemodilution decrease cerebral oxygenation. Both acute and chronic anemia have been associated with cognitive dysfunction. Aggressive blood conservation protocols have been instituted across all age groups without conclusive evidence for their impact upon outcome. Aged subjects are at the greatest risk of cognitive sequelae after major surgery associated with significant blood loss. We hypothesize that cerebral physiologic changes associated with "normal" aging may compromise cerebral oxygenation in the presence of severe anemia.Fischer 344 rats, the NIH National Institute of Aging normal aging rat model, underwent a stepwise isovolemic hemodilution protocol. Age groups (Age Grp) studied were as follows: Age Grp-A (3 months), n=14; Age Grp-B (9 to 12 months), n=14; and Age Grp-C (24 months), n=14. Brain oxygen tension (PBrO2), laser Doppler flow, and mean arterial pressure were measured. Final hemoglobin averaged 6.1+/-0.9 g/dL. PBrO2 levels decreased from a baseline of 18.1+/-4.1 to 17.5+/-6.8 mm Hg (P=0.49), and laser Doppler flow increased by 18+/-20% (P<0.0001) after hemodilution. Employing repeated measures multiple regression, Age Grp (P=0.30) was not a significant controlling covariate of PBrO2 in response to isovolemic hemodilution. PBrO2 levels were actually higher in Age Grp-C animals at all time points of the hemodilution protocol, although this was not statistically significant. Aged animals were also fully capable of mounting a robust local cerebral hyperemic response to the anemic challenge that was not separable from the response of younger animals.

A multiparametric assessment of oxygen efflux from the brain

A quantitative understanding of unidirectional versus net extraction of oxygen in the brain is required because an important factor in calculating oxidative metabolism by calibrated functional magnetic resonance imaging (fMRI) as well as oxygen inhalation methods of positron emission tomography (15O2-PET) and nuclear magnetic resonance (17O2-NMR)) is the degree of oxygen efflux from the brain back into the blood. Because mechanisms of oxygen transport from blood to brain are dependent on cerebral metabolic rate of oxygen consumption (CMRO2), cerebral blood flow (CBF), and oxygen partial pressure (pO2) values in intravascular (Piv) and extravascular (Pev) compartments, we implemented multimodal measurements of these parameters into a compartmental model of oxygen transport and metabolism (i.e., hemoglobin-bound oxygen, oxygen dissolved in plasma and tissue spaces, oxygen metabolized in the mitochondria). In the alpha-chloralose anesthetized rat brain, we used magnetic resonance (7.0 T) and fluorescence quenching methods to measure CMRO2 (2.5+/-1.0 micromol/g min), CBF (0.7+/-0.2 mL/g min), Piv (74+/-10 mm Hg), and Pev (16+/-5 mm Hg) to estimate the degree of oxygen efflux from the brain. In the axially distributed compartmental model, oxygen molecules in blood had two possible fates: enter the tissue space or remain in the same compartment; while in tissue there were three possible fates: enter the blood or the mitochondrial space, or remain in the same compartment. The multiparametric results indicate that the probability of unmetabolized (i.e., dissolved) oxygen molecules reentering the blood from the tissue is negligible and thus its inclusion may unnecessarily complicate calculations of CMRO2 for 15O-PET, 17O-NMR, and calibrated fMRI methods.

A three-compartment model of the hemodynamic response and oxygen delivery to brain

We describe a mathematical model linking changes in cerebral blood flow, blood volume and the blood oxygenation state in response to stimulation. The model has three compartments to take into account the fact that the cerebral blood flow and volume as measured concurrently using laser Doppler flowmetry and optical imaging spectroscopy have contributions from the arterial, capillary as well as the venous compartments of the vasculature. It is an extension to previous one-compartment hemodynamic models which assume that the measured blood volume changes are from the venous compartment only. An important assumption of the model is that the tissue oxygen concentration is a time varying state variable of the system and is driven by the changes in metabolic demand resulting from changes in neural activity. The model takes into account the pre-capillary oxygen diffusion by flexibly allowing the saturation of the arterial compartment to be less than unity. Simulations are used to explore the sensitivity of the model and to optimise the parameters for experimental data. We conclude that the three-compartment model was better than the one-compartment model at capturing the hemodynamics of the response to changes in neural activation following stimulation.

A theoretical model of oxygen delivery and metabolism for physiologic interpretation of quantitative cerebral blood flow and metabolic rate of oxygen

The coupling of cerebral blood flow (CBF) and metabolic rate of oxygen (CMRO2) during physiologic and pathophysiologic conditions remains the subject of debate. In the present study, we have developed a theoretical model for oxygen delivery and metabolism, which describes the diffusion of oxygen at the capillary-tissue interface and the nonlinear nature of hemoglobin (Hb) affinity to oxygen, allowing a variation in simple-capillary oxygen diffusibility, termed "effective oxygen diffusibility (EOD)." The model was used to simulate the relationship between CBF and CMRO2, as well as oxygen extraction fraction (OEF), when various pathophysiologic conditions were assumed involving functional activation, ischemia, hypoxia, anemia, or hypo- and hyper-capnic CBF variations. The simulations revealed that, to maintain CMRO2 constant, a variation in CBF and Hb required active change in EOD. In contrast, unless the EOD change took place, the brain allowed small but significant nonlinear change in CMRO2 directly dependent upon oxygen delivery. Application of the present model to quantitative neuroimaging of CBF and CMRO2 enables us to evaluate the biologic response at capillary level other than Hb- and flow-dependent properties of oxygen transport and may give us another insight regarding the physiologic control of oxygen delivery in the human brain.

Neuroprotection in hypothermia linked to redistribution of oxygen in brain

Hypothermia improves the outcome of acute ischemic stroke, traumatic injury, and inflammation of brain tissue. We tested the hypothesis that hypothermia reduces the energy metabolism of brain tissue to a level that is commensurate with the prevailing blood flow and hence allows adequate distribution of oxygen to the entire tissue. To determine the effect of 32 degrees C hypothermia on brain tissue, we measured the sequential changes of physiological variables by means of PET in pigs. Cerebral blood flow and oxygen consumption (cerebral metabolic rate of oxygen) declined to 50% of the baseline in 3 and 5 h, respectively, thus elevating the oxygen extraction fraction to 140% of the baseline at 3 h. The results are consistent with the claim that cooling of the brain to 32 degrees C couples both energy metabolism and blood flow to a lower rate of work of the entire tissue.

Relation between cerebral blood flow and metabolism explained by a model of oxygen exchange

The cerebral blood flow (CBF) and cerebral metabolic rate of oxygen (CMRo(2)) are major determinants of the contrast in functional magnetic resonance imaging and optical imaging. However, the coupling between CBF and CMRo(2) during cerebral activation remains controversial. Whereas most of the previous models tend to show a nonlinear coupling, experimental studies have led to conflicting conclusions. A physiologic model was developed of oxygen transport through the blood-brain barrier (BBB) for dynamic and stationary states. Common model simplifications are proposed and their implications for the CBF/CMRo(2) relation are studied. The tissue oxygen pool, the BBB permeability, and the hemoglobin dissociation curve are physiologic parameters directly involved in the CBF/CMRo(2) relation. We have been shown that the hypothesis of a negligible tissue oxygen pool, which was admitted by most of the previous models, implies a tight coupling between CBF and CMRo(2). By relaxing this hypothesis, a real uncoupling was allowed that gives a more coherent view of the CBF/CMRo(2) relation, in better agreement with the hypercapnia data and with the variability reported in experimental works for the relative changes of those two variables. This also allows a temporal mismatch between CBF and CMRo(2), which influences the temporal shape of oxygenation at the capillary end.

Carbon monoxide disposition and permeability-surface area product in the foetal circulation of the perfused term human placenta

In order to estimate the placental barrier to gas transfer, a novel carbon monoxide (CO) wash-in method was used to estimate the permeability-surface area (PS) product for the transfer of gas across the foetal circulation in the perfused human term placenta. The PS product for CO was 0.0096+/-0.006 ml/s/g or 0.012+/-0.007 ml/s/g using compartmental or Crone-Renkin analysis, respectively. Using this result and a published estimate of the placental capillary surface area, the permeability coefficient to CO across the foetal circulation was found to be approximately 4 x 10(-5)cm/s. This result is compatible with the hypothesis that the foetal circulation of the human placenta imposes a potentially significant barrier to gas transfer.

Distribution kinetics of solutes in the isolated in-situ perfused rat head using the multiple indicator dilution technique and a physiological two-barrier model

The purpose of this study was to determine the pharmacokinetics of [14C]diclofenac, [14C]salicylate and [3H]clonidine using a single pass rat head perfusion preparation. The head was perfused with 3-[N-morpholino] propane-sulfonic acid-buffered Ringer's solution. 99mTc-red blood cells and a drug were injected in a bolus into the internal carotid artery and collected from the posterior facial vein over 28 min. A two-barrier stochastic organ model was used to estimate the statistical moments of the solutes. Plasma, interstitial and cellular distribution volumes for the solutes ranged from 1.0 mL (diclofenac) to 1.6 mL (salicylate), 2.0 mL (diclofenac) to 4.2 mL (water) and 3.9 mL (salicylate) to 20.9 mL (diclofenac), respectively. A comparison of these volumes to water indicated some exclusion of the drugs from the interstitial space and salicylate from the cellular space. Permeability-surface area (PS) products calculated from plasma to interstitial fluid permeation clearances (CL(PI)) (range 0.02-0.40 mL s(-1)) and fractions of solute unbound in the perfusate were in the order: diclofenac > salicylate > clonidine > sucrose (from 41.8 to 0.10 mL s(-1)). The slow efflux of diclofenac, compared with clonidine and salicylate, may be related to its low average unbound fraction in the cells. This work accounts for the tail of disposition curves in describing pharmacokinetics in the head.

Changes of cerebral blood flow, oxygenation, and oxidative metabolism during graded motor activation

In the present studies fMRI and a hypercapnic calibration procedure were used to monitor simultaneous changes in cerebral blood flow (CBF), cerebral blood oxygenation, and cerebral metabolic rate of oxygen (CMRO(2)) during activation in the sensorimotor cortex. In the first set of experiments seven volunteers performed bilateral, self-paced finger tapping and in the second set of experiments six volunteers performed bilateral finger tapping with six different frequencies (0.5-3 Hz). During the latter task relative CBF and BOLD signal intensity changes varied linearly as a function of stimulus frequency. In good agreement with recent PET and fMRI data increases in CMRO(2) were smaller than the corresponding changes in CBF during self-paced finger tapping and at all levels of graded motor activation. At a single level of activation and during graded activation there was a positive linear relationship between CBF and CMRO(2) with ratios of approximately 3:1. Comparable proportionality constants have been found in the visual cortex and primary sensory cortex, indicating similarities between the relationship of CBF and CMRO(2) in various cortical regions.

Quantitative functional imaging of the brain: towards mapping neuronal activity by BOLD fMRI

Quantitative magnetic resonance imaging (MRI) and spectroscopy (MRS) measurements of energy metabolism (i.e. cerebral metabolic rate of oxygen consumption, CMR(O2)), blood circulation (i.e. cerebral blood flow, CBF, and volume, CBV), and functional MRI (fMRI) signal over a wide range of neuronal activity and pharmacological treatments are used to interpret the neurophysiologic basis of blood oxygenation level dependent (BOLD) image-contrast at 7 T in glutamatergic neurons of rat cerebral cortex. Multi-modal MRI and MRS measurements of CMR(O2), CBF, CBV and BOLD signal (both gradient-echo and spin-echo) are used to interpret the neuroenergetic basis of BOLD image-contrast. Since each parameter that can influence the BOLD image-contrast is measured quantitatively and separately, multi-modal measurements of changes in CMR(O2), CBF, CBV, BOLD fMRI signal allow calibration and validation of the BOLD image-contrast. Good agreement between changes in CMR(O2) calculated from BOLD theory and measured by (13)C MRS, reveals that BOLD fMRI signal-changes at 7 T are closely linked with alterations in neuronal glucose oxidation, both for activation and deactivation paradigms. To determine the neurochemical basis of BOLD, pharmacological treatment with lamotrigine, which is a neuronal voltage-dependent Na(+) channel blocker and neurotransmitter glutamate release inhibitor, is used in a rat forepaw stimulation model. Attenuation of the functional changes in CBF and BOLD with lamotrigine reveals that the fMRI signal is associated with release of glutamate from neurons, which is consistent with a link between neurotransmitter cycling and energy metabolism. Comparisons of CMR(O2) and CBF over a wide dynamic range of neuronal activity provide insight into the regulation of energy metabolism and oxygen delivery in the cerebral cortex. The current results reveal the energetic and physiologic components of the BOLD fMRI signal and indicate the required steps towards mapping neuronal activity quantitatively by fMRI at steady-state. Consequences of these results from rat brain for similar calibrated BOLD fMRI studies in the human brain are discussed.

Blood flow and oxygen delivery to human brain during functional activity: theoretical modeling and experimental data

Coupling of cerebral blood flow (CBF) and cerebral metabolic rate for oxygen (CMRO(2)) in physiologically activated brain states remains the subject of debates. Recently it was suggested that CBF is tightly coupled to oxidative metabolism in a nonlinear fashion. As part of this hypothesis, mathematical models of oxygen delivery to the brain have been described in which disproportionately large increases in CBF are necessary to sustain even small increases in CMRO(2) during activation. We have explored the coupling of CBF and oxygen delivery by using two complementary methods. First, a more complex mathematical model was tested that differs from those recently described in that no assumptions were made regarding tissue oxygen level. Second, [(15)O] water CBF positron emission tomography (PET) studies in nine healthy subjects were conducted during states of visual activation and hypoxia to examine the relationship of CBF and oxygen delivery. In contrast to previous reports, our model showed adequate tissue levels of oxygen could be maintained without the need for increased CBF or oxygen delivery. Similarly, the PET studies demonstrated that the regional increase in CBF during visual activation was not affected by hypoxia. These findings strongly indicate that the increase in CBF associated with physiological activation is regulated by factors other than local requirements in oxygen.

Interdependence of regional and global cerebral blood flow during visual stimulation: an O-15-butanol positron emission tomography study

The authors investigated the influence of variations in global cerebral blood flow (gCBF) on regional flow changes during visual stimulation. Global flow was varied using different end-expiratory CO2 values (PETCO2) between 20 and 70 mm Hg. Visual stimulation was performed with a red LED-array flashing at 8 Hz. Blood flow was measured with 0-15-butanol, continuous arterial blood sampling, and positron emission tomography (PET). Global flow changes surpassed the published values of O-15-H2O studies, better fitting the results of the inert gas technique (gCBF at 20, 40, and 70 mm Hg PETCO2 +/- SD was 31 +/- 4, 48 +/- 13, and 160 +/- 50 mL 100 g(-1) min(-1), respectively). The relation between PETCO2 and CBF in the current study was best described by an exponential rather than a linear function. At low PETCO2, the activation-induced flow changes are moderately damped, whereas at high PETCO2, they are nearly lost (deltaCBF (+/-SD): 52% +/- 25%, 68% +/- 22%, 16% +/- 25% at PETCO2 = 20, 40, 70 mm Hg, respectively).

Carbon monoxide wash-in method to determine gas transfer in vascular beds: application to rat hindlimb

The vascular barrier to gas transfer is an important physiological parameter; however, no readily applicable technique exists to quantitate the process. A simple technique to measure the permeability-surface area (PS) product for gas transfer in vascular beds is proposed using wash in of carbon monoxide (CO) and Crone-Renkin analysis. Wash-in experiments were performed on the perfused hindlimbs of male Wistar rats (n = 15) by using CO as a surrogate marker for oxygen and technetium-99m-labeled albumin as the vascular marker. The use of CO and erythrocyte-free perfusate and the collection of outflow samples into tubes preloaded with erythrocytes obviated the need for an anaerobic collection device or consideration of Hb binding in the analysis. The PS product for CO was determined from the early extraction as 0.013 +/- 0.006 ml. s(-1). g(-1). Compartmental analysis revealed that the fractional recovery of CO was 0.45 +/- 0.14 and the volume of distribution was 2.31 +/- 0.76 ml/g. This technique detected a small measurable barrier to the transfer of CO across the hindlimb vasculature and is potentially applicable to other vascular beds in health and disease.

On the oxygenation of hemoglobin in the human brain

We test three hypotheses arising from a model of oxygen delivery to brain tissue. The hypotheses claim that mitochondrial oxygen is negligible in brain tissue such that oxygen consumption depends solely on the mean capillary oxygen tension for a given capillary density; that capillary density is adjusted to satisfy the average steady-state oxygen requirement; and that sudden changes of brain function are subserved by changes of blood flow which adjust the mean capillary oxygen tension in the required direction. The results of the tests did not reject the two former hypotheses and only partly rejected the latter: Sudden changes of blood flow are not always accompanied by increases of oxygen consumption. When they are, changes of apparent capillary density (physiological recruitment) can occur.

Model of blood-brain transfer of oxygen explains nonlinear flow-metabolism coupling during stimulation of visual cortex

The coupling between cerebral metabolic rate of oxygen (CMRO2) and blood flow (CBF) in response to visual stimulation was evaluated by means of a model of oxygen delivery. The model predicted a nonlinear relationship between stimulus-evoked changes of oxygen consumption and blood flow. The magnitude of the CMRO2/CBF ratio index (IO2) was used to indicate the degree of flow-metabolism coupling prevailing in specific areas of the brain during physiological stimulation. Therefore, the index provided a measure of the blood oxygenation level dependent (BOLD) magnetic resonance contrast. To evaluate the changes of IO2 in response to visual stimulation, the model was applied to the effect of a changing flicker rate of a visual stimulus on the magnitudes of CBF, CMRO2, and oxygen diffusion capacity, in the human brain. Positron emission tomography (PET) was used to measure the CBF and the CMRO2 in 12 healthy volunteers who viewed a cross-hair (baseline) or a yellow-blue annular checkerboard reversing at frequencies of 1, 4, or 8 Hz. The magnitude of CBF in the primary visual cortex increased as a function of the checkerboard reversal rate and reached a maximum at the frequency of 8 Hz (z=16.0), while the magnitude of CMRO2 reached a maximum at 4 Hz (z=4.0). Therefore, the calculated IO2 was lower at 8 Hz than at 1 and 4 Hz, in contrast to the oxidative metabolic rate that reached its maximum at 4 Hz. The model explained the increase of oxygen consumption as the combined effect of increased blood flow and increased oxygen diffusion capacity in the region of visual activation.

Dependence of oxygen delivery on blood flow in rat brain: a 7 tesla nuclear magnetic resonance study

Magnetic resonance imaging (MRI) and spectroscopy (MRS) were used at a magnetic field strength of 7 T to measure CBF and CMRO2 in the sensorimotor cortex of mature rats at different levels of cortical activity. In rats maintained on morphine anesthesia, transitions to lower activity and higher activity states were produced by administration of pentobarbital and nicotine, respectively. Under basal conditions of morphine sulfate anesthesia, CBF was 0.75 +/- 0.09 mL x g(-1) x min(-1) and CMRO2 was 3.15 +/- 0.18 micromol x g(-1) x min(-1). Administration of sodium pentobarbital reduced CBF and CMRO2 by 66% +/- 16% and 61% +/- 6%, respectively (i.e., "deactivation"). In contrast, administration of nicotine hydrogen tartrate increased CBF and CMRO2 by 41% +/- 5% and 30% +/- 3%, respectively (i.e., "activation"). The resting values of CBF and CMRO2 for alpha-chloralose anesthetized rats were 0.40 +/- 0.09 mL x g(-1) x min(-1) and 1.51 +/- 0.06 micromol x g(-1) x min(-1), respectively. Upon forepaw stimulation, CBF and CMRO2 were focally increased by 34% +/- 10% and 26% +/- 12%, respectively, above the resting nonanesthetized values (i.e., "activation"). Incremental changes in CBF and CMRO2, when expressed as a percentage change for "deactivation" and "activation" from the respective control conditions, were linear (R2 = 0.997) over the entire range examined with the global and local perturbations. This tight correlation for cerebral oxygen delivery in vivo is supported by a recent model where the consequence of a changing effective diffusivity of the capillary bed for oxygen, D, has been hypothetically shown to be linked to alterations in CMRO2 and CBF. This assumed functional characteristic of the capillary bed can be theoretically assessed by the ratio of fractional changes in D with respect to changes in CBF, signified by omega. A value 0.81 +/- 0.23 was calculated for omega with the in vivo data presented here, which in turn corresponds to a supposition that the effective oxygen diffusivity of the capillary bed is not constant but presumably varies to meet local requirements in oxygen demand in a similar manner with both "deactivation" and "activation."

An isolated in-situ rat head perfusion model for pharmacokinetic studies

PURPOSE

To develop a viable, single pass rat head perfusion model useful for pharmacokinetic studies.

METHODS

A viable rat head preparation, perfused with MOPS-buffered Ringer's solution, was developed. Radiolabelled markers (red blood cells, water and sucrose) were injected in a bolus into the internal carotid artery and collected from the posterior facial vein over 28 minutes. The double inverse Gaussian function was used to estimate the statistical moments of the markers.

RESULTS

The viability of the perfusion was up to one hour, with optimal perfusate being 2% bovine serum albumin at 37 degrees C, pH 7.4. The distribution volumes for red blood cells, sucrose and water (from all studies, n = 18) were 1.0 +/- 0.3 ml, 6.4 +/- 4.2 ml and 18.3 +/- 11.9 ml, respectively. A high normalised variance for red blood cells (3.1 +/- 2.0) suggests a marked vascular heterogeneity. A higher normalised variance for water (6.4 +/- 3.3) is consistent with additional diffusive/permeability limitations.

CONCLUSIONS

Analysis of the physiological parameters derived from the moments suggested that the kinetics of the markers were consistent with distribution throughout the head (weight 25 g) rather than just the brain (weight 2 g). This model should assist in studying solute pharmacokinetics in the head.

Increased inspired oxygen concentration as a factor in improved brain tissue oxygenation and tissue lactate levels after severe human head injury

OBJECT

Early impairment of cerebral blood flow in patients with severe head injury correlates with poor brain tissue O2 delivery and may be an important cause of ischemic brain damage. The purpose of this study was to measure cerebral tissue PO2, lactate, and glucose in patients after severe head injury to determine the effect of increased tissue O2 achieved by increasing the fraction of inspired oxygen (FiO2).

METHODS

In addition to standard monitoring of intracranial pressure and cerebral perfusion pressure, the authors continuously measured brain tissue PO2, PCO2, pH, and temperature in 22 patients with severe head injury. Microdialysis was performed to analyze lactate and glucose levels. In one cohort of 12 patients, the PaO2 was increased to 441+/-88 mm Hg over a period of 6 hours by raising the FiO2 from 35+/-5% to 100% in two stages. The results were analyzed and compared with the findings in a control cohort of 12 patients who received standard respiratory therapy (mean PaO2 136.4+/-22.1 mm Hg). The mean brain PO2 levels increased in the O2-treated patients up to 359+/-39% of the baseline level during the 6-hour FiO2 enhancement period, whereas the mean dialysate lactate levels decreased by 40% (p < 0.05). During this O2 enhancement period, glucose levels in brain tissue demonstrated a heterogeneous course. None of the monitored parameters in the control cohort showed significant variations during the entire observation period.

CONCLUSIONS

Markedly elevated lactate levels in brain tissue are common after severe head injury. Increasing PaO2 to higher levels than necessary to saturate hemoglobin, as performed in the O2-treated cohort, appears to improve the O2 supply in brain tissue. During the early period after severe head injury, increased lactate levels in brain tissue were reduced by increasing FiO2. This may imply a shift to aerobic metabolism.

Frequency-dependent changes in cerebral metabolic rate of oxygen during activation of human visual cortex

To test the hypothesis that brain oxidative metabolism is significantly increased upon adequate stimulation, we varied the presentation of a visual stimulus to determine the frequency at which the metabolic response would be at maximum. The authors measured regional CMR(O2) in 12 healthy normal volunteers with the ECAT EXACT HR+ (CTI/Siemens, Knoxville, TN, U.S.A.) three-dimensional whole-body positron emission tomograph (PET). In seven successive activating conditions, subjects viewed a yellow-blue annular checkerboard reversing its contrast at frequencies of 0, 1, 4, 8, 16, 32, and 50 Hz. Stimulation began 4 minutes before and continued throughout the 3-minute dynamic scan. In the baseline condition, the subjects began fixating a cross hair 30 seconds before the scan and continued to do so for the duration of the 3-minute scan. At the start of each scan, the subjects inhaled 20 mCi of (15)O-O2 in a single breath. The CMR(O2) value was calculated using a two-compartment, weighted integration method. Normalized PET images were averaged across subjects and coregistered with the subjects' magnetic resonance imaging in stereotaxic space. Mean subtracted image volumes (activation minus baseline) of CMR(O2) then were obtained and converted to z statistic volumes. The authors found a statistically significant focal change of CMR(O2) in the striate cortex (x = 9; y = -89; z = -1) that reached a maximum at 4 Hz and dropped off sharply at higher stimulus frequencies.

An adiabatic approximation to the tissue homogeneity model for water exchange in the brain: I. Theoretical derivation

Using the adiabatic approximation, which assumes that the tracer concentration in parenchymal tissue changes slowly relative to that in capillaries, we derived a time-domain, closed-form solution of the tissue homogeneity model. This solution, which is called the adiabatic solution, is similar in form to those of two-compartment models. Owing to its simplicity, the adiabatic solution can be used in CBF experiments in which kinetic data with only limited time resolution or signal-to-noise ratio, or both, are obtained. Using computer simulations, we investigated the accuracy and the precision of the parameters in the adiabatic solution for values that reflect 2H-labeled water (D2O) clearance from the brain (see Part II). It was determined that of the three model parameters, (1) the vascular volume (Vi), (2) the product of extraction fraction and blood flow (EF), and (3) the clearance rate constant (kadb), only the last one could be determined accurately, and therefore CBF must be determined from this parameter only. From the error analysis of the adiabatic solution, it was concluded that for the D2O clearance experiments described in Part II, the coefficient of variation of CBF was approximately 7% in gray matter and 22% in white matter.

A model for the regulation of cerebral oxygen delivery

On the basis of the assumption that oxygen delivery across the endothelium is proportional to capillary plasma PO2, a model is presented that links cerebral metabolic rate of oxygen utilization (CMRO2) to cerebral blood flow (CBF) through an effective diffusivity for oxygen (D) of the capillary bed. On the basis of in vivo evidence that the oxygen diffusivity properties of the capillary bed may be altered by changes in capillary PO2, hematocrit, and/or blood volume, the model allows changes in D with changes in CBF. Choice in the model of the appropriate ratio of Omega identical with (DeltaD/D)/(DeltaCBF/CBF) determines the dependence of tissue oxygen delivery on perfusion. Buxton and Frank (J. Cereb. Blood Flow. Metab. 17: 64-72, 1997) recently presented a limiting case of the present model in which Omega = 0. In contrast to the trends predicted by the model of Buxton and Frank, in the current model when Omega > 0, the proportionality between changes in CBF and CMRO2 becomes more linear, and similar degrees of proportionality can exist at different basal values of oxygen extraction fraction. The model is able to fit the observed proportionalities between CBF and CMRO2 for a large range of physiological data. Although the model does not validate any particular observed proportionality between CBF and CMRO2, generally values of (DeltaCMRO2/CMRO2)/(DeltaCBF/CBF) close to unity have been observed across ranges of graded anesthesia in rats and humans and for particular functional activations in humans. The model's capacity to fit the wide range of data indicates that the oxygen diffusivity properties of the capillary bed, which can be modified in relation to perfusion, play an important role in regulating cerebral oxygen delivery in vivo.

Dynamics of blood flow and oxygenation changes during brain activation: the balloon model

A biomechanical model is presented for the dynamic changes in deoxyhemoglobin content during brain activation. The model incorporates the conflicting effects of dynamic changes in both blood oxygenation and blood volume. Calculations based on the model show pronounced transients in the deoxyhemoglobin content and the blood oxygenation level dependent (BOLD) signal measured with functional MRI, including initial dips and overshoots and a prolonged poststimulus undershoot of the BOLD signal. Furthermore, these transient effects can occur in the presence of tight coupling of cerebral blood flow and oxygen metabolism throughout the activation period. An initial test of the model against experimental measurements of flow and BOLD changes during a finger-tapping task showed good agreement.

A model for the coupling between cerebral blood flow and oxygen metabolism during neural stimulation

A general mathematical model for the delivery of O2 to the brain is presented, based on the assumptions that all of the brain capillaries are perfused at rest and that all of the oxygen extracted from the capillaries is metabolized. The model predicts that disproportionately large changes in blood flow are required in order to support small changes in the O2 metabolic rate. Interpreted in terms of this model, previous positron emission tomography (PET) studies of the human brain during neural stimulation demonstrating that cerebral blood flow (CBF) increases much more than the oxygen metabolic rate are consistent with tight coupling of flow and oxidative metabolism. The model provides a basis for the quantitative interpretation of functional magnetic resonance imaging (fMRI) studies in terms of changes in local CBF.