MRI Measurement of the Temporal Evolution of Relative CMRO 2 During Rat Forepaw Stimulation

Transcription

1 Magnetic Resonance in Medicine 4: (1999) MRI Measurement of the Temporal Evolution of Relative CMRO During Rat Forepaw Stimulation Joseph B. Mandeville, 1, * John J.A. Marota, 1,3 C. Ayata, 4 Michael A. Moskowitz, 4 Robert M. Weisskoff, 1, and Bruce R. Rosen 1, This study reports the first measurement of the relative cerebral metabolic rate of oxygen utilization (rcmro ) during functional brain activation with sufficient temporal resolution to address the dynamics of blood oxygen level-dependent (BOLD) MRI signal. During rat forepaw stimulation, rcmro was determined in somatosensory cortex at 3-sec intervals, using a model of BOLD signal and measurements of the change in BOLD transverse relaxation rate, the resting state BOLD transverse relaxation rate, relative cerebral blood flow (rcbf), and relative cerebral blood volume (rcbv). Average percentage changes from 10 to 30 sec after onset of forepaw stimulation for rcbf, rcbv, rcmro, and BOLD relaxation rate were 6 16, 17, 19 17, and 6 1, respectively. A poststimulus undershoot in BOLD signal was quantitatively attributed to the temporal mismatch between changes in blood flow and volume, and not to the role of oxygen metabolism. Magn Reson Med 4: , Wiley-Liss, Inc. Key words: CMRO ; BOLD; undershoot; temporal mismatch; rat 1 MGH-NMR Center, Massachusetts General Hospital, Boston, Massachusetts. Department of Radiology, Massachusetts General Hospital, Boston, Massachusetts. 3 Department of Anesthesia and Critical Care, Massachusetts General Hospital, Boston, Massachusetts. 4 Department of Neurology, Massachusetts General Hospital, Boston, Massachusetts. Grant sponsor: National Institutes of Health; Grant numbers: DA09467; DA00384; R01HL *Correspondence to: Joseph B. Mandeville, MGH-NMR Center, Building 149, Room 301, 13th Street, Charlestown, MA jbm@nmr.mgh.harvard.edu Received 16 December 1998; revised March 1999; accepted 0 July Wiley-Liss, Inc. The presumption that functional brain activation should induce similar magnitude changes in relative cerebral blood flow (rcbf) and the relative metabolic rates of oxygen (rcmro ) and glucose (rcmrglu) utilization was challenged by the seminal PET measurements reported by Fox and Raichle and coworkers during the late 1980s (1,). Those experiments found that rcbf and rcmrglu far exceeded rcmro during human visual and somatosensory stimulation. The discovery that blood oxygen leveldependent (BOLD) signal (3,4) could be used to map changes in neuronal activity (5,6), by means of functional MRI (fmri) supported the original PET findings, as BOLD signal should not increase unless rcbf outstrips the combined effects of increases in rcmro and relative cerebral blood volume (rcbv). Whereas measurements by positron emission emission (PET) () and autoradiography (7) have consistently shown similar magnitudes of rcbf and rcmrglu after a functional challenge, the issue of how these observables couple to rcmro has not been definitively settled, primarily because existing methods for quantifying rcmro are indirect and arduous. Subsequent to the original Fox and Raichle report, PET and Kety-Schmidt experiments in a variety of paradigms reported a wide range of results, including little or no task-induced increase in rcmro (,8,9), similar magnitude changes in rcmro and rcbf during visual imagery (10), and stimulus-specific coupling in the human visual system (11). One group used NMR spectroscopy of 13 C-labeled glucose in rat somatosensory cortex during forepaw stimulation to infer rcmro, using a metabolic model and reported that oxygen consumption increased by % (1,13), a far greater change than that reported for autoradiographic measurements of rcmrglu or rcbf during the same paradigm (14). In principle, changes in CMRO can be inferred from the interaction of oxidative metabolism with blood oxygenation, which is related to BOLD signal. However, two primary obstacles have previously hindered quantification of rcmro through BOLD signal. First, the temporal profile of rcbv has been difficult to measure with most existing methods. Second, functional changes in hemodynamic and metabolic observables are related to BOLD signal by a normalization factor that depends on regional baseline physiology. Two recent reports assumed a coupling relationship between rcbf and rcbv and then calculated rcmro during human visual stimulation from interleaved measurements of BOLD signal and rcbf. Kim and Ugurbil (15) used a global parameterization of the BOLD normalization factor based upon work by Ogawa et al. (16) with estimated physiological input parameters, whereas Davis et al. (17) determined regional normalization maps on an empirical basis. In order to understand the multiphasic nature of BOLD signal, which is presumed to arise from temporal mismatches between underlying hemodynamic and metabolic alterations, it is necessary to characterize the magnitude and temporal responses of rcbf, rcbv, and BOLD signal in the same stimulation paradigm. Exogenous intravascular contrast agents with long blood half-lives have provided a sensitive new functional imaging tool for animal studies of sensory stimuli (18 1). The slow return of rcbv to baseline has now been implicated as the origin of the BOLD poststimulus undershoot (18). A temporal mismatch between rcbf and rcbv was hypothesized by the balloon model of Buxton et al. (). This mismatch was observed and further modeled using Windkessel theory (3), which suggested venous delayed compliance as the cause of the temporal mismatch. In this study, we empirically determined the BOLD normalization constant (4,5) and then combined measurements of rcbf, rcbv, and BOLD signal to calculate rcmro in rat somatosensory cortex with 3-sec temporal resolution during electrical stimulation of the contralateral forepaw. 944

2 CMRO Contribution to BOLD Signal 945 A preliminary account of this work has been presented in abstract form (4); subsets of these data have been presented in other reports (18,3). MATERIALS AND METHODS Calculation of rcmro A general model of BOLD signal based on Fick s principle is described in the Appendix. From Eq. [A5], four independent measurements must be combined to determine the change in CMRO as a function of time (t): (a) the change in BOLD transverse relaxation rate, R* (t), (b) rcbf(t), (c) rcbv(t), and (d) R* (BOLD) (0), which is the baseline value of the transverse relaxation rate attributable to BOLD effects. The first three of these variables can be directly measured during a functional challenge. However, R* (BOLD) (0) is much more difficult to measure than R*(t), because factors unrelated to the BOLD phenomenon contribute to the resting state transverse relaxation rate of MRI signal. Although rough estimates of this value can be obtained by model calculations with empirical constraints (15,16), R* (BOLD) (0) is expected to be a regional variable (17). In particular, rat cortex exhibits a large gradient in resting state CBV from the outer to inner layers (6). Thus, it is important for quantitative calculations of rcmro to determine R* (BOLD) (0) empirically. R* (BOLD) (0) can be determined in a model-consistent way through Eq. [A5] by measuring R*, rcbf, and rcbv during a functional challenge for which it known a priori that the hemodynamic response is not accompanied by a change in CMRO (4,5). Hypercapnia is just such a challenge (7 9), unless it is extreme and prolonged. This was the strategy employed by Davis et al. (17). As in the Davis calculation, we assumed a magnitude coupling between rcbf and rcbv during hypercapnia, F/F 0 (V/V 0 ) ;in Grubb s hypercapnia measurements by PET, a best fit to the data was obtained with.6 (30). Thus, we determined R* (BOLD) (0) according to Eq. [A5] from MRI measurements of BOLD R* and rcbv in rat somatosensory cortex during hypercapnia: R* R* (BOLD) (0) [1] 1 (V/V 0 ) 1 To determine rcmro in rat somatosensory cortex during forepaw stimulation, we measured BOLD R *(t) and rcbv(t) using MRI, and we measured rcbf(t) using laser doppler flowmetry. We then employed two analysis strategies: 1. We calculated the temporal evolution of rcmro ( M/M) in terms of relative changes in CBF ( F/F), CBV ( V/V) and the BOLD relaxation rate ( R */ R * (BOLD) ) using Eq. [A5]. 51 F(t)/F(0)6 M(t)/M(0) 51 V(t)/V(0)6 / 51 R *(t)/r * (BOLD) (0)6 1/ 1 []. In order to reduce potential systematic error due to partial volume issues between the MRI and LDF data sets, we estimated the magnitude of rcmro in a manner consistent with the calculation of Eq. [1] for the BOLD resting state relaxation rate; rcbf was inferred from rcbv, using Grubb s relationship. Since the time constants for changes in blood flow and blood volume are different (3), this method cannot provide information about rcmro during hemodynamic transitions. Because rcbv did not quite reach a steady state value during the 30-sec stimulus, we estimated steady-state rcbv for each experiment using the asymptotic value of a monoexponential fit (18). The steady-state magnitude of rcmro was thus calculated as M/M 51 V/V6 / 51 R */R * (BOLD) (0)6 1/ 1 [3] As discussed in the Appendix, we used 1 and 1.5 as canonical parameters, and we evaluated the sensitivity of the calculation to our choice of parameters. CO Responsivity For measurements of the BOLD baseline transverse relaxation rate, R*(t) and rcbv(t) were measured at Tesla during transitions of P a CO from normocarbia to hypercarbia in rats that were anesthetized with -chloralose and paralyzed with pancuronium (n 3). The same multislice gradient echo planar imaging sequence that was used for stimulation studies was used to record MRI signal during each transition to hypercarbia. BOLD R*(t) and rcbv(t) were measured in somatosensory cortex during sequential cycles of P a CO in the same animal; MION contrast agent (10 mg iron per kg) was injected intravenously between the first and second cycles. For each cycle from normocarbia to hypercarbia and back, blood gases were sampled at the baseline state and at the hypercarbic plateau about 15 min after the addition of 5% CO to the inhalation gas. Hypercapnia and stimulation experiments were performed in separate sets of animals. To locate somatosensory cortex for determination of R* (BOLD) (0), images from the three hypercapnia studies were registered with images from three studies in which each forepaw was electrically stimulated. Registration was performed manually using three position offsets and a rotation in the image plane; other rotation angles were constrained during the experiments by head fixation. A 6-mm 3 bilateral volume of somatosensory cortex was selected from a single slice of the average map of functional forepaw brain activation; this volume included most of the activated region, where the average BOLD contrast to noise ratio was 5 (computed using a pooled T statistic). This region was transferred to the hypercapnia image set for calculation of the average values of R*(t) and rcbv(t) on the hypercapnic plateaus of MRI signal. For each animal, R* (BOLD) (0) was then determined from Eq. [1]. Functional Imaging Techniques Animal preparation and monitoring, stimulation parameters, and functional imaging techniques have been de-

3 946 Mandeville et al. scribed previously (18,1,3). The data for changes in BOLD R *(t) and rcbv(t) caused by this forepaw stimulation paradigm have previously been presented (18), as has the response of rcbf(t) (3). This section is included for completeness; the reader is referred to those earlier reports for additional details. Briefly, hypercapnia and forepaw stimulation studies were performed on rats that were anesthetized with -chloralose and paralyzed with pancuronium using continuous infusion of both agents. Blood gases and body temperature were monitored and controlled. For forepaw stimulation studies, average P a CO levels (mean SE) for MRI and LDF experiments were and mm Hg, respectively. During stimulation, electrical pulses of 5 V were applied for 0.3 msec at 3 Hz. To ensure complete recovery of functional signals, 150 sec of rest followed each 30-sec stimulation period; this epoch was typically repeated 6 times on each forepaw using BOLD contrast. To weight signal by blood volume, a large dose of a monocrystalline iron oxide nanocolloid (MION) was then injected, and an equal number of stimulations of each forepaw were repeated. Functional imaging was performed at field strengths of Tesla (7 paws, 5 rats) and 4.7 Tesla (6 paws, 5 rats); in addition to the previously reported data (18), one additional animal was imaged at Tesla. fmri studies employed multislice gradient echo planar imaging with a repetition time of 3 sec, an excitation angle of 90, an echo time (T E ) of typically 5 msec, and a spatial resolution of typically 0.6 mm 3. BOLD transverse relaxation rate was calculated from BOLD signal (S)as R *(t) ln5s(t)/s(0)6/ T E. rcbv(t) was calculated as previously described (18), using a linear relationship between R *(t) and the blood volume fraction after injection of the contrast agent. Region-of-interest (ROI) analyses were applied to time series for BOLD and CBV-weighted imaging. To select regions in somatosensory cortex, each image voxel was subjected to a Student s T-test to determine the statistical significance of signal change between resting and stimulated states. A 3-mm 3 volume of interest was then selected from the core of activation determined from the BOLD and CBV image series. Robust activation was observed in all cases contralateral to the stimulated forepaw, whereas statistically significant signal changes were not observed in ipsilateral somatosensory cortex. Representative maps of functional activation using BOLD and CBV contrast have been presented previously (18,1). For our analysis of rcmro (t), data for BOLD R *(t) and rcbv(t) at.0 and 4.7 Tesla were averaged after first scaling BOLD R *(t) by the ratio of field strengths (0.43). From the literature, it is expected that parenchymal BOLD R *(t) should increase in an approximately linear manner with field strength (31), whereas rcbv(t) should be independent of field strength when a sufficient amount of contrast agent is used (18). To verify that our data were consistent with these assumptions, we applied pooled T-tests between each data set ( and 4.7 Tesla) for both rcbv and BOLD R * after applying the scaling factor to R *. These statistical tests were applied on (a) temporally averaged responses during the 30 sec of stimulation, and (b) temporally averaged responses from sec after stimulus cessation, which corresponded to a region of undershoot in BOLD signal. Measurement of rcbf(t) was performed using an LDF spectrometer (PeriMed Periflux PFB, Sweden) with a sampling rate of 00 msec and a bandwidth of 1 khz. Two craniotomies were drilled under saline cooling at the location of somatosensory cortex in each hemisphere, and probes were placed on dura in pools of mineral oil. Based on the MRI analysis of functional activation and the known location of somatosensory cortex, probes were placed 0.3 mm posterior of bregma and 4.0 mm lateral to the midline. Otherwise, protocols for surgery, anesthesia, and stimulation were identical with those used in MRI studies. For comparison with MRI results, rcbf(t) was resampled to a temporal resolution of 3 sec. RESULTS CO Responsivity Within each animal, the values of P a CO that were determined from the separate ventilation cycles using BOLD and CBV contrast never differed by more than mm Hg during normocarbia or hypercarbia. For ventilation cycles using BOLD signal, transitions occurred between P a CO levels of and mm Hg. For ventilation cycles using CBV contrast, transitions occurred between P a CO levels of and mm Hg. The average value of BOLD R* with respect to normocarbia was sec 1, and the average value of rcbv was 4 4%. By using Eq. [1] to compute R* (BOLD) (0) in each animal, the average value of this quantity was calculated to be sec 1 at the lower value of P a CO (35 mm Hg) and sec 1 at the higher value (58 mm Hg). Since the average level of P a CO during forepaw stimulation studies (40 mm Hg) was slightly higher than the normocarbic baseline (35 mm Hg) in these studies, a linear interpolation was used to obtain a value for R* (BOLD) (0) of s sec 1 at 40 mm Hg. An estimate of R* (BOLD) (0) at 4.7 Tesla was obtained by scaling the Tesla result by the ratio of field strengths, in accordance with model predictions (16) and empirical results (16,3). The validity of this approach was tested using a pooled-t comparison between forepaw stimulation results for BOLD R* at Tesla and BOLD R*/.35 at 4.7 Tesla. These data sets were not significantly different (P 0.34). Forepaw Stimulation Excluding one additional animal in the data set at Tesla, results for R*(t) and rcbv(t) during this forepaw stimulation paradigm have been presented previously (18), and results for rcbf(t) have also been reported (3). Figure 1 shows the separate measurements of rcbv(t) and R*(t)/ R* (BOLD) (0) at field strengths of and 4.7 Tesla. Error bars on the BOLD data include contributions from both R*(t) and R* (BOLD) (0). The average responses of both rcbv and R*/ R* (BOLD) (0) during stimulation were slightly smaller in the data set at 4.7 Tesla relative to the Tesla results. Moreover, the average poststimulus overshoot of R*(t)/R * (BOLD) (0) and the delayed return of rcbv(t) to baseline after stimulus cessation were more pronounced in the 4.7 T data set.

4 CMRO Contribution to BOLD Signal 947 FIG. 1. Average percentage changes in CBV (filled circles) and BOLD R * (open circles) as a function of time during rat forepaw stimulation at Tesla (left; 7 paws, 5 rats) and 4.7 Tesla (right; 6 paws, 5 rats). The gray shaded region depicts the temporal window of stimulation. Pooled-T tests over temporally averaged regions were used to determine whether any of these trends were statistically significant (P 0.05). During the stimulus (0 30 sec), neither rcbv nor R */R * (BOLD) (0) was statistically different between these data sets. Similarly, neither rcbv nor R */ R * (BOLD) (0) were found to be different in the overshoot region from sec after stimulus cessation. Therefore, rcbv(t) and R *(t)/r * (BOLD) (0) were averaged across field strengths. Figure a compares rcbf(t), rcbv(t), and R *(t)/ R * (BOLD) (0) during forepaw stimulation; the change in sign on the BOLD relaxation rate gives this data a similar appearance to BOLD signal, which is more commonly shown in the literature. About 6 sec after stimulus cessation, the BOLD time course began a poststimulus undershoot; this occurred when rcbf(t) dropped below rcbv(t). The BOLD relaxation rate returned to the prestimulus baseline when rcbv(t) finally returned to baseline. Figure b shows the calculation of rcmro (t) using Eq. []. As rcmro (t) was calculated from group average results, error bars were determined by propagating standard errors on the separate measurements of rcbf(t), rcbv(t), R *(t), and R * (BOLD) (0). rcmro (t) was found to be roughly constant during the stimulus duration. After stimulus cessation, rcmro (t) returned to baseline with a time constant similar to that for rcbf(t). The solid line in Fig. is a calculation of rcmro (t) using the model of Buxton and Frank (33), which predicts that rcmro (t) is temporally coupled to rcbf(t) with a nonlinear magnitude relationship. This calculation depends on only rcbf(t) and the baseline oxygen extraction fraction, which was assumed to be 40%. Table 1 summarizes our estimate of the magnitude relationship between rcbf and rcmro using two different analyses as described by Eqs. [] and [3] under Methods. In the first analysis, the average responses from 10 to 30 sec after stimulus onset were determined, and rcmro was calculated using Eq. []. The value of rcmro (19 17%) was much smaller than our LDF measurement of rcbf (6 16%). In the second analysis, Grubb s relationship was used to infer rcbf from rcbv in order to eliminate partial volume uncertainties between the MRI and LDF data sets. The calculated values for rcmro at and 4.7 Tesla showed good agreement. The estimated value of rcbf (83 1%) was not significantly different from the LDF result. The best estimate of rcmro (9 15%) using this analysis was slightly higher than in the first analysis, but the ratio of average rcbf to average rcmro was about 3 in each case. Table shows the magnitude of model-dependent error as the parameters and were varied in the two analyses. Uncertainty arising from model parameters produced systematic uncertainties in rcmro and rcbf/rcmro that were smaller than our statistical error bars. Table 1 Averages Values in Rat Somatosensory Cortex for the BOLD Resting State Relaxation Rate at Tesla (3 Rats), rcbv and BOLD Signal During Forepaw Stimulation as Measured by MRI at Tesla (7 Paws, 5 Rats), and 4.7 Tesla (6 Paws, 5 Rats), and rcbf During Forepaw Stimulation as Measured by LDF (4 Paws, 3 Rats)* Tesla 4.7 Tesla Average R * (BOLD) (0) sec sec 1a,b BOLD R * sec sec 1 R */ R * (BOLD) (0) b 3 11% 0 5% 6 1% Analysis I: Average responses from 10 to 30 sec after stimulus onset (Eq. []) rcbv 4% 13 % 17 % rcbf (LDF) 6 16% rcmro b 19 17% Analysis II: MRI steady-state analysis (Eq. [3]) FIG.. Left: Average percentage changes and standard errors in CBF (crosses), CBV (closed circles), and negative BOLD relaxation rate (open circles). The gray shaded regions depict the period of forepaw stimulation. Right: Calculated values for the percentage change in CMRO. The solid line is the prediction of the Buxton-Frank model (33), using a resting state oxygen extraction fraction of 0.4. rcbv c 7 5% 4 4% 5 3% rcbf d 89 18% 78 16% 83 1% rcmro b 5 18% 33 13% 9 15% *Relative CMRO was determined by two analyses described under Methods. a Calculated by scaling the Tesla result by the ratio of field strengths. b Error bars determined by propagating standard errors of the mean. c Monoexponential fits were used to determine steady-state values of rcbv. d Calculated from rcbv using Grubb s relationship (30): F/F 0 (V/V 0 ).6.

5 948 Mandeville et al. Table Evaluation of Model-Dependent Errors Using the Two Analyses Described Under Methods* R * (BOLD) (0) 4.0 sec 1.4 sec sec sec 1.1 sec 1 R */ R * (BOLD) (0) 16% 6% 35% 19% 30% Analysis I: Average responses from 10 to 30 sec after stimulus onset (Eq. []) rcmro 17% 19% 1% 7% 15% rcbf/rcmro Analysis II: MRI steady-state analysis (Eq. [3]) rcmro 3% 9% 31% 18% 36% rcbf/rcmro *Parameter describes the dependence of the BOLD relaxation rate on blood oxygenation, and parameter relates rcbf to rcbv as F/F 0 (V/V 0 ). rcmro and the ratio of rcbf to rcmro were found to be relatively insensitive to model parameters. DISCUSSION BOLD Poststimulus Undershoot A poststimulus undershoot in BOLD signal has been apparent in human studies of sensory stimulation since the first report of the use of this contrast mechanism for mapping human brain function (5). It has been widely assumed that the BOLD undershoot arises from a temporal mismatch between underlying hemodynamic and metabolic alterations. Transient features of BOLD signal have generated considerable interest in the spatiotemporal and magnitude relationships between changes in oxidative metabolism and perfusion. The hypothesis that the undershoot arises from a temporal mismatch between rcbf(t) and rcmro (t) (34 36) is fundamentally incompatible with the diffusion-limited model of oxygen delivery to brain tissue (33). A temporal mismatch between rcbf(t) and venous blood volume, as suggested by recent biomechanical models (,3), would resolve the diffusionlimited hypothesis of oxygen delivery to brain tissue with the observation of a BOLD poststimulus undershoot, as well as a generally smaller BOLD overshoot soon after stimulation onset. The development of intravascular contrast agents with long blood half-lives has enabled measurements of rcbv(t) during functional stimulation in animal models. As seen in Fig., the onset of the BOLD poststimulus undershoot occurred when rcbf(t) dropped below rcbv(t) about 6 sec after stimulus cessation, and the end of the BOLD undershoot occurred as rcbv(t) resolved to the pre-stimulus baseline value. As seen in Fig. 1, percentage changes in the BOLD relaxation rate and rcbv(t) and were approximately equal after 15 0 sec after stimulus cessation. This result is predicted by the BOLD model if CBF and CMRO have returned to baseline values at these late time points (see Eq. []). We therefore ascribe the BOLD poststimulus undershoot in this model to a temporal mismatch between rcbf(t) and rcbv(t). Using a more rapid sampling rate, we recently reported two distinct temporal phases of rcbv(t) during onset and cessation of stimulation (3); a rapid response of rcbv(t) was attributed to the elastic response of capillaries and veins, while a slow and delayed phase of continued rcbv(t) evolution was attributed to the viscoelastic characteristics of smooth muscle surrounding veins, which exhibit pronounced delayed compliance in ex vivo studies (37,38). A temporal mismatch between rcbf(t) and rcbv(t) can be reproduced within a conventional model of brain vasculature in which arterioles actively modulate CBF and capillaries and veins respond passively to pressure changes in the respective compartments (,3). These data and models suggest that rcbv(t) can be viewed as a correlate of rcbf(t) that reflects a temporal low-pass filter applied by venous stress relaxation. Magnitude of rcmro The calculated average change in CMRO (19 17%) during 30 sec of forepaw stimulation was slightly more than one standard error above the baseline. The observed relationship between rcmro and rcbf during stimulation was found to be broadly consistent with the original PET observations of Fox and Raichle and the prediction of the Buxton-Frank model, which falls within statistical error bars on this measurement across the entire temporal range. The small change in rcmro determined from this study stands in striking contrast to estimates based on 13 C NMR spectroscopy that CMRO changes by % during forepaw stimulation (1,13). The voltage, frequency, and duration of electrical pulses used in those studies were identical to the stimulation parameters used in this study. The observation of a positive BOLD signal change during forepaw stimulation requires that rcbf exceed rcmro during this paradigm. Although stimulation protocols and anesthetic regimens differ slightly throughout the literature, other measurements of rcbf by LDF during forepaw stimulation have yielded increases of 40 10% (39,40), whereas the gold-standard iodoantipyrene technique showed an average CBF increase of 33 1% across contralateral somatosensory cortex (7). The magnitude of CMRO change is further restricted by the observation that CBV increases in this paradigm and that a significant proportion of this increase is likely attributable to capillary and venous blood volume, based on the temporal discordance between rcbf(t) and rcbv(t) and the large fraction of postarteriole blood volume, which is about 85% of total CBV (41,4). The average increase in glucose utilization across somatosensory cortex during forepaw stimulation was reported to be 55 18% (7). Our results and the available experimental data suggest that the basic assumptions (43) or experimental corrections (1,13) in the 13 C- NMR calculation of rcmro need to be revisited. Sources of Error Errors in our measurement of rcmro can be divided into three types: (a) statistical errors, (b) systematic errors from model uncertainties, and (c) systematic errors from other sources, including registration and partial volume issues. The error bars on rcmro in Fig. primarily reflect biological variability and illustrate the difficulty of obtaining high precision in calculations derived from multiple sequential biological measurements. By contrast, system-

6 CMRO Contribution to BOLD Signal 949 atic uncertainties from model parameters were found to somewhat smaller for any reasonable assumptions, as illustrated in Table. Model uncertainties in rcmro using this method are generally small, owing to the selfcorrecting nature of the model-based empirical determination of R * (BOLD) (0), as discussed by Davis et al. (17). There are three sources of partial volume and registration uncertainties. First, LDF and MRI experiments were performed in separate animal groups. Although the location of somatosensory cortex was taken from a standard atlas and confirmed by the MRI results, the exact volume of optimal LDF sensitivity, particularly with respect to depth from the cortical surface, was unknown with respect to the selected MRI volume. However, these rcbf measurements are roughly concordant with other literature results during forepaw stimulation. Moreover, the value of rcbf recorded by LDF and the value predicted from measurements of rcbv and Grubb s relationship were roughly concordant (Table 1). Second, small misregistrations between the hypercapnia and stimulation images sets could introduce systematic error into our determination of R * (BOLD) (0), but effects on calculation of rcmro would be modest. For example, even a factor of systematic error in R * (BOLD) (0) would not change the average value of rcmro beyond our current statistical error bars. Finally, the different dependencies of BOLD signal and CBV-weighted fmri on the resting state blood volume fraction produced a subtle shift between BOLD and CBV activation centroids as a result of the strong cortical blood volume gradient (unpublished). Our region of interest analysis attempted to properly account for this effect. It should be noted that the most important feature of our data the BOLD poststimulus undershoot results from a temporal mismatch between blood flow and volume is less sensitive to partial volume issues and systematic uncertainties than the calculated magnitude of rcmro. The time window for the BOLD poststimulus undershoot is completely independent of the scaling factor determined from the hypercapnia measurements. Moreover, the time at which rcbf(t) falls below rcbv(t) after stimulus cessation is not very sensitive to the peak magnitudes of those quantities because the time constant for decrease of rcbf(t) is much faster than the corresponding time constant for rcbv(t). Human Measurements of rcmro Recent MRI measurements of rcmro during visual stimulation in humans have been reported by Davis et al. (17) and Hoge et al. (44) (R.D. Hoge, private communication) using this same conceptual approach. In those studies, rcmro was found to be statistically elevated but smaller than rcbf by factors of 3. Steady-state results for rcmro in those experiments showed smaller statistical errors than the results of this study because of (a) the use of simultaneous BOLD and CBF acquisitions, and (b) determination of the BOLD baseline transverse relaxation rate in each subject in a registered volume of interest. Systematic error because of uncertainty in the coupling relationship between rcbf and rcbv is probably small due to the selfcorrecting nature of a model-based empirical determination of R * (BOLD) (0) (17). However, the accuracy of ASL measurements of CBF during focal and global changes in blood flow is still an open issue. As a result of the current inability to measure rcbv(t) in humans, methods that assume a flow-volume coupling relationship (15,17) cannot determine rcmro (t)onatime scale shorter than sec, the observed reaction time for rcbv(t). Several recent studies have described the spatiotemporal characteristics of the undershoot in the human visual cortex (45,46). The dependence of the undershoot magnitude on stimulus duration appears to be quite consistent with the observed dynamics of blood volume and the hypothesis of venous delayed compliance. Unfortunately, the anatomic resolution of our studies was not sufficient to address regional variations in BOLD transients and whether these correlate with different time constants or magnitudes of rcbv arising from vascular heterogeneity. Ultimately, a complete description of BOLD physiology in awake human brain will require dynamic blood volume measurements using this method or complementary noninvasive modalities such as optical imaging. APPENDIX From the first observation of signal loss in T*-weighted images around cerebral veins in rats (3), it has been apparent that deoxygenated hemoglobin, which has a paramagnetic susceptibility proportional to the number of deoxygenated hemes (47), is a potent endogenous intravascular contrast agent. Changes in the local concentration of deoxyhemoglobin ([dhb]) are reflected in the transverse relaxation rate ( R*) of bulk magnetization. In terms of signal (S) at any time (t), S(t) S(0) exp5 R*(t) T E 6, where T E is the gradient echo time of the MRI sequence. We used a simple model for the BOLD part of the transverse relaxation rate (R* (BOLD) ) that was generated by (a) assuming a functional form for R* (BOLD) versus the blood volume fraction (V) and the concentration of deoxygenated hemoglobin in the blood ([dhb] BLOOD ), and (b) applying Fick s law of conservation of oxygen flux to describe relaxation rate changes ( R* R* (BOLD) ) in terms of rcbf, rcbv, and rcmro. In a general form, R * (BOLD) KV [dhb] BLOOD. [A1] To rewrite [dhb] BLOOD in terms of the ratio of CBF (F) to CMRO (M), we employed both the definition of hemoglobin oxygen saturation (Y), [dhb] BLOOD [Hb] BLOOD (1 Y) [A] and Fick s law, which conserves oxygen flux across the capillary bed. Using the unidirectional flow of oxygen across the blood-brain barrier as the presumptive measure of CMRO, F[Hb] (1 Y VENOUS ) M. [A3] Neglecting arterial blood, which represents only about 15% of total CBV (41,4), Y Y VENOUS. Then Eqs. [A1] [A3] can be combined as R * (BOLD) KV (M/F), [A4]

7 950 Mandeville et al. where V is the blood volume fraction in the image voxel. During a functional challenge, R * can be expressed in terms of rcbf [f(t) F(t)/F(0)], rcbv [v(t) V(t)/V(0)], and rcmro [m(t) M(t)/M(0)]: R *(t) R *(t) R *(0) where R * (BOLD) (0) 51 v (t) m (t)/f (t)6, R * (BOLD) (0) KV (0)M (0)/F (0) [A5] [A6] is a time-independent normalization constant that depends on regional baseline physiology. Equation [A5] is a generalization of Ogawa s formulation (16), as presented in Eqs. [8] and [9] of that manuscript. Ogawa s formulation results when 1and Eq. [A5] is linearized for small changes (i.e., terms higher than first order in any combination of F/F, V/V, or M/M are ignored). Ogawa s formula was used by Kim et al. (15) to calculate rcmro using an estimate of R* (BOLD) (0) as a global constant, and Eq. [A5] was used by Davis et al. (17) to determine rcmro after empirically determining regional R* (BOLD) (0). 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