NMR IN BIOMEDICINE NMR Biomed. 2001;14:413–431 DOI:10.1002/nbm.733

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

Fahmeed Hyder,1,2,5* Ikuhiro Kida,1 Kevin L. Behar,3 Richard P. Kennan,6 Paul K. Maciejewski4 and Douglas L. Rothman1,2,5 1Departments of Diagnostic Radiology, Magnetic Resonance Center for Research in Metabolism and Physiology, Yale University, New Haven, CT, USA 2Department of Biomedical Engineering, Yale University, New Haven, CT, USA 3Department of Psychiatry, Yale University, New Haven, CT, USA 4Department of Internal Medicine, Magnetic Resonance Center for Research in Metabolism and Physiology, Yale University, New Haven, CT, USA 5Section of Bioimaging Sciences, Yale University School of Medicine, New Haven, CT, USA 6Department of Diagnostic Radiology, Albert Einstein College of Medicine, Bronx, NY, USA

Received 22 February 2001; Revised 22 August 2001; Accepted 22 August 2001

ABSTRACT: Quantitative magnetic resonance imaging (MRI) and spectroscopy (MRS) measurements of energy metabolism (i.e. cerebral metabolic rate of oxygen consumption, CMRO2), 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 CMRO2, 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 CMRO2, CBF, CBV, BOLD fMRI signal allow calibration and validation of the BOLD image-contrast. Good agreement between changes in CMRO2 calculated from BOLD theory and measured by 13C 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 CMRO2 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. Copyright  2001 John Wiley & Sons, Ltd. KEYWORDS: oxygen; glucose; lactate; glutamate; glutamine; glycogen; neuron; astrocyte; cerebral activity; lamotrigine

*Correspondence to: F. Hyder, 126 MRC, 330 Cedar Street, Yale INTRODUCTION University, New Haven, CT 06510, USA. Email: [email protected] Functional imaging of mammalian brain with magnetic Abbreviations used: BOLD, blood-oxygenation level dependent; CBF, resonance imaging (MRI) has become a popular modality cerebral blood flow; CBV, cerebral blood volume; CMRglc, cerebral 1 metabolic rate for glucose consumption; CMRglc(ox), cerebral metabolic in neuroscience, but the exact relationship between the rate for glucose oxidation; CMRO2, cerebral metabolic rate for oxygen measured blood-oxygenation level dependent (BOLD) consumption; D, effective mass transfer coefficient for oxygen in the capillary bed; DANTE, delays alternating with nutations for tailored signal and the underlying neurophysiological parameters excitation; EPI, echo planar imaging; FLASH, fast low-angle shot; fMRI, remains unclear. The BOLD functional MRI (fMRI) functional MRI; ICED PEPSI, in vivo carbon edited detection with proton method allows detection of changes in blood oxygenation echo planar spectroscopic imaging; MRI, magnetic resonance imaging; during a physiological stimulation with gradient-echo MRS, magnetic resonance spectroscopy; OEF, oxygen extraction 2 fraction; PET, positron emission tomography; POCE, 1H observed 13C and spin-echo MRI. The BOLD image-contrast relies on editing; R1, longitudinal relaxation rate of tissue water; R2*, apparent physiologically induced changes in the magnetic proper- tissue water relaxation rate; R2, absolute tissue water relaxation rate; TE, ties of blood (oxyhemoglobin is diamagnetic and echo time; TIR, inversion recovery time; TR, recycle time; VTCA, tricarboxylic acid cycle flux; Y, blood oxygenation. deoxyhemoglobin is paramagnetic), where an increase

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 414 F. HYDER ET AL. in the fractional BOLD fMRI signal-change (DS/S > 0) is In this paper, we explore the neurophysiological basis consistent with a drop in venous deoxyhemoglobin of BOLD fMRI at 7 T in rat brain for the purpose of concentration.1–5 At steady-state, DS/S is given by neuronal activity mapping at steady-state. We present changes in neurophysiological parameters based on multi-modal measurements of changes in CMRO2, CBF, Fick’s principle3–5 CBV, and BOLD signal in rat cerebral cortex at 7 T over a wide range of neuronal activity and pharmacological  ÁS=S ˆ A‰ ÁCBF/CBF À ÁCMRO2=CMRO2† treatments. This approach differs from others in the 1† 10–12 = 1 ‡ ÁCBF/CBF†ÀÁCBV/CBVŠ field because each parameter in eqn (1) that influences the image-contrast is measured independently where A´ is a measurable physiological and static in rat cerebral cortex. Furthermore this approach allows magnetic field dependent constant and DCMRO2/CMRO2, validation of BOLD image-contrast, because the pre- DCBF/CBF and DCBV/CBV are the changes in cerebral dicted changes in CMRO2 based on BOLD theory metabolic rate of oxygen consumption, cerebral blood [rearrangement of eqn (1)] can be compared with the flow and cerebral blood volume, respectively (see independently measured changes in CMRO2 based on in Appendix A). Of these physiological parameters, vivo 13C MRS.6 The method of indirect 13C MRS 1 13 DCMRO2/CMRO2 is the most relevant for studying detection (i.e. using H instead of C) for CMRglc(ox) and 6,7 functional brain activity, because it is proportional to CMRO2 measurements is discussed. Insights into energy the change in energy consumption associated with metabolism and oxygen delivery of glutamatergic changes in neuronal activity induced by the stimulation. neurons are gained from comparisons of CMRO2 and Methods which provide direct measurement of the rate CBF over a wide range of activity. of cortical energy utilization or production are considered as ‘gold-standards’ for detection of neuronal activity. In the autoradiography method8 a 14C labeled analog of MATERIAL AND METHODS glucose, 2-deoxyglucose, is infused into the blood stream in trace amounts. The radioactive analog crosses the Animal preparation blood–brain barrier and is phosphorylated much like glucose. Since the 14C labeled phosphate cannot be Adult, male, Sprague–Dawley rats (110–280 g; fasted metabolized further, its concentration is proportional to >16 h) were tracheotomized under halothane (0.7–1.2%) the cerebral metabolic rate of glucose consumption anesthesia and artificially ventilated (70% N2O/30% O2). (CMRglc). The positron emission tomography (PET) A femoral artery was cannulated for continuous mean fluoro-deoxyglucose method uses similar principles to arterial blood pressure monitoring and periodic sampling deoxyglucose autoradiography but measures the distribu- for measurement of blood gases, pH, pressure, and tion of fluoro-deoxyglucose-6-phosphate. In vivo 13C glucose. Femoral veins were cannulated for intravenous magnetic resonance spectroscopy (MRS) detection of (i.v.) infusions of nicotine hydrogen tartrate, iron oxide infused 13C labeled glucose, a stable isotope, can provide contrast agent (AMI-227; Advanced Magnetics Inc., 6,7 13 13 important information on brain energy metabolism. Cambridge, MA), and/or D-[1- C] or [1,6- C]glucose The flow of 13C label from glucose to glutamate can be (99 atom %; Cambridge Isotopes, Andover, MA). used to calculate the tri-carboxylic acid cycle flux Intraperitoneal (i.p.) lines were inserted for administra- (VTCA), cerebral metabolic rates of glucose oxidation tion of anesthetic, paralyzing, and/or pharmacological (CMRglc(ox)) which is proportional to CMRO2. Under agents. The scalp was retracted and a layer of Saran Wrap normal physiological conditions, glucose is the major was placed over the skull. The rat was placed prone in a energy substrate in the mammalian cortex and it is cradle and covered with a water blanket to maintain body metabolized9 either in the presence of oxygen (via temperature (37 °C). Halothane was discontinued after glucose oxidation generating 32–34 ATP/glucose, CO2, the positioning and anesthesia was maintained through- and H2O) or absence of oxygen (via glycolysis and/or out with either morphine sulfate or a-chloralose and glycogen shunt generating 1–2 ATP/glucose and lactate). paralyzed with D-tubocurarine chloride (initial 0.5 mg/ BOLD fMRI has become the method of choice for human kg; supplemental 0.25 mg/kg/30 min; i.p.). The head brain mapping, because of its high spatial and (relative to was secured with a bite-bar and tightly fixed by foam PET) temporal resolution, as well as its being non- cushions on either side of the head. The center of the hazardous and non-invasive. As shown in eqn (1), in radio-frequency surface-coil was placed above the principle the BOLD fMRI signal, in combination with bregma. measurements of CBF and CBV, can be used to map regional changes in CMRO2 (or CMRglc(ox)). Such quantitative BOLD fMRI approaches which allow maps General MRI and MRS experimental setups of regional energy metabolism with the spatial resolution of MRI, would pay great dividends towards mapping of All in vivo MRI and MRS data were obtained on a neuronal activity in the intact human brain. modified 7 T Bruker Biospec or AVANCE horizontal-

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T 415 bore spectrometer (Bruker Instruments, Billerica, MA) Protocols and methods for BOLD calibration operating at 300.6 and 75.5 MHz for 1H and 13C, studies respectively. Indirect 13C MRS [i.e. 1H observed 13C editing (POCE) experiments] and all MRI data were Multi-modal measurements were divided into five acquired with an 1H resonator radio-frequency transmit treatment groups, but prior to the start of each MRI and (8 cm diameter) for homogeneous transmission and a 1H MRS protocol, a delays alternating with nutations for radio-frequency surface-coil receiver (10 mm diameter) tailored excitation (DANTE) method was used (see for local reception. This radio-frequency coil arrange- below) for estimation of static magnetic field distortion in ment13 allows better shimming, minimizes sensitivity the region of interest.23,24 Values of BOLD fMRI signal loss in the receiver coil, and results in high signal-to- (both gradient-echo and spin-echo), CBF and CBV were noise ratio for 1H. A concentric 13C radio-frequency obtained (by averaging) from the same region of interest surface-coil (20 mm diameter) was used for transmission (48 or 8 ml) as the CMRO2 measurements were made 23,24 and decoupling in the POCE experiments (for CMRO2 from. measurements; see below). High signal-to-noise ratio 1H The rats in group a (‘control I’) were anesthetized with spectra with 13C composite pulse decoupling14 were morphine sulfate (initial 50 mg/kg; supplemental 30 mg/ acquired every 5 min. Direct 13C MRS data were kg/30 min; i.p.), where the rats in groups b and g received acquired with a dual surface radio-frequency coil system in addition sodium pentobarbital (initial 45 mg/kg initial; consisting of a circular 13C coil (10 mm diameter) for supplemental 10 mg/kg/30 min; i.p.) and nicotine hydro- transmission and a butterfly 1H coil for decoupling gen tartrate (dose of 4 mg/kg; rate of 16.7 ml/min; i.v.), where the 13C radio-frequency excitation pulse was respectively.13,23,24 The rats in group  (‘control II’) were optimized for cortical signal detection.15 High signal-to- anesthetized with a-chloralose (initial 80 mg/kg; supple- noise ratio 13C spectra with nuclear Overhauser enhance- mental 20 mg/kg/30 min; i.p.), where the rats in group e ment and 1H broadband decoupling14 were acquired received electrical stimulation (2–3 V square pulses of every 10 min. 0.3 ms duration at 3 Hz; Harvard Apparatus Limited, High-resolution, multi-slice, fast low-angle shot Kent, MA) of the forepaw13,25 using a pair of thin copper (FLASH) coronally oriented anatomical images electrodes. [weighted by longitudinal (R1) relaxation rate of tissue For each rat in group a, BOLD fMRI signal (both water] were acquired [image matrix = 128 Â 128; in- gradient-echo and spin-echo), CMRO2, CMRglc(ox) and plane resolution = 156 Â 156 mm2; slice thickness = CBF were measured together under basal conditions of 500 mm; repetition time (TR) = 250 ms; echo time (TE)= morphine/nitrous oxide anesthesia. For each rat in group 20 ms; inversion recovery time (TIR) = 300 ms]. These b, the BOLD fMRI signal (both gradient-echo and spin- images provided coordinates for the placement of a echo) and CBF were measured before pentobarbital 7.5 Â 1.6 Â 4.0 mm3 region of interest for the POCE administration under basal conditions, then BOLD fMRI 16,17 experiments. The static magnetic field homogeneity signal (both gradient-echo and spin-echo), CMRO2, 3 of a 8 Â 2 Â 5mm volume in the sensorimotor cortex CMRglc(ox) and CBF were measured together after was optimized. Details of the localized POCE pulse pentobarbital administration. For each rat in group g, sequence have been described earlier.16–18 Chemical shift the BOLD fMRI signal (both gradient-echo and spin- imaging 13C turnover data were obtained using in vivo echo) and CBF were measured before nicotine adminis- carbon edited detection with proton echo planar spectro- tration under basal conditions, then BOLD fMRI signal scopic imaging (ICED PEPSI), which combines echo- (both gradient-echo and spin-echo), CMRO2, CMRglc(ox) planar imaging (EPI) with 13C-1H J-editing and semi- and CBF were measured together after nicotine admin- selective water suppression of POCE.19,20 Multi-modal istration. In two cases, each group received an anesthetic MRI data were acquired with EPI using sequential dose of a-chloralose (initial 80 mg/kg; supplemental sampling.21 The distortions in EPI associated with spin- 20 mg/kg/30 min; i.p.) balanced with nitrous oxide either echo were minimal22 because the total acquisition time alone (group ) or in combination with forepaw of all echoes was 20.48 ms. All multi-parametric MRI stimulation (group e) to increase focal activity in the measurements were made with coronally oriented multi- sensorimotor region.16 For each rat in Groups  and e, slice EPI acquisitions with 1 mm slice separation (image BOLD fMRI signal (both gradient-echo and spin-echo), matrix = 32 Â 32 or 32 Â 64; in-plane resolution = CMRO2, CMRglc(ox) and CBF were measured at rest 320 Â 320 or 430 Â 430 mm2; slice thickness = (‘control II’) and during stimulation of both forepaws. 1000 mm; TR  5000 ms). A sinc pulse was used for For relative CBV measurements separate groups of rats slice excitation and an adiabatic fast passage hyperbolic were divided into the same five treatment groups secant pulse was used for slice refocusing as well as described above (i.e. groups a–e) and BOLD fMRI signal inversions. All data were acquired under steady-state (both gradient-echo and spin-echo) were mapped with conditions. AMI-227 for each condition. Single-exponential fits of the multi TE (ranging from 10 to 80 ms) gradient-echo and spin-echo MRI data were

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 416 F. HYDER ET AL. used to obtain transverse relaxation rates of tissue water, R2*(obs) and R2(obs), respectively. We used the follow- ing relaxation rate term to describe the BOLD fMRI signal (see Appendix A) 0 à à R2 Y†ˆR2 obs†ÀR2 obs†ÀR2 ÁBo† 2† where R2*(DBo) is the relaxation component of tissue water relaxation rate attributed to macroscopic distor- tions of static magnetic field (DBo), and R2'(Y) is the reversible relaxation component tissue water relaxation rate due to blood oxygenation effects. The R2*(DBo) component within the region of interest was estimated by an MRI sequence26 with a double spin tagging sequence using DANTE pulses as described previously.23,24 The BOLD fMRI signal-change at steady-state in eqn (1) is Figure 1. Schematic representation of the metabolic model also given by at isotopic mass balance.16,17,31,32 The [1-13C] or [1,6- 13C]glucose in plasma 2G ) and brain 2G ) exchange via 0 o i ÁS=S ˆ exp ÀÁR2 Y†ÂTE†À1 3† Michaelis±Menten kinetic parameters Km 2half-saturation concentration for transport) and Vmax 2maximum transport where TE is 25 ms and DR2'(Y) is the change in the rate), where Km ranges from 10 to 15 mM and Vmax/CMRglc relaxation rate term described by eqn (2). The advantage ranges from 5 to 25. Under most conditions the calculated VTCA is insensitive to the reported range of these par- of this definition for the BOLD signal is that the common 16 13 ameters. The C label ¯ows at the rate 2  CMRglc and unknown terms between R2*(obs) and R2(obs) are through the glycolytic intermediates 2negligible concentra- 24 subtracted away leaving only the pure oxygenation tions) and arrives at C3-pyruvate and C3-lactate, represented term which can be described as1–5 by L 21.5 mmol/g). Two sources of 12C entrance into the tri- carboxylic acid cycle are exchange of blood±brain pyruvate 0 R2 Y†ˆCmax 1 À Y†b Hct 4† and lactate pool 2Vex) and the ketone body ¯ux 2Vket), both of which dilute the 13C fractional enrichment of intermediates where C is a BOLD proportionality constant, max is the in the tri-carboxylic acid cycle. The ef¯ux at L, Vout, causes magnetic field-dependent deoxyhemoglobin susceptibil- some 13C label to be lost to blood. The 13C label enters the acetyl CoA pool at a rate of 2  CMR prior to its entry ity frequency shift, b is the blood volume fraction, glc2ox) into the tri-carboxylic acid cycle. The 13C label enters the tri- (1 À Y) is the blood deoxygenation, and Hct is the blood carboxylic acid cycle and labels C4-a-ketoglutarate, aKG4, hematocrit (see Appendix A for other details). and C4-glutamate 212.0 mmol/g), Glu4. These two pools are 31,32 The relative changes in CBV from the baseline to in very rapid isotopic exchange, Vx, where Vx/VTCA  1. lower or higher conditions were measured by adminis- There is an exchange between C4-glutamate and C4- glutamine 26.2 mmol/g), Gln4, at a rate of Vgln 2where Vgln/ tration of a high susceptibility MRI contrast agent to 16 VTCA ranges from 0.25 to 1. ). VTCA is approximately equal enhance blood volume induced changes in R2(obs) or to 1/3CMRO2 2see Appendix B for other details). In the ®rst 13 R2*(obs). The blood volume susceptibility was raised pass of the tri-carboxylic acid cycle the C label arrives at C4- through serial injections (2 mg/kg/0.9 ml bolus) of an glutamate 2i.e. Glu4), which re¯ects pyruvate dehydrogenase activity 2in the neuron), whereas in the second and iron oxide contrast agent AMI-227 which remains in the 13 intravascular space for several hours.27 The relative subsequent passes of the cycle the C label arrives at C2- and C3-glutamate. However, some pyruvate carboxylase changes in CBV were calculated by DCBV/CBV w w/o w w/o w w/o activity 2in the astrocyte) could lead to labeling of C3- =(DR À DR )/(R À R ), where R and R are oxaloacetate which would subsequently lead to labeling of the rates at the reference conditions with and without C3-glutamate also. Since each metabolic modeling was agents, respectively, and DRw and DRw/o are the rate carried out with the 13C isotopic turnover rate of C4- differences as a consequence of transition from baseline glutamate, which represents labeling from C1,6 or C1- glucose in the ®rst turn of the tri-carboxylic acid cycle and to lower or higher conditions with and without agents, pyruvate dehydrogenase activity in the neuron, the pyruvate respectively. Details of relative experimental errors have carboxylase activity in the astrocyte will not modify our 24,27,28 been described earlier. results of VTCA estimates The absolute CBF maps were obtained using the spin- echo slice selective and non-slice selective inversion- recovery weighted EPI data.13,29 A single-exponential water () was assumed to be 0.95 ml/g.29 Absolute recovery fit to the multi TIR data (ranging from 200 to perfusion was calculated by CBF = 60  (R1app À R1b), 2200 ms) was used to create R1 maps for the slice where R1app is the apparent relaxation rate given by selective (R1s) and non-slice selective (R1n) images. The [R1b ‡ (R1s À R1n)/(1 ‡ À)] and À is a small correction longitudinal relaxation rate of arterial blood water (R1b) factor, given by 3/4(1 À R1b/R1n), which accounts for the was determined (0.50 Æ 0.03 sÀ1) from high-resolution difference between longitudinal relaxation rates of tissue CBF data,13 and the brain–blood partition coefficient for water and arterial blood water.29 Details of the associ-

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T 417 estimates. Inflows from other unlabeled substrates (e.g. ketone bodies, Vket; pyruvate and lactate blood–brain exchange, Vex) can dilute the acetyl CoA pool. Compari- son of the measured 13C fractional enrichment of C4- glutamate and C1,6 or C1-glucose permits determination of the total dilution of the acetyl CoA pool, Vdil (see Appendix B). The values of CMRO2 and CMRglc(ox) were determined by

CMRglc ox† ˆ 1=2 VTCA À Vdil† 5†

CMRO2 ˆ 3 VTCA À 3=4Vdil† 6† Equations (5) and (6) describe metabolic fluxes derived from a [1-13C] or [1,6-13C]glucose experiment which primarily reflects flows through pyruvate dehydrogenase which is localized in the neuron, whereas a [2-13C]glu- cose experiment reflects flows through pyruvate carbox- ylase which is localized in the astrocyte (see Fig. 2; ‘Measurements of neuroenergetics using 13C MRS’ in Discussion). Partial-volume corrected CMRO2 and CMRglc(ox) were obtained for the forepaw stimulation data (group e) as previously described17 using the ! ! À À  13 13 relationship of (activated) = [ (observed) (1 f) Figure 2. 2A) In the [1- C]glucose experiment, the C label ! f f ¯ows from C1-glucose to C3-pyruvate and C3-lactate, and (rest)]/ , where represents the fraction of activated through the tri-carboxylic acid cycle intermediates, into C4- tissue in the compartment using the activated CBF maps glutamate due to fast isotopic exchange between C4- thresholded at the resting CBF value, and ! represents the glutamate and C4-a-ketoglutarate. C4-glutamate in the metabolic rates CMRglc(ox) and/or CMRO2. The modeling neuron serves as a precursor for C4-glutamine in the parameters which have secondary effects on V , astrocyte. Since C4-glutamine labeling lags behind C4- TCA 13 CMRO2 and CMRglc(ox) have been described pre- glutamate under these situations, the [1- C]glucose experi- 6,7,13,16,17,31,32 ment mainly re¯ects neuronal pyruvate dehydrogenase viously (Fig. 1; Appendix B). 2PDH) activity. 2B) In the [2-13C]glucose experiment, the 13C label ¯ows from C2-glucose to C2-pyruvate and C2-lactate and enters the tri-carboxylic acid cycle resulting in C5- 13 13 Calibration of the BOLD fMRI signal glutamate labeling. However, this C label is lost as CO2 in the ®rst turn of the tri-carboxylic acid cycle via the pyruvate dehydrogenase reaction in the neuron. However, 13C label The determination of DCMRO2/CMRO2 from measure- can also lead to consequent C3 labeling in intermediates of ments of DS/S requires that the values of A´ , DCBF/CBF the tri-carboxylic acid cycle via the pyruvate carboxylase 2PC) D reaction in the astrocyte. Thus in the [2-13C]glucose and CBV/CBV be measured. The majority of studies experiment C3-glutamine labeling is detected prior to C3- attempting this calibration have measured just DCBF/ glutamate under steady-state conditions, which indicates CBF, assumed DCBV/CBV, and determined A´ either that the [2-13C]glucose experiment mainly re¯ects astrocytic from theoretical calculations or by measuring DS/S and pyruvate carboxylase activity. In both of these experiments DCBF/CBF during transient manipulations of blood CO the time lag observed between labeling of glutamate and 2 glutamine can be modeled7 to determine glutamate- levels. Our approach differs in that we have directly glutamine neurotransmitter ¯ux 2Vcyc) measured, over a wide range of brain activity induced by variable anesthesia and functional activation, the relative differences of fractional changes in four parameters [eqn (1)]; DS/S (measured by MRI), DCBF/CBF (measured by D D ated experimental errors have been described pre- MRI), CBV/CBV (measured by MRI), and CMRO2/ 13,29,30 CMRO2 (measured by MRS). The determination of the viously. ´ Details of the direct and indirect 13C MRS experi- normalization constant A was obtained by dividing both sides of eqn (1) by DCBF/CBF and rearranging to result ments for measurements of VTCA have been described.6,7,13,16,17,31,32 Time courses of C4-glutamate in 13 labeling were normalized to the C fractional enrich- A ˆ =‰ 1 À Ɇ= 1 ‡ ÁCBF/CBF†ÀÊ 7† ment of C1,6 or C1-glucose. A set of coupled differential equations were used to describe the model (Fig. 1; where  =(DS/S)/(DCBF/CBF), É =(DCMRO2/CMRO2)/ Appendix B), and an iterative method was used to fit the (DCBF/CBF), and à =(DCBV/CBV)/(DCBF/CBF). It model to the C4-glutamate turnover data to yield VTCA should be emphasized that, while the CBV method in this Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 418 F. HYDER ET AL. study measures changes in total plasma vascular space, experiment with FLASH consisted of a pre-stimulation the BOLD measurement is sensitive to venous blood rest period followed by forepaw stimulation and a post- volume compartment. Since each term in eqns (1) and (7) stimulation rest period. The interval between successive was measured over a wide range of neuronal activity at scans was 10 min. Three control BOLD experiments 7 T in rat cortex, the parameter A´ was determined purely were completed before injection of lamotrigine (6-[2,3- from experimental data. The normalized approach to dichlorophenyl]-1,2,4-triazine-3,5-diamine; 25 mg/kg; determination of A´ [eqn (7)] avoids biases towards i.p.), which is a neuronal voltage-dependent Na‡ channel arbitrary values of DS/S, which has potential to be blocker and neurotransmitter glutamate release inhibitor. affected by the resting baseline value.33 The BOLD and CBF experiments were performed approximately every 15 min, before and after lamotrigine treatment. Validation of the calibrated BOLD fMRI signal by comparison with MRS High-resolution CMRO2 mapping by calibrated BOLD fMRI In order to calculate DCMRO2/CMRO2 from multi-modal MRI measurements, eqn (1) was rearranged to In another group of a-chloralose anesthetized rats (initial Á = ˆ Á À‰ Á = †= CMRO2 CMRO2 CBF/CBF S S A † 40 mg/kg; supplemental 20 mg/kg/30 min; i.p.), an MRI 8 36 ‡ ÁCBV/CBVŠ 1 ‡ ÁCBF/CBF† method was used that allows the measurement of changes in BOLD signal (both gradient-echo and spin- which can be further simplified by the relationship echo), CBF and CBV in a rapid manner (1 min). We 34 between CBV and CBF refer to the method as blood oxygenation level dependent ' exponential decays adjusted for flow attenuated inversion ÁCBV/CBV ˆ 1 ‡ ÁCBF/CBF† À 1 9† recovery (BOLDED AFFAIR). The method allows to allow calculation of DCMRO2/CMRO2 from only interleaved measurements of both transverse (R2 and BOLD and CBF measurements (by MRI only) R2*) and longitudinal (R1) relaxation rates of tissue water in conjunction with pulsed arterial spin labeling. The Á = ˆ Á CMRO2 CMRO2 CBF/CBF image-contrasts are intrinsically oxygenation and flow ' À‰ ÁS=S†=A ‡ 1 ‡ ÁCBF/CBF† À 1Š 10† weighted but each contrast is made quantitative by two TE and TIR acquisitions with EPI. This method has been 1 ‡ ÁCBF/CBF† validated in rat brain by comparison of multi-modal maps The value of A´ was calculated from the calibration curve obtained by using the two-point and multi-point fitting described above [eqn (7)]. Although the relationship approaches during varied levels of activity, and the basic expressed by eqn (10) is similar to others,10–12 we have theory and associated experimental/systematic errors for 36 sought to measure each parameter on the right-hand side multi-slice imaging have been discussed. By use of an 23,24 MRI contrast agent and repeated measurements of of eqn (8) to predict DCMRO2/CMRO2. Comparison of predicted [by eqn (8) using MRI data] and measured changes in R2 and R2* with stimulation (in the same subject), the CBV changes can be determined with the (by POCE using MRS data) values of DCMRO2/CMRO2 under conditions of variable anesthesia and sensory same method. Prior to the start of data acquisition a 26 D 23,24 stimulation allowed validation of this method DANTE method was used to calculate R2*( Bo) and to be used in eqn (2) to determine DR2'(Y) for ÁCMRO2=CMRO2‰predicted by eqn 8†Š calculating DS/S [see eqn (3)]. The BOLDED AFFAIR 11† ˆ m‰ÁCMRO2=CMRO2 measured by POCE†Š sequence was initiated with a TR of 64 s (eight raw images, where each image was acquired every 8 s). The where m approaches unity if the predicted and measured first and last five images represented the control values DCMRO2/CMRO2 are in agreement. This valida- conditions, whereas during the middle five images the tion is essentially a test of how well a single value of A´ rat experienced forepaw stimulation. In each rat, this (with TE ranging from 20 to 34 ms) is able to normalize protocol was repeated with and without the MRI contrast the BOLD signal over a large range of activity. agent AMI-227. The R1 data obtained (at rest and during activation) without the contrast agent were used to calculate CBF maps, whereas the R2* and R2 maps (at Neurochemical basis of BOLD fMRI rest and during activation) obtained without the contrast agent were used to calculate BOLD signal-changes. The Details of this experiment have been described pre- R2* and R2 maps (at rest and during activation) obtained viously.35 In a separate group of a-chloralose anesthe- with and without the contrast agent were used to tized rats, BOLD and CBF maps were obtained during calculated the CBV changes. CMRO2 maps were created rest and forepaw stimulation (see above). A BOLD fMRI based on eqn (8) [or eqn (10)].

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T 419

Figure 3. Typical 13C turnover spectral data from 2A) direct 13C and 2B) indirect 13C 2i.e. POCE) experiments localized in the somatosensory area of a- chloralose anesthetized rats 2group ), where the chemical shift position of C4-glutamate is shown with a gray dot. These spectra were exponentially line-broadened by 10±20 Hz. The VTCA determined from the time-courses of C4-glutamate were similar for both rats, and are in good agreement with previous measurements.7,13,16,17

RESULTS POCE has increased several-fold in the last few years,13,16,17,37,38 and recently indirect 13C in conjunction Measurements of cerebral metabolism and perfu- with chemical shift imaging has been implemented using sion by MRS and MRI methods ICED PEPSI to obtain 8 ml voxels in rat cortex.19,20 Typical ICED PEPSI data for 13C detection of C4- Serial spectra obtained from the somatosensory region of glutamate in vivo in 8 ml voxels used for CMRO2 mapping rat brain by direct and indirect 13C MRS methods are is shown in Fig. 4 and compared with BOLD [shown in shown in Fig. 3 for a-chloralose anesthetized rats (group terms of an R2'(Y) map as in eqn (2)] CBF and CBV maps ) during [1-13C]glucose infusion. The time-courses of (from the same rat: group a). The CBV map is C4-glutamate signal increase were similar for both rats represented by a spin-echo MRI which reveals the (i.e. VTCA of 0.44 Æ 0.05 and 0.49 Æ 0.08 mmol/g/min) distribution of the MRI contrast agent (AMI-227) at indicating that both methods have comparable sensitivity baseline. Although the spatial resolution in the CMRO2 towards 13C turnover in glutamatergic neurons of map is lower than the other MRI-derived maps, the cerebral cortex. Although the spectral resolution of direct observed regional correlations of metabolism (by MRS), 13C data is notably superior, the main advantage of the perfusion (by MRI), and BOLD signal support neuro- indirect method for 13C turnover of C4-glutamate is the vascular coupling.39,40 spatial resolution (i.e. 50 ml and 300 ml for indirect Figure 5 shows typical metabolic and perfusion data and direct 13C, respectively) since the 13C signal is obtained from rat brain in the different conditions:13 detected at the sensitivity of 1H. The sensitivity of control condition of morphine anesthesia (group a),

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 420 F. HYDER ET AL.

Figure 4. High-resolution multi-modal MRI and MRS data of 2A) absolute CBF, 2B) absolute CMRO2, 2C) absolute R2'2Y), and 2D) relative CBV maps from rat brain. Each measurement was made under steady-state metabolism and perfusion in the same rat under morphine anesthesia 2group a). The scale bars in 2A)±2C) represent absolute units of CBF 2ml/g/min), CMRO2 2mmol/g/min), and À1 R2'2Y)2s ), respectively, whereas the scale bar in 2D) represents a relative scale of resting CBV. The nominal spatial resolutions in 2A), 2C) and 2D) were 320 Â 320 Â 1000 mm3, whereas in 2B) was 1250 Â 1250 Â 5000 mm3.As shown, the data were differently interpolated

followed by either pentobarbital administration (group relative magnitudes in CBV changes for the two control b), or nicotine infusion (group g); another control conditions (groups a and ) were different (i.e. 5 Æ 3vs condition was a-chloralose anesthesia (group ), fol- 14 Æ 9%), the value of ' determined from eqn (9) was of lowed by forepaw stimulation (group e). Figure 5(A) the same magnitude (i.e. 0.10 Æ 0.06) for all perturba- demonstrates that, relative to ‘control I’ condition (group tions. Therefore, the relative changes in CBV in relation a), VTCA and CBF are lowered with pentobarbital (group to the absolute changes in CBF could be scaled to the b; i.e. ‘deactivation’) and increased with nicotine (group awake resting CBF value for the non-anesthetized resting g; i.e. ‘activation I’). Figure 5(B) demonstrates that awake condition and used in eqn (10) for the calibration. relative to ‘control II’ condition (group ), VTCA and CBF In Fig. 6(A), the changes in CBV (measured by MRI) and are increased with forepaw stimulation (group e; i.e. CMRO2 (measured by MRS) shows that (DCMRO2/ ‘activation II’) with a mean value of 0.7 Æ 0.2 for f (see CMRO2)  (DCBV/CBV) over the same range of ‘Protocols and methods for BOLD calibration studies’ in changes in CBF (measured by MRI). Because the 13 Materials and Methods). Since the C fractional measured DCMRO2/CMRO2 values above the non- enrichment ratio of C4-glutamate/C1-glucose at the end anesthetized resting awake condition [group e; top right of each experiment for each condition was insignificantly quadrant in Fig. 6(A)] were partial-volume corrected, a different from the others (0.4 Æ 0.1),13 the 12C dilution of nonlinear fit over the whole dynamic range is a better the acetyl CoA pool was constant over a wide range of representative for the relationship between CMRO2 and cerebral metabolism. CBF [see below and Fig. 7(C)]. The changes in CBV (measured by MRI) and CMRO2 (measured by MRS) are compared with changes in CBF (measured by MRI) in Fig. 6(A). The relative changes in Probing BOLD image-contrast of glutamatergic CBV for the global perturbations (groups b and g) were neurons small, ranging from 2 to 7% with respect to the ‘control I’ condition (group a), whereas the localized changes in The BOLD signal-changes [see eqn (3)] were measured CBV measured during forepaw stimulation (group e) for the same physiological perturbations as described in were slightly larger, ranging from 7 to 21% with respect Fig. 5. Figure 6(B) shows the summary of all multi-modal to the ‘control II’ condition (group ). The relationship MRI and MRS data which have been used to standardize between CBV and CBF [eqn (9)] shows that, although the the BOLD fMRI signal-changes over a wide range of

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T 421

Figure 5. Measurements of CBF and VTCA in the same rat, by MRI and MRS methods, for global 2A) and focal 2B) 13 perturbations. The color bar at the bottom shows the scaling for the CBF data, whereas VTCA is depicted by the C4-glutamate time courses from the POCE data 2*) and the best-®ts of the metabolic model 2Ð) 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 rectangle in each CBF map represents the localized region from where the metabolic data were obtained from. 2A) Group a is the `control I' condition of morphine sulfate anesthesia 2VTCA = 1.1 Æ 0.1 mmol/g/min; CBF = 0.8 Æ 0.1 ml/g/min); group b is `deactivation' from group a with addition of sodium pentobarbital 2VTCA = 0.4 Æ 0.1 mmol/g/min; CBF = 0.3 Æ 0.1 ml/g/min); and group g is `activation I' from Group a with infusion of nicotine hydrogen tartrate 2VTCA = 1.4 Æ 0.1 mmol/g/min; CBF = 1.1 Æ 0.1 ml/g/min). 2B) Group  is `control II' condition of a-chloralose anesthesia 2VTCA = 0.5 Æ 0.1 m mol/g/min; CBF = 0.4 Æ 0.1 ml/g/min), and group e is `activation II' from group  with forepaw stimulation, where f = 0.7 Æ 0.2 from thresholded activated CBF maps 2VTCA = 1.7 Æ 0.4 mmol/g/min; CBF = 1.6 Æ 0.4 ml/g/min). The values in brackets are the mean Æ standard deviation values 2n = 22).13 Modi®ed from Hyder et al.13,41

neuronal activity (groups a–e). The average contribution Figure 7(B) shows the comparison of the predicted À1 of DBo to R2*(obs) was 7 Æ 1s (n = 28) in the region of DCMRO2/CMRO2 [by eqn (8)] and measured DCMRO2/ 24 interest. The average values (n = 28) of É, Ã and  in CMRO2 (by POCE). Because most of the data points eqn (7) were 0.75 Æ 0.16, 0.12 Æ 0.07 and 0.10 Æ representing the MRI-predicted and MRS-measured 0.06, respectively, to provide a standardized value of values of DCMRO2/CMRO2 lie close to the line of 0.36 Æ 0.09 for A´ (TE = 26 Æ 4 ms) representing the non- identity over a wide dynamic range of neuronal activity anesthetized resting awake condition. To gain insight into (groups a–e), there is high confidence [m = 0.9 Æ 0.1; eqn the relative importance of the oxygenation-dependent (11)] of the BOLD fMRI signal calibration at 7 T in relaxation term in relation to the BOLD signal-change rat cortex (n = 28). Figure 7(C) indicates that CBF [eqn (1)], we defined the rate by the difference between (measured by MRI) and CMRO2 (measured by MRS) R2*(obs) and R2(obs), after removal of the R2*(DBo) change near proportionately in the rat somatosensory 23,24 13 component, leaving only the R2'(Y) term [see eqn (2); cortex over a wide dynamic range. Because the BOLD Appendix A]. Figure 7(A) shows that the R2'(Y) term [eqn signal calibration described above [Fig. 7(B)] is valid for (2)] is linearly correlated with the ratio of CMRO2/CBF. the same range of activity [Fig. 7(C)], eqn (8) can be used This indicates a negative correlation between BOLD in conjunction with multi-modal measurements of BOLD signal and oxygen extraction fraction (OEF), as shown in signal, CBF and CBV to calculate changes in CMRO2. Appendix A, which has been qualitatively observed by Figures 6 and 7 reveal that CBF and CMRO2 play a more others42,43 and provides experimental verification for dominant role in modulation of the BOLD fMRI signal at assumptions used in description of the BOLD theory.1–5 7 T in rat cortex.

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 422 F. HYDER ET AL.

Figure 6. 2A) Comparisons of DCBV/CBV 2Â) and DCMRO2/CMRO2 2‡) vs DCBF/CBF for the different conditions 2groups a±e). The ratios of 2DCMRO2/CMRO2)/2DCBF/CBF) and 2DCBV/ CBV)/2DCBF/CBF), given by É and Ã, respectively, in eqn 27), are signi®cantly different 2slopes through origin are 0.8 and 0.1, respectively). The origin represents the resting awake state for rat cerebral cortex.13 Modi®ed and updated from Hyder et al.13,41 and Kida et al.23,24 2B) Summary of quantitative MRI and MRS measurements of relative changes in CBF, CMRO2, CBV and BOLD signal, over a wide range of neuronal activity 2groups a±e). For each condition, the changes in CBF, CMRO2, CBV and BOLD signal were normalized by changes in CBF which resulted in ratios of DCBF/CBF 2normalized to 1), É, à and , respectively [eqn 27)]. This normalization procedure provides a comparison of relative changes in each parameter during changes in neuronal activity. These ®ndings show that CBF and CMRO2 play a more dominant role in modulation of BOLD image-contrast at 7 Tin glutamatergic neurons of rat brain. The error bars represent the standard deviation from the mean

Figure 7. The neuroenergetic basis of BOLD is investigated with multi-modal MRS and MRI measurements. 2A) The transverse relaxation rate term of R2'2Y), as shown in eqn 22), is positively correlated with the ratio of CMRO2/CBF which is related to OEF 2see Appendix A). This relationship, which has been qualitatively observed,42,43 provides quantitative experimental veri®cation of BOLD theory.1±5 Modi®ed and updated from Kida et al.23,24 2B) The predicted DCMRO2/CMRO2 [by eqn 210)] and measured DCMRO2/CMRO2 2by POCE) values are compared to provide validation of BOLD calibration at 7 Tin glutamatergic neurons of rat cerebral cortex. Thedotted line represents the line of identity and a linear regression analysis of the data provides a value of m = 0.9 Æ 0.1 [eqn 211)] with R2 = 0.95. These results indicate that at very high static magnetic ®elds strengths deoxygenation effects in blood dominates relaxation effects in tissue1,2 which can be accentuated by combining the gradient-echo and spin-echo data [eqn 22)]. Since the validation of BOLD calibration relies on standard errors of independent measures for relaxation rate, blood ¯ow, and volume, by comparing the calculated and measured DCMRO2/CMRO2 it can be calculated that the validation accuracy for high-resolution CMRO2 mapping by multi-modal MRI at 7 Tin rat cortex 23,24 is at least 80%. Modi®ed and updated from Kida et al. 2C) Comparison of CMRO2 2measured by MRS) vs CBF 2measured by MRI) for the different conditions 2groups a±e). For the observed relationship between CBF and 13,44,45 CMRO2, the tissue pO2 has to remain signi®cantly lower than vessel pO2 values, which supports a situation in which the effective mass transfer coef®cient for oxygen 2D) must change 2see Appendix C). Since the ratio of 2DD/ D)/2DCBF/CBF) expressed as a constant was determined to be 0.8 Æ 0.2, it is suggested that the ef®ciency of oxygen delivery plays an important role for the regulation of oxygen delivery in vivo. The ®lled symbol represents the resting awake state for rat cerebral cortex.13 The error bars represent the standard deviation from the mean. Modi®ed and updated from Hyder et al.13

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T

Plate 1. The neurochemical basis of BOLD is investigated with pharmacological treatment of lamotrigine, which is a neuronal voltage-dependent Na‡ channel blocker and glutamate release inhibitor.35 Since the localized BOLD response #in the forelimb area of the somatosensory cortex in multi-slice data) during forepaw stimulation after lamotrigine treatment signi®cantly declined #from 0.07 Æ 0.01 to 0.03 Æ 0.02 after lamotrigine induction; n = 6), the activation of voltage-dependent Na‡ channels and neuronal glutamate release are involved in the BOLD fMRI response during somatosensory activation of the rat cortex. The localized BOLD responses were obtained by averaging activated pixels across slices that remained above the same statistical threshold. The color bar represents a t-scale thresholded at p < 0.01 #yellow)

Plate 2. Multi-modal maps of localized changes in CBF, CBV, and BOLD signal #eqn 3) obtained during forepaw stimulation in an a-chloralose anesthetized rat which were used to calculate a relative CMRO2 map using eqn 8. The rats in this group #n = 4) received an initial a-chloralose dose of 40 mg/kg #i.p.). The magnitude of changes in CBF, CBV and BOLD signal were 1.17 Æ 0.41, 0.07 Æ 0.04 and 0.06 Æ 0.02, respectively, and the localized change in CMRO2 was 0.93 Æ 0.33 for this rat only #2 Â 2 voxel focus). Each map is scaled differently. The regional correlation observed between changes in CMRO2 and CBF is very similar to regional correlation 46 between changes in CMRglc and CBF for the same rat model.

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T 423 To investigate the neurochemical basis of BOLD fMRI which are directed towards mapping neuronal activity by signal, pharmacological treatment with lamotrigine, BOLD fMRI. Since 13C MRS can provide measurements which is a neuronal voltage-dependent Na‡ channel of brain energy metabolism, we review some methodo- blocker and glutamate release inhibitor, was used in the logical details of the method for neuroenergetics. Multi- rat forepaw stimulation model.35 The magnitudes of modal experiments which deal with the neurophysio- BOLD and CBF responses to forepaw stimulation logical basis of BOLD fMRI are also discussed in detail. declined in a time-dependent manner within the first 2 h Methodological pitfalls of perfusion (CBF and CBV) after lamotrigine treatment. The increases in BOLD and imaging by MRI methods are discussed else- CBF during stimulation were reduced by 50 and 90%, where.13,24,27–30 Consequences of these results and use respectively, after lamotrigine treatment. Plate 1 (Figure of these methods for high-resolution CMRO2 (i.e. 8) shows the localized BOLD response during forepaw neuronal activity) mapping by BOLD fMRI are dis- stimulation before and after lamotrigine treatment in the cussed. same rat, where the BOLD signal-change declined from 0.07 Æ 0.01 before lamotrigine injection to 0.03 Æ 0.02 after lamotrigine induction (n = 6). These results suggest Measurements of neuroenergetics using 13C MRS that activation of voltage-dependent Na‡ channels are involved in the BOLD fMRI response. 13C MRS provides a unique window on cerebral metab- olism of 13C labeled glucose6,7,9,33 (Fig. 1). In contrast to 14C isotopes detected in 2-deoxyglucose autoradiogra- 813 13 CMRO2 mapping by calibrated BOLD fMRI phy, C isotopes in conjunction with C MRS allow measurement of one or more metabolites at different Plate 2 (Figure 9) shows the mapping of localized carbon positions in real time. Furthermore, placement of 13 changes in CBF, CBV, and BOLD signal [using R2'(Y)as C label in different carbon positions of a substrate can in eqn (3)] during forepaw stimulation in a lightly also provide information about fluxes through different anesthetized rat. The magnitude of localized changes in enzymes. For example, [1-13C]glucose and [2-13C]glu- CBF, CBV and BOLD signal were 1.22 Æ 0.45, 0.08 cose experiments are used to measure fluxes through Æ 0.05 and 0.06 Æ 0.02, respectively (n = 4). Comparison pyruvate dehydrogenase and pyruvate carboxylase, of the localized changes in CBV and CBF shows that the which are localized in the neuron and astrocyte, value of ' for the functional data (0.1) in this lightly respectively7 (Fig. 2). Since the enzymes for glutamate anesthetized condition is in agreement with the other and glutamine synthesis (i.e. glutaminase51 and gluta- conditions measured in Fig. 6(A) (see above). Therefore, mine synthetase,52 respectively) are localized in the eq. (10) could be used with the high confidence of the neuron and astrocyte, respectively, glutamate and linear regression in Fig. 7(B) (R2 = 0.95) to predict glutamine are considered neuronal and astrocytic 53–57 regional alterations in CMRO2 from the localized changes pools. in CBF and BOLD signal and the experimentally In the studies used to calibrate the BOLD effect at 7 T ´ determined values of A [eqn (7)] and ' [eqn (9)]. The for CMRO2 determination in rat brain (Figs 3–7), the rate 13 regional alterations in CMRO2 was estimated to be of neuronal glucose oxidation was determined from C 0.97 Æ 0.36 using eqn (10) for the lightly anesthetized labeling of C4-glutamate during infusion of [1-13C]glu- condition (n = 4). Alternatively, using eqn (8) with cose. In this experiment the 13C label flows from C1- fractional changes in CBF, CBV and BOLD signal glucose to C3-pyruvate and C3-lactate, via the tri- yielded insignificantly different predictions of DCMRO2/ carboxylic acid cycle intermediates, into C4-glutamate CMRO2 (0.97 Æ 0.36 vs 0.93 Æ 0.40; p > 0.3). While due to fast isotopic exchange between C4-glutamate and magnitudes of changes in CBF and CMRO2 were smaller C4-a-ketoglutarate, and finally into C4-glutamine due to than previous values for forepaw stimulation,13 the value glutamate release by the neuron and uptake by the 6 of É [eqn (7)], which is given by the ratio of (DCMRO2/ astrocyte (i.e. neurotransmitter cycling). As long as 13 CMRO2)/(DCBF/CBF) for the lightly anesthetized con- [1- C]glucose infusion is continuous under steady-state dition in the current study (0.7 Æ 0.3), is in good conditions, the first turn of the tri-carboxylic acid cycle agreement with previous observations13 under deeper will always lead to the scenario described above. Because anesthesia (0.8 Æ 0.2). C4-glutamine labeling lags behind C4-glutamate under these situations, the [1-13C]glucose experiment mainly reflects neuronal pyruvate dehydrogenase activity (i.e. DISCUSSION neuronal glucose oxidation). A [1,6-13C]glucose experi- ment is identical to a [1-13C]glucose experiment except The main goal of functional imaging methods is to that the 13C fractional enrichment of each pool is doubled delineate neural processes from the neuroimaging since C1,6-glucose forms two identical 13C labeled signals. This papers deals with quantitative functional trioses and labels C3-pyruvate and C3-lactate twice per imaging studies of rat brain by MRI and MRS methods glucose molecule.

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 424 F. HYDER ET AL. The metabolic model for the [1-13C] or [1,6-13C]glu- continuous supply of oxygen for normal function and any cose experiment, which yields CMRO2 and CMRglc(ox),is reduction in supply of oxygen leads to permanent schematically shown in Fig. 113,16,17,31,32 and elaborated neuronal damage. Therefore normal brain function in Appendix B. Several modeling parameters have requires that oxygen delivery be regulated in relation to secondary effects upon the calculated metabolic fluxes, the oxidative metabolic requirements of nerve cells.48 An and the magnitude of these effects can be evaluated by important point is that, while there is no requirement for a sensitivity analyses,31,32 or have been measured in constant stoichiometry between changes in CBF and 16,17,31,32 separate experiments. Since these analyses CMRO2, there is a prescribed stoichiometric ratio reveal that many of these parameters have relatively between changes in CMRO2 and CMRglc if glucose small effects on VTCA, CMRO2, and CMRglc(ox) (Æ10% to oxidation is to be maintained from rest to higher and/or Æ15%) for the dynamic range covered in our anesthe- lower levels of activity.9 Our investigations in rat brain tized rat studies13 (Figs 5 and 6), the derived metabolic over a wide range of neuronal activity (Fig. 5) have 13 13 fluxes with [1- C] or [1,6- C]glucose can provide allowed relationships between CMRglc(ox), CMRO2, and important information on neuroenergetics.6,7,9,33 CBF to be explored (Fig. 6), which reveals that more The observation that glutamate is packaged within than 95% of neuronal ATP production is accounted for vesicles in pre-synaptic terminals58 led to the suggestion via glucose oxidation over a wide range of activity.13 that there may be independent transmitter and metabolic These results indicate that ATP homeostasis is main- pools of glutamate that are turning over at different tained over a wide range of conditions by altered rates,59 where the transmitter pool is essentially metab- metabolic rates.64 olically inactive, being taken up by the nerve terminal The relationship between CMRO2 and CBF [Fig. 7(C)] after release into the synaptic cleft. An alternative model reveals that substrate delivery is tightly associated with which links the transmitter pool of glutamate directly to brain energy metabolism.48 These results have important metabolism is the idea of cycling of glutamate and implications for theories on cerebral oxygen deliv- glutamine between neurons and astrocytes (i.e. gluta- ery.13,44,45 Based on the assumption that the flow of mate-glutamine neurotransmitter cycle).60 Several inde- oxygen across the blood-brain barrier is proportional to pendent observations support the glutamate-glutamine the partial pressure of oxygen (pO2) in the capillary, a 44 cycle and argue against the idea of separate transmitter model was presented which links CMRO2 to CBF (and and metabolic glutamate pools:55 active astrocytic uptake CBV) through an effective mass transfer coefficient for of extracellular glutamate61 which is coupled to astro- oxygen (D) of the capillary bed (see Appendix C). Based cytic glucose metabolism,62 enzymes for glutamate and upon in vivo evidence that the effective mass transfer glutamine synthesis are localized in neurons and astro- coefficient for oxygen may be altered by changes in 51,52 65–68 cytes respectively, and the precursors of glutamate capillary pO2, hematocrit and/or blood volume, the and glutamine are each other.53–57 Recent 13C MRS model allows changes in D with changes in CBF. Choice studies in vivo6,7 have demonstrated an approximately in the model of the appropriate ratio of , which is given 1:1 relationship between increases in the rates of by (DD/D)/(DCBF/CBF), determines the dependence of neuronal glucose oxidation (via glutamate turnover) and tissue oxygen delivery upon perfusion. While the model neurotransmitter cycling (via glutamate and glutamine does not predict any particular observed proportionality turnovers) with increasing electrical activity. Therefore, between CBF and CMRO2, the model’s capacity to fit the the derived metabolic fluxes with [1-13C]glucose provide wide range of data indicates that the oxygen diffusion information on functional neuroenergetics6,7 because the properties of the capillary bed, which can be modified in metabolic and transmitting roles of glutamate are almost relation to perfusion (i.e. 1 > > 0; see Appendix C), completely coincident with ATP production and signal plays an important role in regulating cerebral oxygen propagation by the neuron. delivery. The effective mass transfer coefficient for oxygen, D, is derived under the assumption that oxygen delivery is proportional to local vessel pO2 (Appendix C). Regulated cerebral metabolism and perfusion The evidence that oxygen delivery is proportional to local 69 vessel pO2 is based on studies which have shown that At rest, approximately 20% of energy produced in the tissue pO2 is lower than vascular pO2, and very little awake human body is used in the brain, which is less than tissue oxygen diffuses back out into the microvascula- 63 70 5% in total weight. It is generally believed that under ture. Measurements of tissue pO2 suggest that under the normal physiological conditions in the adult mammalian conditions studied here it remains significantly lower 69 brain, almost all of the energy required for ATP than vessel pO2 values, which supports a situation in generation is supplied via oxidation of glucose through which D must change to explain the observed relation- 13 the tri-carboxylic acid cycle leading to oxidative ship between CBF and CMRO2 in Fig. 7(C). The phosphorylation.48 Roy and Sherrington40 suggested that relationship between CBF and D, expressed as , was cerebral perfusion is locally adjusted to meet the regional determined in vivo13 to be 0.8 Æ 0.2 over the dynamic metabolic needs. Brain cells rely on an abundant and range. These results support an important role for the

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T 425 capillary bed to modulate the efficiency of oxygen use of BOLD signal, CBF and CBV measurements to 44,45 delivery in vivo. map CMRO2 at 7 T (see below; Plate 2 (Figure 9)). However, a limitation in this approach is that voxels at the MRI spatial resolution with very high or low values of Neurophysiology of BOLD fMRI in rat brain at 7 T CMRO2, which may not be reliably characterized by the BOLD calibration, could be averaged out. Since The approach we employed to calibrate the BOLD calibrating the BOLD effect [eqn (11)] is limited by image-contrast differs from previous animal studies standard errors in independent measures of relaxation which used non-physiological challenges (e.g. hypoxia rate, blood flow and volume (maximally expected to be or hypercapnia) to perturb CBF.42,43 In previous studies Æ5, Æ10 and Æ5%, respectively24), by comparing the changes in CBV were assumed to follow the the calculated DCMRO2/CMRO2 with the measured dependence proposed by eqn (9) for hypercapnic DCMRO2/CMRO2 (where the associated errors are within 34 13 challenges in primates and changes in CMRO2 and Æ15% at maximum ) we conclude that the validation CBV were not measured. The value of ' from eqn (9) accuracy for neuroenergetics of BOLD image-contrast at was determined to be 0.4 by Grubb et al.34 in a PET 7 T is at least 80%. study, whereas the value of ' determined in the current We expect the accuracy of the BOLD calibration at 7 T MRI study was 0.1 for a wide range of activity in rat in the rat cortex to be high over a wide range of neuronal brain [Fig. 6(A)]. This discrepancy could be partially activity [Fig. 7(B)] because of the linear relationship attributed to different tracers used in the MRI and PET observed between CBF and CMRO2 over the same range. methods for CBV measurements. Because the distribu- Figure 7(C) indicates that CBF (measured by MRI) and tion spaces and half-lives of PET and MRI tracers are CMRO2 (measured by MRS) change nearly propor- different, the changes in tracer kinetics of each label tionately in the rat somatosensory cortex over a wide reflect changes in different compartments of blood (e.g. dynamic range.13 Since the normalization of the BOLD plasma vs hemoglobin). Alternatively, hypoxia and signal described above is valid for the same range of hypercapnia induce some level of uncoupling between activity [Fig. 7(B)], eqn (8) can be used in conjunction oxygen delivery and consumption, and alterations in with multi-modal measurements of BOLD signal, CBF 48 blood pH and/or hematocrit, which may lead to a and CBV to calculate changes in CMRO2. While use of different coupling between CBF and CBV than with the long half-life superparamagnetic MRI contrast agent physiological stimulation. for the CBV measurements27,28 provides valuable data in The BOLD calibration was tested by comparison of these experiments, the use of these agents for human DCMRO2/CMRO2 predicted [by eqn (8)] and measured experiments is not yet approved. Alternatively, BOLD (by POCE). The accuracy of the BOLD calibration in Fig. and CBF data can be used in conjunction with 7(B) [m = 0.9 Æ 0.1; eqn (11)] is consistent over a wide experimentally derived values of A˚ and ' to calculate range of neural activity, from the deeply anesthetized changes in CMRO2 [eqn (10); see Plate 2 (Figure 9)]. condition (bottom left quadrant) to highly activated Recent BOLD fMRI experiments in the awake human condition (top right quadrant). The highest levels of visual cortex71,72 and in the anesthetized rat sensorimotor activity are above the non-anesthetized resting awake cortex36,73 have shown that DS/S and DCBF/CBF are condition (origin). Although the confidence limit of linearly correlated. These observations, in conjunction calibration of the BOLD signal is quite high [Fig. 7(B)] with eqn (8), indicate that the relationship between there are limitations to the calibration. One potential DCBF/CBF and DCMRO2/CMRO2 would also be linear source of uncertainty in comparing the MRI-predicted with functional activation as we have observed experi- CMRO2 data [by eqn (10)] with the MRS-measured mentally in the rat cortex [Fig. 7(C)]. CMRO2 data (by POCE) is the heterogeneity in metab- Since the linear relationship between CBF and CMRO2 olism within larger MRS voxels in comparison to DCBF/ has been observed in rat and human cortex under a CBF, DCBV/CBV, and DS/S measurements which all variety of conditions,44,45 this BOLD calibration ap- have substantially superior spatial resolution. This proach may be applied to human studies. Recent fMRI heterogeneity is greater under conditions of sensory studies by Hoge et al.11 and Kim et al.12 in the human stimulation than non-stimulated conditions. The CMRO2 visual cortex also suggest a linear relationship between measured (by POCE) in the region of interest is CBF (measured by MRI) and CMRO2 (predicted by equivalent to the average of CMRO2 predicted [by eqns MRI), where the predicted value of É [eqn (7)] given by (8) or (10)] from all MRI sub-voxels. If theory is correct, the ratio of (DCMRO2/CMRO2)/(DCBF/CBF) ranged by calculating DCMRO2/CMRO2 in each voxel from the from 0.5 to 0.7, which is in good agreement with the MRI data and then summing, the average value value of É in the current rat studies (0.7 Æ 0.3). The determined from the BOLD calibration should agree slight difference in the relationship between CBF vs with the MRS measurement. The finding of good CMRO2 for rats and humans may be due to an actual experimental agreement between these independent species difference in the mechanisms of cerebral oxygen measures [Fig. 7(B)] strongly supports the combined delivery. However, experimentally measured values of A˚

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 426 F. HYDER ET AL. and ' along with some validation experiments in human magnetic field strength of 4 T and higher, the effects of brain studies may improve the agreement between the rat BOLD on gradient-echo and spin-echo MRI signals are and human data. predominantly associated with the extravascular com- Much of BOLD fMRI research interest pertains to partment,1–5 which may provide localization of neural measurements of activation-dependent changes in the activation.77 physiological parameters mentioned above (e.g. see other Plate 2 (Figure 9) shows an example of quantitative papers in this issue). Thus it is important to characterize high-resolution CMRO2 mapping in rat brain at 7 T the molecular mechanisms linking the observed BOLD during functional activation of the forepaw. The regional signal-change to neurophysiology at the cellular level. correlation between changes in CMRO2 and CBF Under physiological conditions Ca2‡ dependent vesicu- observed here supports the concept of neurovascular lar release of neurotransmitters (e.g. an excitatory amino coupling.39,40 The correlation of region specific perfusion acid like glutamate) occurs in response to depolarization and metabolism has been observed during functional which results from influx of Na‡ ions through pre- activation elicited by forepaw46 and whisker78 stimula- synaptic voltage-dependent Na‡ channels.74 Neuronal tions in anesthetized rats using [14C]-2-deoxyglucose excitability and neurotransmitter release can both be autoradiography. Furthermore, ultra-high resolution suppressed by inhibitors of these channels and the Na‡ [14C]-2-deoxyglucose autoradiography studies79 have current that these channels mediate. Thus Na‡ channel revealed that the neuropil is the site of the highest blockers can be applied in treatment of epilepsy and other metabolic activity. These autoradiography and MRI/ neurodegenerative disease where excessive release of MRS studies suggest that functional neuroenergetic neurotransmitters is believed to contribute to neuronal response of glutamatergic neurons can be represented injury.75,76 The hypothesis that activation of voltage- to a great extent by changes in neuronal glucose dependent Na‡ channels is a necessary step in the oxidation. Since the BOLD effect at 7 T has been neurochemical pathway leading to the BOLD and CBF validated within 80% accuracy [see Fig. 7(B) and above]. responses during somatosensory activation in rat was BOLD maps can represent neuronal glucose oxidation as tested.35 After lamotrigine treatment, significant depres- suggested by regional correlation between changes in sion of localized hemodynamic and neuroenergetic CMRO2 and CBF during functional activation (Plate 2 responses (see Fig. 8) imply that voltage-dependent (Figure 9)). Na‡ channels is involved in the BOLD fMRI response, although more studies are required to determine the extent to which glutamate release or other neurotrans- mitters and modulators are involved in the generation of CONCLUSIONS the BOLD neuroimaging signal.35 The BOLD image-contrast in rat cortex at 7 T has been calibrated by multi-modal MRI measurements, and the High-resolution CMRO2 mapping by calibrated neuroenergetic weighting of the BOLD effect has been 13 and validated BOLD fMRI validated with the C MRS measurements of CMRO2 (i.e. neuronal activity) over a wide range of activity. In Using the description of BOLD theory shown in support of the neurovascular coupling concept, regional Appendix A, the fractional changes in CMRO2 were correlation was observed for changes in CMRO2 and CBF calculated by eqn (8) where we defined the transverse with functional activation. Physiological and pharmaco- relaxation rate by eqn (2). There was good agreement logical studies reveal that BOLD signal-changes are between measured and predicted values of DCMRO2/ closely linked with alterations in neuronal glucose CMRO2 [Fig. 7(B)], which strongly supports theoretical oxidation and neuronal glutamate release. Although the description of BOLD theory.1–5 A detailed discussion of exact cellular processes that underlie the BOLD phenom- the biophysical consequences of these results has been enon are yet to be revealed, the current findings strongly described earlier.24 In summary, the results indicate that confirm the neuroenergetic and neurochemical makeup the strongest modulator of the BOLD fMRI signal is the of BOLD and indicate the necessary steps towards R2'(Y) component [eqn (2)], utilized here by differencing mapping neuronal activity by fMRI. of R2*(obs) and R2(obs) after removal of the R2*(DBo) term, which is associated with the extravascular compart- ment at high static magnetic field strength.1–5 At the Acknowledgements optimal TE and within the physiologic range of water diffusion coefficients, gradient-echo contrast is sensitive The authors would like to thank Professor Robert G. to both small and large vessels, whereas spin-echo Shulman for helpful discussions. The authors also thank contrast is more sensitive to small vessels because the engineers T. Nixon, P. Brown and S. McIntyre for motional narrowing effects in large vessels are refocused maintenance of the spectrometer and the radio-frequency [see eqns (A11) and (A12) in Appendix A4,24]. At a static probe designs, and B. Wang and J. Wall for technical

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T 427 support. Supported by National Institutes of Health grants physiologic perturbation, NS-32126 (DLR), HD-32573 (KLB), NS-34813 (KLB), and NS-37203 (FH); and a National Science Foundation ÁOEF ÁY ˆÀ A9† grants DBI-9730892 (FH) and DBI-0095173 (FH). OEF 1 À Y

The BOLD fMRI signal3–5 is defined as

0 APPENDIX A. PHYSIOLOGICAL BASIS OF S ˆ So exp‰ÀTE  R2 Y†Š A10† BOLD fMRI SIGNAL USING FICK'S RELATION- SHIP where TE is the echo time, R2'(Y) is the transverse relaxation rate of tissue water to be described below, and The equilibrium between deoxyhemoglobin and oxyhe- So is the signal at TE of zero. The relaxation rates 47 moglobin (Hb and HbO2) can be shifted by altering the observed with gradient-echo and spin-echo MRI are blood oxygenation, R à obs†ˆR 0 Y†‡R Y†‡R other†‡R à ÁB † A11† † ‡ † 2 2 2 2 2 o Hb O2 n + Hb nO2 A1 R2 obs†ˆR2 Y†‡R2 other† A12† where 4  n > 1. Since Hb and HbO2 are paramagnetic and diamagnetic respectively, BOLD image-contrast is where R2'(Y) and R2(Y) are the reversible and non- materialized because hemoglobin acts as an endogenous reversible relaxation components due to blood oxygena- MRI contrast agent. The blood oxygenation, Y, is based tion effects on tissue water relaxation rate, R2*(DBo)is on the oxygen dissociation curve for hemoglobin which the relaxation component attributed to static magnetic describes the chemical reaction of eqn (A1) at equi- field distortions (DBo), and R2(other) is the relaxation librium component assigned to non-susceptibility-based effects. The difference between R2*(obs) and R2(obs), after CHb O2†n D 23,24 Y ˆ A2† removal of the R2*( Bo) component as shown by eqn † ‡ CHb O2 n CHb (2) in the main text, leaves only the R2'(Y) term which is devoid of the common and unknown terms between where C and C are [Hb(O ) ] and [Hb], Hb(O2)n Hb 2 n R *(obs) and R (obs) with only the pure oxygenation respectively. If the sum of (C ‡ C ) is equal to 2 2 Hb(O2)n Hb term which can be described by eqn (4)1–5 in the main the total hemoglobin (i.e. CHb(total)) then text. Since R2'(Y) in eqn (A10) varies as a function of C blood oxygenation level, hemoglobin acts as an endo- 1 À Y ˆ Hb A3† C † genous MRI contrast agent. The relationship between Y, Hb total 48 CBF and CMRO2 may be derived from Fick’s principle Since the capillary arteriovenous oxygen difference is À given by (Ca Cv) and the arterial oxygenation is CMRO2 ˆ CBFCHb total† 1 À Y† A13† assumed to be very close to 1, then it can be shown that

and the fractional changes in CBF and CMRO2 are related to the oxygenation changes Ca À Cv ˆ CHb A4† À and ÁY ÁCBF ÁCMR ÁCBF 1 ˆ À O2 1 ‡ 1 À Y CBF CMR CBF Ca  CHb total† A5† O2 A14† Then eqn (A3) rearranges to

1 À Cv=Ca ˆ 1 À Y A6† Given the baseline BOLD signal by eqn (A10), it can be shown that a perturbation leads to an expression for DS/S 47 Since Crone has shown that the oxygen extraction as shown by eqn (3) in the main text. The DR '(Y) term in   2 fraction [OEF CMRO2/(CBF Ca)] is given by eqn (3) in the main text can be expanded from the relationship of eqn (4) in the main text OEF ˆ 1 À Cv=Ca A7†  Á 0 † Á Á then eqn (A6) rearranges to ‡ R2 Y ˆ À Y ‡ b † 1 0 † 1 À 1 A15 OEF ˆ 1 À Y A8† R2 Y 1 Y b When fractional changes in OEF are considered due to a which can be expanded further based on eq. [A.14] to

Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 428 F. HYDER ET AL. show the physiological basis of DR2'(Y) eqn (B3) into (B6) results in  0 ÁCMRO2 ÁCBV CMRO2 ˆ 3VTCA À 3=4Vket B7† ÁR2 Y†ˆ 1 ‡ 1 ‡ CMRO2 CBV which calculates the oxygen consumption from the tri-  À1 carboxylic acid cycle. Therefore, for each value of VTCA ÁCBF 0 1 ‡ À1ŠR2 Y† the values of CMRglc(ox) and CMRO2 can be calculated CBF from eqns (B4) and (B7), respectively. The value of total ´ dilution of the acetyl CoA pool, V , is given by where A in eqn (1) is given by the product of R2'(Y) and dil TE. 1 À‰C4-glutamate13C fractional enrichmentŠ Vdil ˆVTCA ‰glucose13C fractional enrichmentŠ B8† APPENDIX B. DETERMINATION OF CMRO2 13 AND CMRglc=ox) BY C MRS provided that the enrichment of the glutamate pool has reached steady-state (where m = 1/2 and 1 for [1-13C]glu- If glucose is the only source of carbon for the tri- cose and [1,6-13C]glucose experiments, respectively). carboxylic acid cycle and all the [1-13C]glucose enters the acetyl CoA pool, then the stoichiometry of fluxes for the breakdown of glucose is given by

CMRglc ˆ 1=2VTCA B1† APPENDIX C. MODEL OF CEREBRAL OXYGEN DELIVERY AND ITS RELATION WITHBOLD ˆ † CMRO2 3VTCA B2 fMRI and the 13C fractional enrichment of C4-glutamate should be exactly half that of C1-glucose. However, experi- The oxyhemoglobin dissociation curve [eqn (A2)] mentally we find that 13C fractional enrichment of describes the oxygen carrying propensity of blood. The C4-glutamate is less than half that of C1-glu- amount of oxyhemoglobin, CHb(O2)n, is in equilibrium 7,13,16,17,31,32 with deoxyhemoglobin, CHb, and oxygen, CO2 [eqn cose. Two metabolic pathways that may 44,45 contribute to the dilution of C4-glutamate are 12C (A1)]. The model proposes that for a given microscopic capillary segment the rate of oxygen influxes from ketone bodies, Vket, and pyruvate (and delivery is proportional to the vessel-to-tissue pO2 lactate) blood-brain exchange, Vex, both of which contribute unlabeled carbons to the acetyl CoA pool. gradient. Most of the dissolved oxygen molecules that cross the blood- brain barrier radially diffuse into the Vout represents a net efflux of pyruvate (and lactate) into the blood from the brain.9 Under these conditions, the tissue and are consumed. The maximum vessel pO2 is equal to the pO2 of arteriolar blood and oxygen diffusion mass balance between VTCA and CMRglc, based on the fact that a hexose forms two trioses, is given by constant is hypothesized to be constant. Extraction of oxygen into the tissue from an infinitesimally thin blood CMRglc ˆ 1=2‰VTCA À Vket ‡ VoutŠ B3† bolus occurs all through transit, where the temporal profile of the total oxygen content of blood (CB) can be where the oxidative portion is described in relation to the oxygen content in the plasma C CMRglc ox† ˆ 1=2‰VTCA À VketŠ B4† ( P)by =  ˆÀ 0 À † † and the non-oxidative portion is dCB d k CP 1 q C1 where the C is equivalent to C , C is equivalent to CMRglc nonÀox† ˆ 1=2Vout B5† B Hb(O2)n P CO2, q is related to the dissolved oxygen in the Although Vout cannot be measured by this approach, by extravascular space (CT) in relation to CP, and the 13 comparison of CMRglc(ox) from C MRS and CMRglc constant k' is determined by the spatial gradients of from autoradiography under a variety of conditions13,16,17 oxygen tension radially around the bolus, and is the first- can allow the determination of Vout [i.e. CMRglc(ox) as in order rate constant of oxygen loss from the capillary. The 44,45 eqn (B5)]. Likewise, the stoichiometry between VTCA and main assumptions in eqn (C1) have been described. If CMRO2 is given by it is assumed that through an elapsed time of Dt the ratio of transient oxygen contents in plasma and blood is CMRO2 ˆ 3‰2CMRglc À VoutŠ‡21=4Vket B6† constant, i.e. r = CP/CB, then À where the different factors for [2 CMRglc Vout] and Vket C  ‡ Á†ˆC † exp ÀkrÁ† C2† in eqn (B6) signify that different precursors for acetyl B P CoA (i.e. glucose and ketone bodies) are coupled where k is given by the product of k' and (1 À q) and Dt is 31,32 differently to oxidative metabolism. Substituting the mth equivalent fraction of the circulation time (Tc). Copyright  2001 John Wiley & Sons, Ltd. NMR Biomed. 2001;14:413–431 NEUROPHYSIOLOGICAL BASIS OF BOLD fMRI AT 7 T 429 Equation (C2) leads to the arterial value. Highly non-linear relationship between

†ˆ † À‰ Š † † CMRO2 and CBF is predicted by the model with =0 CB Tc CP 0 exp kr netTc C3 and these predictions are heavily dependent on basal OEF D D where [kr] is the net-averaged kr product. The values. For the case where D/D and CBF/CBF are net hypothetical resistance of oxygen transport is distributed equal (i.e. = 1), oxygen delivery increases linearly with over a range of physiological episodes which occur in perfusion with no change in average vessel pO2. various locations and/or phases of oxygen transport, However, in this case a highly linear relationship between which together are termed as the effective mass transfer CMRO2 and CBF is predicted where the changes in coefficient for oxygen [see eqn (C7)], rather than one metabolism and perfusion are exactly proportional, with particular site and/or period. Oxygen extraction around no dependence on basal OEF values. In contrast when > > the capillary may be calculated from 1 0, oxygen delivery may be increased both through an increase in vessel pO2 and D. The prediction ˆ‰ †À †Š= † † OEFc CT 0 CB Tc CB 0 C4 of this model is a linear relationship between CMRO2 and CBF with minimal dependence on basal OEF values. A > where CB(0) CB(Tc) and given eqn (C3), OEFc is also qualitative but substantial validation of these different equivalent to situations is the ability to predict the BOLD fMRI image- contrast. The changes in CMR and CBF observed OEFc ˆ 1 À exp À‰krŠ Tc† C5† O2 net during activation reflect a decrease in OEF from its The total oxygen extraction per capillary can be depicted basal value (i.e. DOEF/OEF < 0) which is equal to an by the summation of the effect of an infinitesimally thin increased venous blood oxygenation. 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