Home | About | Journals | Submit | Contact Us | Français |

**|**HHS Author Manuscripts**|**PMC4830424

Formats

Article sections

- Abstract
- 1 Introduction
- 2 Theory
- 3. Materials and methods
- 4 Results
- 5 Discussion
- Supplementary Material
- References

Authors

Related links

Neuroimage. Author manuscript; available in PMC 2017 April 1.

Published in final edited form as:

Published online 2016 January 11. doi: 10.1016/j.neuroimage.2016.01.001

PMCID: PMC4830424

NIHMSID: NIHMS751118

Aaron B. Simon,^{1,}^{5} David J. Dubowitz,^{2} Nicholas P. Blockley,^{3} and Richard B. Buxton^{2,}^{4,}^{*}

The publisher's final edited version of this article is available at Neuroimage

Calibrated blood oxygenation level dependent (BOLD) imaging is a multimodal functional MRI technique designed to estimate changes in cerebral oxygen metabolism from measured changes in cerebral blood flow and the BOLD signal. This technique addresses fundamental ambiguities associated with quantitative BOLD signal analysis; however, its dependence on biophysical modeling creates uncertainty in the resulting oxygen metabolism estimates. In this work, we developed a Bayesian approach to estimating the oxygen metabolism response to a neural stimulus and used it to examine the uncertainty that arises in calibrated BOLD estimation due to the presence of unmeasured model parameters. We applied our approach to estimate the CMRO_{2} response to a visual task using the traditional hypercapnia calibration experiment as well as to estimate the metabolic response to both a visual task and hypercapnia using the measurement of baseline apparent R_{2}′ as a calibration technique. Further, in order to examine the effects of cerebral spinal fluid (CSF) signal contamination on the measurement of apparent R_{2}′, we examined the effects of measuring this parameter with and without CSF-nulling. We found that the two calibration techniques provided consistent estimates of the metabolic response on average, with a median R_{2}′-based estimate of the metabolic response to CO_{2} of 1.4%, and R_{2}′- and hypercapnia-calibrated estimates of the visual response of 27% and 24%, respectively. However, these estimates were sensitive to different sources of estimation uncertainty. The R_{2}′-calibrated estimate was highly sensitive to CSF contamination and to uncertainty in unmeasured model parameters describing flow-volume coupling, capillary bed characteristics, and the iso-susceptibility saturation of blood. The hypercapnia-calibrated estimate was relatively insensitive to these parameters but highly sensitive to the assumed metabolic response to CO_{2}.

Functional magnetic resonance imaging (fMRI) based on Blood Oxygenation Level Dependent (BOLD) contrast is an important tool for the study of human cognition because of its impressive ability to localize sources of evoked neural activity and its safe and noninvasive nature. However, while BOLD imaging has been highly useful for answering the question of *where* cognitive processes take place, it has had much less success in answering *how much* activity is associated with a particular process. This is largely because BOLD imaging is not directly sensitive to the electrical events that mediate neural signaling, nor to any single activity-related physiological process (e.g. blood flow, oxygen metabolism), but rather to fluctuations in the rate of MR signal decay attributable to changes in the quantity of deoxyhemoglobin in the cerebral vasculature –a quantity that depends on the relative values of several physiological variables (Buxton, 2013).

The fundamental gap between what BOLD measures —namely the change in R_{2}* between two neurophysiological states —and what is typically of interest, a metric of state change-associated neural activity, has inspired considerable effort on understanding the biophysical processes that transform neural activity changes into detectible changes in R_{2}*, with the goal of making it possible to quantitatively interpret BOLD signal changes in terms of fundamental physiological processes. From the inception of BOLD imaging, the link between deoxyhemoglobin and MR contrast was understood (Bandettini et al., 1992; Ogawa et al., 1992), and seminal biophysical modeling work in the early 1990s established the first quantitative links between physiological variables such as hemoglobin oxygen saturation, blood volume, and hematocrit and MR signal evolution (Ogawa et al., 1993; Yablonskiy and Haacke, 1994). In 1998 Davis et al. made a critical step in linking BOLD contrast changes to changes in neural activity by positing that by combining BOLD imaging with arterial spin labeling (ASL), an MR contrast directly sensitive to cerebral blood flow (CBF) (Detre et al., 1992; Wong et al., 1997), and a simple biophysical model of R_{2}* decay, one could quantitatively estimate a stimulus-evoked change in cerebral oxygen metabolism (CMRO_{2}), a physiological parameter thought to capture the integrated energy costs of the underlying neural activity (Davis et al., 1998).

The Davis model was a breakthrough for the quantitative experimental study of the BOLD response because it presented a straightforward approach to converting BOLD and ASL measurements into CMRO_{2} measurements. The model divided the physiological basis of the BOLD response into three general components: (1) Changes in the Oxygen Extraction Fraction (OEF), captured by the ratio of CMRO_{2}-CBF changes, (2) changes in cerebral venous blood volume (CBV), captured by literature-derived relationships between CBF and CBV, and (3) the quantity of deoxyhemoglobin in the baseline state, a scaling parameter captured through a separate “calibration” experiment. Originally this calibration experiment entailed the experimentally demanding measurement the BOLD and CBF responses to hypercapnia (Davis et al., 1998); however, recently, theoretical and experimental studies have suggested that the measurement of R_{2}′, the rate of signal decay that may be refocused by a spin echo, in the baseline state provides similar information without the need for inhaled gases (Blockley et al., 2012; 2015).

The results of numerous calibrated BOLD studies emphasize the new information beyond what is available from the BOLD response that measurements of CMRO_{2} can provide as well as the feasibility of obtaining this information experimentally (Buxton et al., 2014). However, estimates of the CMRO_{2} response can depend significantly on assumptions about unmeasured and often unknown physiological parameters, parameters that are implicit to, but not explicitly defined in the Davis model. These physiological parameters could be factors relevant for the BOLD signal model, such as vascular volume changes, or factors relevant for the calibration experiment, such as the assumption of an iso-metabolic response to hypercapnia, or assumptions about the method used to measure R_{2}′. These unmeasured parameters constitute sources of uncertainty in experimental estimates of the CMRO_{2} response that are not easily accounted for using the Davis model or other similarly heuristic models (Griffeth et al., 2013).

In this work we describe a novel approach to account for this uncertainty in an experimental context. In this framework a detailed biophysical model that incorporates a range of important physiological variables is used as a forward model, allowing one to predict experimental measurements for a given set of physiological parameters. In addition to predicting the BOLD response to activation, the model also predicts the experimental results of the calibration experiment, either the BOLD change in the hypercapnia experiment or the signal decay curve during a spin echo experiment for the R_{2}′ approach.

In order to use this model to estimate the CMRO_{2} response consistent with a particular set of measurements, it must be inverted. To do this we adopt a Bayesian approach, assigning a prior probability distribution to each parameter in the model, then sampling the parameter space according to the likelihood that a given set of parameters could generate our measured data given an explicitly stated statistical model, building up a collection of samples that can be used to determine a posterior probability distribution for the CMRO_{2} response that reflects the uncertainty of that estimate given our *a priori* uncertainty about the values of the unmeasured model parameters.

We applied this approach to an experiment in which we measured BOLD and CBF responses in the human visual cortex to a visual stimulus (flickering checkerboard) and to a hypercapnia stimulus. In addition, we measured local baseline R_{2}′ using a modified technique that was designed to control for uncertainty due to partial volume effects of tissues with different T2 values, and to test for the contribution of cerebrospinal fluid (CSF) effects to the apparent value of R_{2}′. We then sought to answer the following questions: What is the uncertainty associated with an estimate of the CMRO_{2} response if only the CBF and R_{2}* (BOLD) responses to a stimulus are measured? How much does the uncertainty decrease if the baseline apparent R_{2}′ is measured in addition to the CBF and R_{2}* responses? How much does the uncertainty decrease if the CO_{2} stimulus is assumed to be iso-metabolic and is used to inform the estimate of the response to the visual task?

Through this analysis we found that, while considerable uncertainty in the CMRO_{2} response may exist even in the absence of population variability or measurement noise, this uncertainty can be reduced by improving our prior knowledge of just a few of the many unmeasured parameters in the model. Through focused investigation of these parameters and better understanding of how they vary across populations of interest, much more precise estimates of the CMRO_{2} response may be obtainable through functional MRI techniques.

BOLD signal decay has its origin in the paramagnetic nature of deoxygenated hemoglobin. In the presence of a strong magnetic field, deoxyhemoglobin, which is found in increasingly high concentrations as one moves down the vascular tree from arteries to veins, produces a magnetic dipole that perturbs the local magnetic field around it, leading to a loss of coherence in the precession of proton magnetic moments across an imaging voxel and ultimately signal decay. A complete model of this process would require precise knowledge of the architecture of the tissue vasculature as well as the hemoglobin oxygen saturation at each point in the vascular tree (Gagnon et al., 2015). Similarly, precisely capturing the shape of this signal decay curve in an experiment would require many closely spaced and high signal-to-noise samples. At this time, neither of these is available for estimating the CMRO_{2} response to a neural stimulus in the human brain. As a result, we must necessarily make many simplifications to our model of signal decay, through which we hope to capture most of the salient features. Similarly, in our experimental measurements, time constraints limit both the signal-to-noise of our measurements and the number of samples we can obtain from a decay curve, requiring that we use simple metrics to capture the salient features of the signal decay (here apparent R_{2}′ in the baseline state and the apparent change in R_{2}* in response to a stimulus).

In the discussion that follows we will first describe the forward signal model that we have adopted for this work, identifying the key physiological parameters that arise from it and motivating the modeling decisions that went into its development. We will then describe how we invert this model using a Bayesian probabilistic framework to compare simulated decay curves with experimental data.

Brain tissue within an imaging voxel of typical volume (~30–100mm^{3}) or region of interest (ROI) is highly heterogeneous, consisting of neural parenchyma, a diverging and converging vascular tree that continuously changes in vessel diameter and oxygen saturation as one moves from artery to vein, and, potentially, non-cellular compartments such as cerebral spinal fluid (CSF). The best way to discretize this structure into a finite and tractable number of compartments is unclear, and investigators have made different choices in how to do so. The original Davis model considers only signal coming from an extravascular parenchymal compartment, which is subject to field inhomogeneity produced by a single, uniformly oxygenated venous compartment (Davis et al., 1998). Xiang He et al. expanded this model to include the signal from a single, uniform intravascular compartment as well as a CSF compartment (He and Yablonskiy, 2006). Following He et al., Dickson et al. adopted a model with intravascular, extravascular, and interstitial/CSF compartments, although they attempted to relax the assumption of uniform vessel diameter in the He model by modeling the vascular compartment as containing vessels coming from a distribution of sizes (Dickson et al., 2010), though with uniform saturation. Uludag et al., and later Griffeth et al., excluded the CSF compartment but subdivided the vascular compartment into arteries, capillaries, and veins, assigning unique but uniform vessel sizes and oxygen saturations to each sub-compartment (Griffeth and Buxton, 2011; Uludağ et al., 2009). For this work we have attempted to balance these approaches, adopting a five compartment model containing parenchyma, arteries, capillaries, veins, and CSF. Each of these compartments is assigned a fractional volume of the total imaging volume, denoted *V _{p}*,

$$S(t)={\sum}_{x=p,a,c,v,e}{\rho}_{x}{V}_{x}{W}_{x}{S}_{x}(t)$$

(1)

where the parameters *ρ _{x}, W_{x},* and

Transverse signal decay in the parenchymal compartment (*S _{p}(t)*) is caused by magnetic field inhomogeneity that arises from deoxyhemoglobin molecules in the intravascular space. Multiple factors affect the rate of parenchymal signal decay, as well as its behavior in response to a spin echo pulse. Important factors include the saturation of the blood, the blood volume, the orientation of the blood vessels to the main magnetic field, and the blood vessel diameters. As discussed above, none of these parameters has a single value in a physical volume of brain tissue; however, with some simplifying assumptions, an approximate model of the tissue signal behavior becomes mathematically tractable. The key assumptions made in this model are as follows: (1) within each vascular sub-compartment, oxygen saturation and vessel radius are uniform; (2) the vessels that comprise each sub-compartment may be thought of as randomly oriented and distributed, infinitely long cylinders of uniform magnetic susceptibility; (3) vessels in the arterial and venous compartments are large enough (diameter 10μm) that the signal decay they produce is not affected by the diffusion of protons through the extravascular space; while those in the capillary compartment are small enough (diameter<10μm) to be significantly effected by diffusion; (4) the effects of each vascular compartment on the tissue compartment are multiplicative. In the limit where the decay produced by each vascular compartment is truly mono-expontential R

Under these conditions we can describe the parenchymal signal evolution with the equation

$${S}_{p}(t)={e}^{-{R}_{2,p}t}\xb7{S}_{p,a}(t)\xb7{s}_{p,c}(t)\xb7{s}_{p,v}(t)$$

(2)

where *R _{2,p}* is the deoxyhemoglobin independent rate of R

$${S}_{p,x}(t)=\{\begin{array}{cc}{e}^{-{V}_{x}\xb7{f}_{c,x}\left({\scriptstyle \frac{t}{{\tau}_{c,x}}}\right)}& t<{\scriptstyle \frac{SE}{2}}\\ {e}^{-{V}_{x}\xb7{f}_{c,x}\left({\scriptstyle \frac{SE-t}{{\tau}_{c,x}}}\right)}& {\scriptstyle \frac{SE}{2}}\le t<SE\\ {e}^{-{V}_{x}\xb7{f}_{c,x}\left({\scriptstyle \frac{t-SE}{{\tau}_{c,x}}}\right)}& SE\le t\end{array}$$

(3)

$${f}_{c,x}\phantom{\rule{0.16667em}{0ex}}\left({\scriptstyle \frac{t}{{\tau}_{c,x}}}\right)={\scriptstyle \frac{\mathbf{1}}{\mathbf{3}}}{\int}_{\mathbf{0}}^{\mathbf{1}}du{\scriptstyle \frac{(2+u)\sqrt{1-u}}{{u}^{2}}}\left(1-{J}_{0}\phantom{\rule{0.16667em}{0ex}}\left(1.5\phantom{\rule{0.16667em}{0ex}}\left({\scriptstyle \frac{t}{{\tau}_{c,x}}}\right)\phantom{\rule{0.16667em}{0ex}}u\right)\right)$$

(4)

$${\tau}_{c,x}^{-1}={\scriptstyle \frac{4}{3}}\gamma \xb7\pi \xb7\mathrm{\Delta}{\chi}_{0}\xb7\mathit{Hct}(\mid {Y}_{\mathit{off}}-{Y}_{x}\mid )\xb7{B}_{0}$$

(5)

In Equations 3–5, *τ _{c,x}* describes the fundamental rate constant for signal decay. The parameters

Water, proteins, and lipids, the chief constituents of blood and neural tissues, are all diamagnetic, with magnetic susceptibilities of −0.719, −0.774, and −0.670ppm, respectively (He and Yablonskiy, 2009). Because red blood cells (RBCs) contain more protein than the surrounding plasma, when fully oxygen saturated they are actually more diamagnetic than the plasma and produce field inhomogeneity. Based on the relative concentrations of protein and water in RBCs and plasma, Spees and others determined that RBCs have the same susceptibility as the surrounding plasma when hemoglobin is 95% saturated (Spees et al., 2001). Reasoning that plasma should have a similar biochemical composition to brain tissue, Uludag et al. and also Griffeth et al. assumed that at an oxygen saturation of 95%, blood ceases to produce the field inhomogeneity that leads to signal decay (Griffeth and Buxton, 2011; Uludağ et al., 2009). Others have not considered this term in their analysis, simply assuming *Y _{off}* = 1 (Dickson et al., 2010; He and Yablonskiy, 2006). Based on literature values for the biochemical composition and magnetic susceptibility of grey matter (He and Yablonskiy, 2009), and using the formula from Spees et al. for calculating blood susceptibility we calculate that

The effect of the capillary compartment on parenchymal signal decay is more challenging to model. In the capillary compartment, the vessels are considered to be small enough that the analytic equations describing signal evolution around large vessels cannot be applied. At this scale, water proton diffusion through the inhomogeneous magnetic field leads to signal dephasing that cannot be completely recovered by a spin echo pulse. Several investigators have developed Monte Carlo models to describe extravascular signal evolution due to blood vessels of this scale and have summarized their results in phenomenological models that describe the apparent rates of *R _{2}* and

Briefly, the tissue is treated as a collection of rectangular prisms each containing a single vessel. The vessels are treated as very long, straight cylinders of a specified radius and the volume of the enclosing prisms was determined such that the vessels would occupy a specified fractional volume of their prisms. The affect of a vessel on the surrounding magnetic field is determined by its oxygen saturation (*Y _{c}*), fractional volume (

To save computational time, the capillary model was not computed for every combination of *Y*, *Hct, V _{c}*

The magnetic environment within a blood vessel is highly complex and heterogeneous due to the presence of red blood cells. Without knowledge of the distribution, shape, and movement of these cells, as well as the plasma around them, it is very challenging to develop a theoretical framework for describing the transverse signal evolution in the intravascular compartments. For this reason, we have adopted an empirically derived phenomenological model of intravascular signal decay based on the work of Blockley et al. and Zhao et al. (Blockley et al., 2012; Zhao et al., 2007). In this model, intravascular signal decay at time *t* about a spin echo at time SE is described by the piecewise continuous mono-exponential decay function

$${S}_{x}(t)=\{\begin{array}{cc}{e}^{-{R}_{2x}^{\ast}t}& t<{\scriptstyle \frac{SE}{2}}\\ {e}^{-{R}_{2x}(2t-SE)-{R}_{2x}^{\ast}(SE-t)}& {\scriptstyle \frac{SE}{2}}\le t<SE\\ {e}^{-{R}_{2x}SE-{R}_{2x}^{\ast}(t-SE)}& SE\le t\end{array}$$

(6)

where *R _{2,x}* and

$${R}_{2,x}^{\ast}=(14.9{\mathit{Hct}}_{x}+14.7)+(302.1{\mathit{Hct}}_{x}+41.8){(1-{Y}_{x})}^{2}$$

(7)

$${R}_{2,x}=(16.4{\mathit{Hct}}_{x}+4.5)+(165.2{\mathit{Hct}}_{x}+55.7){(1-{Y}_{x})}^{2}$$

(8)

In their model for transverse signal decay, He et al. suggested that an imaging volume nominally containing brain tissue contains a finite volume of CSF or extracelluar fluid (He and Yablonskiy, 2006). Due to the differing biochemical makeups of grey matter and CSF, they reasoned that the magnetic moment of the CSF compartment could precess about the transverse plane at a slightly different frequency than that of the brain tissue. Because the measured signal is a complex sum of its constituents, they proposed that dephasing between a CSF compartment and a parenchymal compartment could contribute to signal loss. Fitting experimental data to their model, they estimated that this compartment had an off resonance frequency of approximately 5Hz at 3T and comprised ~5% of an average nominally gray matter voxel. Using this same model, Dickson et al. estimated the off resonance frequency to be approximately 7Hz and the fractional volume to be ~4% of a gray matter volume (Dickson et al., 2010). Since this dephasing could be refocused by a spin-echo pulse, we reasoned that such an effect could contribute significantly to the apparent rate of R_{2}′, biasing the baseline measurement used to calibrate an estimate of CMRO_{2}. As such we included such a compartment in our model, with a signal contribution described by the equation

$${S}_{e}(t)=\{\begin{array}{cc}{e}^{-{R}_{2,e}t-2\pi i\xb7\mathrm{\Delta}v\xb7t}& t<{\scriptstyle \frac{SE}{2}}\\ {e}^{-{R}_{2,e}t-2\pi i\xb7\mathrm{\Delta}v\xb7(SE-t)}& {\scriptstyle \frac{SE}{2}}\le t<SE\\ {e}^{-{R}_{2,e}t-2\pi i\xb7\mathrm{\Delta}v\xb7(t-SE)}& SE\le t\end{array}$$

(9)

where R_{2,e} is the rate of R_{2} decay for CSF and *Δν* is the off resonance frequency between gray matter parenchymal tissue and CSF.

The signal model described above is used to simulate the signal decay that would be measured for experiments with three different types of pulse sequences. The first sequence is a PICORE QUIPSS-II ASL sequence with a dual echo readout designed for the simultaneous measurement of *R _{2}** and CBF-weighted signals (Wong et al., 1998). The second sequence is a Gradient Echo Sampling of Spin Echo (GESSE) sequence (Yablonskiy and Haacke, 1997) used to measure the baseline apparent

$${W}_{x}=\{\begin{array}{cc}1-{e}^{-{\scriptstyle \frac{{TI}_{2}}{{T}_{1,x}}}}& \mathit{ASL}\\ 1-{e}^{-{\scriptstyle \frac{TR}{{T}_{1,x}}}}& \mathit{GESSE}\\ 1-\left(2-{e}^{-{\scriptstyle \frac{TR-TI}{{T}_{1,x}}}}\right)\phantom{\rule{0.16667em}{0ex}}{e}^{-{\scriptstyle \frac{TI}{{T}_{1,x}}}}& \mathit{FLAIR}\phantom{\rule{0.16667em}{0ex}}\mathit{GESSE}\end{array}$$

(10)

where TI refers to the time between the inversion and excitation pulses in the FLAIR GESSE sequence, and TI2 refers to the time between inversion and excitation pulses in the ASL sequence. This inversion time (TI2) is the relevant time for T_{1} relaxation because a pre-saturation pulse is applied to the imaging volume immediately before the inversion pulse. For the CSF compartment a T_{1} of 4000ms was assumed based on literature findings (Lin et al., 2001; Lu et al., 2005) and similarly the T_{1} of the parenchyma was taken to be 1200ms (Lu et al., 2005; Wansapura et al., 1999), values appropriate for a field strength of 3T. The T_{1} of blood was calculated for each vascular compartment as a function of hematocrit and oxygen saturation using linear interpolation of the functions described by Lu et al. for 92% and 69% oxygen-saturated blood (Lu et al., 2004). Inline Supplemental Figure 2 displays calculated blood T_{1} values across the hematocrit and oxygen saturation ranges relevant to this study.

The signal model described above approximates the MR signal behavior for a given set of arterial, capillary, and venous oxygen saturations and compartment volumes, as well as additional model parameters such as hematocrit. As the model is designed to describe changes in metabolism in response to a stimulus, CMRO_{2} must be related to oxygen saturation in the baseline and stimulus states. The fundamental equation used to relate oxygen saturation to CMRO_{2} is the Fick equation, *CMRO*_{2} = *ε* · *CBF* · (*Y _{a}* –

$$r={\scriptstyle \frac{{\mathit{CMRO}}_{2,\mathit{stim}}}{{\mathit{CMRO}}_{2,0}}}={\scriptstyle \frac{{\mathit{CBF}}_{\mathit{stim}}{Y}_{a,\mathit{stim}}{\mathit{OEF}}_{\mathit{stim}}}{{\mathit{CBF}}_{0}{Y}_{a,0}{\mathit{OEF}}_{0}}}$$

(11)

where the subscript *stim* indicates the stimulus state and the subscript 0 indicates the baseline state. The change in CBF is measured, and *Y _{a}* is easily measured through pulse oximetry. Thus determining the change in CMRO

$${Y}_{c}=(1-\kappa )\xb7{Y}_{a}+\kappa \xb7{Y}_{v}.$$

(12)

Blood volume changes are modeled through exponential flow-volume coupling constants as described by Griffeth et al. (Griffeth and Buxton, 2011). Because some experimental work has been done to ground these models for venous volume (Chen and Pike, 2009), capillary volume (Stefanovic et al., 2008), and total CBV (Grubb et al., 1974), the models used here are described by the equations
${\scriptstyle \frac{{V}_{v,\mathit{stim}}}{{V}_{v,0}}}={\left({\scriptstyle \frac{{\mathit{CBF}}_{\mathit{stim}}}{{\mathit{CBF}}_{0}}}\right)}^{{\varphi}_{v}},{\scriptstyle \frac{{V}_{c,\mathit{stim}}}{{V}_{c,0}}}={\left({\scriptstyle \frac{{\mathit{CBF}}_{\mathit{stim}}}{{\mathit{CBF}}_{0}}}\right)}^{{\varphi}_{c}}$, and
${\scriptstyle \frac{CB{V}_{\mathit{stim}}}{CB{V}_{0}}}={\left({\scriptstyle \frac{{\mathit{CBF}}_{\mathit{stim}}}{{\mathit{CBF}}_{0}}}\right)}^{\varphi}$, where the subscript *stim* indicates the stimulus state and the subscript 0 indicates the baseline state, and the flow-volume coupling parameters *ϕ*, *ϕ _{v}*, and

The discussion above describes our approach to simulating the signal decay curve associated with a particular experiment and a particular set of model parameters. From these decay curves, we can simulate the characteristic measurements that we would make during a particular experiment. For the dual echo ASL experiment, these measurements are the fractional change in CBF and the absolute change in apparent value of *R _{2}** between rest and stimulation. For the GESSE and FLAIR GESSE experiments the measurement is the apparent baseline

Note that we refer to both R_{2}* and R_{2}′ as ‘apparent’ in this work. We do this because, strictly speaking, characterizing signal decay by the parameters R_{2}* and R_{2}′ only describes systems undergoing mono-exponential decay. Under such ideal conditions, signal decay at time *t* after excitation may be described simply by the equation

$$S(t)={S}_{0}{e}^{-{R}_{2}^{\ast}t}={S}_{0}{e}^{-({R}_{2}+{R}_{2}^{\prime})t}$$

(13)

where R_{2}′ represents the rate of signal loss than can be recovered by a spin-echo pulse and R_{2} represents the rate of decay that is irrecoverable. In the system described here, certain components are modeled as undergoing strict mono-exponential decay (e.g. the intravascular compartments); however, the aggregate system is not. As such, if R_{2}* and R_{2}′ are measured, their apparent values will depend on precisely when (i.e. at what time points on the decay curve) signal measurements are made. Thus the value of R_{2}′ measured by one experimental protocol (e.g. GESSE) is not the same as the value of R_{2}′ measured in the same system by a different protocol (e.g. asymmetrical spin-echo). To account for this, we calculate R_{2}* and R_{2}′ from our simulated decay curves in the same way that we do for the experiments themselves, which is described in detail in Section 3.6 below.

To estimate the uncertainty in an estimate of the CMRO_{2} response attributable to uncertainty in our measurements, as well as to unmeasured model parameters, we adopted a Bayesian probabilistic model. In the context of this model, the probability that the underlying, unmeasured model parameters, denoted here by the array ** ξ**, and the measurement parameters,

$$p(\xi ,\psi \mid y)\propto p(\mathit{\xi})p(\mathit{\psi})p(\mathit{y}\mid \mathit{\xi},\mathit{\psi})$$

(14)

In this equation *p*(**ξ**, ** ψ** |

Because Equation 14 cannot be solved analytically, we estimate *p*(**ξ**, ** ψ** |

Six healthy adult subjects (three female) participated in this study (ages 22–29 years). The study was approved by the institutional review board at the University of California San Diego, and written informed consent was obtained from all participants.

Simultaneous BOLD and CBF-weighed images were acquired on a GE Discovery 750 3T scanner with a dual-echo arterial spin labeling (ASL) PICORE QUIPSS II sequence (Wong et al., 1998) with a spiral readout. Eight slices (5mm thick/1mm gap) were acquired, with slices 2–5 (from inferior to superior) aligned by visual inspection with the calcarine sulcus. Pulse sequence parameters were as follows: TR 3.0s, TI1/TI2 700/1800ms, TE1 3.3ms, TE2 30ms, 90° flip angle, FOV 256mm, matrix 64×64. In addition, a cerebral spinal fluid (CSF) reference scan and a minimum contrast scan were acquired for use in quantifying CBF (Chalela et al., 2000; Wang et al., 2005). The CSF and minimum contrast scans were single-shot spiral EPI images with TE 3.3ms, TR 4s and TE 11ms TR 2s, respectively, and the same in-plane parameters as the ASL scan. A field map was also acquired for use in correcting distortions in the spiral images due to the inhomogeneity of the magnetic field.

Measurements used to estimate R_{2}′ were made using a gradient echo sampling of spin echo (GESSE) imaging sequence (Yablonskiy and Haacke, 1997). The GESSE image slices were aligned with the centers of the ASL images and had the same in plane resolution and field of view. However, in order to reduce the effects of through-plane gradients on the estimate of R_{2}′, these images were acquired with a slice thickness of 2mm, with the gap between slices increased to 4mm. Two pairs of GESSE image series were collected for this study. Each pair of images consisted of an early spin echo series and a late spin echo series, which were acquired as separate scans. The early spin echo occurred 48ms after excitation and the late spin echo, 98ms after excitation. The samples of each spin echo decay curve were collected asymmetrically. Around the early spin echo curve, 64 samples were collected from 42.77–82.59ms after excitation at intervals of 0.63ms. Around the late spin echo curve, samples were collected from 62.78–102.59ms with the same interval spacing. For the first pair of image series, no T1 preparation pulses were used, and the TR was 2s. For the second pair of image series, an inversion pulse was added before the excitation pulse with the intention of minimizing the cerebral spinal fluid (CSF) signal in the 2^{nd}–5^{th} slices from the bottom of the image stack. A TR of 3.5s and inversion time (TI) of 1.38s was chosen to null the CSF signal, based on an assumed CSF *T _{1}* of approximately 4000ms (Lin et al., 2001; Lu et al., 2005). The third slice from the bottom of the stack was chosen to occur at the CSF null time. Each image slice was acquired sequentially from inferior to superior with a spacing of 110ms. Based on equation 10, we estimated that the CSF signal in the FLAIR GESSE images would be less than 8% of its completely relaxed value in the 5th slice, which was least optimally nulled, or less than 20% of the CSF signal in the standard GESSE images. Inline Supplemental Figure 3 displays FLAIR GESSE signal intensity as a fraction of GESSE signal intensity across slices 2–5 for a single subject, with signal suppression in the ventricles consistent with the theoretical prediction.

Visual Stimuli were produced using MATLAB® (2009a, The MathWorks, Natick, MA) with the Psychophysics Toolbox extensions (Pelli, 1997). The visual stimulus consisted of an 8Hz black and white flickering radial checkerboard with a central region (visual angle ~1.5deg) that was maintained an iso-luminescent gray. The visual stimulus was projected onto a screen, which the subject could view through a head coil mounted mirror.

Each study contained two visual task runs during which simultaneous BOLD and CBF weighted images were acquired. During each scan cardiac and respiratory activity were recorded using a pulse oximeter and respiratory bellows that were built into the MRI scanner. Throughout each of the runs, subjects were asked to fixate on the center of the screen. In order to maintain the subjects’ attention, random numbers (0–9) were displayed in the gray central region of the screen at 1s intervals. The subjects were instructed to press a button on a response box each time a number was displayed twice in a row. The first functional run was used to locate a region of interest (ROI) in the visual cortex. The stimulus paradigm began with 24s of rest followed by 6 cycles of 24s-stimulus, 24s-rest. The second functional run was used to quantify the CBF and BOLD responses to a visual stimulus. The visual stimulus used for this run was the same as that used for ROI localization, however the timing of the stimuli was altered to improve estimation of the baseline signal and to allow for full recovery from the post-stimulus undershoot between stimulus cycles. This functional run began with 72s rest, followed by 6 cycles of 24s-stimulus, 48s-rest and ended with an additional 60s period of rest.

Throughout the imaging session, each subject wore a non-rebreathing facemask (Hans Rudolph, KS, USA). The inspiratory port was connected to a tube that was open to the air in the scanner room but could be connected to a large gas-tight bag filled with a premixed gas (5% CO_{2}, 21% O_{2}, balance N_{2}) by turning a valve.

Each study contained a CO_{2} stimulus run during which BOLD and CBF weighted images were again acquired. The duration of the run was 9min. For the first 3.5 minutes the inspiratory port was open to room air while baseline measurements were acquired. A valve was then turned, switching the source of air to the 5% CO_{2} mixture for a period of three minutes. For the final 2.5 minutes, the inspiratory port was again open to room air. Throughout the run, the subject was asked to keep his or her eyes open and focus on the center of the projection screen. To maintain subject attention, the number repetition task was again employed throughout the run.

Raw ASL images were first corrected for distortions due to the inhomogeneity of the magnetic field (Noll et al., 2005). The first four images of each scan were discarded to allow the MRI signal to reach steady state. All functional runs were motion corrected and registered to the first visual task run using AFNI software (Cox, 1996). In order to minimize BOLD contamination of the CBF measurements, CBF-weighted image series were produced from the raw first-echo ASL images by surround subtraction (Liu and Wong, 2005). R_{2}* -weighted (i.e. BOLD-weighted) images were produced from both the first echo and second echo ASL images by surround averaging (Liu and Wong, 2005) and used to calculate quantitative *R _{2}** image series as described below.

All quantitative analysis was performed in a region of interest (ROI) within the visual cortex, which was defined by the BOLD and CBF response of each subject to the first visual task. Statistical analysis for ROI selection was performed with a general linear model approach for the analysis of ASL data as described by Perthen (Perthen et al., 2008). Briefly, a stimulus regressor was produced by convolving the stimulus pattern with a gamma density function (Boynton et al., 1996). Cardiac and respiratory signals were used as regressors to account for the non-stimulus related signal variance produced by physiological processes (Glover et al., 2000; Restom et al., 2006). A constant and a linear term were also included as regressors. An anatomical mask that included only gray matter voxels in the posterior half of the brain and within slices 2–5 from inferior to superior was produced for each subject, and ROI selection was restricted to this region. Voxels exhibiting CBF or BOLD activation were detected after correcting for multiple comparisons using AFNI AlphaSim (Cox, 1996), using an overall significance threshold of p = 0.05 given a minimum cluster size of four voxels. For each subject, an active visual cortex region of interest (ROI) was defined as those voxels exhibiting both CBF and BOLD activation independently.

Estimates of the deoxyhemoglobin-related R_{2}′ in the brain may be biased by the presence of air-tissue interfaces, which produce magnetic field inhomogeneity across the brain that, in turn, produces R_{2}′-type signal decay that is unrelated to the quantity and distribution of deoxyhemoglobin in an imaging voxel (Dickson et al., 2010; He and Yablonskiy, 2006). We used a method described by Dickson and others to correct our GESSE images for the effects of through-plane gradients before using them for quantitative analysis, using phase images derived from the GESSE image series themselves to generate field maps and making the assumptions that the slice profile was approximately rectangular and that the field inhomogeneity could be approximated as linear gradients through each voxel. Details of the field correction procedure may be found in (Dickson et al., 2010). After correction, all GESSE images series were registered to the first visual task ASL image series using AFNI software (Cox, 1996).

Before performing quantitative analysis on each subject, the CBF-weighted and *R _{2}**-weighted image series from the second visual task run and CO

To estimate the apparent *R _{2}′* in the baseline state, the GESSE time series were assumed to represent mono-exponential signal decay around a spin echo, which can be described by the equation

$$S(t)=\{\begin{array}{cc}{S}_{0}{e}^{-({R}_{2}+{R}_{2}^{\prime})t}& t<{\scriptstyle \frac{SE}{2}}\\ {S}_{0}{e}^{-({R}_{2}-{R}_{2}^{\prime})t-{R}_{2}^{\prime}SE}& {\scriptstyle \frac{SE}{2}}\le t<SE\\ {S}_{0}{e}^{-({R}_{2}+{R}_{2}^{\prime})t+{R}_{2}^{\prime}SE}& SE\le t\end{array}$$

(15)

During the period when the signals are both sampled, the early (48ms) spin-echo decay curve is in the third time regime and the late (98ms) spin-echo decay curve is in the second time regime. The apparent R_{2}′ could thus be calculated as one half the difference in slopes between the logarithms of the late and early spin echo decay curves (Figure 2)

$${R}_{2}^{\prime}={\scriptstyle \frac{1}{2}}\left({\scriptstyle \frac{d\text{ln}(S{(t)}_{SE=98ms})}{dt}}-{\scriptstyle \frac{d\text{ln}(S{(t)}_{SE=48ms})}{dt}}\right)={\scriptstyle \frac{({R}_{2}^{\prime}-{R}_{2})+({R}_{2}^{\prime}+{R}_{2})}{2}}$$

(16)

To sample the posterior probability density of *r*, the activation CMRO_{2} value normalized to the baseline CMRO_{2} value, we used a simple algorithm we designed to efficiently gather samples while fully exploring the parameter space. For this work, we wished to isolate uncertainty in the CMRO_{2} estimate stemming from two sources: 1) uncertainty in the measured values due to measurement error and response variability across the population sample; and 2) uncertainty due to unknown values of underlying physiological variables in the model. For this reason, we considered two cases in the analysis: “absolute” uncertainty, which includes contributions from both measurement uncertainty and physiological uncertainty (case 1); and “intrinsic” uncertainty due just to the physiological uncertainty (case 2). Our approach was as follows:

- We first chose a statistical model for each measurement
*y*(e.g._{i}*f*,*ΔR*,_{2}**R*,_{2}′*Y*). In order to assess the uncertainty attributable to variance in the measurements across the sample population, we assumed a simple model, that each per subject measurement ${y}_{i}^{j}$ comes from a Gaussian distribution of unknown mean_{a}*μ*and variance ${\sigma}_{i}^{2}$, and that each measurement is independent and identically distributed. To isolate the intrinsic uncertainty due to uncertainty in the unmeasured model parameters alone, we assumed that the sample mean for each measurement is identical to the population mean._{i} - Because the population variance of the measurements,
*σ*^{2}, was not a parameter of interest, we next marginalized the joint posterior probability distribution by integrating over*σ*^{2}.$$p(\mathit{\xi},\mathit{\mu}\mid \mathit{y})\propto {\int}_{{\sigma}_{1}^{2}}\dots {\int}_{{\sigma}_{1}^{2}}p(\mathit{\xi})p(\mathit{\mu})p({\mathit{\sigma}}^{2})p(\mathit{y}\mid \mathit{\xi},\mathit{\mu},{\mathit{\sigma}}^{2})d{\sigma}_{1}^{2}\dots d{\sigma}_{i}^{2}$$(17)Because the likelihood function*p*(*y*|_{i},*ξ*,*μ**σ*) depends only on^{2}*μ*and ${\sigma}_{i}^{2}$, Equation 17 may be rewritten as_{i}$$p(\mathit{\xi},\mathit{\mu}\mid \mathit{y})\propto p(\mathit{\xi}){\prod}_{i}{\int}_{{\sigma}_{i}^{2}}p({\mu}_{i})p({\sigma}_{i}^{2})p({y}_{i}\mid {\mu}_{i},{\sigma}_{i}^{2})d{\sigma}_{i}^{2}\propto p(\mathit{\xi}){\prod}_{i}p({\mu}_{i}\mid {y}_{i})$$(18) - For the Gaussian statistical model, assuming the non-informative prior $p({\mu}_{i},{\sigma}_{i}^{2})\propto {\scriptstyle \frac{1}{{\sigma}_{i}^{2}}}$, the marginal posterior probability function
*p*(*μ*|_{i}*y*) has the form of a_{i}*t*-distribution (Gelman et al., 2014)$${\scriptstyle \frac{{\mu}_{i}-\overline{{y}_{\iota}}}{{s}_{i}/\sqrt{n}}}|{y}_{i}~{t}_{n-1}$$(19)where $\overline{{y}_{\iota}}$ and*s*denote the sample mean and standard deviation of measurement_{i}*i*and*n*is the number of samples. In the case in which measurement variance is ignored, the parameters inare irrelevant, and marginal posterior probability function for μ*σ*^{2}_{i}can be written$$p({\mu}_{i}\mid {y}_{i})\propto \{\begin{array}{ll}1\hfill & {\mu}_{i}=\overline{{y}_{\iota}}\hfill \\ 0\hfill & {\mu}_{i}\ne \overline{{y}_{\iota}}\hfill \end{array}$$(20) - To construct samples of the posterior distribution,
*p*(,*ξ*|*μ*), we drew random samples from the prior distributions*y**p*() and marginal posterior distributions*ξ**p*(|*μ*) such that for each set of samples, the forward model would generate the sampled population means of*y**R*and_{2}′*ΔR*. To do this we first drew random samples from the prior distributions,_{2}**p*(*ξ*), of each of the unmeasured physiological variables with the exceptions of OEF_{i}_{0}and OEF_{stim}. The prior distribution used for each variable inwas uniform (i.e. equal probability density) within a finite range of values (see Table 1), which we denote as*ξ**p*(*ξ*)~U(_{i}*ξ*,_{i,a}*ξ*) where ξ_{i,b}_{i,a}is the lowest non-zero probability value of parameter ξ_{i}and ξ_{i,b}is the highest non-zero probability value. - We then drew random samples of
*μ*from_{i}*p*(*μ*|_{i}*y*) for each measurement used in the estimation process._{i} - If no calibration data was used in the estimation process (either from measuring R
_{2}′ or from measuring the CBF and R_{2}***responses to CO_{2}), then*OEF*was simply drawn from the prior distribution_{0}*p(OEF*. If calibration data was used, then the value of_{0})*OEF*was fit such that the forward model for R_{0}_{2}′ or the forward model for the ΔR_{2}* response to CO_{2}would produce the sampled value of ${\mu}_{{R}_{2}^{\prime}}$ or ${\mu}_{\mathrm{\Delta}{R}_{2,{CO}_{2}}^{\ast}}$, respectively, depending upon the chosen calibration experiment. - After sampling or fitting for
*OEF*, the parameter_{0}*OEF*was fit such that the forward model of the ΔR_{stim}_{2}* response to the stimulus of interest would produce the sampled value of ${\mu}_{\mathrm{\Delta}{R}_{2,\mathit{stim}}^{\ast}}$. - Because
*p(OEF*and_{0})*p(OEF*were uniform, if the fit values of_{stim})*OEF*and_{0}*OEF*were within the supported domains of their prior distributions, the sample was accepted, and the value of_{stim}*r*was calculated for that sample using Equation 11. Otherwise the sample was rejected. - Steps 4–7 were repeated until sufficient samples were obtained. Samples were processed in batches of 1000. After each batch was processed, half of the complete sample set was randomly and repeatedly resampled. The 95% central interval was calculated for each partial sample, and sufficient samples were assumed to have been collected when the upper and lower bounds of the 95% central intervals from the partial data sets achieved variances of less than 1%.

Across subjects average measured baseline apparent R_{2}′ was 3.94+/−0.64s^{−1} using the standard GESSE protocol and 3.05+/−0.41s^{−1} using the FLAIR GESSE protocol (mean +/− std). Average CBF responses to CO_{2} and to the visual stimulus, with respect to baseline, were 24+/−5% and 69+/−16%, respectively. The average ΔR_{2}* responses to CO_{2} and the visual stimulus were −0.63+/−0.16s^{−1} and −0.74+/−0.17s^{−1}, respectively. The average arterial oxygen saturation (*Y _{a}*) was 0.99+/−0.01. Responses for individual subjects may be seen in Table 2.

Quantitative estimation of the CMRO_{2} response typically involves a calibration experiment, which is designed to capture characteristics of the baseline state that affect the magnitude of the BOLD response associated with a given change in CBF and CMRO_{2}. Our first question was what could be determined about the magnitude of the CMRO_{2} response, given our prior uncertainty about the unmeasured variables in our model, without such a calibration experiment. Figure 3 shows the posterior probability distributions of the CMRO_{2} responses to (a) CO_{2} and (b) the visual stimulus with and without consideration of measurement noise. The shaded bars represent 95% central intervals for each estimate. Even without the effect of measurement uncertainty, little may be concluded about the magnitude of the CMRO_{2} response without additional information. To the CO_{2} stimulus, the estimated responses were −1.5% [−62 – 10%] (median [95% CI]) and −1.2% [−62 – 8.6%], accounting for and ignoring measurement uncertainty, respectively. To the visual stimulus, the estimated responses were 22% [−51 – 44%] and 22% [−50 – 39%].

We next asked how much our estimate of the CMRO_{2} response would be improved by using a baseline measurement of the apparent R_{2}′ to calibrate the BOLD response to each stimulus. Figure 4 shows the uncertainty associated with estimating the CMRO_{2} response based on R_{2}′ calibration. Compared with no calibration, R_{2}′ calibration greatly decreased uncertainty in the estimate of the CMRO_{2} response. Using the FLAIR preparation to suppress CSF contamination of the signal further reduced the uncertainty in the estimate. The estimated response to the CO_{2} stimulus, accounting for measurement noise, was 1.4% [−7.6 – 9.1%] (median [95% CI]) for the FLAIR GESSE estimate and 1.0% [−23 – 10%] for the standard GESSE estimate. The estimated response to the visual stimulus was 27% [9.9 – 43%] for the FLAIR GESSE estimate and 25% [−15 – 43%] for the standard GESSE estimate. Accounting only for intrinsic uncertainty, the estimated response to the CO_{2} stimulus was 1.5% [−2.5 – 5.3%] for the FLAIR GESSE estimate and 1.9% [−22 – 7.0%] for the standard GESSE estimate. The estimated response to the visual stimulus was 27% [19 – 34%] for the FLAIR GESSE estimate and 27% [−15 – 37%] for the standard GESSE estimate.

Often, the CMRO_{2} response to a stimulus of interest is calibrated by measuring the CBF and R_{2}* changes that result from breathing air containing elevated levels of CO_{2}, under the assumption that it does not produce a change in CMRO_{2} (Barzilay et al., 1985; Chen and Pike, 2010; Davis et al., 1998; Mark et al., 2011; Sicard and Duong, 2005). However, this assumption remains controversial and some studies have shown either increases (Horvath et al., 1994; Yang and Krasney, 1995) or decreases (Xu et al., 2011; Zappe et al., 2008). As we reported above, our estimates of the CO_{2} response based on apparent R_{2}′ are consistent with CO_{2} having a negligible effect on CMRO_{2}, albeit with some uncertainty. As such we asked what the uncertainty in our estimate of the CMRO_{2} response to a visual stimulus would be if we either assumed that the CMRO_{2} response to CO_{2} was negligible or assigned to it a modest prior uncertainty (*p(r _{CO2}~U(0.95,1.05)*) and used it to calibrate the response to the visual stimulus instead of using the baseline R

Figure 5 displays the posterior uncertainty of the CMRO_{2} response to the visual stimulus under these conditions. When it was assumed that the CMRO_{2} response to CO_{2} was negligible, CO_{2} calibration significantly reduced the uncertainty in the estimate of the response to the visual stimulus. Accounting for measurement uncertainty, the response was estimated to be 24% [5.6 – 36%] and ignoring measurement uncertainty, 25% [22 – 27%]. However, even a small amount of uncertainty in the CO_{2} response produced considerable uncertainty in the estimate of the response to the visual stimulus. Accounting for measurement uncertainty, the response was estimated to be 24% [1.8 – 37%], and ignoring measurement uncertainty, 24% [16 – 33%].

In this work we developed a novel Bayesian approach to estimating the CMRO_{2} response to a neural stimulus based on calibrated BOLD data and used it to examine the uncertainty that arises in estimates of the CMRO_{2} response when the values of unmeasured physiological model parameters are not precisely known. We examined estimates calibrated by a traditional hypercapnia experiment, in which the measured changes in CBF and R_{2}* in response to breathing elevated levels of CO_{2} are used to obtain information about baseline deoxyhemoglobin, as well as estimates calibrated by the more novel technique of measuring baseline apparent R_{2}′. In order to minimize the effect of multi-exponential T_{2} decay on the estimate of R_{2}′, we employed a novel measurement approach using two GESSE imaging sequences with different spin-echo times. Further, in order to examine the effects of CSF-contamination on the measurement of apparent R_{2}′, we measured this parameter with and without a CSF-nulling preparation pulse. We found that the two calibration approaches provided highly comparable CMRO_{2} response estimates on average. However, we found that while uncertainty due to measurement variance was a significant source of uncertainty in our estimates, likely due to the small sample size of the study, we also found that prior uncertainty in the unmeasured model parameters produced considerable intrinsic uncertainty in our estimates, and that the magnitude of this uncertainty depended upon the choice of calibration experiment.

As originally envisioned, the calibration experiment was designed to capture information about the quantity of deoxyhemoglobin (approximately the product of hematocrit, venous blood volume, and oxygen extraction fraction) in a voxel in the baseline state, a quantity determined in theoretical work to strongly influence the magnitude of the R_{2}* (BOLD) response to a given change in CBF and CMRO_{2} (Davis et al., 1998). In both theoretical and experimental work, the apparent spin echo-recoverable transverse relaxation rate, R_{2}′, has been found to reflect this baseline deoxyhemoglobin state, making it a potentially valuable calibration metric (Blockley et al., 2012; Fujita et al., 2006; Kida et al., 2000; Yablonskiy, 1998). We found that measuring baseline apparent R_{2}′ did significantly reduce the uncertainty associated with the CMRO_{2} estimate, compared with that of a calibration-free estimate, but that several unmeasured model parameters contributed significantly to the intrinsic uncertainty associated with the measurement.

The largest source of this uncertainty in our analysis was associated with the potential for CSF contamination of a nominally gray matter imaging volume in the R_{2}′ experiment, which in this model could produce spin-echo recoverable signal loss. Figure 6 illustrates the how CSF partial volume produces estimation uncertainty. Figures 6a and 6b display simulations of apparent R_{2}′ as a function of CSF fractional volume and resonance frequency offset for an otherwise fixed set of model parameters. Figure 6a displays simulations associated with a standard GESSE protocol, while Figure 6b displays simulations associated with a protocol optimized to minimize the CSF signal. In this simulation, even a very small (<0.05) CSF fraction could bias the measurement of R_{2}′ by as much as 50% using the standard approach. Suppression of the CSF signal minimized this bias. Figure 6c displays simulations of apparent ΔR_{2}* for an iso-metabolic 50% increase in CBF. CSF volume and off-resonance also affected the value of ΔR_{2}* in this simulation; however, the effect size was on the order of a few percent, orders of magnitude smaller than the R_{2}′ effect. Because the measurement bias produced by CSF contamination is greater for R_{2}′ than for ΔR_{2}*, it may cause one to overestimate the CMRO_{2} response if it is not accounted for. If the size and off resonance frequency of this compartment are unknown, then attempting to account for them through a prior distribution introduces uncertainty into the CMRO_{2} estimate. Figures 6d and 6e show how uncertainty in CSF volume and off-resonance create uncertainty in the estimated CMRO_{2} response to the CO_{2} stimulus when R_{2}′ is measured without or with CSF suppression, respectively. While these parameters strongly influence the estimate based on the standard GESSE measurement, they have negligible influence on the FLAIR GESSE estimate. Figure 6f shows the probability distributions associated with standard or FLAIR GESSE derived estimates of the CMRO_{2} response to CO_{2} if, instead of defining a finite prior uncertainty on *V _{e}* and

Even after suppression of CSF contamination, the intrinsic uncertainty associated with R_{2′}′ calibration is not negligible. This is because while R_{2}′ and ΔR_{2}* are similarly sensitive to variation in the baseline hematocrit, oxygenation and volume of the venous compartment (the drivers of the first-order BOLD effect) they are disparately sensitive to variation in several other unmeasured model parameters. The parameters for which this is particularly problematic are the blood-tissue iso-susceptibilty parameter *Y _{off}*, the flow-volume coupling parameters (e.g.

The effects of *κ* and *a* on the estimate of CMRO_{2} are more subtle. Both parameters scale the magnitude of the effect the capillary compartment has on extravascular signal decay, the first by determining the oxygen saturation of the capillary vessels, the second by defining the characteristic size of the capillary vessels. As capillary oxygen saturation drops and size increases, the rate of extravascular signal decay produced by those vessels is increased. Some of this decay is refocused by a spin echo, and is thus captured by the measurement of R_{2}′. However, some of this decay is not refocused, and may be thought of as more R_{2}-like decay. As a result of the increase in R_{2} decay, the ΔR_{2}* produced by a given set of model parameters increases more with increases in *κ* and *a* than does R_{2}′. The result is that if *κ* and *a* are assumed to be larger, the estimated CMRO_{2} response also will be larger (Figure 8).

In this work, we suggested that we could reduce the uncertainty associated with CSF contamination by adding a FLAIR preparation to the GESSE imaging sequence, and it is important to consider whether this FLAIR preparation achieved its intended purpose. While it is difficult to directly measure the effect of CSF contamination on signal decay, the measurements we made of R_{2}′ with and without CSF-nulling were consistent with our imaging volume containing a CSF compartment of similar size and off-resonance frequency as measured previously (Dickson et al., 2011; He and Yablonskiy, 2006). Further, while a direct measurement of the effect size of CSF contamination on R_{2}′ estimation has not been previously reported, a first-order comparison of other recent R_{2}′ estimates with our own suggests some consistency in effect size across studies and imaging methods. For example, in a 2006 study at 1.5T, Fujita et al. measured baseline apparent R_{2}′ in the visual cortex using a gradient echo sampling of free induction decay and echo (GESFIDE) sequence without CSF-nulling (Fujita et al., 2006), calculating an average apparent R_{2}′ of 2.48s^{−1} across subjects. Because to a first order approximation, apparent R_{2}′ is expected to be proportional to magnetic field strength (Yablonskiy, 1998), this would equate to an R_{2}′ of ~5s^{−1} at 3T, the field strength in this study. In this study we measured an average apparent R_{2}′ of ~4s^{−1} without and ~3s^{−1} with CSF-nulling. The relatively high numbers reported by Fujita et al. compared with our own are consistent with the hypothesis that CSF contributes to R_{2}′*-*like decay, with remaining quantitative discrepancies possibly explained by differences in the pulse sequences used to measure apparent R_{2}′. Similarly, in a recent study using asymmetrical spin echo (ASE) to measure R_{2}′ without CSF suppression our group found an average R_{2}′ of ~3s^{−1} (Blockley et al., 2015). Again, accounting for differences in the methodologies used to estimate apparent R_{2}′ this estimate is consistent with the CSF-contaminated R_{2}′ estimate in this work (in our simulations ASE estimates of R_{2}′ are approximately ~1s^{−1} lower than those made using our current dual-GESSE technique due to the effect of approximately quadratic exponential signal decay near the spin echo (Yablonskiy, 1998) – data not shown).

It is possible that some of the difference in R_{2}′ that was observed between the GESSE and FLAIR GESSE-based measurements is attributable not to CSF contamination, but to white matter contamination. White matter has a T_{1} of ~800ms, and thus has increased T_{1} weighting in the FLAIR GESSE images vs. the GESSE images (1.56 vs. 1.13 relative to gray matter based on Equation 10) (Lu et al., 2005; Wansapura et al., 1999). Because blood volume is significantly lower in white matter than gray matter, significant white matter contamination of a nominally gray matter voxel will decrease the apparent R_{2}′, and this effect should be magnified in the FLAIR GESSE images relative to the GESSE images. We considered the effect size that white matter contamination could have on the measurement of R_{2}′ and ΔR_{2}*, as well as the uncertainty associated with estimating the CMRO_{2} response, in order to determine whether a white matter compartment of uncertain volume needed to be included in our model. Inline Supplemental Figure 4 displays the difference between simulated R_{2}′ measurements for GESSE AND FLAIR GESSE-based measurements as a function of increasing white matter contamination. In these simulations, significant white matter contamination explained a small portion of the observed difference in apparent R_{2}′ between GESSE and FLAIR GESSE measurements, but concomitant CSF contamination was required to fully explain the observed difference. Further, because white matter contamination affects ΔR_{2}* measurements similarly to R_{2}′ measurements, it is less likely to contribute strongly to uncertainty in the CMRO_{2} response (Inline Supplemental Figure 4).

These findings lend support to the idea that CSF partial-volume effects have an effect on signal decay that is reasonably well-approximated by the model proposed in (He and Yablonskiy, 2006), which was adopted here, and suggest that CSF-suppression should be included in protocols designed to measure R_{2}′. However, it will be important in the future to consider whether the highly simplified CSF compartment model adopted here and in previous work is sufficient to describe the range of effects such a compartment could have on the MR signal.

Breathing air containing elevated concentrations of CO_{2} was the original technique proposed for calibrating BOLD studies and is still the most commonly used today. Though performing this calibration experiment is challenging and may be contraindicated in some patient populations, we found here that it has the advantage of being much less susceptible to the sources of uncertainty that affect R_{2}′ calibration, likely because variation in the unmeasured parameters of the model affects the measurement of apparent ΔR_{2}* similarly in both the calibration and activation experiment. We did find, however, that this technique is highly sensitive to the assumption that the response to CO_{2} is iso-metabolic, such that even slight prior uncertainty in this response eliminates its advantage over R_{2}′. This could be important to an investigator interested in measuring the CMRO_{2} response to a neural stimulus in a population that could be metabolically sensitive to CO_{2} or who is interested in the response to CO_{2} itself.

In this study we found the median estimates of the CMRO_{2} response to the visual stimulus based on R_{2}′ and CO_{2} calibration to be highly comparable (26% and 24%, respectively). Similarly we found the median R_{2}′-calibrated estimate of the CMRO_{2} response to CO_{2} (~1.5%) to be consistent with the assumption that the CO_{2} response is approximately iso-metabolic. This is encouraging because it suggests that these two calibration techniques, at least on average, provide comparable calibration and thus have the potential to be used interchangeably based on the experimental needs of the investigator.

Interestingly, while the intrinsic uncertainty associated with hypercapnia calibration (taking the iso-metabolic assumption to be valid) was found to be significantly lower than the intrinsic uncertainty associated with R_{2}′ calibration, the absolute uncertainty of the two estimates was highly comparable in this study. To get an idea of how many subjects would be required before hypercapnia calibration would demonstrate a significant advantage over R_{2}′ calibration given the measurement variance and noise model employed in this study, we repeated the estimates of the CMRO_{2} response for each modality, assuming the same measurement variances that were found here but an increased sample size. Figure 9 shows simulated estimates of the median and 95% central interval for each approach as a function of increasing sample size. For R_{2}′ calibration, absolute uncertainty became dominated by intrinsic uncertainty for samples greater than approximately 24 subjects, while for hypercapnia, uncertainty continued to decrease for larger samples. This suggests that hypercapnia calibration may demonstrate more significant advantages over R_{2}′ calibration in studies with large cohorts, provided that the iso-metabolic assumption is valid given the experimental conditions.

There are several limitations to this study. First, as we have acknowledged above, while we have made an effort here to incorporate into our model of blood oxygenation sensitive signal decay parameters that capture the most salient features of a realistic imaging volume, including multiple intravascular compartments, an extravascular parenchymal compartment, and a contaminating CSF compartment, we have by necessity greatly reduced the complexity of a true vascular network. The decisions we made in this process have introduced an additional source of uncertainty into our estimates, uncertainty that is difficult to quantify without a gold standard for comparison. As efforts continue, for now in animal models, to better understand and describe the vascular structure and characteristics of brain tissue (Gagnon et al., 2015), resulting model improvements should be readily incorporable into the framework we have presented here.

Second, in choosing particular prior probability distributions for each of the parameters in this model, we have undoubtedly influenced the estimated posterior probability distribution of the CMRO_{2} response. In choosing prior distributions, we often had few reports from the literature with which to constrain our decisions, and so typically simply tried to make each distribution broad enough that it would encompass reported estimates by a wide margin. As such, we recognize that some might consider the prior constraints on some of the variables too tight and others too broad. In addition, some might consider it inappropriate to make the priors on each parameter independent, when it could be reasonable to assume that some, such as intravascular compartment volumes, are correlated. In this work, we are not advocating the use of these particular priors in future studies and would certainly expect that if another investigator had additional information to constrain one or more of them further, that she would do so. Rather we are describing an analysis framework within which an investigator may explicitly state her assumptions about each model parameter in terms of prior probability distributions and account for the uncertainty in her findings given those stated assumptions. In addition, we have identified several parameters of which prior uncertainty strongly influences posterior uncertainty and which therefore deserve focused study if suspected to vary systematically across different populations of interest. For example *Y _{off}* is dependent upon the concentration of non-heme iron both in blood and in brain tissue and thus could change significantly with aging (Zecca et al., 2004), while flow-volume coupling constants and capillary characteristics could be affected by vascular disease.

Third, as is the case with any statistical analysis, the model we have chosen to represent the uncertainty in our measurements influences the level of uncertainty in our estimates of the CMRO_{2} response. Because we did not make sufficient independent measurements at the individual subject level to confidently estimate measurement variance, we chose to assume that the variance in measurements across subjects was attributable to measurement error with a distribution that was Gaussian and independent across measurements. This may prove to be a somewhat conservative approach to modeling this variability, as it is likely that some of the variance across measurements is correlated (e.g. subjects with a large CBF response also have a large BOLD response) and that accounting for this correlation would reduce the uncertainty in our final estimates. Given enough repeated and independent measurements at the individual subject level to estimate measurement error, a more optimal approach might be to apply the approach described here to the analysis of each individual subject and then to combine the resulting posterior probability distributions within a hierarchical model to determine the group posterior probability distribution. Such an approach would, of course, require additional consideration of how to treat the prior uncertainty of the unmeasured parameters, for example whether a given parameter should be assumed to have an uncertain but constant value across the experimental population, or whether it should be assumed to vary across the group. We are investigating the effects of such assumptions in an upcoming study, but felt that such an investigation was beyond the scope of this present work, which was primarily to investigate the intrinsic sources of uncertainty in estimates of the CMRO_{2} response.

In order to examine the sources of uncertainty in our estimate of the CMRO_{2} response, we developed a detailed model that explicitly takes into account what we believe to be the salient physiological parameters of the BOLD response. The model itself is not particularly novel, as it is built from the collected work of many previous investigators. However, our application of such a detailed model to the analysis of experimental data, instead of a more heuristic model such as the Davis model or Griffeth model (Davis et al., 1998; Griffeth et al., 2013), is, to our knowledge, unique to the calibrated BOLD literature. There are both advantages and disadvantages to this approach. We found the chief disadvantage to be the computational time required to invert the model in order to estimate the CMRO_{2} response from the BOLD and CBF measurements, which is trivial with a model such as the Davis model. Sampling the posterior distribution of the CMRO_{2} response, which we implemented in MATLAB, took between 15 minutes and an hour depending on the calibration experiment used and the number of samples needed to stabilize the estimate of the 95% central interval. Improvements in computational time are very likely obtainable with more a efficient sampling algorithm; however, for investigators interested in making voxel-wise estimates, time costs could prove to be an important consideration.

However, this approach also offers several important advantages. First, as we have discussed at length here, it allows an investigator to explicitly state her assumptions about the parameters of the model, incorporate any experimental information she deems appropriate to constrain these parameters, and state her uncertainty about her conclusions explicitly in terms of the assumptions she has made and the measurements she has acquired. Second, the more flexible framework of the detailed model makes it possible to analyze experimental data that cannot be easily handled by a more heuristic model. For example, the Davis model considers only the effects of a single venous-like compartment on signal decay, implicitly assuming that more saturated arterial blood does not contribute significantly to the BOLD response. This is not an unreasonable assumption in a population of young, healthy subjects whose arterial blood is near the iso-susceptibility oxygen saturation (*Y _{off}*). However, it is unclear how this model would accommodate a population of hypoxemic subjects, whose arterial blood could contribute significantly to the BOLD response. Investigators interested in studying subjects with cardiovascular or pulmonary disease, or who are interested in the effects of altitude on CMRO

Third, this approach allows the relatively simple incorporation of many sources of data that are challenging to integrate into existing heuristic models. For example, an investigator could measure each subject’s hematocrit and integrate this information directly into the model if it were thought to vary systematically across populations of interest. Alternatively, an investigator could employ one of several recently developed techniques (e.g. TRUST, VSEAN, QUIXOTIC, PROM) to directly measure baseline venous oxygen saturation in order to further constrain the estimate of baseline OEF (Bolar et al., 2011; Fan et al., 2012; Guo and Wong, 2012; Lu and Ge, 2008).

The need to use biophysical models with unmeasured parameters in order to estimate the CMRO_{2} response to a neural stimulus from a calibrated BOLD experiment introduces uncertainty into the estimated response. We have described here an approach to accounting for this uncertainty and examined the principal sources of uncertainty associated with two promising methods of calibration, measurement of baseline apparent R_{2}′ and measurement of the CBF and *R _{2}** responses to CO

- New method of accounting for uncertainty in fMRI-based estimates of CMRO
_{2}activity - Identifies key sources of uncertainty in hypercapnia- and R
_{2}′-calibrated BOLD - Adaptation of R
_{2}′ estimation technique increases precision of gasless calibration

Click here to view.^{(209K, eps)}

Click here to view.^{(49K, eps)}

Click here to view.^{(1.4M, eps)}

We would like to thank Zachary Smith for his assistance with performing the hypercapnia experiments for this project. This work was supported by NIH grants NS036722, NS085478, NS081405, NS053934, NS075812 and EB000790.

**Publisher's Disclaimer: **This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

- Bandettini PA, Wong EC, Hinks RS, Tikofsky RS, Hyde JS. Time course EPI of human brain function during task activation. Magn Reson Med. 1992;25:390–397. [PubMed]
- Barzilay Z, Britten AG, Koehler RC, Dean JM, Traystman RJ. Interaction of CO2 and ammonia on cerebral blood flow and O2 consumption in dogs. Am J Physiol. 1985;248:H500–7. [PubMed]
- Blockley NP, Griffeth VEM, Buxton RB. A general analysis of calibrated BOLD methodology for measuring CMRO2 responses: Comparison of a new approach with existing methods. NeuroImage. 2012;60:279–289. doi: 10.1016/j.neuroimage.2011.11.081. [PMC free article] [PubMed] [Cross Ref]
- Blockley NP, Griffeth VEM, Simon AB, Dubowitz DJ, Buxton RB. Calibrating the BOLD response without administering gases: comparison of hypercapnia calibration with calibration using an asymmetric spin echo. NeuroImage. 2015;104:423–429. doi: 10.1016/j.neuroimage.2014.09.061. [PMC free article] [PubMed] [Cross Ref]
- Bolar DS, Rosen BR, Sorensen AG, Adalsteinsson E. QUantitative Imaging of eXtraction of oxygen and TIssue consumption (QUIXOTIC) using venular-targeted velocity-selective spin labeling. Magn Reson Med. 2011;66:1550–1562. doi: 10.1002/mrm.22946. [PMC free article] [PubMed] [Cross Ref]
- Boynton GM, Engel SA, Glover GH, Heeger DJ. Linear systems analysis of functional magnetic resonance imaging in human V1. J Neurosci. 1996;16:4207–4221. [PubMed]
- Buxton RB. The physics of functional magnetic resonance imaging (fMRI) Rep Prog Phys. 2013;76:096601. doi: 10.1088/0034-4885/76/9/096601. [PMC free article] [PubMed] [Cross Ref]
- Buxton RB, Griffeth VEM, Simon AB, Moradi F. Variability of the coupling of blood flow and oxygen metabolism responses in the brain: a problem for interpreting BOLD studies but potentially a new window on the underlying neural activity. Frontiers in Neuroscience. 2014:8. doi: 10.3389/fnins.2014.00139. [PMC free article] [PubMed] [Cross Ref]
- Chalela JA, Alsop DC, Gonzalez-Atavales JB, Maldjian JA, Kasner SE, Detre JA. Magnetic resonance perfusion imaging in acute ischemic stroke using continuous arterial spin labeling. Stroke. 2000;31:680–687. [PubMed]
- Chen JJ, Pike GB. BOLD-specific cerebral blood volume and blood flow changes during neuronal activation in humans. NMR Biomed. 2009:n/a–n/a. doi: 10.1002/nbm.1411. [PubMed] [Cross Ref]
- Chen JJ, Pike GB. Global cerebral oxidative metabolism during hypercapnia and hypocapnia in humans: implications for BOLD fMRI. Journal of Cerebral Blood Flow & Metabolism. 2010;30:1094–1099. doi: 10.1038/jcbfm.2010.42. [PMC free article] [PubMed] [Cross Ref]
- Cox RW. AFNI: software for analysis and visualization of functional magnetic resonance neuroimages. Comput Biomed Res. 1996;29:162–173. [PubMed]
- Davis TL, Kwong KK, Weisskoff RM, Rosen BR. Calibrated functional MRI: mapping the dynamics of oxidative metabolism. Proc Natl Acad Sci USA. 1998;95:1834–1839. [PubMed]
- Detre JA, Leigh JS, Williams DS, Koretsky AP. Perfusion imaging. Magn Reson Med. 1992;23:37–45. [PubMed]
- Dickson JD, Ash TWJ, Williams GB, Harding SG, Carpenter TA, Menon DK, Ansorge RE. Quantitative BOLD: The effect of diffusion. J Magn Reson Imaging. 2010;32:953–961. doi: 10.1002/jmri.22151. [PubMed] [Cross Ref]
- Dickson JD, Ash TWJ, Williams GB, Sukstanskii AL, Ansorge RE, Yablonskiy DA. Quantitative phenomenological model of the BOLD contrast mechanism. Journal of Magnetic Resonance. 2011;212:17–25. doi: 10.1016/j.jmr.2011.06.003. [PubMed] [Cross Ref]
- Fan AP, Benner T, Bolar DS, Rosen BR, Adalsteinsson E. Phase-based regional oxygen metabolism (PROM) using MRI. Magn Reson Med. 2012;67:669–678. doi: 10.1002/mrm.23050. [PMC free article] [PubMed] [Cross Ref]
- Fujita N, Matsumoto K, Tanaka H, Watanabe Y, Murase K. Quantitative study of changes in oxidative metabolism during visual stimulation using absolute relaxation rates. NMR Biomed. 2006;19:60–68. doi: 10.1002/nbm.1001. [PubMed] [Cross Ref]
- Gagnon L, Sakadzic S, Lesage F. Quantifying the microvascular origin of BOLD-fMRI from first principles with two-photon microscopy and an oxygen-sensitive nanoprobe. … of Neuroscience 2015 [PMC free article] [PubMed]
- Gelman A, Carlin JB, Stern HS, Dunson DB, Vehetari A, Rubin DB. Bayesian Data Analysis. 3. CRC Press; Boca Raton: 2014.
- Glover GH, Li TQ, Ress D. Image-based method for retrospective correction of physiological motion effects in fMRI: RETROICOR. Magn Reson Med. 2000;44:162–167. [PubMed]
- Griffeth VEM, Blockley NP, Simon AB, Buxton RB. A New Functional MRI Approach for Investigating Modulations of Brain Oxygen Metabolism. PLoS ONE. 2013;8:e68122. doi: 10.1371/journal.pone.0068122. [PMC free article] [PubMed] [Cross Ref]
- Griffeth VEM, Buxton RB. A theoretical framework for estimating cerebral oxygen metabolism changes using the calibrated-BOLD method: Modeling the effects of blood volume distribution, hematocrit, oxygen extraction fraction, and tissue signal properties on the BOLD signal. NeuroImage. 2011;58:198–212. doi: 10.1016/j.neuroimage.2011.05.077. [PMC free article] [PubMed] [Cross Ref]
- Grubb RL, Raichle ME, Eichling JO, Ter-Pogossian MM. The effects of changes in PaCO2 on cerebral blood volume, blood flow, and vascular mean transit time. Stroke. 1974;5:630–639. [PubMed]
- Guo J, Wong EC. Venous oxygenation mapping using velocity-selective excitation and arterial nulling. Magn Reson Med. 2012;68:1458–1471. doi: 10.1002/mrm.24145. [PMC free article] [PubMed] [Cross Ref]
- Haynes WM, editor. CRC Handbook of Chemistry and Physics. 94. CRC Press/Taylor and Francis; Boca Raton, FL: 2014. Internet Version 2014.
- He X, Yablonskiy DA. Quantitative BOLD: Mapping of human cerebral deoxygenated blood volume and oxygen extraction fraction: Default state. Magn Reson Med. 2006;57:115–126. doi: 10.1002/mrm.21108. [PMC free article] [PubMed] [Cross Ref]
- He X, Yablonskiy DA. Biophysical mechanisms of phase contrast in gradient echo MRI. Proc Natl Acad Sci USA. 2009;106:13558–13563. doi: 10.1073/pnas.0904899106. [PubMed] [Cross Ref]
- Horvath I, Sandor NT, Ruttner Z, McLaughlin AC. Role of nitric oxide in regulating cerebrocortical oxygen consumption and blood flow during hypercapnia. Journal of Cerebral Blood Flow & Metabolism. 1994;14:503–509. doi: 10.1038/jcbfm.1994.62. [PubMed] [Cross Ref]
- Kida I, Kennan RP, Rothman DL, Behar KL, Hyder F. High-Resolution CMRO2 Mapping in Rat Cortex: A Multiparametric Approach to Calibration of BOLD Image Contrast at 7 Tesla. Journal of Cerebral Blood Flow & Metabolism. 2000;20:847–860. doi: 10.1097/00004647-200005000-00012. [PubMed] [Cross Ref]
- Lin C, Bernstein M, Huston J, Fain S. Measurements of T1 Relaxation times at 3.0T: Implications for clinical MRA. Proceedings of the 9th Annual Meeting of ISMRM; Glasgow. 2001; 2001. p. 1391.
- Liu TT, Wong EC. A signal processing model for arterial spin labeling functional MRI. NeuroImage. 2005;24:207–215. doi: 10.1016/j.neuroimage.2004.09.047. [PubMed] [Cross Ref]
- Lu H, Clingman C, Golay X, van Zijl PCM. Determining the longitudinal relaxation time (T1) of blood at 3.0 Tesla. Magn Reson Med. 2004;52:679–682. doi: 10.1002/mrm.20178. [PubMed] [Cross Ref]
- Lu H, Ge Y. Quantitative evaluation of oxygenation in venous vessels using T2-Relaxation-Under-Spin-Tagging MRI. Magn Reson Med. 2008;60:357–363. doi: 10.1002/mrm.21627. [PMC free article] [PubMed] [Cross Ref]
- Lu H, Nagae-Poetscher LM, Golay X, Lin D, Pomper M, van Zijl PCM. Routine clinical brain MRI sequences for use at 3.0 Tesla. J Magn Reson Imaging. 2005;22:13–22. doi: 10.1002/jmri.20356. [PubMed] [Cross Ref]
- Mark CI, Fisher JA, Pike GB. Improved fMRI calibration: Precisely controlled hyperoxic versus hypercapnic stimuli. NeuroImage. 2011;54:1102–1111. doi: 10.1016/j.neuroimage.2010.08.070. [PubMed] [Cross Ref]
- Nicoll D, Lu C, Pignone M, McPhee SJ, editors. Pocket Guide to Diagnostic Tests. 6. McGraw-Hill; New York: 2012.
- Noll DC, Fessler JA, Sutton BP. Conjugate phase MRI reconstruction with spatially variant sample density correction. IEEE Trans Med Imaging. 2005;24:325–336. doi: 10.1109/TMI.2004.842452. [PubMed] [Cross Ref]
- Ogawa S, Menon RS, Tank DW, Kim SG, Merkle H, Ellermann JM, Ugurbil K. Functional brain mapping by blood oxygenation level-dependent contrast magnetic resonance imaging. A comparison of signal characteristics with a biophysical model. Biophys J. 1993;64:803–812. doi: 10.1016/S0006-3495(93)81441-3. [PubMed] [Cross Ref]
- Ogawa S, Tank DW, Menon R, Ellermann JM, Kim SG, Merkle H, Ugurbil K. Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging. Proc Natl Acad Sci USA. 1992;89:5951–5955. [PubMed]
- Pelli DG. The VideoToolbox software for visual psychophysics: transforming numbers into movies. Spat Vis. 1997;10:437–442. [PubMed]
- Perthen JE, Lansing AE, Liau J, Liu TT, Buxton RB. Caffeine-induced uncoupling of cerebral blood flow and oxygen metabolism: A calibrated BOLD fMRI study. NeuroImage. 2008;40:237–247. doi: 10.1016/j.neuroimage.2007.10.049. [PMC free article] [PubMed] [Cross Ref]
- Restom K, Behzadi Y, Liu TT. Physiological noise reduction for arterial spin labeling functional MRI. NeuroImage. 2006;31:1104–1115. doi: 10.1016/j.neuroimage.2006.01.026. [PubMed] [Cross Ref]
- Sakai F, Igarashi H, Suzuki S, Tazaki Y. Cerebral blood flow and cerebral hematocrit in patients with cerebral ischemia measured by single-photon emission computed tomography. Acta Neurol Scand, Suppl c. 1989;127:9–13. [PubMed]
- Sicard KM, Duong TQ. Effects of hypoxia, hyperoxia, and hypercapnia on baseline and stimulus-evoked BOLD, CBF, and CMRO2 in spontaneously breathing animals. NeuroImage. 2005;25:850–858. doi: 10.1016/j.neuroimage.2004.12.010. [PMC free article] [PubMed] [Cross Ref]
- Spees WM, Yablonskiy DA, Oswood MC, Ackerman JJ. Water proton MR properties of human blood at 1.5 Tesla: Magnetic susceptibility, T1, T2, T* 2, and non-Lorentzian signal behavior. Magn Reson Med. 2001;45:533–542. [PubMed]
- Stefanovic B, Hutchinson E, Yakovleva V, Schram V, Russell JT, Belluscio L, Koretsky AP, Silva AC. Functional reactivity of cerebral capillaries. Journal of Cerebral Blood Flow & Metabolism. 2008;28:961–972. doi: 10.1038/sj.jcbfm.9600590. [PMC free article] [PubMed] [Cross Ref]
- Uludağ K, Müller-Bierl B, Uğurbil K. An integrative model for neuronal activity-induced signal changes for gradient and spin echo functional imaging. NeuroImage. 2009;48:150–165. doi: 10.1016/j.neuroimage.2009.05.051. [PubMed] [Cross Ref]
- Wang J, Qiu M, Constable RT. In vivo method for correcting transmit/receive nonuniformities with phased array coils. Magn Reson Med. 2005;53:666–674. doi: 10.1002/mrm.20377. [PubMed] [Cross Ref]
- Wansapura JP, Holland SK, Dunn RS, Ball WS. NMR relaxation times in the human brain at 3.0 tesla. J Magn Reson Imaging. 1999;9:531–538. [PubMed]
- Wong EC, Buxton RB, Frank LR. Implementation of quantitative perfusion imaging techniques for functional brain mapping using pulsed arterial spin labeling. NMR Biomed. 1997;10:237–249. [PubMed]
- Wong EC, Buxton RB, Frank LR. Quantitative imaging of perfusion using a single subtraction (QUIPSS and QUIPSS II) Magn Reson Med. 1998;39:702–708. [PubMed]
- Xu F, Uh J, Brier MR, Hart J, Yezhuvath US, Gu H, Yang Y, Lu H. The influence of carbon dioxide on brain activity and metabolism in conscious humans. Journal of Cerebral Blood Flow & Metabolism. 2011;31:58–67. doi: 10.1038/jcbfm.2010.153. [PMC free article] [PubMed] [Cross Ref]
- Yablonskiy DA. Quantitation of intrinsic magnetic susceptibility-related effects in a tissue matrix. Phantom study. Magn Reson Med. 1998;39:417–428. [PubMed]
- Yablonskiy DA, Haacke EM. Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime. Magn Reson Med. 1994;32:749–763. [PubMed]
- Yablonskiy DA, Haacke EM. An MRI method for measuring T2 in the presence of static and RF magnetic field inhomogeneities. Magn Reson Med. 1997;37:872–876. [PubMed]
- Yang SP, Krasney JA. Cerebral blood flow and metabolic responses to sustained hypercapnia in awake sheep. Journal of Cerebral Blood Flow & Metabolism. 1995;15:115–123. doi: 10.1038/jcbfm.1995.13. [PubMed] [Cross Ref]
- Zappe AC, Uludağ K, Oeltermann A, Ugurbil K, Logothetis NK. The Influence of Moderate Hypercapnia on Neural Activity in the Anesthetized Nonhuman Primate. Cerebral Cortex. 2008;18:2666–2673. doi: 10.1093/cercor/bhn023. [PubMed] [Cross Ref]
- Zecca L, Youdim MBH, Riederer P, Connor JR, Crichton RR. Iron, brain ageing and neurodegenerative disorders. Nat Rev Neurosci. 2004;5:863–873. doi: 10.1038/nrn1537. [PubMed] [Cross Ref]
- Zhao JM, Clingman CS, Närväinen MJ, Kauppinen RA, van Zijl PCM. Oxygenation and hematocrit dependence of transverse relaxation rates of blood at 3T. Magn Reson Med. 2007;58:592–597. doi: 10.1002/mrm.21342. [PubMed] [Cross Ref]

PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers. |