Synopsis

Keywords: YIA, Diffusion/other diffusion imaging techniques, Blood-brain barrier, water exchange, diffusion weighted perfusion imaging

We developed an innovate pulse sequence and acquired diffusion weighted pCASL signals from a wide range of PLDs with improved SNR and spatial resolution. A 3-compartment single-pass approximation (SPA) model, which includes an additional venous compartment, was proposed to capture the full dynamics of the labeled blood bolus passing through capillaries while exchanging into tissue space before flowing into venules, and a LRL method was proposed for individual kw quantification.

Background:

A diffusion prepared pseudo-continuous arterial spin labeling (DP-pCASL) method was proposed for quantification of water exchange rate (kw) across the blood-brain barrier (BBB)^1-3. However, the non-CPMG de-phasing of the diffusion preparation module leads to half signal loss. In this study, we present an innovate pulse sequence and acquired signals from a wide range of PLDs with improved SNR and spatial resolution⁴. A 3-compartment single-pass approximation (SPA) model, which includes an additional venous compartment, was proposed to capture the full dynamics of the labeled blood bolus passing through capillaries while exchanging into tissue space before flowing into venules. A comprehensive set of parameters including cerebral blood flow (CBF), capillary transit time (τc) and kw were quantified and permeability surface product of water (PSw), total extraction fraction (Ew) and capillary volume (Vc) were derived simultaneously. With information (i.e., Vc and τc) obtained from 3-compartment SPA modeling, a simplified Linear-Regression of Logarithm (LRL) approach was proposed for individual kw quantification.

Methods:

Separation of vascular/tissue compartments of ASL signals: Due to the large (pseudo)-diffusion coefficients difference (~100 fold) between ASL water in the tissue (0.0009 mm²/sec) and vascular compartments (0.09 mm²/sec), a small diffusion weighting will null the vascular compartment while has minimal impact on the tissue compartment (1-3).
Pulse sequence (Fig. 1): We proposed an embedded first-order Motion Compensated Diffusion Weighting scheme (MCDW) with a BIR-4 (B1-insensitive rotation) non-selective refocusing pulse (Fig. 1B) for robust refocusing and motion compensation in the presence of B1⁺/B₀ field inhomogeneities (5).
3-compartment SPA model: ASL signal can be expressed as the convolution between arterial input function (AIF) and residue functions of vascular (R_v) and tissue (R_t) compartments:
$$\frac{\Delta M}{M_0}=\frac{CBF}{\lambda}(R_v(t)+R_t(t))*AIF(t)\tag*{…[1]}$$
AIF for pCASL and residue functions for SPA (6) model can be expressed as:
$$AIF(t)=\begin{cases}0 & t \in [0,ATT),[ATT+\delta,\inf) \\ e^{-ATT \cdot R_{1a}} & t \in [ATT,ATT+\delta) \end{cases}\tag*{…[2]}$$
$$R_v(t)=\begin{cases}e^{-(k_w+R_{1a}) \cdot t} & t \in [0,\tau _c) \\e^{-k_w\cdot \tau _c}\cdot e^{-R_{1a}\cdot t} & t \in[\tau_c, \inf) \end{cases}\tag*{…[3]}$$
$$R_t(t)=\begin{cases}\frac{k_w}{k_w+R_{1a}-R_{1t}} \cdot (e^{-R_{1t} \cdot t} -e^{-(k_w+R_{1a}) \cdot t})& t \in [0,\tau _c) \\ \frac{k_w}{k_w+R_{1a}-R_{1t}} \cdot (1-e^{-\frac{PS_w}{CBF}-(R_{1a}-R_{1t}) \cdot \tau _c}\cdot e^{-R_{1t} \cdot t}) & t \in[\tau_c, \inf) \end{cases}\tag*{…[4]}$$
where λ is the partition coefficient of water in the brain (0.9 g/ml), δ is the labeling duration, R_1a and R_1t are the longitudinal relaxation rate of arterial blood and tissue. τ_c is the capillary transit time. V_c and PS_w can be derived:
$$V_c=CBF \cdot \tau _c\tag*{…[5]}$$
$$PS_w=k_w \cdot V_c\tag*{…[6]}$$
Eq. [3,4] demonstrate the ASL labeled water starts exchanging into tissue compartment when bolus arrives (t=0), and then reaches the non-exchanging venous compartment at t=τ_c. Fig. 2 shows simulated residue functions (A) and ASL signals (B). Vascular contribution (blue) decreases rapidly when t=[0, τ_c] due to fast exchange across the BBB, then decays with R_1a in the non-exchange venous compartment.
LRL method for individual k_w quantification: When venous contribution is small for moderate PLDs (<2.5s according to 3-compartment SPA modeling results), 2-compartment SPA model can be a good approximation (4,6,7):
$$\Delta M_c(t)=-\frac{2\epsilon \cdot CBF \cdot M_0 }{\lambda \cdot(k_w+R_{1a})}\cdot e^{k_w \cdot ATT} \cdot (e^{-(k_w+R_{1a} )(t-\delta)} - e^{-(k_w+R_{1a}) t})\tag*{…[7]}$$
We proposed a LRL method to estimate kw from ΔMc acquired at multi-PLDs. Eq. [7] can be simplified by taking logarithm of both sides:
$$\log(\Delta M_c(t))=\log(-\frac{2\epsilon \cdot CBF \cdot M_0}{\lambda \cdot(k_w+R_{1a})}\cdot e^{k_w \cdot ATT} \cdot (e^{(k_w+R_{1a})\delta} -1) \cdot e^{-(k_w+R_{1a})t})=A+S \cdot t\tag*{…[8]}$$
$$A=\log(-\frac{2\epsilon \cdot CBF \cdot M_0}{\lambda \cdot(k_w+R_{1a})}\cdot e^{k_w \cdot ATT} \cdot (e^{(k_w+R_{1a})\delta} -1))\tag*{…[9]}$$
$$S=-(k_w+R_{1a}) \space or \space k_w=-S-R_{1a}\tag*{…[10]}$$
where A and S are the intercept and slope of the linear function log(ΔM_c(t)). Eq. [10] demonstrates that the rate of the exponential decay of ΔM_c(t) equals to k_w + R_1a. A k_w map can be generated by voxel-wise linear regression of multi-PLD log(ΔM_c) signals.
MRI experiments/data analysis: Imaging parameters were: FOV=224mm², 36 slices (20% oversampling), 3.5mm³ isotropic resolution, 3-fold acceleration along partition direction with spatiotemporal TGV regularized reconstruction (8), TE = 47.7 msec, label duration=1870 msec. Eighteen label/control pairs were acquired with b=0 or 40.4 sec/mm² at five PLDs: [1590,1890,2190,2490,2790] msec. Total scan time was 35 mins. 11 subjects (8M/3F, age = 26±3 years) underwent MRI scans on a Siemens 3T Prisma system using a 32‐channel head coil.
Perfusion images of each subject were normalized into the MNI space. CBF, k_w and τ_c were simultaneously estimated by 3-compartment SPA modeling on the group-averaged signals using least-square non-linear curve fitting in MATLAB (lsqcurvefit). PS_w and V_c were derived by Eqs. [5,6].

Results & Discussion:

Fig. 3 (left) shows one representative slice of group-averaged perfusion images acquired at five PLDs. ΔM_b=0 has overall higher intensity, and the difference (vascular compartment) is shown in the third row. Signal intensity in the vascular compartment decreased at longer PLD. Vascular contribution was relatively higher in GM at short PLD (1590msec) and became relatively higher in WM at long PLD (2790msec).
Fig. 4 shows group-averaged 3-compartment SPA modeling results. CBF, τ_c, k_w, V^c and PS_w maps were simultaneously obtained from voxel-wise 3-compartment SPA modeling. Average CBF = 51.5/36.8 ml/100g/min, k_w = 126.3/106.7 min^-1, PS_w = 151.6/93.8 ml/100g/min, τ_c = 1409.2/1431.8 msec and V_c = 1.2/0.9 ml/100g in grey and white matter, respectively.
Fig. 5 shows k_w maps obtained from the proposed LRL method (top) and DP-pCASL (bottom) techniques from one representative subject (F, 25 years). 12 slices with moderate thickness (8 mm) were acquired in DP-pCASL scans (3). 36 thinner slices (3.5 mm) were acquired by the proposed MCDW-pCASL. Additionally, the proposed LRL approach, which does not require spatial regularized reconstruction, improved spatial resolution of k_w map.

Conclusion:

MCDW-pCASL allows visualization of intra-/extra-vascular ASL signals across multiple PLDs. Three-compartment SPA model provides a comprehensive measurement of BBB water dynamics from group-averaged data, and a simplified LRL method was proposed for individual k_w quantification

Acknowledgements

This work was supported by National Institute of Health (NIH) grant UF1-NS100614, R01-NS114382 and R01-EB028297