Hyunyeol Lee^{1} and Felix W Wehrli^{1}

In qBOLD, the accuracy of local deoxygenated blood volume (DBV) and hemoglobin oxygen saturation (Yv) maps is impaired because of coupling of these two parameters in the signal model. Here, we introduce an interleaved qBOLD method that combines extravascular R2’ and intravascular R2 mapping in a single pulse sequence. Prior knowledge for DBV and Yv is obtained from the velocity-selective-spin-labeling module in the sequence, subsequently used as priors for qBOLD processing. Data obtained in eight subjects demonstrates significantly improved performance yielding plausible values averaging 60.1±3.3% for Yv and 3.1±0.5% and 2.0±0.4% for DBV in gray and white matter, respectively.

Quantitative BOLD (qBOLD)^{1,2} enables local
estimation of deoxygenated blood volume (DBV) and
hemoglobin oxygen saturation (Yv) by means of an analytical model
for the temporal evolution of the extravascular signal in the presence of blood
vessel networks, valid in the static dephasing regime^{3}, described as:

$$S(t)=S_{0}e^{-R_{2,t}t-DBV\cdot f(t/t_{c})} (1) $$

$$f(t/t_{c})=\frac{1}{3}\cdot\int_{0}^{1}u^{-2}\cdot(u+2)\cdot\sqrt{1-u}\cdot(1-J_{0}(1.5\cdot u\cdot t/t_{c}))du (2)$$

$$t_c^{-1}=\frac{4\pi}{3}\gamma\cdot B_{0}\cdot \Delta \chi_{0}\cdot Hct\cdot(1-Y_{v}) (3)$$

Here, $$$\Delta \chi_{0}$$$ is
the susceptibility difference between fully oxygenated and deoxygenated red
blood cells ($$$\Delta \chi_{0}$$$~
0.27 ppm in CGS units^{4}). However, DBV and Y_{v} are mutually coupled in the
signal model, making the parameter estimation challenging to achieve a unique
set of solutions^{5}. To address this issue, we had previously proposed
to combine conventional qBOLD (based on extravascular R_{2}’ mapping)
with a velocity-selective-spin-labeling (VSSL)-based venous R_{2} (or Y_{v}
upon conversion via R_{2}-Y_{v} calibration) measurement^{6}
to obtain prior information of Y_{v} in the qBOLD parameter estimation^{7}.
Here, the method was further developed in that, besides the Y_{v}
prior, venous cerebral blood volume (CBV_{v}) was also extracted from
the VSSL data acquisition as an initial estimate of DBV in the qBOLD
processing.

**Imaging technique:** Figures 1a,b show a schematic of the proposed
pulse sequence with six blocks to achieve: 1) sensitivity to deoxyhemoglobin-induced
modulations of extravascular R_{2}’ using an asymmetric spin echo (ASE)
sequence, and 2) selective labeling of venous blood spins via VSSL.
Furthermore, RF pulses for saturation, flip-down, and inversion are applied to pertinent
spatial regions judiciously timed so as to suppress both arterial blood and CSF
(Fig. 1c, 1d) and thus ensuring exclusive labeling of venous blood in the VSSL
module.

**Estimation of CBV _{v} and Y_{v} via VSSL: **Voxel signals in control (S

$$S_{con}=C\cdot\left((1-CBV_{v})\cdot M_{z,t}^{-1}\cdot e^{-\frac{T_{VSSL}}{T_{2,t}}}+CBV_{v}\cdot M_{z,v}^{-1}\cdot e^{-\frac{T_{VSSL}}{T_{2,v}}}\right) (4)$$

$$S_{tag}=C\cdot(1-CBV_{v})\cdot M_{z,t}^{-1}\cdot e^{-\frac{T_{VSSL}}{T_{2,t}}} (5)$$

where C is the hardware-determined voxel scaling, $$$M_{z,t}^{-1}$$$ and $$$M_{z,v}^{-1}$$$ represent longitudinal magnetization of brain
tissue and venous blood, respectively, immediately prior to VSSL, and T_{VSSL}
is the duration of the VSSL block. The control/tag difference yields:

$$S_{diff}=S_{con}-S_{tag}=C\cdot CBV_{v}\cdot M_{z,v}^{-1}\cdot e^{-\frac{T_{VSSL}}{T_{2,v}}} (6)$$

Multiple pairs of control/tag scans with varying T_{VSSL}
enables estimation of T_{2,v} using Eq. (6) and subsequently Y_{v}
via T_{2,v} –
Y_{v}
calibration^{6}. The normalization of S_{diff} to S_{con}
yields CBV_{v} as:

$$\frac{S_{diff}}{S_{con}}=\frac{ CBV_{v}\cdot M_{z,v}^{-1}\cdot e^{-\frac{T_{VSSL}}{T_{2,v}}}}{(1-CBV_{v})\cdot M_{z,t}^{-1}\cdot e^{-\frac{T_{VSSL}}{T_{2,t}}}+CBV_{v}\cdot M_{z,v}^{-1}\cdot e^{-\frac{T_{VSSL}}{T_{2,v}}}}\approx CBV_{v} (7)$$

Here, two approximations were made: 1) $$$T_{2,t} \approx T_{2,v}$$$ valid at a 3 T field strength and 2) $$$M_{z,t}^{-1} \approx M_{z,v}^{-1}$$$ based on the numerical simulation of Bloch equation (Fig. 1c).

** **

**Data
acquisition:** Data were acquired at 3 T (Siemens
Tim Trio) in eight healthy subjects (mean age = 31 ± 7
years, 4 females) for an imaging slice locating immediately superior to the
corpus callosum. Imaging parameters: TR = 3000 ms, TI = 1150 ms, TS = 1650 ms,
FOV = 240^{2} mm^{2}, slice thickness = 6 mm, matrix size = 64^{2},
and phase partial Fourier = 6/8. Twelve sets of ASE signals were acquired with
SE temporal offsets (Δ) of
0, 3, 6,…, 33 ms. A pair of tag and control
VSSL scans were repeated with T_{VSSL }= 30 ms, 60 ms, 90 ms, 120 ms.
Total imaging time was 10 min with two signal averages. Additionally, data were
acquired using a 3D dual-echo GRE pulse sequence to obtain high-resolution
magnitude images for brain segmentation and a B_{0} field map for
correction of macroscopic field inhomogeneities in ASE signals.

**Data
Processing: **Gaussian smoothing with a 3 x 3 kernel
size was applied to all acquired images. CBV_{v} and Y_{v}
parameter maps, derived by VSSL, served as priors for DBV and Y_{v} in
the qBOLD processing in which acquired ASE signals in the given range of Δ
were fitted to the model in Eqs. (1-3). For comparison, conventional qBOLD
processing was also performed with no priors. Extracted
DBV and Y_{v} in each voxel were averaged over GM and WM masks and over
the entire brain, respectively, in the eight study subjects and tabulated.

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