INTRODUCTION

Top Abstract Introduction Methods Results Discussion Appendix A Appendix B Appendix C References

UNDER BASAL CONDITIONS, most of the energy required for cerebral ATP generation is supplied by oxidation of glucose through the tricarboxylic acid cycle (60). Roy and Sherrington (58) suggested that the cerebral metabolic rates of oxygen and glucose use (i.e., CMR_O2 and CMR_Glc, respectively) are locally adjusted to meet the metabolic needs through local regulation of cerebral blood flow (CBF) and volume (CBV). The mechanisms for these couplings have remained elusive, and even the measured stoichiometries have been somewhat variable, reflecting a variety of experimental methods and conditions. Generally, tight proportionality between fractional changes in CMR_O2 and CBF measured regionally has been observed at rest with a ratio of ~1:1 (29, 54). However, recent results from positron emission tomography (PET) have demonstrated that, during brain activation, CBF increases by a greater fraction than does CMR_O2 (11, 12). The greater fractional increase in CBF than in CMR_O2 has been interpreted as an uncoupling between perfusion and oxidative metabolism within the normal physiological range of activity. An important point is that although there is no requirement for a constant stoichiometry between fractional changes in CBF and CMR_O2, there is a prescribed stoichiometric ratio between fractional changes in CMR_O2 and CMR_Glc, if oxidative glycolysis is to be maintained from rest to higher and/or lower levels of activity (60).

Recently, Buxton and Frank (6) presented a model in which the higher increase in CBF than in CMR_O2 during cerebral activation (11, 12) is not uncoupling but rather represents a mechanistic limitation on the ability to increase cerebral oxygen delivery through CBF. There are two main assumptions in their model: 1) they assumed that cerebral tissue oxygen tension is low, for which there is considerable evidence (37-39, 41), such that the capillary-tissue PO₂ gradient is determined primarily by the capillary PO₂ (26, 33, 34); and 2) they assumed that oxygen delivery is only increased through perfusion. There is no change in the effective diffusivity of oxygen from blood to tissue; thus it was proposed that the capillary bed has no flexibility with respect to changes in CBF. Their model shows that as the capillary PO₂ approaches the arterial input value, the relationship between changes in CBF and CMR_O2 becomes highly nonlinear, because a large increase in CBF is required to achieve a small increase in the capillary PO₂. Their model is able to fit the PET data of Fox and co-workers (11, 12), who reported a ratio of ~0.2:1 for relative changes in CMR_O2 and CBF. With the assumptions made, their model predicts that the ability of the brain to increase oxygen consumption is severely limited, and low ratios for relative changes in CMR_O2 and CBF should be the norm for all brain activations at the oxygen extraction fraction (OEF) values reported in the literature.

The stated goal of the model of Buxton and Frank (6) was to relate changes in CBF and CMR_O2 during functional activation in awake humans and to compare results with PET activation data. A more comprehensive survey of the literature reporting changes in CBF and CMR_O2, including measurements from additional PET activation studies and resting graded anesthesia studies, shows proportionalities not allowed by their model. For example, with sensory stimulation in awake humans, ratios of ~0.5:1 have been observed for relative changes in CMR_O2 and CBF (59), and during cognitive stimulation, ratios of ~1:1 have been reported (56). In addition, PET studies have shown that, at rest, human cortical gray matter values of CBF, CMR_O2, and CMR_Glc are regionally coupled (17, 54, 56). Similar high ratios have been reported for local correlations in animals, showing close agreement with CBF, CMR_O2, and CMR_Glc (5, 35, 64). A further limitation of their model is that it predicts a highly nonlinear relationship between CBF and CMR_O2, which does not agree with the close-to-linear relationships between CBF and CMR_O2 measured across ranges of graded anesthesia in rats (20, 24, 45, 46, 64) and humans (29, 51, 61).

We present an extended model where certain characteristics are derived from a number of recent models (3, 6, 8, 15, 16, 52, 55, 60, 68). Our model relaxes one of the constraints in the model of Buxton and Frank (6) by allowing for changes in effective diffusivity (D) of the capillary bed with changes in CBF. The change in effective diffusivity of the capillary bed may result from altering capillary PO₂, hematocrit, and/or blood volume, as has been reported on the basis of microscopic measurements (9, 10, 21, 31, 32, 36, 42, 43). Consequently, oxygen delivery is allowed to be responsive to perfusion by an increase in the effective diffusivity of the capillary bed. The model of Buxton and Frank (6) is the limiting case of the present model, in which the ratio (D/D)/(CBF/CBF) is equal to zero. The present model is able to fit the large body of data in which the observed ratios (CMR_O2/CMR_O2)/(CBF/CBF), although generally close to unity, are sometimes significantly smaller. The ability of the current model to fit the wide range of data indicates that the diffusivity properties of the capillary bed, which may be altered by changes in capillary PO₂, hematocrit, and/or blood volume, play an important role in regulating cerebral oxygen delivery in vivo. However, the model does not validate any particular value of (CMR_O2/CMR_O2)/(CBF/CBF); only more reliable in vivo experiments can do that. Implications of this analysis for the interpretation of functional magnetic resonance imaging (fMRI) are also discussed.

Glossary

BOLD	Blood oxygenation level dependent
CBF and CBV	Cerebral blood flow and volume
CMRO2 and CMRGlc	Cerebral metabolic rates of oxygen and glucose consumption
OEF	Tissue oxygen extraction fraction
Y	Venous blood oxygenation
D	Effective diffusivity for oxygen in the capillary bed
Ca and Cv	Arterial and venous oxygen concentrations
T	Transit time of capillary bed
and	Coupling parameter for changes in D and CMRO2 with changes in CBF
[Hb(O2)n]	Oxyhemoglobin concentration
[Hb]	Deoxyhemoglobin concentration
[Hb(total)]	Total hemoglobin concentration
S	BOLD fMRI signal
A	Magnetic field-dependent physiological constant
max	Magnetic field-dependent deoxyhemoglobin susceptibility frequency shift
b	Blood volume fraction
TE	Gradient-echo time
C	BOLD proportionality constant
	Magnetic susceptibility constant for deoxyhemoglobin
B0	Static magnetic field
	Apparent transverse relaxation rate of tissue water

	THEORY AND METHODS

Top Abstract Introduction Methods Results Discussion Appendix A Appendix B Appendix C References

Model. Oxygen in blood exists in two discrete components, hemoglobin and plasma, with the oxygen affinity and concentration significantly higher in the former. Oxygen extraction by the tissue from an infinitesimally thin element of blood occurs during capillary transit and may be described by the temporal profile of the changing total oxygen content of blood [C_T()]. At any time during the transit the rate of loss of oxygen is proportional to the oxygen concentration in the plasma [C_P()]

(1)

The constant k is determined by the spatial gradients of PO₂ across the volume element and is the first-order rate constant of oxygen loss from the capillary (3, 6, 8, 15, 16, 52, 55). If it is assumed that the ratio of transient oxygen content values in plasma and blood is constant, i.e., r = C_P/C_T, during an elapsed time of , then it can be shown that

(2)

If is the nth equivalent fraction of the capillary transit time (T_c), then it can be shown that

(3)

where (kr)_net is the net kr product for the whole transit time T_c (see APPENDIX A). If k is a constant all through transit, then Eq. 3 becomes

(4)

As pointed out by Gjedde (15), in this case r_net may be estimated from C_T(0), OEF, and the mathematical relationship between hemoglobin fractional oxygenation and C_P. However, in the more general case, as presented here, the term (kr)_net in Eq. 3 may not be separated. Note that r is determined by the relationship between hemoglobin fractional oxygenation and the average capillary PO₂. Because of the cooperativity of oxygen binding, r will not be a constant but will vary with , in contrast to the model of Buxton and Frank (6). Although the mathematical description of Eq. 3 is similar to the Renkin-Crone relationship (8, 55) and the model of Buxton and Frank (6), there is no localization of the major point of resistance to the capillary endothelium. This localization may be inferred from the use of the permeability-surface area product in the Renkin-Crone relationship and from the assumption of Buxton and Frank that the PO₂ is negligible throughout the brain extracellular and intracellular space. The OEF around the capillary (OEF_c) may be calculated (3, 6, 8, 15, 16, 52, 55, 60, 68) from

(5)

which is equivalent to

(6)

Because at steady state perfusion is constant at all points along the capillary, so T_c may be calculated from the relationship

(7)

which, by substitution, leads to

(8)

where D_c is the effective diffusivity for oxygen from the capillary to the point of consumption, presumably the mitochondria, and is equal to

(9)

Thus the net oxygen extraction per capillary can be described by the cumulative effect of an infinitesimally thin element of blood moving down a capillary during transit as it loses oxygen to the tissue and which experiences changing spatial PO₂ gradients between the traversing volume element and the abluminal side of the capillary endothelium. The changing ratio of total to plasma oxygen contents in the traversing volume element reflects the cooperative binding of oxygen by hemoglobin in whole blood within the capillary. Extension to the macroscopic picture is achieved through averaging across an ensemble of identical capillaries, which yields macroscopic terms: effective diffusivity of the capillary bed (D), transit time of the capillary bed (T), perfusion in the capillary bed (CBF), OEF, and CMR_O2, such that

(10)

Equation 10 is similar to previous analytic expressions of a microvascular tissue unit, which consists of a mass of tissue irrigated by a collection of identical capillaries that are uniformly separated (3, 6, 8, 15, 16, 52, 55, 60, 68), although the interpretation of the diffusivity constant, D, is somewhat different here. It has been shown previously that, for a distribution of transit times, an expression similar to Eq. 10 is valid, provided the distribution is reasonably symmetrical and peaked about the average value (52, 68). An alternate expression for OEF determined from Fick's equation is given by (60)

(11)

where C_a is the average capillary arterial oxygen concentration in the bed. The unidirectional flow of oxygen molecules across the endothelium is very efficient (26, 37-39, 41), and this process is driven by the average capillary PO₂. Combination of Eqs. 10 and 11 shows that

(12)

Equation 12 shows that oxygen utilization is linked to perfusion via the effective diffusivity of the capillary bed. By rearrangement of Eq. 11, the relationship between fractional changes in CMR_O2, CBF, and OEF may be expressed as

(13)

In Eq. 13 and subsequently, the terms without and with  indicate basal and relative differences, respectively, due to a physiological perturbation. In the present analysis, the effective diffusivity for oxygen permeability within the capillary bed is assumed to be coupled to perfusion according to a parameter , which we define as

(14)

The term  is a measure of the coupling between the changes in effective diffusivity of the capillary bed for oxygen delivery. If  is constant over the range of CBF changes, then Eq. 14 may be substituted into Eq. 13 to yield

(15)

where  = [1 + (CBF/CBF)],  = [1 + (CBF/CBF)], and

(16)

Provided that CBF/CBF, , and the basal value of OEF are known, the values of CMR_O2/CMR_O2 and OEF/OEF may be calculated using the above relationships. The model of Buxton and Frank (6) may be shown to be equivalent to the model proposed here at the limiting case of  = 0 (see APPENDIX B), when

(17)

It is also useful to define a parameter that measures the coupling between changes in oxidative metabolism and perfusion, which we define as

(18)

Depending on  and the basal value of OEF, the calculated  may be close to constant over the physiological range of changes in perfusion or highly nonlinear, as proposed by Buxton and Frank (6), allowing a wide range of data to be fitted. As such the model does not validate any particular reported value of ; only reliable experiments can do that.

Assumptions. The model for the microvascular unit, which consists of a mass of tissue irrigated by a collection of identical capillaries that are uniformly separated, has the following assumptions.

Implications of the model for blood oxygenation level-dependent functional magnetic resonance image contrast. The experimental fractional changes in CMR_O2 and CBF observed during functional activation reflect a decrease in OEF from its basal value (i.e., OEF/OEF < 0), which is commensurate with an increased venous blood oxygenation (Y ) in cerebral capillaries; i.e., |OEF/OEF| = Y/(1  Y ) > 0, where the arterial oxygenation is assumed to be very close to 1 (see APPENDIX C). Recent advancements in fMRI have allowed the detection of changes in cerebral blood oxygenation during functional challenges with the -weighted or gradient-echo image contrast (where is the apparent transverse relaxation rate of tissue water). This is the most commonly used image contrast in fMRI and has been termed blood oxygenation level dependent (BOLD) (47, 48). The BOLD fMRI image contrast relies on physiologically induced changes in the magnetic properties of blood: oxyhemoglobin is diamagnetic, and deoxyhemoglobin is paramagnetic. An increase in the physiologically induced BOLD fMRI signal (S/S > 0) is consistent with a drop in venous deoxyhemoglobin concentration. Near-infrared spectrophotometry (23, 66) and intrinsic optical reflectance studies (14, 44) have shown that deoxyhemoglobin concentration decreases after stimulation onset in awake or anesthetized mammalian brains, which provides qualitative support for the BOLD fMRI hypothesis (47, 48). The physiologically induced BOLD fMRI signal change (S/S) can be approximated in various ways, and a common approximation is

(19)

where A is a magnetic field-dependent physiological constant and  is a constant that modulates the blood volume component (4, 6, 22, 25, 28, 30, 47, 48, 70). To relate the change observed in BOLD fMRI studies to changes in CMR_O2 and CBF, it is necessary to establish a relationship between these physiological parameters and Y/(1  Y ) and CBV /CBV. A restatement of Eq. 13 is

(20)

and a common expression for blood volume changes by Grubb et al. (19) is

(21)

where  = [1 + (CBF/CBF)] and  = 0.38 (from Ref. 19). There is a general agreement in the various expressions for S/S (4, 6, 22, 25, 28, 30, 47, 48, 70), although there is some discrepancy about the constants. Equations 19-21 can be simplified to

(22)

Simulations. For simulations, the effects of  on the relationship between CBF and CMR_O2 and the relationship between BOLD fMRI image contrast and CBF were examined for OEF of 0.2 and 0.4, which cover the range of basal OEF values reported in the literature for normal, adult, awake, nonstimulated human cortex (11, 12, 40, 49, 56, 59). The cases examined here are  > 0 and  = 0.

View larger version (17K): [in this window] [in a new window]   Fig. 1.   Calculated effects of  on proportionalities between CBF/CBF and CMRO2/CMRO2 for basal OEF values of 0.2 and 0.4. Highly nonlinear relationship between CBF/CBF and CMRO2/CMRO2 is observed when  = 0 (dashed curves), as observed in model of Buxton and Frank (6). A linear relationship between CBF/CBF and CMRO2/CMRO2 is observed when  > 0 (solid curves). Values of  in solid curves are 0.31, 0.28, and 0.23 (, , and , respectively) in A and 0.23, 0.17, and 0.14 (, , and , respectively) in B. See Glossary for definition of abbreviations.

View larger version (16K): [in this window] [in a new window]   Fig. 2.   Impact of model on BOLD fMRI image contrast simulated (using Eqs. 19-22) as follows: A = Cmax(1  YOEF)bTE (4, 22, 28, 47, 48, 70), where (1  YOEF) is arteriovenous blood oxygenation difference (i.e., blood deoxygenation) at basal OEF and Cmax(1  YOEF)b is equal to basal , which gives rise to basal BOLD signal. S/S, Bold fMRI signal changes. Curves are simulated with  = 1, max = 267.5B0 (where B0 = 4 T and  = 0.01 ppm), b = 0.03, TE = 0.03, C = 72.70, and (1  YOEF) at 2 different basal values of OEF (i.e., 0.2 and 0.4, which correspond to  = 7.00 ± 2.33 s1 and A = 0.14 ± 0.05 as in Ref. 30) for  > 0 (solid curves) and  = 0 (dashed curves) at basal OEF values of 0.2 (A) and 0.4 (B). For  > 0, reduced S/S is due to effect of increasing  to tighten proportionality between CBF/CBF and CMRO2/CMRO2; for higher values of  there is also a tendency for S/S to decrease above a threshold CBF/CBF. This decrease in S/S is due to greater blood volume at higher CBF/CBF values because of power law dependence on perfusion (see Eq. 21). See Fig. 1 legend for  values. See Glossary for definition of abbreviations.

	RESULTS

Top Abstract Introduction Methods Results Discussion Appendix A Appendix B Appendix C References

The in vivo rat and human data are fitted to determine values of . Basal values of CBF/CBF and CMR_O2/CMR_O2 at different levels of wakefulness are obtained from the literature for rats (20, 24, 45, 46, 64) and humans (29, 51, 61). In rat and human data sets the awake CBF and CMR_O2 values were used to obtain curves of CMR_O2/CMR_O2 vs. CBF/CBF, and linear regression analysis was used to obtain in vivo values of  for the rat and human cortices of 0.88 ± 0.06 and 0.96 ± 0.09, respectively (R² = 0.97 and 0.93). Respective  values are calculated with these  values, with use of Eq. 23, at basal OEF of 0.2, 0.3, and 0.4

(23)

where  = ln [1  OEF(/)] and  = ln (1  OEF). The result of the linear fits to the data are shown in Table 1. In Fig. 3 the in vivo data are plotted against the curve predicted with  > 0 (solid curves) and  = 0 (dashed curves) for three basal OEF values. The fits to the in vivo data are clearly better when  > 0, showing how the flexibility in the present model allows these well-established results to be explained. In contrast, the approach of Buxton and Frank (6) cannot be extended below the awake level.

View larger version (21K): [in this window] [in a new window]   Fig. 3.   Experimental reported values of CBF/CBF and CMRO2/CMRO2 at different levels of activity due to anesthesia in rat cortex with  = 0.88 ± 0.06 (20, 24, 45, 46, 64) and in human cortex with  = 0.96 ± 0.09 (29, 51, 61). For basal OEF = 0.2, 0.3, and 0.4, corresponding  values are 0.88, 0.87, and 0.86 in A, B, and C, respectively, and 0.95, 0.94, and 0.93 in D, E, and F, respectively. Fits to in vivo data are clearly better when  > 0 (solid curves) than when  = 0 (dashed curves), supporting an important role for coupling between effective diffusivity for oxygen of capillary bed and perfusion. See Table 1 for details on in vivo data and results of CMRO2 (%) predicted when  > 0 and  = 0.

Values of  have been obtained from functional activation data sets of awake humans with different stimulation paradigms (11, 12, 56, 59). In each case, a linear regression analysis is carried out for each data set to obtain an in vivo value of , and the reported basal OEF value is used when an in vivo value of  is calculated (using Eq. 23). For each functional data set, as shown in Table 2, the negative value(s) of oxygen utilization reported is not included in the regression analysis, and the best fits are pivoted at the origin. The cases for  > 0 and  = 0 are examined. The results of the linear regression analysis for each data set are shown in Table 2. Fits similar to those in Fig. 3 are made to data available for physiologically activated tissue in the awake humans. For each study the data are fit to determine a value of , which leads to a value of  calculated using the OEF reported in that study, as shown in Table 2. In Fig. 4, for each study the in vivo human data are plotted against the curve predicted with  > 0 (solid curves) and  = 0 (dashed curves) at the corresponding basal OEF value for that study. Although Fig. 4 shows that  varies with different stimulation paradigms and laboratories, the fits to the in vivo data are clearly better when  > 0 (solid curves) than when  = 0 (dashed curves). However, in most of these functional studies the scatter in the data is so large that the ability to distinguish  > 0 from  = 0 is less conclusive than for the data obtained from variable depths of anesthesia (Fig. 3). Table 2 summarizes the results of fits when  > 0 and  = 0 given the data for physiologically activated tissue in awake humans. For each study, the mean value of CMR_O2/CMR_O2 predicted with  > 0 is in excellent agreement with raw in vivo observations and significantly larger than the values predicted with  = 0 (Table 2).

View larger version (27K): [in this window] [in a new window]   Fig. 4.   Analysis similar to Fig. 3 performed on data available from literature for physiologically activated tissue in awake humans (Table 2). For each study, data are fit to determine a value of , which leads to a value of  calculated using OEF reported in that study, as shown in Table 2. For each study, in vivo human data are plotted against curve predicted with  > 0 (solid curves) and  = 0 (dashed curves) at corresponding basal OEF for that study: visual study (A), sensory study (B), sensory study (C), and cognitive study (D). Although  varies with different stimulation paradigms and laboratories, fits to in vivo data are clearly better when  > 0 (solid curves) than when  = 0 (dashed curves). See Table 2 for details of study, stimulus paradigm, and results of CMRO2 (%) predicted when  > 0 and  = 0.

	DISCUSSION

Top Abstract Introduction Methods Results Discussion Appendix A Appendix B Appendix C References

Some, but not all (56, 59), human brain functional data of PET studies have demonstrated that, during brain activation, CBF/CBF  CMR_O2/CMR_O2 (11, 12). This has been interpreted as an uncoupling between perfusion and oxidative metabolism. Buxton and Frank (6) proposed that the greater fractional increase in CBF than in CMR_O2 during activation is a consequence of oxygen delivery to tissue being proportional to the capillary-tissue PO₂ gradient. At low basal OEF values, their model predicts a highly nonlinear relationship, with low coupling ratios between changes in CMR_O2 and CBF because of the limited ability of perfusion to increase the capillary-tissue PO₂ gradient. Gjedde (15) presented a model in which oxygen delivery is limited by the maximum partial pressure difference achievable between the capillary plasma and the oxygen-consuming mitochondria. Although no specific barrier to oxygen diffusion is required in this model for a low initial OEF, the ability of CBF to increase oxygen delivery to the tissue is similarly limited (15). Here we extend this approach by considering the effect of a changing effective diffusivity of the capillary bed for oxygen. For a fixed ratio between changes in effective diffusivity of the capillary bed and perfusion, signified by a physiological parameter  (Eq. 14), a close-to-constant proportionality is maintained between changes in CBF and CMR_O2 throughout the physiological activity range (60). This model provides a better fit to the majority of in vivo human data of changes in CBF and CMR_O2 than does the model of Buxton and Frank, which is the limiting case when  = 0.

The effect of an increased  is to increase the ratio  between CMR_O2/CMR_O2 and CBF/CBF (Fig. 1; see RESULTS). A major assumption in the model is that changes in perfusion and effective diffusivity of the capillary bed are tightly regulated and coupled to maintain a low cerebral PO₂, and as a consequence, oxygen delivery is primarily determined by the capillary PO₂. Reports of very low cerebral PO₂ (37-39, 41) suggest that the capillary-tissue PO₂ gradient is proportional to the capillary PO₂. Consistent with this view, a multiple-tracer study has shown that most of the oxygen that enters the tissue is metabolized (26). Alternatively, similar trends would be observed if the cerebral PO₂ were not negligible, provided that it was maintained at a constant and lower value than the capillary PO₂. With a constant cerebral PO₂, changes in oxygen delivery would still be determined primarily by changes in the capillary PO₂ and the coupled effective diffusivity for oxygen of the capillary bed (8, 55).

The microscopic physiological picture of this model is the ability of the capillary bed to increase effective diffusivity for oxygen, caused by the increase in capillary PO₂, hematocrit, and/or blood volume (9, 10, 21, 31, 32, 36, 42, 43) during increased brain activity. Increased CBV in the activated cortex is a well-accepted occurrence (11, 12, 56, 59) and supports the proposal of Roy and Sherrington (58) that changes in CMR_O2 and CMR_Glc are regulated by alterations in CBF and CBV. During altered brain function, the swelling of capillary diameter (2, 7, 14, 44, 57, 66, 67), variation in the number of plasmatic capillaries (1, 13, 18, 31, 50, 63, 65, 67, 69), and/or intracapillary stacking of erythrocytes (10, 21, 32, 36, 42, 43, 62, 67) can contribute to the change in capillary PO₂, hematocrit, and/or blood volume. Much evidence has been presented in support of changes in the number of plasmatic capillaries (1, 13, 18, 31, 50, 63, 65, 67, 69) or intracapillary stacking of erythrocytes (10, 21, 32, 36, 42, 43, 62, 67) being critical events that can modulate oxygen delivery and demand. Because some type of capillary readjustment, with respect to capillary PO₂, hematocrit, and/or blood volume, would modify the effective diffusivity for oxygen of the capillary bed, it is not necessary to assume that there is absolutely no capillary readjustment within a microvascular tissue unit, as did Buxton and Frank (6). Although the term capillary readjustment generally reflects increases in the blood volume of the capillary bed, the term presented here suggests a modifying capillary bed with respect to capillary PO₂, hematocrit, and/or blood volume. The generally better fits obtained by the current model to in vivo data than in the case of no increase in effective diffusivity of the capillary bed suggest that one or all mechanisms may be operational in increasing this parameter in vivo.

An implication of the model of Buxton and Frank (6) is that low values of  should be the norm, because CMR_O2 is limited by the PO₂ gradient. However, examination of a range of PET activation data indicates that, in contrast to the results of Fox and co-workers (11, 12), the data are generally fit better with  > 0 (Fig. 4). Furthermore, all the global measurements (Fig. 3) show very strong proportionalities of CMR_O2 and CBF, which are in agreement with higher  values, such as those found by Roland and co-workers (56, 59) (Tables 1 and 2). A possible explanation for the variation in the activation data in the literature is that stimuli may only be activating a fraction of the tissue within an image voxel. Depending on the measurement methodology, the effect of this partial volume on CMR_O2 and CBF may be considerably different. In contrast, in the graded anesthesia studies, such partial-volume effects are reduced, because the perturbations are global. In addition, the human graded anesthesia studies were performed by arteriovenous difference methodology, for which measurements of CMR_O2 and CBF are relatively straightforward compared with imaging methodologies (for review, see Ref. 53). However, arteriovenous difference methods represent an average value for the entire brain, so that small regions with values of  that are substantially different from the mean value may have been missed. Because methodological and partial volume differences may not account for all the variation in the human activation data, it is clearly necessary to design experiments with better sensitivity and spatial resolution to better determine the coupling between CMR_O2 and CBF under different states of activation and/or different stimulation paradigms.

Conclusion. Recent models of cerebral oxygen delivery (6, 15) have suggested that, at low values of OEF, oxygen delivery is limited by the inefficiency of perfusion in raising capillary PO₂. We have presented a model that weakens this limitation by allowing changes in the capillary effective diffusivity to oxygen with changes in perfusion. The change in capillary effective diffusivity to oxygen with respect to perfusion, i.e., , allows oxygen delivery to be more sensitive to changes in perfusion. An appropriate value of  asserts an ~1:1 ratio between changes in CBF and CMR_O2 throughout a wide range of activity. The model of Buxton and Frank (6), in which  = 0, is the limiting case of our model. The present model shows that when  > 0 the limitation imposed by oxygen delivery on increases in CMR_O2 predicted by the model of Buxton and Frank does not hold within the physiological range. In contrast to the model of Buxton and Frank, where the data could only fit data where  = 0, our model can fit a wide range of data, so it makes no claims to establishing the relationship between changes in CBF and CMR_O2; only good data can do that. The present model is able to fit all available in vivo data and depicts the transition of hemodynamic and metabolic events for a large range of physiological cases. This characteristic of the model signifies that the oxygen diffusivity properties of the capillary bed, which are adjusted with respect to perfusion, play a crucial part in regulating cerebral oxygen delivery in vivo.