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Neuroimage. Author manuscript; available in PMC 2013 July 16.

Published in final edited form as:

Published online 2012 April 23. doi: 10.1016/j.neuroimage.2012.04.036

PMCID: PMC3376222

NIHMSID: NIHMS372552

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

See other articles in PMC that cite the published article.

Multimodal imaging improves the accuracy of the localization and the quantification of brain activation when measuring different manifestations of the hemodynamic response associated with cerebral activity. In this study, we incorporated cerebral blood flow (CBF) changes measured with arterial spin labeling (ASL), Diffuse Optical Tomography (DOT) and blood oxygen level-dependent (BOLD) recordings to reconstruct changes in oxy- (ΔHbO_{2}) and deoxyhemoglobin (ΔHbR). Using the Grubb relation between relative changes in CBF and cerebral blood volume (CBV), we incorporated the ASL measurement as a prior to the total hemoglobin concentration change (ΔHbT). We applied this ASL fusion model to both synthetic data and experimental multimodal recordings during a 2-sec finger-tapping task. Our results show that the new approach is very powerful in estimating ΔHbO_{2} and ΔHbR with high spatial and quantitative accuracy. Moreover, our approach allows the computation of baseline total hemoglobin concentration (HbT_{0}) as well as of the BOLD calibration factor M on a single subject basis. We obtained an average HbT_{0} of 71 μM, an average M value of 0.18 and an average increase of 13 % in cerebral metabolic rate of oxygen (CMRO_{2}), all of which are in agreement with values previously reported in the literature. Our method yields an independent measurement of M, which provides an alternative measurement to validate the hypercapnic calibration of the BOLD signal.

Multimodal brain imaging aims to enhance the localization and the quantification of cerebral activity by combining the strengths of each individual modality (Moseley and Donnan, 2004). Moreover, multimodal imaging allows the study of cerebral activity with different physiological contrast, such as the electrical activity of the neurons and the related hemodynamic response. The relationship between these two phenomena is known as neurovascular coupling and has been studied extensively by combining electrophysiological recordings with hemodynamic measurements. Examples include functional Magnetic Resonance Imaging (fMRI) combined with intracortical recordings of neural signals (Logothetis et al., 2001), Intrinsic Optical Imaging with electrophysiological recording (Jones et al., 2005; Devor et al., 2003), Diffuse Optical Tomography (DOT) with electroencephalography (EEG) (Opitz et al., 1999; Kennan et al., 2002), and DOT with magnetoencephalography (MEG) (Ou et al., 2009).

Simultaneous measurements of functional magnetic resonance imaging (fMRI) and diffuse optical tomography (DOT) have been used in animals (Kida et al., 1996; D’Arceuil et al., 2005) and in humans (Kleinschmidt et al., 1994; Toronov et al., 2001; Strangman et al., 2002; Steinbrick et al., 2006; Tak et al., 2010) to study the normal functioning brain, as well as to investigate pathophysiology (Tak et al., 2011). DOT and fMRI elegantly complement one another. On one hand, the hemodynamic response is reconstructed with higher spatio-temporal resolution by combining the high temporal resolution of DOT with the high spatial resolution of fMRI. On the other, the ability of DOT to independently measure absolute changes in oxyhemoglobin (HbO_{2}) and deoxyhemoglobin (HbR) (and therefore absolute changes in total hemoglobin (HbT)) allows the computation of important physiological parameters (e.g., the BOLD calibration factor and relative changes in CMRO_{2}) more robustly than with fMRI alone (Hoge et al., 2005; Huppert et al., 2009; Tak et al., 2010).

Of the various multimodal approaches, bottom-up fusion models have been used extensively in the literature (Riera et al., 2005; Huppert et al., 2008, Huppert et al., 2009). Bottom-up modeling relates the spatio-temporal evolution of physiological parameters to the measurements through an observation model describing the biophysics of each modality. For DOT-fMRI fusions, these physiological parameters are the concentration of HbO_{2} and HbR. Huppert et al. (2008) successfully constructed such a model integrating DOT and blood oxygen level-dependent (BOLD) fMRI measurements. Their linear model reconstructed the hemoglobin changes in space and time and computed a numerical correspondence between relative changes in the BOLD signal at 3T and absolute changes in HbR. This method has two major limitations: (1) Although the method provides a robust reconstruction of HbR, the reconstructed HbO_{2} is subject to greater errors; and (2) due to the lack of baseline HbT concentration (HbT_{0}), the numerical correspondence between HbR and the BOLD changes cannot be compared against the traditional hypercapnia calibration factor M (Davis et al., 1998), and furthermore cannot be used to compute relative changes in the cerebral metabolic rate of oxygen (CMRO_{2}) from independent relative changes in BOLD and cerebral blood flow (CBF) measurements.

In this paper, we address these two drawbacks by adding an arterial spin labeling (ASL) fMRI CBF measurement to the fusion model. The CBF measurement constrains the reconstruction of the HbT image, thus informing the reconstruction of HbO_{2}. Moreover, measurements of absolute changes in HbT from DOT and relative changes in CBF from ASL enable the estimation of baseline total hemoglobin concentration (HbT_{0}) from a simple assumption of the flow-volume relationship (Grubb et al., 1974). The estimated HbT_{0} combined with simultaneous measurements of relative changes in the BOLD signal and absolute changes in HbR allows calibration of the BOLD signal (Davis et al., 1998) in a framework consistent with the hypercapnic calibration method but without the need for a hypercapnic challenge. Finally, the calibrated BOLD signal is used together with a separate measurement of CBF from ASL to compute relative changes in CMRO_{2} (Davis et al., 1998; Hoge et al., 1999; Buxton et al., 2010) during a motor task in human subjects.

We first quantify the accuracy of the method with numerical simulations over a realistic human head model obtained from anatomical MRI. Reconstructed hemoglobin concentrations from simultaneous NIRS, BOLD and ASL recordings during 2-sec finger-tapping tasks are then presented. The parameter HbT_{0}, the BOLD calibration factor M and relative changes in CMRO_{2} are then calculated from the reconstructed hemodynamic responses for each subject individually.

Our bottom-up NIRS-BOLD-ASL fusion model is a straightforward extension of the NIRS-BOLD fusion model described by Huppert et al. (2008). Essentially, it consists of a multidimensional linear model describing HbO_{2} and HbR, an observation model relating HbO_{2} and HbR to the measurements, and a least-squares minimization method. The model is briefly summarized here. Further details can be found in (Huppert et al., 2008).

The changes in HbR and HbO_{2} are represented as linear combinations of temporal (*T*) and spatial basis functions (*G*) in order to reduce the dimensionality of the problem. As in Huppert et al. (2008), we used four distinct pairings of spatial and temporal basis functions to describe the hemodynamic response in the cortex and other hemodynamic fluctuations across the head. The task-evoked hemodynamic response was modeled by a set of overlapping Gaussian spheres with a 6-mm standard deviation. The spheres were separated by 6 mm in a hexagonal pattern (Huppert et al., 2008) and were constrained to the gray and white matter tissue of the contralateral side of the finger tapping stimulus. The temporal basis used to model this evoked hemodynamic response was a linear combination of a gamma-variant function and its derivative with a resolution of 2 Hz 0 to 20 sec after the stimulus onsets. Systemic hemodynamic fluctuations were modeled independently in the brain; the CSF and the skin were modeled using a set of sine and cosine functions (from 1/20 Hz to 1.0 Hz in 1/20-Hz increments) to describe the temporally oscillating systemic physiology. Fluctuations from the brain are reflected in both the DOT and fMRI measurements while skin and CSF fluctuations are reflected only in the DOT measurements. The CSF fluctuations originate mainly from the hemodynamic response occurring in the pial veins present above the surface of the cortex (Gagnon et al., 2012), while skin fluctuations result from respiration and heartbeats. The multidimensional linear model represents the hemoglobin changes as a product of the spatial-temporal basis function (*GT*) and a vector of unknown coefficients (*β*).

$$\left[\begin{array}{l}\mathrm{\Delta}{\mathit{HbO}}_{2}\hfill \\ \mathrm{\Delta}\mathit{HbR}\hfill \end{array}\right]=\mathit{GT}\xb7\beta $$

(1)

The reader is referred to (Huppert et al., 2008) for more information about the geometry, the analytical expression and the values of the parameters used in the spatial and temporal basis functions.

Light propagation in tissue is described by the photon diffusion equation. Under the Rytov approximation (i.e. when the perturbation is smooth spatially), a linear equation is sufficient to predict the changes in DOT measurements produced by a perturbation of the optical properties of the medium (Arridge et al., 1999). The equation takes the following form:

$$\left[\begin{array}{l}{\mathit{Y}}_{\mathit{DOT}}^{830\phantom{\rule{0.16667em}{0ex}}nm}(t)\hfill \\ {\mathit{Y}}_{\mathit{DOT}}^{690\phantom{\rule{0.16667em}{0ex}}nm}(t)\hfill \end{array}\right]=\left[\begin{array}{ll}{\epsilon}_{{\mathit{HbO}}_{2}}^{830\phantom{\rule{0.16667em}{0ex}}nm}(t)\xb7{\mathit{A}}^{830\phantom{\rule{0.16667em}{0ex}}nm}\hfill & {\epsilon}_{\mathit{HbR}}^{830\phantom{\rule{0.16667em}{0ex}}nm}(t)\xb7{\mathit{A}}^{830\phantom{\rule{0.16667em}{0ex}}nm}\hfill \\ {\epsilon}_{{\mathit{HbO}}_{2}}^{690\phantom{\rule{0.16667em}{0ex}}nm}(t)\xb7{\mathit{A}}^{690\phantom{\rule{0.16667em}{0ex}}nm}\hfill & {\epsilon}_{\mathit{HbR}}^{690\phantom{\rule{0.16667em}{0ex}}nm}(t)\xb7{\mathit{A}}^{690\phantom{\rule{0.16667em}{0ex}}nm}\hfill \end{array}\right]\xb7\left[\begin{array}{l}\mathrm{\Delta}{\mathit{HbO}}_{2}(t)\hfill \\ \mathrm{\Delta}\mathit{HbR}(t)\hfill \end{array}\right]+\left[\begin{array}{l}{v}_{\mathit{DOT}}^{830\phantom{\rule{0.16667em}{0ex}}nm}(t)\hfill \\ {v}_{\mathit{DOT}}^{690\phantom{\rule{0.16667em}{0ex}}nm}(t)\hfill \end{array}\right]$$

(2)

where **Y** is the vector of DOT measurements for each source-detector pair, the matrix **A** is the spatial sensitivity of the detected light determined by Monte-Carlo simulations (Boas et al., 2002; Huppert et al., 2006b), *ε* is the spectral extinction coefficient at the denoted wavelength and for the denoted hemoglobin species, and *v* is a noise term specific for each source-detector pair and wavelength. The matrix *A* handles the partial volume error of NIRS by explicitly mapping measurements from the MR space to the source-detector space of NIRS.

The BOLD signal is comprised of an intravascular as well as an extravascular component (Lu and van Zijl, 2005; Obata et al., 2004). In order to retain a linear relationship between absolute changes in HbR and relative changes in BOLD, we consider only the extravascular component of the BOLD signal in our fusion model. This assumption is justified by the fact that the extravascular signal composes the majority of the BOLD signal at 3T (Lu and van Zijl, 2005). The change in relaxation rate is correlated to *v _{o}*, the frequency offset of water at the outer surface of a magnetized vessel;

$$\mathrm{\Delta}{R}_{2E}^{}$$

(3)

The deoxyghemoglobin changes are related to the venous blood volume-to-tissue fraction (*V*) and the venous oxygen saturation (*Y*), and the initial venous oxygen saturation is related to *E _{o}*, the resting oxygen extraction fraction, with the equations below (Obata et al., 2004).

$$\frac{\mathit{HbR}(t)}{{\mathit{HbR}}_{0}}=\frac{V(t)\xb7(1-Y(t))}{{V}_{0}\xb7(1-{Y}_{0})},\phantom{\rule{0.38889em}{0ex}}{E}_{0}=1-{Y}_{0}$$

(4)

Substituting the above equations (Eq. (4)) into Eq. (3), we obtain the linear relationship between relative changes in the BOLD signal and absolute changes in HbR as follows (Davis et al., 1998; Hoge et al., 1999; Obata et al., 2004):

$$\frac{\mathrm{\Delta}S(t)}{{S}_{0}}=\mathit{BOLD}(t)\approx \underset{\alpha}{\underbrace{\frac{-4.3\xb7{v}_{0}\xb7{V}_{0}\xb7{E}_{0}\xb7TE}{{\mathit{HbR}}_{0}}}}\xb7\mathrm{\Delta}\mathit{HbR}(t)$$

(5)

where *TE* is the echo time, and *HbR _{0}* is the baseline HbR concentration. All these parameters are lumped into a single parameter (

$${\mathit{Y}}_{\mathit{BOLD}}(t)=[\begin{array}{ll}0\hfill & \alpha \xb7\mathit{I}\hfill \end{array}]\xb7\left[\begin{array}{l}\mathrm{\Delta}{\mathit{HbO}}_{2}(t)\hfill \\ \mathrm{\Delta}\mathit{HbR}(t)\hfill \end{array}\right]+{v}_{\mathit{BOLD}}(t)$$

(6)

where * Y_{BOLD}* is the vector of BOLD measurements in each voxel and

The calibration factor M widely measured during hypercapnic BOLD calibration is defined as the maximum BOLD signal obtained if all of the deoxyhemoglobin is washed out of the venous pool (Davis et al., 1998; Hoge et al., 1999). Substituting Δ*HbR* = −*HbR*_{0} in Eq. (5) gives *M* = 4.3 · *v*_{0} · *V*_{0} · *E*_{0} · *TE*_{0}. Therefore, the relationship between the parameter α computed with our fusion model and the calibration factor M used in hypercapnic BOLD calibration studies is given by

$$M=\alpha \xb7{\mathit{HbR}}_{0}.$$

(7)

where *HbR _{0}* is obtained from

Arterial Spin Labeling (ASL) is a non-invasive MRI technique that allows measurement of regional tissue perfusion (Detre et al., 1992). In order to better reconstruct changes in HbO_{2} and to estimate *HbT _{0}*, our new model extends the previous model of Huppert et al. (2008) to include ASL measurements in addition to DOT and BOLD measurements.

We use the Grubb relation (Grubb et al., 1974) to compute relative changes in cerebral blood volume (CBV) from relative changes in CBF measured by ASL. This relationship is given by

$$\frac{\mathrm{\Delta}\mathit{CBV}}{{\mathit{CBV}}_{0}}+1={\left(\frac{\mathrm{\Delta}\mathit{CBF}}{{\mathit{CBF}}_{0}}+1\right)}^{g}$$

(8)

where *g* is a parameter called the Grubb exponent. This relation generally holds for steady-state measurements. To take into account the short duration of our stimulus (2 sec), we computed an effective Grubb exponent using a dynamic multi-compartment Windkessel model on the same data set (Huppert et al., 2009). The value of this effective Grubb exponent was found to be *g* = 0.228. This value, which was used in our analysis, is close to the BOLD-specific flow-volume relationship recently reported by Chen and Pike (2009). Under constant hematocrit, changes in HbT are directly related to changes in CBV. This has been verified experimentally using combined NIRS and MION-fMRI measurements. Siegel et al. have shown that changes in cerebral blood volume measured with fMRI are directly related to relative changes in HbT measured with DOT (Siegel et al., 2003). Therefore, we can substitute CBV with HbT in Eq. (8) to obtain

$${\mathit{Y}}_{\mathit{ASL}}={\left(\frac{\mathrm{\Delta}\mathit{CBF}}{{\mathit{CBF}}_{0}}+1\right)}^{g}-1=\frac{\mathrm{\Delta}\mathit{HbT}}{{\mathit{HbT}}_{0}}.$$

(9)

This is further justified by the experimental fact that relative changes in CBF measured with ASL are highly correlated both temporally (Huppert et al., 2006a) and spatially (Huppert et al., 2006b) with absolute changes in HbT measured by DOT. With Eq. (9) the observation model for ASL is given by

$${\mathit{Y}}_{\mathit{ASL}}(t)=\frac{1}{{\mathit{HbT}}_{0}}[\begin{array}{ll}\mathit{I}\hfill & \mathit{I}\hfill \end{array}]\xb7\left[\begin{array}{l}\mathrm{\Delta}{\mathit{HbO}}_{2}(t)\hfill \\ \mathrm{\Delta}\mathit{HbR}(t)\hfill \end{array}\right]+{v}_{\mathit{ASL}}(t).$$

(10)

* Y_{ASL}* in Eq. (9) is the relative volume change obtained using ASL data,

The multidimensional linear models and the three observation models (DOT, BOLD and ASL) can be combined in a single linear equation allowing the recovery of ΔHbO_{2} and ΔHbR simultaneously from all three measurements:

$$\left[\begin{array}{l}{\mathit{Y}}_{\mathit{DOT}}^{830\phantom{\rule{0.16667em}{0ex}}nm}(t)\hfill \\ {\mathit{Y}}_{\mathit{DOT}}^{690\phantom{\rule{0.16667em}{0ex}}nm}(t)\hfill \\ {\mathit{Y}}_{\mathit{BOLD}}(t)\hfill \\ {\mathit{Y}}_{\mathit{ASL}}(t)\hfill \end{array}\right]=\underset{H}{\underbrace{\left[\begin{array}{cc}{\epsilon}_{{\mathit{HbO}}_{2}}^{830\phantom{\rule{0.16667em}{0ex}}nm}(t)\xb7{\mathit{A}}^{830\phantom{\rule{0.16667em}{0ex}}nm}& {\epsilon}_{\mathit{HbR}}^{830\phantom{\rule{0.16667em}{0ex}}nm}(t)\xb7{\mathit{A}}^{830\phantom{\rule{0.16667em}{0ex}}nm}\\ {\epsilon}_{{\mathit{HbO}}_{2}}^{690\phantom{\rule{0.16667em}{0ex}}nm}(t)\xb7{\mathit{A}}^{690\phantom{\rule{0.16667em}{0ex}}nm}& {\epsilon}_{\mathit{HbR}}^{690\phantom{\rule{0.16667em}{0ex}}nm}(t)\xb7{\mathit{A}}^{690\phantom{\rule{0.16667em}{0ex}}nm}\\ 0& \alpha \xb7\mathit{I}\\ {\mathit{HbT}}_{0}^{-1}\xb7\mathit{I}& {\mathit{HbT}}_{0}^{-1}\xb7\mathit{I}\end{array}\right]\xb7\mathit{GT}}}\xb7X+\left[\begin{array}{c}{v}_{\mathit{DOT}}^{830\phantom{\rule{0.16667em}{0ex}}nm}(t)\\ {v}_{\mathit{DOT}}^{690\phantom{\rule{0.16667em}{0ex}}nm}(t)\\ {v}_{\mathit{BOLD}}(t)\\ {v}_{\mathit{ASL}}(t)\end{array}\right]$$

(11)

The values for *α* and *HbT _{0}* are initialized to the estimated values using the raw DOT, BOLD and ASL data. Following this, the state vector

$$\widehat{X}={({\mathit{H}}^{T}{\mathit{R}}^{-1}\mathit{H}+{\mathrm{\Gamma}}^{2}{\mathit{Q}}^{-1})}^{-1}{\mathit{H}}^{T}{\mathit{R}}^{-1}\xb7\mathit{Y}$$

(12)

where **R**^{−1} and *Γ*^{2}**Q**^{−1} are the inverses of the measurement noise covariance and the state noise covariance respectively. The matrix **R** is estimated from the data using the same procedure described in (Huppert et al., 2008). To estimate **R**, we calculated the variance of the residual for each measurement by iteratively solving the state estimate and estimating **R** to be the variance of the residual of the measurements. The initial seed of **R** was calculated from linear regression of the data with the temporal basis. An identity matrix was used for the state covariance matrix **Q**. The value for the regularization tuning parameter *Γ* was taken from our simulation results (see section *Simulations*) and was set to the optimal *Γ* value (*Γ* = 10^{−6}).

Once Eq. (12) is solved, the predicted DOT, BOLD and ASL signals are re-calculated using the estimated HbO_{2} and HbR values via the forward model given by Eq. (11). The *α* and *HbT _{0}* values are then estimated by minimizing the residual between the predicted and measured signals. New estimates of ΔHbO

We used the following equation to calculate changes in CMRO_{2} during functional activity (Davis et al., 1998; adapted version from Lin et al., 2009):

$$\frac{\mathrm{\Delta}{\mathit{CMRO}}_{2}}{{\mathit{CMRO}}_{20}}$$

(13)

where the M value is obtained using Eq. (7), ΔHbT is the sum of the ΔHbO_{2} and ΔHbR changes estimated by the model (Eq. 12), HbT_{0} is also estimated from the model, ΔCBF/CBF_{0} is obtained from the ASL data and *β* = 1.5 is a constant relating the change in transverse relaxation rate (*ΔR _{2}^{*}*) to the concentration of HbR.

The experimental protocol and the data used in this study have been previously reported (Huppert et al., 2008). A subset of four out of five healthy, right-handed subjects was used in this study (between 20–60 years old). The study included simultaneous measurement of NIRS, BOLD and ASL signals during an event-related 2-sec finger-tapping task. Each experiment consisted of 6 runs. For the final analysis, we kept only the runs for which a clear hemodynamic response could be observed. The number of good runs ranged from 3 to 5 per subject. Each run was 6 minutes long and included 27–32 stimuli, with an inter-stimulus interval ranging from 4 to 20 sec with an average of 12 sec. The study was approved by the Massachusetts General Hospital Institutional Review Board and subjects gave written consent.

A multichannel continuous wave optical imager (CW4, TechEn Inc., Milford, Massachusetts), consisting of 18 lasers – half of them at 690 nm (18 mW) and the other half at 830 nm (7 mW) – and 16 detectors, was used for measurements as previously described in (Franceschini et al., 2003). Only four sources and eight detectors were used in this study. The DOT probe was made from flexible plastic strips with plastic caps inserted into them to hold fiber optic bundles. It has two rows of four detectors and one row of four sources arranged in a rectangular grid with 2.9 cm between neighboring source-detector pairs (Fig. 1). During the experiment, the probe was placed on the subject’s head where the contralateral motor cortex was located and secured using Velcro straps and foam padding. 10-m fibers were used to reach the MR scanner while their other end was connected to the DOT instrument in the control room. The DOT data was synchronized to the MRI images as previously described (Huppert et al., 2006a) and downsampled to the same 2-Hz frequency of fMRI using a Nyquist filter. Optical density changes were obtained by taking the negative log of the normalized incident light density. The optical measurement sensitivity profiles were obtained using GPU-accelerated Monte Carlo simulations (10^{8} photons) based on a segmented anatomical MP-RAGE volume with five tissue layers (Fang and Boas, 2009). The locations of optodes in the 3D MR volume were determined with the help of fiducial markers.

ASL-fMRI measurements were performed on a 3 T Siemens Allegra MR Scanner (Siemens Medical Systems, Erlangen Germany) using PICORE labeling geometry (Wong et al., 1997) with Q2TIPS saturation (Luh et al., 1999) to impose a controlled label duration. The sequence had a post-label delay of 1400 ms, a label duration of 700 ms, a repetition time of 2 s and an echo time of 20 ms (α = 90°). EPI was used to image five 6-mm slices (1-mm spacing) with 3.75-mm in-plane spatial resolution. Structural scans were performed using a T1-weighted MPRAGE sequence (1×1×1.33 mm resolution, TR/TE/α = 2530 ms/3.25 ms/7°). The stimulus was jittered evenly on a 500-ms time step, allowing the response to be calculated at 2 Hz. The functional images were motion corrected (Cox and Jesmanowicz, 1999) and spatially smoothed with a 6-mm Gaussian kernel. The ASL scans were separated into the control (BOLD signal) and negatively labeled tag images, which were then interpolated to upsample to 2 Hz using a cubic spline model (de Boor, 1978). Each negatively labeled tag scan was subtracted from the subsequent control scan to get the flow image series.

The DOT data were downsampled using a Nyquist filter to 2-Hz, while the BOLD and ASL data were upsampled to the same frequency. A third order polynomial was applied to the data set to remove task-unrelated physiological drift.

To compare the accuracy of our ASL fusion model with that of the BOLD fusion model previously used by Huppert et al. (2008), a sphere-shaped absorption perturbation was positioned ~25 mm deep in the head and synthetic DOT, BOLD and ASL measurements were generated using the forward model Eq. (11). We added a measurement noise of 5 % for the DOT and the BOLD time courses and a measurement noise of 10 % for the ASL time courses. The noise was higher for ASL to reflect its lower experimental SNR. The maximum values for the simulated ΔHbO_{2} and ΔHbR were 8 μM and −2.5 μM respectively. The hemoglobin changes were then recovered from the synthetic data using the iterative procedure described in the *Fusion Model and Bayesian Inversion Approach* section. Different values for the regularization parameter *Γ* were tested to determine the optimal value for the analysis of the *in vivo* recordings.

The ΔHbO_{2} and ΔHbR reconstructions obtained using DOT-only model, the BOLD fusion model (DOT and BOLD, Huppert et al, 2008) and the ASL fusion model (DOT, BOLD and ASL) are shown in Fig. 2. The BOLD fusion and the ASL fusion models recovered the HbR response successfully while only the ASL fusion model could reconstruct the HbO_{2} response with a high accuracy.

Simulation Results. The reconstructed hemoglobin concentrations are shown for the DOT-only (left), BOLD fusion (middle) and ASL fusion (right) models. (Top) HbO_{2} (Bottom) HbR. The sphere-shaped inclusion was located at a depth of 25 mm. The contrast-to-noise **...**

The mean squared errors (MSE) between the simulated and the reconstructed ΔHbO_{2} and ΔHbR were computed for DOT-only, BOLD fusion and ASL fusion models to compare the accuracy of each model in reconstructing the hemodynamic response. Results are shown in Fig. 3. The ASL fusion model had the lowest MSE values compared to the other two models and was therefore used for the analysis of the finger-tapping data.

Mean squared error between the simulated and the recovered ΔHbO_{2} and ΔHbR for the DOT only, BOLD fusion and ASL fusion models.

The ΔHbO_{2} and ΔHbR values obtained for different values of the regularization parameter *Γ* are shown in Fig. 4. The optimal value of the parameter *Γ* was roughly 1×10^{−5} and 1×10^{−6} for ΔHbO_{2} and ΔHbR respectively but the reconstruction was still reasonably accurate over the range 1×10^{−4} to 1×10^{−8}. Therefore, we used a value of 10^{−6} for both HbO_{2} and HbR for the analysis of the finger-tapping data.

The ΔHbO_{2} and ΔHbR responses obtained with the ASL fusion model from the *in vivo* recordings are shown in Fig. 5 for all subjects. Results were obtained using a regularization parameter *Γ* = 10^{−6} (or 1 μM), which is the optimum regularization value obtained from our simulations. The activation areas were located in the motor and primary somatosensory cortices, which represent finger movement and touch, respectively, during finger tapping.

Regions of interest (ROI) were identified for each subject from the BOLD activation t-map due to the higher SNR of BOLD compared to ASL. The HbO_{2}, HbR, BOLD and CBF signals were then averaged over this ROI to produce the time courses shown in Fig. 6.

The estimated M and HbT_{0} values are shown in Table 1 for each subject. The M values were computed using Eq. (5) assuming a baseline oxygen saturation of 70 % in the venous pool (i.e. E_{0} = 0.3). The average M value obtained was 0.18 and the average HbT_{0} was 71 μM. The changes in CMRO_{2} obtained using Eq. (13) are shown in Table 1. The average CMRO_{2} change and the average flow-consumption ratio observed were 13 % and 1.4 respectively.

In this study, we extended the fusion model proposed by Huppert et al. (2008) to include ASL data with the help of Grubb’s relation. As shown in Figures 2, ,33 and and5,5, this approach brings great improvement to the previous model in terms of estimating ΔHbO_{2}. The simulation results in Fig. 2 show that the ASL fusion model can estimate both ΔHbO_{2} and ΔHbR with high spatial accuracy. The lower MSEs obtained with the ASL fusion model (Fig. 3) indicate that the quantification of the reconstruction is more accurate for the ASL fusion model compared to the previous BOLD fusion model. This improvement was larger for HbO_{2} compared to HbR simply because the simulated changes were three times higher for HbO_{2} compared to HbR. Overall, the better performance of the ASL fusion model is explained by the fact that the model obtains prior information about the spatial location of HbO_{2} information from the ASL data, which is correlated with total blood volume changes and hence total hemoglobin changes. Finally, the simulations at various regularization levels presented in Fig. 4 show that the ASL fusion model is robust in estimating the true ΔHbO_{2} and ΔHbR values for a wide range of the regularization parameter (from 10^{−4} to 10^{−8}).

Overall, the spatial locations of the increases in HbO_{2} and decreases in HbR during the motor task (Fig. 5) are very close and mostly overlapping. Nevertheless, slight differences can be observed regarding the spatial extent of the activation for the two chromophores. Physiologically, the spatial extend of BOLD and ASL maps have been shown to be non-coincident. This is because arterial dilation gives rise to venous HbR washout. While there is also HbO_{2} washout in the veins, our prior work has suggested that HbO_{2} has a greater contribution from the arterial side than does HbR (Huppert et al. 2006a). This could give rise to the spatial discrepancies observed between HbO_{2} and HbR reconstruction in Fig. 5.

The ASL fusion model presented in this paper has the advantage of simultaneously estimating the relationship between changes in HbR and BOLD (α parameter in Eq. (7)) and the baseline total hemoglobin concentration. This allows us to compute an experimental data-driven estimate of the BOLD calibration factor, M, from Eq. (7). This estimate of M can be directly compared with M values obtained from hypercapnic studies. Our M values shown in Table 1 are within a reasonable range compared to the experimental values obtained from hypercapnic and carbogen studies (0.07 to 0.25) (Chiarelli et al., 2007; Gauthier et al., 2011). A potential source of error is the baseline oxygen extraction fraction (E_{0}), which was assumed constant for each subject (E_{0} = 0.3). This assumption could slightly bias our estimation of M but not enough to explain the inter-subject variability since E_{0} directly multiplies HbT_{0} and α to give M. Therefore, an E_{0} range of 0.25–0.35 can only change the M value by ± 12.5 % (in our case 0.18 ± 0.02) (see Eq. (7)). In future work, simultaneous measurements of DOT, BOLD and ASL during hypercapnic challenge and functional activity will allow comparison of M values obtained by the ASL fusion model with those obtained from hypercapnia calibration. This will provide an independent measure of M to validate the widely used hypercapnic BOLD calibration.

Similarly, our HbT_{0} values presented in Table 1 are also within the physiological range reported in the literature (60 to 100 μM) (Torricelli et al., 2001; Gagnon et al., 2008). Future studies could include an independent time-resolved spectroscopy measure of HbT_{0} to compare with those recovered from the ASL fusion model.

Our new approach also provided an estimation of CMRO_{2} changes using the recovered hemoglobin values, estimated M and HbT_{0} values and the ASL data (Eq. (13)). This approach is unique in that the only parameter assumed in calculating CMRO_{2} is the baseline oxygen extraction fraction. However, using only the extravascular component of the BOLD signal may result in slight overestimation of CMRO_{2}. The average CMRO_{2} change we obtained was approximately 13%, which is consistent with previous observations with similar stimulus paradigms (Hoge et al., 2005; Tak et al., 2010; Maciejewski et al., 2004). The CMRO_{2} time courses we obtained follow the same pattern in CBF time courses. This is because of the fact that we obtain CMRO_{2} by direct multiplication of the CBF time course which is the highest source of noise among others.

The flow-consumption ratio we get (1.4) is in good agreement with the value of 1.5 obtained with a multicompartment windkessel model by a previous work on the same data set (Huppert et al., 2009). On the other hand, this value is lower than the values obtained using PET or calibrated-BOLD methods (Buxton, 2010). A possible explanation for the difference between the studies would be the shorter duration of our stimulus which does not allow steady state to be reached. This is supported by the fact that longer stimulation is needed to reach steady-state and therefore maximal flow response (Dunn et al., 2005, Drew et al., 2011). The lower flow responses obtained for shorter stimulation combined with similar CMRO_{2} increases could be a potential explanation for the lower flow-consumption ratio we obtained.

An important assumption we made in this paper was to assume Grubb’s relation between relative changes in CBF and CBV. The value of the Grubb exponent historically has been given as 0.38 for steady-state manipulations of blood flow and volume (Grubb et al., 1974). Recent work has suggested that a smaller value more accurately represents the flow-volume relationship during brain activation. Huppert et al. (2009) estimated the effective Grubb exponent for dynamic activation to 0.228 using a multicompartment windkessel model on the same data set. This value is very close to the BOLD-specific value of 0.23 reported recently by Chen and Pike (2009). As a sanity check, we also reconstructed the hemoglobin concentrations from the *in vivo* recordings assuming the traditional 0.38 value (data not shown) and there was no difference between the model residuals obtained assuming either of the two values. However, we obtained slightly lower HbT_{0} and M values with the higher Grubb value, but these values were still within the physiological range of 0.07 to 0.25 for M and 60 to 100 μM for HbT_{0}. In future work, a dynamic relationship between CBF and CBV such as the Balloon model (Buxton et al., 1998) or multicompartment windkessel model (Huppert et al., 2009) could be included in the ASL fusion model to better account for the temporal dynamics of CBF and CBV.

The overlapping Gaussian basis functions used in this paper were very general and allowed us to reconstruct the hemodynamic response without any spatial restriction. However, better reconstruction methods, such as the wavelet based method developed by Abdelnour and Huppert (2009), could be used to reconstruct the hemoglobin changes. The method uses a surface-based wavelet representation to model the anatomical structure of the brain and this reduces the number of parameters to be estimated in the reconstruction. A similar approach could be incorporated into our ASL fusion model to reduce the dimensionality of the problem and potentially provide a more robust reconstruction.

In this paper, we extended the previous DOT-BOLD fusion model of Huppert et al. (2008) by incorporating ASL measurements in the reconstruction of ΔHbO_{2} and ΔHbR. This resulted in a better reconstruction of ΔHbO_{2} since the ASL measurement acted as a prior for the ΔHbT reconstruction. Moreover, our ASL fusion model allowed the computation of baseline total hemoglobin concentration as well as of the BOLD calibration factor M individually for each subject. We obtained an average HbT_{0} value of 71 μM, an average M value of 0.18 and an average CMRO_{2} change of 13%, all of which agree well with values previously reported in the literature. Our model provides a reasonable alternative to validate with an independent method the celebrated hypercapnic BOLD calibration.

The authors are grateful to Rick Hoge and Frédéric Lesage for initial discussions related to this work. We also thank Qianqian Fang and Jay Dubb for their help with the Monte Carlo simulations and Gary Boas for his comments on the draft of this paper. This work was supported by NIH grants P41-RR14075, R01-EB006385 and R90-DA023427. L. Gagnon was supported by the Advanced Multimodal Neuroimaging Training Program at MIT and the Fonds Québecois de la Recherche sur la Nature et les Technologies (FQRNT).

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