Dependence of Oxygen Delivery on Blood Flow in Rat Brain: A 7 Tesla Nuclear Magnetic Resonance Study

Abstract

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 · g⁻¹ · min⁻¹ and CMRO₂ was 3.15 ± 0.18 μmol · g⁻¹ · 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 α-chloralose anesthetized rats were 0.40 ± 0.09 mL · g⁻¹ · min⁻¹ and 1.51 ± 0.06 μmol · g⁻¹ · 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 Ω. A value 0.81 ± 0.23 was calculated for Ω 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.”

Keywords

Magnetic resonance imaging Magnetic resonance spectroscopy Positron emission tomography Functional magnetic resonance imaging Blood oxygenation level dependent Brain mapping Oxygen Glucose Lactate Glutamate Glutamine Glycogen Kreb's cycle Cerebral energy Perfusion Blood volume Metabolic flux Extraction

Brain cells rely on an abundant and continuous supply of oxygen for normal function. Reductions in the supply of oxygen can readily lead to neuronal damage. This extreme vulnerability of cerebral tissue to oxygen deprivation results from the high rate of metabolism, relatively low intracellular energy reserves, and the low blood volume supplying the oxygenated hemoglobin. Therefore, normal brain function requires that oxygen delivery be regulated in relation to the oxidative metabolic requirements of the nerve cells.

The rate of oxygen delivery to brain tissue from blood depends on the vessel-to-tissue oxygen partial pressure (Po₂) gradient (Krogh, 1919) and the efficiency of oxygen transfer from the capillary bed (Hyder et al., 1998). The value of the Po₂ gradient depends primarily on the oxygen tension in the microvessels because the cerebral tissue oxygen tension is low (Crockard et al., 1976; Metzger and Huber, 1977; Fennema et al., 1989; Vovenko, 1999). Consistent with a low tissue oxygen tension are studies that have found that the flux of oxygen from plasma to brain tissue is unidirectional (Grieb et al., 1985; Sawada et al., 1989; Kassissia et al., 1995), where most of the oxygen molecules that cross the endothelium are believed to be completely metabolized (Krogh, 1919; Tenney, 1974; Kreuzer, 1982). Therefore, at metabolic and hemodynamic steady-state, based on the available evidence, it can be concluded that the rates of oxygen delivery and oxygen consumption are equal.

On basis of the assumption that oxygen delivery across the endothelium is proportional to the vessel Po₂ value, a recent model proposed by Hyder et al (1998) shows that CMRO₂ can be linked to CBF through a hypothetical effective diffusivity term for oxygen (D) of the capillary bed. The assumed functional behavior of the capillary bed can be represented as fractional changes in effective oxygen diffusivity with respect to alterations in cerebral perfusion, that is, (ΔD/D)/(ΔCBF/CBF), signified by Ω, which reflects a measure of the efficiency of oxygen transport from the blood in the capillary to the tissue. For each vessel in a capillary bed, an expression can be derived relating vessel circulation time to oxygen delivery and integration of this expression over an ensemble of capillaries yields a relationship in which the diffusivity term, D, relates to macroscopic oxygen delivery (which at steady-state is equal to CMRO₂).

An extensive reexamination of the relevant rat and human data from the literature (Hyder et al., 1998) demonstrates that at steady-state conditions, CBF and CMRO₂ change in a near-stoichiometric manner from the resting anesthetized condition over a wide dynamic range (including the resting awake condition or higher). As pointed out by Gjedde (1997) and Buxton and Frank (1997), a near-linear relationship between CBF and CMRO₂ cannot be maintained with a constant oxygen diffusivity because of the vessel Po₂ asymptotically approaching the arterial value (Appendix A). It has been proposed that the linear relationship between CBF and CMRO₂ in the cerebral cortex may be explained with an oxygen diffusivity term that varies with perfusion (Hyder et al., 1998). It was found that the full range of results in the literature, ranging from “activation” by sensory stimulation to “deactivation” by anesthesia, could fit well with a nonzero value of Ω (Hyder et al., 1998).

A limitation in inferring a relationship between CBF and CMRO₂ from values reported in the literature is that most of the studies were done by different investigators using different methodologies. In the current study, we use magnetic resonance imaging (MRI) and spectroscopy (MRS) methods to perform combined measurements of CMRO₂ and CBF in rats under different levels of hemodynamic and metabolic activity induced by anesthesia along with sensory stimuli. We find that over a large activity range the data are best fit with a single value of Ω which is nonzero. These results imply an important role for changes in capillary bed diffusivity in regulating oxygen delivery.

MATERIALS AND METHODS

Animal preparation

Sprague-Dawley rats (adult males weighing 140 to 210 g, fasted 24 hours) were tracheotomized and ventilated with a mixture of N₂O/O₂ (70/30) under 1% halothane anesthesia. A femoral artery and vein were cannulated for periodic blood sampling (for measurement of blood gases, pH, pressure, and glucose) and d-[1-¹³C]glucose (99 atom %; Cambridge Isotopes, Andover, MA, U.S.A.) infusion, respectively. The scalp was incised along the midline and the skin was retracted. The skull was cleaned of all tissues between the temporal ridges. A layer of Saran Wrap was placed over the wound to prevent desiccation and avoid contact of moisture with the radiofrequency (RF) surface-coil. After surgery anesthesia was either maintained with morphine sulfate (intraperitoneally 50 mg/kg, initial; 30 mg/kg every 30 minutes, supplemental) or α-chloralose (intraperitoneally 80 mg/kg, initial; 20 mg/kg every 30 minutes, supplemental) and paralyzed with d-tubocurarine chloride (intraperitoneally 0.50 mg/kg, initial; 0.25 mg/kg every 30 minutes, supplemental). The rat was placed prone on a cradle surrounded by a water-heated blanket to maintain core body temperature at approximately 37°C. The head was secured in a holder designed to minimize movement. The RF resonator/surface-coil probe (see later) was placed above the head and centered approximately above the bregma for detection in the sensorimotor region. The rat head was then positioned at the magnet isocenter.

Experimental paradigm

The objective of these experiments was to obtain paired measurements of cortical CBF and CMRO₂ at different levels of cerebral activity. Animals were divided into five treatment groups.

In three cases, each group received an anesthetic dose of morphine sulfate balanced with nitrous oxide either alone (group A) or in combination with sodium pentobarbital (group B) to reduce activity or nicotine hydrogen tartrate (group C) to increase activity. The animals in group A (protocol I) received an initial morphine sulfate intraperitoneal dose of 50 mg/kg with supplemental doses of 25 mg/kg every 30 minutes. The animals in group B (protocol II, “deactivation”) received an initial pentobarbital intraperitoneal dose of 45 mg/kg with supplemental doses of 10 mg/kg every 30 minutes. The animals in group C (protocol III, “activation”) received nicotine hydrogen tartrate at a dose of 4 mg/kg at a constant intravenous infusion rate of 16.7 μL/min. For each animal in group A (n = 5), CBF and CMRO₂ were measured together under basal conditions of morphine/nitrous oxide anesthesia. For each animal in group B (n = 4), the CBF alone was measured before pentobarbital administration under basal conditions, then CBF and CMRO₂ were measured together after pentobarbital administration. For each animal in group C (n = 5), the CBF was measured before nicotine administration under basal conditions, then the CBF and CMRO₂ were measured together after nicotine administration.

In two cases, each group received an anesthetic dose of α-chloralose balanced with nitrous oxide either alone (group D) or in combination with forepaw stimulation (group E) to increase focal activity in the sensorimotor region of both hemispheres (Hyder et al., 1996). The CBF was measured at rest for the animals in group D (protocol IV, n = 4) and during stimulation of both forepaws (i.e., activation) for the animals in group E (protocol V, n = 4). The CMRO₂ values for groups D (n = 4) and E (n = 3) were obtained from unpublished data collected from a protocol described in Hyder et al (1996). A pair of copper electrodes (6 mm long, 1 mm in diameter) were inserted into the skin of each forepaw (between digits 1 and 2, and 3 and 4). An electrical stimulator (Harvard Apparatus Limited, Kent, MA, U.S.A.) provided low-voltage square-wave pulses of 0.3-millisecond duration at 3 Hz (Hyder et al., 1994).

Infusion of 13C-labeled glucose

d-[1-¹³C]Glucose was infused intravenously using a protocol that rapidly elevated and then maintained the labeled glucose at a steady level in the blood (Hyder et al., 1996, 1997). During the infusion, blood samples were obtained every 15 to 30 minutes and centrifuged, and the plasma was removed and frozen.

MRS and MRI measurements

General procedures. All in vivo MRS and MRI data were acquired on a highly modified 7 T Bruker Biospec I horizontal-bore spectrometer (Bruker, Billerica, MA, U.S.A.) operating at 300.6 and 75.5 MHz for ¹H and ¹³C, respectively. The transceiver coils consisted of a ¹H resonator (8-cm diameter) for transmission of RF pulses with an orthogonally oriented ¹H surface-coil as a receiver (1-cm diameter). The two coils were positioned relative to one another such that the homogenous regions of the two RF coils were coincident. The arrangement of the two ¹H RF coils also minimized sensitivity losses in the receiver coil, permitting better localized shimming and homogeneous transmission. The ¹H resonator covered the upper half of the rat's torso, whereas the ¹H surface-coil was positioned over the frontoparietal region of the brain. A concentric surface-coil (20-mm diameter) tuned to the ¹³C frequency was used for the proton observed carbon edited (POCE) experiment (see later).

The static magnetic field homogeneity of the localized volume, which encompassed the bilateral sensorimotor area of the cortex, was optimized by localized shimming before data acquisition. The line-width at half-height for the water signal obtained from the localized volume (x, y, z = 7.5, 1.6, 4.0 mm³) was between 14 and 16 Hz. Coronal, multislice anatomic images (four slices separated by 1 mm, each slice 1-mm thick) provided coordinates for the placement of a 48-μmUL rectangular volume for the POCE experiments. High-resolution R₁ (longitudinal relaxation rate of tissue water) weighted images were acquired with the following parameters: image matrix of 128 × 128 pixels, field of view of 20 mm, repetition time (TR) of 2500 milliseconds, echo time (TE) of 20 milliseconds, and inversion recovery time (TIR) of 300 milliseconds.

Determination of CMRO₂ from [C4]-glutamate turnover. The POCE data were acquired during infusion of [1-¹³C]glucose and localized to the sensorimotor cortex. The experimental details of the localized POCE experiment have been described earlier (Hyder et al., 1996, 1997). Briefly, the sequence included inversion recovery water suppression, image selected in vivo spectroscopy (ISIS; Ordidge et al., 1986) volume selection (x, y, z = 7.5, 1.6, 4.0 mm³), and surface lipid suppression (Hyder et al., 1999a) before the POCE pulse sequence. The POCE segment of the sequence consisted of a spin-echo with TE of 20 milliseconds, and two balanced crusher gradients (each 2 milliseconds in duration) were used in each half of the spin-echo sequence to eliminate nonrefocused magnetization. A ¹H90° composite pulse (θ_yθ_xθ__yθ_x) was followed by a ¹H-180° 2-τ-2 semiselective pulse (θ_xθ_x; τ = 676 microseconds). A ¹³C-180° phase-cycled pulse (θ_xθ_{± x}) was centered at ½J (= 4 milliseconds; J ≈ 125 Hz) from the ¹H-90° pulse. Each free-induction decay was acquired in the presence of a broadband (± 20 ppm) ¹³C composite Waltz-16 decoupling pulse (θ θ θ θ, where θ = 270°__x360°_+x180°__x270°_+x90°__x 180°_+x360°__x180^o_+x270°__x and θ denotes the phases inverted; Shaka et al., 1983) at 2 W during the acquisition time (204.8 milliseconds). The ¹³C inversion pulse, which was applied in alternate scans by alteration of its phase (θ_xθ_{± x}), resulted in more than 98% inversion over a bandwidth of ± 2.5 ppm (in ¹H chemical-shift) based on in vitro samples of [2-¹³C]acetate and glycine. The TR for each acquisition was 2 seconds, and these parameters corresponded to a decoupling duty cycle of approximately 7%, with an average power deposition of 140 mW (at the preamplifier level). The actual power deposition in the brain was several-fold less than this value because the ¹³C RF coil covered a larger region than the brain as well as loss of power within the coil. Consecutive free-induction decays, with and without the ¹³C inversion, were collected in two different memory blocks (64 scans per block). Before Fourier transformation, one block was substracted from the other, zero-filled to 8 K, and exponentially line-broadened (10 Hz). The POCE difference-spectrum was phase corrected between 4.0 and 0.5 ppm (zero- and first-order phase corrections), and the peak height of [C4]-glutamate at 2.35 ppm was measured.

The rat brain was frozen in liquid nitrogen at the end of each in vivo experiment. Each brain was removed from the skull, and an identical region of the cortex (approximately 50 mg), as in the in vivo study (see earlier), was removed. Acid-soluble amino acids were extracted from the frozen tissue using methanol/HCl and 3 M perchloric acid, as previously described (Behar et al., 1986). The ¹³C fractional enrichment of [C4]-glutamate was determined from POCE spectra at 360.13 MHz. Samples of blood plasma (approximately 50 μL) were extracted for quantitation (Behar et al., 1986) of total glucose concentration and ¹³C fractional enrichment of [C1]-glucose.

The details of the metabolic modeling have been described previously (Mason et al., 1992; Hyder et al., 1996, 1997). Bestfit of the metabolic model to the [C4]-glutamate fractional enrichment time course was used to calculate tricarboxylic acid (TCA) cycle flux (V_TCA). For each value of V_TCA, CMRO₂ was determined by relationship 3 × V_TCA. From our previous studies (Hyder et al., 1996, 1997), it was determined that the major source of dilution to the acetyl coenzyme A pool is the pyruvate/lactate blood-brain exchange, which has little effect on the calculated rates. Fits performed with either slow or rapid glucose transport showed that glucose transport is not the rate-limiting factor in glucose metabolism in vivo, and glutamate-glutamine exchange is not the rate-limiting factor in the ¹³C turnover data of [C4]-glutamate (Hyder et al., 1996, 1997). These analyses reveal relatively small effects of flux measurements (≤10%) for the dynamic range covered in this study (Mason et al., 1992; Hyder et al., 1996, 1997). Partial-volume corrected CMRO₂ values were obtained for the forepaw stimulation data, as previously described (Hyder et al., 1997), using the relationship of CMRO₂(activated) = [CMRO₂(observed) – (1 – f) × CMRO₂(rest)]/f, where f represents the fraction of activated tissue in the ISIS compartment using the activated CBF map thresholded at the resting CBF value.

Determination of CBF from absolute R₁ maps. The CBF data were obtained by an inversion recovery method (Schwarzbauer et al., 1996). Coronal, multislice, spin-echo echo-planar imaging (EPI) data (Mansfield, 1977) with R₁-weighting were obtained with 10 TIR values, ranging from 200 to 1800 milliseconds, with delayed acquisition approaches to minimize the effects of vascular artifacts in steady-state arterial spin labeling methods (Calamante et al., 1999). The EPI data were acquired with sequential sampling (Hyder et al., 1995) and the following parameters: TE = 28 milliseconds, image matrix = 32 × 32 pixels, and spatial resolution = 430 × 430 × 1000 μm. A sinc pulse (Mansfield et al., 1979) was used for slice-selective excitation and an adiabatic fast passage hyperbolic secant pulse (Silver et al., 1984) was used for slice refocusing. Excitation and refocusing slice thicknesses were 1 mm, whereas the inverted slice was 5 mm. Two consecutive images corresponding to slice-selective and nonselective inversions were obtained under fully relaxed conditions for each TIR. Adiabatic fast passage hyperbolic secant pulses also were used for inversions. R₁ maps for slice-inverted (R_1s) and nonselect inverted (R_1n) data were calculated with single exponential recovery fits. The use of this method requires the value of R₁ of blood water (R_1b). Because the EPI data were not of sufficient spatial resolution to delineate large arteries in the imaging plane, high spatial resolution spin-echo MRI data (consecutive coronal images of slice-selective and nonselective inversions) were acquired for rats (condition A, n = 3) with the following parameters: TE = 28 milliseconds, image matrix = 256 × 256 pixels, spatial resolution = 75 × 75 × 250 μm, and multiple TIR values ranging from 200 to 2200 milliseconds. R_1b was measured (0.5 ± 0.1 s⁻¹) from pixels in the R_1n images, which clearly delineated large vessels near the cortical surface. The dynamic range of this perfusion imaging method, which is based on absolute R₁ measurements in labeled and control images, was tested by obtaining images before and during hypercapnia (10% CO₂ inhalation) and at death (see later). Absolute CBF was calibrated (Schwarzbauer et al., 1996) on a pixel-by-pixel basis by the relationship of 60 × (λ/(1+∊))(R_1s – R_1n), where λ is the brain-blood partition coefficient for water (0.95 mL/g) and ∈ is a correction coefficient, which is given by ¾(1 – R_1b/R_1n). Another perfusion image was calculated, CBF₀ = 60 × λ(R_1s – R_1n), and a relative error image, δCBF, was calculated as (CBF₀ – CBF)/CBF. From the high spatial resolution perfusion data (see earlier), a systemic error of less than 5% was determined for the dynamic range (Schwarzbauer et al., 1996). Regional values of CBF were obtained by averaging pixels in the rectangular volume of 7.5 × 1.6 × 4.0 mm³ across four slices. The position of the resulting volume in the cortex corresponds to the same region used in the measurement of CMRO₂.

The “tagged” signal in MRI spin tagging methods is not only contingent on tissue perfusion, but also is dependent on vascular transit time effects. Problems of this nature can be minimized (Calamante et al., 1999) with optimal choice of inversion-excitation slice thickness ratio, short pulse lengths, uniform nonselective inversions, and acquisition of each inversion recovery image under fully relaxed conditions. To use optimal conditions for accurate CBF measurement, we performed all of the studies at metabolic and hemodynamic steady-state. Since the pulse duration for each adiabatic inversion was less than 5 milliseconds, the inversion-excitation slice thickness ratio was 5:1, and each tag was made under relaxed conditions (i.e., data acquisition did not have time constraints), the induced systematic errors were negligible (≤5%). Since methods that require subtraction of the control image from the labeled image are heavily dependent on the choice of an optimal TIR value so that the arterial transit time can be accounted for in the difference image (Yang et al., 1998), the approach used here relies on comparison of R₁ maps (Schwarzbauer et al., 1996). The use of a large homogenous RF transmission coil for each nonselective inversion provided a situation that, for each subsequent slice excitation, the “untagged” blood volume was negligible. Specific approaches have been described to reduce systematic errors associated with rapid acquisition of CBF data (Buxton et al., 1998).

Simulations and calculations

Values of CBF and CMRO₂ for graded anesthesia from the literature. Basal values of CBF and CMRO₂ for the conscious condition and graded anesthesia were obtained from the literature for the rat cortex (Hagerdal et al., 1975; Nilsson and Siesjo, 1975, 1976) as shown in Table 1. In each study, the systemic physiologic parameters as measured from blood (e.g., Pco₂, Po₂, pH) all were reported to be within normal limits, whereas the mean arterial blood pressures were slightly different in each case.

TABLE 1.

Values of CBF and CMR_O2 for graded anesthesia in rat from the literature (refer to Fig. 2)

Reference	Condition	CBF (mL · g⁻¹ · min · ⁻¹)	CMR_O2 (μmol · g⁻¹ · min⁻¹)
Nilsson and Siesjo (1975)	Conscious	1.40	5.00
Nilsson and Siesjo (1975)	50 mg/kg phenobarbital	1.11	4.05
Hagerdal et al. (1975)	70% N₂O	1.08	4.60
Nilsson and Siesjo (1976)	70%N₂O, 1.2%halothane	0.80	3.36
Nilsson and Siesjo (1975)	150 mg/kg phenobarbital	0.79	2.95
Nilsson and Siesjo (1975)	250 mg/kg phenobarbital	0.60	2.60

Calculation of Ω, prediction of ΔCMRO₂/CMRO₂, and uncertainty in Ω. Oxygen extraction fraction (OEF) in the vicinity of a capillary bed is given by (Hyder et al., 1998, 1999b)

O E F = 1 - \exp (- D / C B F)

(1)

where the mathematical notation of D as well as the hypothetical makeup, the assumptions involved, and the flexibilities of the parameter are discussed briefly in Appendix B. Assuming equivalence between Eq. 1 and Fick's equation

Δ {C M R}_{O 2} / {C M R}_{O 2} = α [1 - \exp {- (D / C B F) (β / α)}] / O E F - 1

(2)

where $α = (1 + Δ C B F / C B F)$ and $β = (1 + (Δ C B F / C B F) Ω)$ provided that

Ω = (Δ D / D) / (Δ C B F / C B F)

(3)

where the term Ω is hypothesized to reflect the changes in the effective diffusivity of oxygen in relation to circulation (Appendices A and B). The value of Ω (Hyder et al., 1998a, 1999c; Appendix C) can be determined by

Ω = (1 + σ) (ϑ / ς) - σ

(4)

where $σ = (Δ C B F / C B F)^{- 1}, ϑ = \ln [1 - O E F (γ / α)], ς = \ln [1 - O E F], γ = (1 + (Δ C B F / C B F) Ψ)$ , and $Ψ = (Δ {C M R O}_{2} / {C M R O}_{2}) / (Δ C B F / C B F)$ . Respective Ω values were calculated with experimentally determined Ψ using Eq. 4. Values of ΔCMRO₂/CMRO₂ were predicted with Ω = 0, Ω = 1, and 1 > Ω > 0 using Eq. 4. Values of CBF and CMRO₂ for the awake state were obtained from the literature (see earlier). The basal OEF value for the awake condition was assumed to be between 0.2 and 0.4. Since the uncertainty in Ω (i.e., δΩ/Ω) depends on CBF and CMRO₂ (Appendix C), Eq. 4 can be reexpressed

\begin{aligned} δ Ω / Ω = & {(δ α + α - 1)^{- 1} {\ln [1 - O E F (δ γ + γ) / \\ {(δ α + α)] / ς - 1} + \ln [1 - O E F (δ γ + γ) / \\ (δ α + α)] / ς} / {(1 + σ) \ln [1 - O E F (γ + α)] / \\ ς - σ} - 1 \end{aligned}

(5)

where δα and δγ are errors associated with ΔCBF/CBF and ΔCMRO₂/CMRO₂, respectively, at different activity levels. All results are presented as means ± SD.

RESULTS

Cerebral function in terms of “deactivation” and “activation” transitions

Whereas the blood gases (i.e., Po₂, Pco₂) and pH measured over the entire period of each perturbation protocol were insignificantly different from the physiologic condition in each control protocol, changes in mean arterial blood pressure were observed in some cases (Table 2). Pentobarbital and nicotine resulted in slightly lower (75 ± 26 mm Hg, P < 0.11) and higher (115 ± 27 mm Hg, P < 0.12) mean arterial blood pressures, respectively, compared with the control condition (95 ± 7 mm Hg) of the morphine anesthesia. The changes in blood pressure in response to global perturbations were consistent with previous reports (Wei et al., 1993; Chen et al., 1995). However, the observed changes in blood pressure were within the expected range over which cerebral autoregulation occurs in the mature rat brain (60 to 150 mm Hg; Hernandez et al., 1978). In addition, CBF was shown to be independent of mean arterial pressure between 70 to 120 mm Hg for a particular anesthesia level (Harper, 1965, 1966). The ¹³C fractional enrichment ratio of [C4]-glutamate/[C1]-glucose at the end of each experiment for each condition was insignificantly different from the others (Table 2).

TABLE 2.

Systemic physiologic parameters of “deactivation” and “activation” (refer to Figs. 2 and 3)

Condition	Pco₂(mm Hg)	pH	Arterial bloodpressure (mm Hg)	¹³C fractional enrichment ratioof [C4-glutamate]/[Cl-glucose]
Protocol I control condition morphine (A)	37 ± 9	7.35 ± 0.03	95 ± 7	0.42 ± 0.08
Protocol II “deactivation” pentobarbital (B)	34 ± 12*	7.38 ± 0.05†	75 ± 26‡	0.41 ± 0.09
Protocol III “activation” nicotine (C)	35 ± 10§	7.36 ± 0.04‖	115 ± 27¶	0.39 ± 0.07
Protocol IV control condition α-chloralose (D)	37 ± 8	7.37 ± 0.05	88 ± 7	0.38 ± 0.08
Protocol V “activation” forepaw stimulation (E)	38 ± 5#	7.36 ± 0.05**	91 ± 9††	0.42 ± 0.11

Each column represents the mean ± SD value of a physiologic parameter over the entire period of each protocol for all rats (see Materials and Methods). In each protocol Po₂ > 100 mm Hg. Student's paired t-test analyses were applied assuming two samples of unequal variances and one tail. From condition A to B:

Insignificantly different from control condition (Group A) P > 0.54.

†

lnsignificantly different from control condition (Group A) P > 0.72.

‡

Moderately different from control condition (Group A) P < 0.11. From condition A to C.

Insignificantly different from control condition (Group A) P > 0.43.

‖

Insignificantly different from control condition (Group A) P > 0.67.

[Moderately different from control condition (Group A) P < 0.12. From condition D to E;

Insignificantly different from control condition (Group D) P > 0.51.

Insignificantly different from control condition (Group D) P > 0.55.

††

Insignificantly different from control condition (Group D) P > 0.32. The ¹³C fractional enrichment ratio of [C4]-glutamate/[C1]-glucose for each condition was insignificantly different from the others.

The anesthetics and dosage levels were chosen such that “autoregulation” of metabolism and perfusion were maintained over the full range of activity. Additional evidence that autoregulation was maintained in our protocol is that across the full range of activity achieved, the correlation coefficients between regional metabolic and perfusion rates for the anesthetized conditions are nearly identical to those of the awake rat, e.g., 0.84 ± 0.14 versus 0.92 from Des Rosiers et al. (1974) and 0.88 from Sokoloff (1981). These results support the concept that the primary control over cerebral perfusion in the mature brain is related to the regional metabolic demands of the mitochondria (i.e., autoregulation).

Changes in CBF and CMRO2 during global and focal perturbations

Figure 1 shows examples of metabolic and perfusion data obtained from rats during the control condition of morphine anesthesia (group A), pentobarbital administration (group B), and nicotine infusion (group C), another control condition of α-chloralose anesthesia (group D), and forepaw stimulation of α-chloralose anesthetized rats (group E). For global perturbations, Fig. 1 demonstrates that relative to the control condition of morphine anesthesia (group A), V_TCA and CBF are lowered with pentobarbital (group B, “deactivation”) and increased with nicotine (group C, “activation”). Similarly, for focal perturbations, Fig. 1 demonstrates that relative to the control condition of α-chloralose anesthesia (group D) V_TCA and CBF are increased with forepaw stimulation (group E, “activation”). A mean value of 67 ± 18% was determined for f based on thresholded activated CBF maps. Use of high-resolution V_TCA mapping (Hyder et al., 1999c) in conjunction with multiple tissue compartmental analysis of V_TCA (Hyder et al., 1997) would reduce the uncertainties associated with the current partial-volume correction approach.

FIG. 1.

Measurements of CBF and CMRO₂ in the same rat, by MRI and MRS methods, such that changes in cerebral activity induced by barbiturate and narcotic agents, as well as sensory stimulation, could be quantified in the sensorimotor cortex. The right and left columns show the CBF (mean of four slices) and V_TCA (which then is converted to CMRO₂) data, respectively. The color bar at the bottom right shows the scaling for the CBF data. The metabolic information is depicted as [C4]-glutamate time courses from POCE data (•) and the best-fits of the metabolic model (—) to the data, where the vertical axis is the [C4]-glutamate ¹³C fractional enrichment in the brain and the horizontal axis is the time after [1-¹³C]glucose infusion began. The dotted white box in each CBF map represents the localized region from where the metabolic data were obtained. The data are separated into five groups: group A is the control condition of morphine sulfate anesthesia, group B is the lower activity condition (“deactivation” from A) with addition of sodium pentobarbital, group C is the higher activity condition (“activation” from A) with infusion of nicotine hydrogen tartrate, group D is another control condition of α-chloralose anesthesia-nitrous oxide, and group E is the higher activity condition (“activation” from D) with forepaw stimulation. For the global perturbations, CBF is lowered to 0.28 ± 0.05 mL · g⁻¹ · min⁻¹ with pentobarbital (group B) and increased to 0.90 ± 0.10 mL · g⁻¹ · min⁻¹ with nicotine (group C) from the control condition value of 0.77 ± 0.08 mL · g⁻¹ · min⁻¹ (group A), and V_TCA is decreased with the barbiturate to 0.46 ± 0.06 μmol · g⁻¹ · min⁻¹ (group B) and increased with the narcotic to 1.27 ± 0.15 μmol · g⁻¹ · min⁻¹ (group C) from a control value of 0.96 ± 0.11 μmol · g⁻¹ · min⁻¹ (group A). For the focal perturbations, CBF is increased to 1.94 ± 0.24 mL · g⁻¹ · min⁻¹ with forepaw stimulation (group E) from the control condition value of 0.42 ± 0.07 mL · g⁻¹ · min⁻¹ (group D), and V_TCA is increased with the forepaw stimulation to 2.11 ± 0.31 μmol · g⁻¹ · min⁻¹ (group E) from a control value of 0.51 ± 0.06 μmol · g⁻¹ · min⁻¹ (group D). See Fig. 2 for the CBF and CMRO₂ values obtained for each condition.

FIG. 2.

Absolute values of CMRO₂ and CBF for the five levels of activities measured in this study (○) in the rat cortex are compared with conscious data (△) and graded anesthesia data from the literature (•) for rat cortex. See Table 1 for details of the literature data points. Statistical significance were determined by Student's paired Mest assuming two samples of unequal variances with one tail. For the global perturbations, from the control condition of group A, CBF and CMRO₂ were reduced by 66% ± 16% (P < 0.003) and 61% ± 6% (P < 0.001), respectively, with sodium pentobarbital in group B; CBF and CMRO₂ were increased by 41% ± 5% (P < 0.002) and 30% ± 3% (P < 0.001), respectively, with nicotine hydrogen tartrate in group C. For the focal perturbations, from the control condition of group D, CBF and CMRO₂ were increased by 34% ± 10% (P < 0.006) and 26% ± 12% (P < 0.008), respectively, above the resting nonanesthetized values with forepaw stimulation in group E. For the rat sensorimotor cortex, the value of Ψ, which is equal to the slope of the curve or (ΔCMRO₂/CMRO₂)/(ΔCBF/CBF), determined from this study (0.84 ± 0.14) is in excellent agreement with the literature value (0.88 ± 0.06). These results suggest that CBF and CMRO₂ change linearly within the autoregulation range. The error bars represent mean ± SD in each case.

For the whole study, under the control condition of morphine—nitrous oxide, CBF was 0.75 ± 0.09 mL · g⁻¹ · min⁻¹. As shown in Fig. 2, CBF decreased to 0.26 ± 0.06 mL · g⁻¹ · min⁻¹ after pentobarbital treatment (Fig. 2, group B) and increased to 1.06 ± 0.12 mL · g⁻¹ · min⁻¹ in rats treated with nicotine (Fig. 2, group C) from the control condition (Fig. 2, group A). In these same animals, the cortical TCA cycle flux, V_TCA, changed in parallel with changes in CBF (Fig. 2). The V_TCA decreased to 0.41 ± 0.03 μmol · g^_1 · min⁻¹ after pentobarbital treatment and increased to 1.37 ± 0.07 μmol · g⁻¹ · min⁻¹ in rats treated with nicotine, compared with the morphine-nitrous oxide control group (1.05 ± 0.06 μmol · g⁻¹ · min⁻¹). Assuming that glucose is the main substrate for mitochondrial oxidation, the corresponding values of CMRO₂ for groups A to C were 3.15 ± 0.18 μmol · g⁻¹ · min⁻¹ (control), 1.23 ± 0.09 μmol · g⁻¹ · min⁻¹ (pentobarbital), and 4.11 ± 0.21 μmol · g⁻¹ · min⁻¹ (nicotine). Similarly, under the control condition of α-chloralose anesthesia-nitrous oxide, CBF and CMRO₂ were 0.40 ± 0.09 mL · g⁻¹ · min⁻¹ and 1.51 ± 0.06 μmol · g⁻¹ · min⁻¹, respectively, for all rats studied (Fig. 2, group D). Upon forepaw stimulation, CBF and CMRO₂ were focally increased by 34 ± 10% and 26 ± 12%, respectively, above the resting nonanesthetized values (Fig. 2, group E).

Comparison of current findings with previous results in the literature

The values of CMRO₂ and CBF for the five levels of cortical activity (open circles) are plotted in Fig. 2 along with a comparison of cortical CBF and CMRO₂ from studies of awake (solid triangle) and anesthetized rats (solid circles) from the published literature (Table 1). As shown in Fig. 2, the results of the current study (open circles) are in excellent agreement with the reported values (solid symbols). The CBF and CMRO₂ values for the data points in Fig. 2 are replotted in Fig. 3, where the awake condition (solid triangle) is the point of reference. The relationship was nearly linear over a wide range of cerebral activity. The slope of the line defined by the open circles in Fig. 3, given by Ψ = (ΔCMRO₂/CMRO₂)/(ΔCBF/CBF), was 0.84 ± 0.14 (R² = 0.98), which is in good agreement with the previously reported values of 0.88 ± 0.06 for the anesthetized (Hyder et al., 1998, 1999b).

FIG. 3.

The ΔCMRO₂/CMRO₂ and ΔCBF/CBF values for the data points in Fig. 2 have been replotted here, where the conscious condition (△) is the point of reference. This comparison demonstrates that relationship between ΔCBF/CBF and ΔCMRO₂/CMRO₂ over a wide range of cerebral activity is linear. The predictions of the model with Ω = 0.81 (−) and 0.81 ± 0.23 (&) are compared with experimental data (○, current study; •, literature data). The basal OEF for the conscious condition was assumed to be 0.3. This comparison shows that prediction with 1 > Ω > 0 for this model is in great agreement with experimental data over a wide range of cerebral activity.

Comparison of measured changes in CMRO2 and CBF with predictions of the model

For the case where 1 > Ω > 0, a value of Ω was determined using Eq. 4 for each “deactivation” and “activation” transition, with basal OEF values of 0.2, 0.3, and 0.4. No significant differences were found for Ω between the “deactivation” and “activation” transitions of cerebral function (Fig. 4A). The mean value of Ω over all three transitions examined was 0.81 ± 0.23. The ΔCMRO₂/CMRO₂ for each transition was predicted using Eq. 2 with Ω values of 0.0, 0.81 ± 0.23, and 1.00 (Fig. 4B), where 0 and 1 represent the limiting and nonlimiting cases of the model, respectively. A significantly better fit is obtained for Ω = 0.81 ± 0.23 than for Ω = 0, which clearly provides a poorer fit to the results. The predictions of ΔCMRO₂/CMRO₂ with Ω = 1 are not significantly different from the measured values, but in this nonlimiting case of oxygen transport the blood oxygenation level dependent (BOLD) functional MRI (fMRI) signal change (Ogawa et al., 1993) would be null (or even negative) because the predicted ΔCMRO₂/CMRO₂ would be equal to the measured ΔCBF/CBF (Appendix A; see Discussion).

FIG. 4.

(A) The value of Ω was determined using Eq. 4 for each “deactivation” and “activation” transition with basal OEF values of 0.2, 0.3, and 0.4. The different transitions are as follows: group A to group B (white solids, “deactivation”), group A to group C (light gray solids, “activation”), and group D to group E (dark gray solids, activation). No significant differences were found for Ω between the “deactivation” and “activation” transitions, where the error bars represent the SD about the mean. The mean value of Ω over all transitions was 0.81 ± 0.23. (B) The ΔCMRO₂/CMRO₂ for each transition was predicted using Eq. 2 with Ω values of 0.00, 0.81 ± 0.23, and 1.00. A significantly better fit is obtained for Ω = 0.81 ± 0.23 than for Ω = 0, which clearly provides a poorer fit to the results. The predictions of ΔCMRO₂/CMRO₂ with Ω = 1 are not significantly different from the measured values, but in this nonlimiting case of oxygen transport the BOLD fMRI signal change would be zero because the predicted changes in CMRO₂ would be equal to the measured changes in CBF (Appendix A).

The uncertainty in the calculated value of Ω can be determined with Eq. 5. For similar magnitudes of systematic error in both CBF and CMRO₂ measurements, the maximum misestimation in Ω would be less than ± 0.5% of the calculated value. If the CMRO₂ measurements were underestimated by 10%, then the respective Ω values also would be underestimated by 9% to 14%. However, a similar magnitude of underestimation in CBF measurements would correspond to an overestimation of Ω values by 13% to 15%. An assumed maximum systematic error of ± 10% in both CBF and CMRO₂ measurements would correspond to a maximum of ± 25% misestimation of Ω. Based on this analysis, it is concluded that even with some degree of misestimation of Ω caused by systematic error in measurements, the calculated value of Ω still would be significantly nonzero.

The prediction of ΔCMRO₂/CMRO₂ with Ω of 0.81 ± 0.23 were compared with the experimental (open circles) and literature (filled symbols) data (Fig. 3). The ΔCBF/CBF and ΔCMRO₂/CMRO₂ values for the data points in Fig. 3 are plotted with the awake resting condition as the point of reference (Table 1). This comparison demonstrates that relationship between CBF and CMRO₂ over a wide range of cerebral activity is linear and shows that prediction with 1 > Ω > 0 for this model is in great agreement with experimental data.

DISCUSSION

In this study, we used MRI and MRS methods to make paired measurements of CBF and CMRO₂ in the same rat sensorimotor cortex under conditions in which global cerebral activity was altered pharmacologically and focal activity was altered with sensory stimulation (Fig. 1). The values of CBF and CMRO₂ obtained at the different levels of activity agree well with data trends from the literature (Fig. 2). A close to linear relationship was observed between changes in oxidative metabolism and perfusion over a wide range of activity (Fig. 3). The derived values of Ω for “deactivation” and “activation” were found to be approximately equal, and an average value of 0.81 ± 0.23 was determined for Ω covering the entire range of activity (Fig. 4). The results support an important role of modulation of capillary bed diffusivity in regulating oxygen delivery.

Comparison with previous measurements of CBF and CMRO2

In this study, pentobarbital and nicotine were administered to decrease and increase, respectively, global cerebral activity from the control condition of morphine anesthesia. In the sensorimotor cortex, the changes in CBF and CMRO₂ with pentobarbital and nicotine were consistent with previous studies (Otsuka et al., 1991a, 1991b; Grunwald et al., 1987, 1991). The CBF value for the control condition achieved with moderate dose morphine anesthesia was approximately 40% lower than the awake state value for the sensorimotor cortex of the rat (Fig. 2). A similar degree of CBF depression was observed in the cat cortex when administered a comparable dose of morphine (Buchweitz et al., 1984). In the rat brain, Nilsson and Siesjo (1975) demonstrated well-correlated decreases of CBF and CMRO₂ with increasing doses of phenobarbital, whereas Michenfelder and Theye (1975) showed a similar trend for CMRO₂ and EEG activity with increasing doses of halothane. In the human brain, similar dose-dependent results for CBF and CMRO₂ have been obtained with thiopental (Pierce et al., 1962; Smith and Wollman, 1972). Likewise, in α-chloralose anesthetized rats, focal activity was altered with forepaw stimulation, which is in good agreement with previous observations (Ueki et al., 1988; Hyder et al., 1996, 1997; Silva et al., 1999). Notice that the absolute values of CBF and CMRO₂ on sensory activation with α-chloralose anesthetized rats rise above the resting nonanesthetized value (Figs. 2 and 3), and these types of changes are typical of certain anesthetics used for sensory activation studies (Shulman et al., 1999).

Role of diffusivity in regulating oxygen delivery

The primary goal of this study was to determine whether the theoretically defined terms of oxygen diffusivity in the capillary bed increases with increased cerebral activity. We have previously shown that the change in oxygen diffusivity with a change in perfusion referred to as Ω, as in Eq. 3, may be determined by plotting changes in CMRO₂ versus changes in CBF (Appendix A). If D is a constant and Ω = 0, then the efficiency of oxygen delivery decreases as CBF is increased because of the vessel Po₂ approaching the arterial value. Once this asymptote is reached, increases in CBF are no longer able to increase oxygen delivery. In contrast, in the case where Ω = 1 (i.e., ΔD/D and ΔCBF/CBF are equal), oxygen delivery increases linearly with perfusion with no change in average vessel Po₂. For the predictions of ΔCMRO₂/CMRO₂, shown in Fig. 4B, the best agreement to the measured values are obtained with 1 > Ω > 0, whereas the poorest fit was obtained with Ω = 0. Although the predicted values of ΔCMRO₂/CMRO₂ for Ω = 0.81 ± 0.23 (determined in this study) were not significantly different from those determined with Ω = 1, a value of unity is not consistent with the change in the BOLD fMRI signal because ΔCMRO₂/CMRO₂ and ΔCBF/CBF would be identical (Appendix A). However, the fact that BOLD signals are readily observed for both global (Kida et al., 1999a, 1999b) and focal (Hyder et al., 1994, 1996, 1997) perturbations suggest strongly that cerebral oxygen delivery occurs through alterations in vessel Po₂ (via CBF) as well as D (Appendix A).

The hypothetically defined term of effective diffusivity, D, which relates oxygen delivery to perfusion, is derived under the assumption that in every segment of each capillary oxygen delivery is proportional to local vessel Po₂ (Appendices A and B). Therefore, at steady-state, CMRO₂ is equivalent to the rate of oxygen delivery. The evidence that oxygen delivery is proportional to local vessel Po₂ is based on studies showing that tissue Po₂ always is found to be lower than the vascular Po₂ (Crockard et al., 1976; Metzger and Huber, 1977; Fennema et al., 1989; Vovenko, 1999) and little oxygen diffuses back into the vasculature (Grieb et al., 1985; Sawada et al., 1989; Kassissia et al., 1995). An alternative possibility to explain the data is that there is no change in diffusivity, but that the vessel-to-tissue Po₂ gradient is small because of a high tissue Po₂. A low vessel-to-tissue Po₂ gradient enhances the effectiveness by which CBF may increase oxygen delivery through small changes in vessel Po₂. The current results cannot distinguish this interpretation from a changing oxygen diffusivity. However, measurements of tissue Po₂ suggest that under the conditions studied, it remains significantly lower than vessel Po₂ values (Crockard et al., 1976; Metzger and Huber, 1977; Fennema et al., 1989; Vovenko, 1999), which supports a hypothesized situation in which diffusivity must change to explain the observed relationship between CBF and CMRO₂.

The value of D is theoretically defined to be dependent on characteristics of capillaries within the tissue, such as their number, geometry, blood volume, and circulation time distribution. Each of these parameters has been proposed to be of importance in regulating oxygen delivery (Mochizuki, 1966; Lawson and Foster, 1967; Moss et al., 1976; Homer et al., 1981), and maintaining cerebral energy homeostasis (Betz, 1977; Elkof and Siesjo, 1971).

Although the use of the term capillary bed readjustment in the literature generally reflects changes in blood volume (Kuschinsky and Paulson, 1992), there are several mechanisms by which the capillary bed may increase its oxygen diffusivity, thereby increasing the efficiency of oxygen delivery. Among these mechanisms are the dilating of capillaries (Cox et al., 1993; Narayan et al., 1995), decreases in the number of plasmatic capillaries (Francois-Dainville et al., 1986; Tajima et al., 1992), and intracapillary stacking of erythrocytes (Mochizuki, 1966; Lawson and Foster, 1967; Moss et al., 1976). The relative importance of these mechanisms in causing the assumed changes in the capillary bed diffusivity remains to be determined (Niimi and Yamakawa, 1985; Tsai and Intaglietta, 1989; Duling, 1994; Kleinfeld et al., 1998).

In the current modeling scheme, no attempt is made to define which particular physiologic events or episodes regulate CBF. Blood flow in brain circulation serves many functions (e.g., CO₂ and heat clearance) in addition to substrate delivery, and several models in the field (Ursino et al., 1989a, 1989b; Ye et al., 1994) deal with some of these other functions of perfusion and the effects of these factors on tissue oxygen levels. However, notice that good fits to the results may be obtained through theoretical consideration of oxygen delivery alone.

Cerebral metabolism and perfusion above the resting awake condition

The discussion has dealt with the regulation of cerebral metabolism and perfusion below the awake condition as observed with graded anesthesia (Figs. 2 and 3). In this range, both the current results and previous published results support a near linear relationship between CBF and CMRO₂. Should the regulation of cerebral metabolism and perfusion above the awake condition be the same as observed with graded anesthesia? In the current study, on sensory activation of α-chloralose anesthetized rats (Fig. 1), the absolute values of CBF and CMRO₂ rose above the resting nonanesthetized values (Fig. 2), the derived value of Ω for sensory activation was indistinguishable from the other “deactivation” and “activation” paradigms studied (Fig. 4), and a single value of Ω produced excellent predictions of ΔCMRO₂/CMRO₂ for the entire activity range, which spanned from deeply anesthetized conditions to the functionally activated state (Fig. 3). This suggests that cerebral metabolism and perfusion above and below the awake condition may be regulated in the same manner.

Position emission tomography studies of functional activation in the activated human brain show that in some cases the changes in CMRO₂ and CBF are close to proportional (Katayama et al., 1986; Roland et al., 1987; Seitz and Roland, 1992; Blomqvist et al., 1994; Hatazawa et al., 1995; Marrett and Gjedde, 1997; Vafaee et al., 1998), whereas in others, there is a much larger increase in CBF than CMRO₂ (Fox and Raichle, 1986; Fox et al., 1988). The studies which have found a relatively greater increase in CBF have been interpreted as being consistent with there being no increase in oxygen diffusivity with increases in perfusion in the activated brain (Buxton and Frank, 1997; Gjedde, 1997).

A possible explanation for the inconsistency in the activation results is that certain stimuli may only activate a fraction of the tissue within an image voxel, and the effect of this partial-volume on CMRO₂ and CBF may be considerably different (Lebrun-Grandie et al., 1983). Support of this idea comes from studies of effects of graded anesthesia on human brain (for recent reviews see Hyder et al., 1998, 1999b), where a linear relationship has been observed for changes in CMRO₂ and CBF (Pierce et al., 1962; Smith and Wollman, 1972). Under these conditions, heterogeneity in the responses of different regions (similar to effects of partial-volume) are reduced because of the global nature of the perturbation. Alternatively, it has been reported that variations in stimuli frequency and context may affect the magnitude of changes in CBF and CMRO₂ differentially (Katayama et al., 1986; Sadato et al., 1997; Vafaee et al., 1998; Zhu et al., 1998). To definitively assess these possibilities, it is necessary to obtain measurements of CBF and CMRO₂ at a sufficiently high spatial resolution to encompass uniformly activated regions of the cortex. However, it would be surprising if there is no increase in oxygen diffusivity in the activated state given the considerable evidence, both from the current and previous studies, for its critical role in modulating oxygen delivery at and below the awake condition (Hyder et al., 1998, 1999b).

Implications for BOLD fMRI

The principle of Fick prescribes that the functional increases in CMRO₂ and CBF observed during functional activation should reflect a decrease in OEF from its basal value, which is commensurate with an increased venous blood oxygenation in cerebral capillaries, as in the BOLD fMRI method (Ogawa et al., 1993). The BOLD fMRI method allows the detection of changes in cerebral blood oxygenation during functional challenges with gradient-echo MRI. The gradient-echo image contrast relies on physiologically induced changes in the magnetic properties of blood (oxyhemoglobin is diamagnetic and deoxyhemoglobin is paramagnetic), where an increase in the fractional BOLD fMRI signal change (ΔS/S > 0) is consistent with a drop in venous deoxyhemoglobin concentration. Results from near infrared spectrophotometry (Hoshi and Tamura, 1993) and intrinsic optical reflectance studies (Narayan et al., 1995), which have shown that deoxyhemoglobin concentration decreases after stimulation onset in the adult mammalian brain, provide qualitative support for the BOLD fMRI hypothesis. A common expression for BOLD fMRI signal change, ΔS/S, is A (ΔCBF/CBF – ΔCMRO₂/CMRO₂), where A is a magnetic field-dependent physiologic constant. This expression reveals that the relative difference between ΔCBF/CBF and ΔCMRO₂/CMRO₂ creates the small positive values of ΔS/S observed in vivo. Therefore, it is not necessary for ΔCMRO₂/CMRO₂ to be close to zero for the BOLD fMRI image contrast mechanism to be observed (Ogawa et al., 1993; Buxton and Frank, 1997; Gjedde, 1997). Recent BOLD fMRI experiments in the human visual cortex (Sadato et al., 1997; Zhu et al., 1998) and in the rat sensorimotor cortex (Kida et al., 1999a; Silva et al., 1999) show that ΔS/S and ΔCBF/CBF are linearly related. These observations, in conjunction with the equation earlier, indicate that the relationship between ΔCBF/CBF and ΔCMRO₂/CMRO₂ also would be linear with functional activation. We have shown experimentally (Fig. 3) that this is the case. Proper calibration of the BOLD fMRI signal (Kida et al., 1999a, 1999b), however, requires measurements of changes in CMRO₂ and CBF over a wider range of activity and conditions. This relationship is further strengthened by the strong correlation between evoked electrical activity and BOLD response during functional activation (Yang et al., 1997).

CONCLUSIONS

The results of this study indicate that CBF and CMRO₂ change near proportionately in the rat somatosensory cortex over a wide range of cortical activity. The results were fit to a model relating the efficiency of oxygen delivery in the capillary bed. It was found that the model, various limits of which have been proposed by several investigators, is best fit to the results when the diffusivity term changes linearly with perfusion. The relationship between CBF and D, expressed as a constant Ω, was determined in vivo to be 0.81 ± 0.23. These results support an important role for the ability of the capillary bed to modulate the efficiency of oxygen transport for the regulation of oxygen delivery in vivo.

APPENDIX A

The models proposed by Buxton and Frank (1997), Gjedde (1997), Hyder et al. (1998), and Hudetz (1999) are based on the premise that for a given microscopic capillary segment, the rate of oxygen delivery is proportional to the vessel-to-tissue Po₂ gradient. Most of the oxygen molecules that cross the blood-brain barrier radially diffuse into the tissue and are consumed. The maximum vessel Po₂ is equal to the Po₂ of arterial blood, and the oxygen diffusion constant is hypothesized to be unvarying over a wide range of activity. The difference between these models arises in the treatment of the effective diffusivity parameter, D, the value of which is theoretically dependent on vascular geometry, distribution of circulation times, and the distribution of erythrocytes. The choice in each model of the appropriate value of Ω, which can be viewed theoretically as a parameter that reflects the efficiency of oxygen delivery, is hypothesized by altered changes in vessel Po₂ (via CBF) and the value of D.

In the models proposed by Buxton and Frank (1997) and Gjedde (1997), D is constant (i.e., Ω = 0) such that oxygen delivery may increase only through an increase in the arterial Po₂. Because the maximum vessel-to-gradient Po₂ gradient is limited to the Po₂ of arterial blood, the ability to increase CMRO₂ by increasing CBF is reduced at high perfusion rates, where the average vessel Po₂ approaches the arterial value. A highly nonlinear relationship between CMRO₂ and CBF is predicted by these models, and these predictions are heavily dependent on basal OEF values. For the case where ΔD/D and ΔCBF/CBF are equal (i.e., Ω = 1), as in the model proposed by Hudetz (1999), oxygen delivery increases linearly with perfusion with no change in average vessel Po₂. However, in this model, a highly linear relationship between CMRO₂ and CBF is predicted, where the changes in metabolism and perfusion are exactly proportional, with no dependence on basal OEF values. In contrast, in the model proposed by Hyder et al. (1998), D is altered with CBF (i.e., 1 > Ω > 0) such that oxygen delivery may be increased both through an increase in arterial Po₂ and D. The prediction of this model is a linear relationship between CMRO₂ and CBF with minimal dependence on basal OEF values.

A qualitative but substantial validation of these models is the ability to predict the BOLD fMRI image contrast, which relies on physiologically induced alterations in the magnetic properties of blood. The fractional changes in CMRO₂ and CBF observed during functional activation reflect a decrease in OEF from its basal value (i.e, ΔOEF/OEF < 0), which is equal to an increased venous blood oxygenation. An increase in BOLD fMRI signal change (ΔS/S) is consistent with a decrease in venous deoxyhemoglobin concentration, and ΔS/S > 0 can be predicted only with 1 > Ω > 0.

APPENDIX B

The oxyhemoglobin dissociation curve describes the oxygen carrying propensity of blood,

Y = C_{H b (O 2) n} / (C_{H b (O 2) n} + C_{H b})

(B1)

where Y is the blood oxygenation, and C_Hb(O2)n and C_Hb are the contents of oxyhemoglobin and deoxyhemoglobin, respectively. Based on mass transfer relations, the amount of oxyhemoglobin, C_Hb(O2)n > is equal to the sum of deoxyhemoglobin, C_Hb, and oxygen, C_O2. Extraction of oxygen into the tissue from an infinitesimally thin blood bolus occurs all through transit. The temporal profile of the total oxygen content of blood (C_T) can be described in relation to the oxygen content in the plasma (C_P) by

d C_{T} / d τ = - k C_{P}

(B2)

where the C_T is equivalent to C_Hb(O2)n > C_P is equivalent to C_O2, and the constant k is determined by the spatial gradients of oxygen tension radially around the bolus, and is the first-order rate constant of oxygen loss from the capillary. The main assumptions in Eq. B2 have been described (Hyder et al., 1998, 1999b). If it is assumed that through an elapsed time of Δτ the ratio of transient oxygen content values in plasma and blood is constant, i.e., r = C_P/C_T, then

C_{T} (τ + Δ τ) = C_{P} (τ) \exp (- k r Δ τ)

(B3)

which is equivalent to

C_{T} (T_{c}) = C_{P} (0) \exp (- [k r]_{n e t} T_{c})

(B4)

where Δτ is the rath equivalent fraction of the circulation time (T_c) and [kr]_net is the net kr product. Since r is determined by the relationship between hemoglobin fractional oxygenation and the average capillary oxygen tension, from Eq. B1 it can be shown that

r = (1 / n) (2 - 1 / Y)

(B5)

where r varies with t because of cooperativity of oxygen binding. The hypothetical resistance of oxygen transport is distributed over a range of physiologic episodes, which occur in various locations or phases of oxygen transport, which together are termed as the effective diffusivity for oxygen (Eq. B9), rather than one particular site or period. Oxygen extraction around the capillary may be calculated from (Renkin, 1959; Crone, 1963)

{O E F}_{c} = (C_{T} (0) - C_{T} (T_{c})) / C_{T} (0)

(B6)

where C_T(0) > C_T(T_C), and given Eq. B4, OEF_c also is equivalent to

{O E F}_{c} = 1 - \exp (- [k r]_{n e t} T_{c})

(B7)

The total oxygen extraction per capillary can be depicted by the summation of the effect of an infinitesimally thin blood bolus flowing down a capillary during transit as it deposits oxygen, and as a consequence of which the flowing blood goes through changing spatial gradients of oxygen tension between the traversing volume element and the albuminal side of the capillary endothelium. The changing values of C_T and C_P in the traversing bolus reflect the cooperative binding of oxygen by hemoglobin in whole blood within the capillary (Eq. B5). Since perfusion is assumed to be constant all through transit, T_c is related to flowing bulk (CBV_c) and rate (CBF_c) in the circulating blood by stationarity and linearity principles (Stewart, 1894; Meier and Zierler, 1954), then Eq. B7 leads to

{O E F}_{c} = 1 - \exp (- D_{c} / {C B F}_{c})

(B8)

where D_c is theoretically defined as the effective diffusivity for oxygen from the capillary to the mitochondria, which is the point of efficient consumption,

D_{c} = [k r]_{n e t} {C B V}_{c}

(B9)

The macroscopic picture is derived through averaging across an ensemble of capillaries.

APPENDIX C

Division of both sides of Eq. 2 with ΔCBF/CBF results in

Ψ = (1 + σ) [1 - \exp {- (D / C B F) (β / α)}] / O E F - σ

(C1)

where Ψ = (ΔCMRO₂/CMRO₂)/(ΔCBF/CBF) and σ = (ΔCBF/CBF)⁻¹. The Ω term can be expressed by rearrangement of Eq. C1 as follows:

Ω = (1 + σ) (ϑ / ς) - σ

(C2)

where $ϑ = \ln [1 - O E F (γ / α)], ς = \ln [1 - O E F]$ , and $γ = (1 + (Δ C B F / C B F) Ψ)$ . Assuming that the uncertainty in Ω (i.e., δΩ/Ω) depends on systematic errors in measured parameters, then Eq. C2 can be expressed as

\begin{aligned} δ Ω / Ω = & [(δ σ + σ) {(δ ϑ + ϑ) / ς - 1} + (δ ϑ + ϑ) / ς] / \\ [(1 + σ) (ϑ / ς) - σ] - 1 \end{aligned}

(C3)

where δσ and δϑ represent errors associated with each parameter.

Footnotes

Acknowledgments

The authors thank Drs. R.G. Shulman, E.J. Novotny, and N.R. Sibson for helpful discussions. The authors also thank engineers T. Nixon, P. Brown, and S. McIntyre for maintenance of the spectrometer and the RF probe design, and X. Ma, Y. Ping, and B. Wang for technical support.

Abbreviations used

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