Repeatability of diffusion-weighted arterial spin labeling MRI for mapping blood–brain barrier water exchange rate at different postlabel delays

Abstract

Purpose:

This study sought to determine the intrasession repeatability of the diffusion-weighted (DW) arterial spin labeling (ASL) sequence at different postlabel delays (PLDs).

Methods:

We first performed numerical simulations to study the accuracy of the two-compartment water exchange rate (Kw) fitting model with added Gaussian noise for DW PLDs at 1500, 1800, and 2100 ms. Ten young, healthy participants then underwent a structural T₁ scan and two intrasession in vivo DW ASL scans at each PLD on a 3T MRI. The Kw, arterial transit time (ATT), and cerebral blood flow maps were linearly registered to the structural images, which were then segmented using FreeSurfer into masks with 35 bilateral gray-matter regions.

Results:

Simulation results showed that the Kw fitting model performed at an error rate less than 10% at physiological ATTs and Kw values, but that error and bias increased at a PLD of 2100 ms and at ATT ranges where the overall blood signal fraction (A₁) is low. In vivo analysis showed a significant positive correlation between intrasession measurements of regional Kw at a DW PLD of 1800 ms $(\beta =0.33,p<0.001)$ only. Furthermore, a significant positive relationship between Kw and cerebral blood flow was seen at a DW PLD of 1500 ms $(\beta =0.26,p=0.005)$ and DW PLD of 2100 ms $(\beta =0.39,p=0.006)$.

Conclusion:

Overall, DW ASL provides the strongest intrasession repeatability at a PLD of 1800 ms in young, healthy subjects, and a simulation study shows accurate Kw fits at physiologic range of ATTs and Kw values.

1 |. INTRODUCTION

Altered blood–brain barrier (BBB) function and permeability have been shown to be a feature of many common neurological and neuropsychiatric disorders.^1–4 Diffusion-weighted (DW) arterial spin labeling (ASL) MRI is an emerging and promising noninvasive, nonionizing, and contrast-free technique to assess BBB water exchange rate (Kw)—a proxy measure of BBB integrity and function. Use of magnetically labeled blood water molecules as endogenous tracer makes applications in young, healthy brains and longitudinal studies possible without having to worry about contrast toxicity or ionization effects.^5–8 Additionally, the relatively small size of water molecules (~18 Da) compared with gadolinium-based contrast agents (Gd-DTPA 550 Da) enables the detection of different and potentially more subtle BBB impairment. Thus, a validated, noninvasive ASL method to measure BBB Kw will provide researchers with a new and more sensitive tool to study the brain.⁹

In an ASL scan, the postlabel delay (PLD) is an important sequence parameter that represents the time after the labeling duration at which an image of the magnetically labeled bolus in the brain is taken. The labeling plane for pseudo-continuous ASL is positioned at the major neck arteries.¹⁰ Once the blood water molecules are labeled, it takes a certain amount of time for those molecules to reach the brain capillaries and cross the BBB into the brain parenchyma. Depending on this arterial transit time (ATT), a physiological parameter formally defined as the amount of time a magnetically labeled water molecule takes to travel from the labeling plane to the capillary of a given brain voxel, the PLD needs to be optimized to allow labeled spins enough time to reach the brain region of interest (ROI) and maintain sufficient signal-to-noise ratio (SNR). Although the optimal PLD has been studied extensively for assessing cerebral blood flow (CBF) with single-delay ASL,¹¹ there is a lack of studies that examine the effect of PLD on the reliability of Kw assessment. Furthermore, ATT has been shown to increase with disease that alters brain vascular health as well as with age.^12–14 Thus, PLD selection is a critical aspect of BBB ASL study design especially when applied in populations with altered ATT.

Water flows freely, although controlled, across the BBB primarily through transmembrane aquaporin channels whose aberrant expression contributes to decreased Kw measured in different disease states using the DW ASL method.^15–20 Nevertheless, findings using different BBB imaging techniques^21,22 and disease-related impact on alternate routes of water exchange have complicated this interpretation and, to date, the field is still uncertain about the direction of Kw change with disease and aging. The theory behind how Kw is estimated in this sequence, called the two-stage single-pass approximation model, was first published by St. Lawrence et al.^23,24 and relies on the approximate 100-fold difference in pseudo-diffusivities (D) of blood and tissue²⁵ to separate the overall ASL signal into an intravascular (blood) and extravascular (tissue) component from which Kw can then be extracted. The three-dimensional (3D) single-delay DW ASL sequence was pioneered by Shao et al.,²⁶ whereby a diffusion gradient ($b$-factor) is applied to crush the fast-flowing spins to differentiate the intravascular and extravascular components from the total signal for every voxel. Initial tests were performed on healthy participants before applications in a cohort with small vessel disease.²⁶ Test–retest MRI scans done approximately 6 weeks apart reported a range of intraclass correlation coefficients (ICCs) across regions from 0.17 in the para hippocampal gyrus, a relatively smaller structure, to as high as 0.72 in the frontal lobe.

Additional studies are needed to affirm the reliability of ASL MRI sequences that assess Kw.^25,26 Thus, the purpose of our work is to assess the intrasession repeatability of a DW ASL sequence at different PLDs to examine the effect of PLD on regional Kw measurements between two intrasession scans. Furthermore, we performed simulation studies by generating simulated ASL signals with the two-compartment model at a range of ATTs and at three different Kw values and PLDs to understand the robustness of the Kw fitting algorithm to added Gaussian noise.

2 |. THEORY

2.1 |. Two-compartment model

The two-compartment model was founded on the principle that the ASL signal, $\Delta M\left(t\right)$, originates from either a vascular (blood), $\Delta M_{bl}\left(t\right)$, or extravascular (tissue), $\Delta M_{ex}\left(t\right)$, component characterized by the unique relaxation times and diffusion coefficients of the spin labels in those compartments, as follows²²:

$$\Delta M\left(t\right)=\Delta M_{bl}\left(t\right)+\Delta M_{ex}\left(t\right)$$ (1)

The general kinetic model²⁷ defines the components of the ASL signal as the convolution over the input function, $c\left(t\right)$, with residue functions that generally model signal loss due to different factors such as blood-to-tissue water exchange, $r_{\text{exch}}$, magnetization decay, $m$, and venous outflow, $r_{\text{out}}$, as follows:

$$\Delta M_{bl}\left(t\right)=2\cdot M_{a,0}\cdot CBF\cdot {\int }_0^{t}c\left(t^{\prime }\right)\cdot r_{\mathit{\text{exch}}}\left(t-t^{\prime }\right)\cdot m_{bl}\left(t-t^{\prime }\right)\cdot r_{bl,out}\left(t-t^{\prime }\right)d{t}^{\prime }$$ (2)

$$\Delta M_{ex}\left(t\right)=2\cdot M_{a,0}\cdot CBF\cdot {\int }_0^{t}c\left(t^{\prime }\right)\cdot \left(1-r_{\mathit{\text{exch}}}\left(t-t^{\prime }\right)\right)\cdot m_{ex}\left(t-t^{\prime }\right)\cdot r_{ex,out}\left(t-t^{\prime }\right)d{t}^{\prime }$$ (3)

where $CBF$ is perfusion in mL/100 g/min, and $M_{a,0}$ is the arterial longitudinal equilibrium magnetization. The $ATT$ and labeling duration $LD$ represent the limits of integration for $c\left(t\right)$ (Eq. [A1]). Refer to the Appendix A for the full model.

2.2 |. Diffusion-weighted ASL

The blood and tissue components of the signal $\Delta M_{bl}\left(t\right)$ and $\Delta M_{ex}\left(t\right)$, respectively, can be separated by their different sensitivities to diffusion-encoding gradients so that the ASL signal collected at a given PLD with multiple diffusion weighting (i.e., $b$ values) can thus be modeled by a bi-exponential equation as follows²⁸:

$$\frac{\Delta M(t,b)}{\Delta M(t,0)}=A_1(t)e^{-b{D}_1}+A_2(t)e^{-b{D}_2}$$ (4)

where the weighting factors $A_1$ and $A_2$ are the fractions of the blood and tissue components, respectively, of the ASL signal curve (Figure 1A), and $D_1$ and $D_2$ are the corresponding apparent diffusion coefficients. Using the definitions of $\Delta M_{bl}\left(t\right)$ and $\Delta M_{ex}\left(t\right)$, the weighting factors are given by

$$A_1(t)=\frac{\Delta M_{bl}\left(t\right)}{\Delta M_{bl}\left(t\right)+\Delta M_{ex}\left(t\right)}$$ (5)

and

$$A_2(t)=\frac{\Delta M_{ex}\left(t\right)}{\Delta M_{bl}\left(t\right)+\Delta M_{ex}\left(t\right)}$$ (6)

Here, the expressions for $A_1$ and $A_2$ contain two unknown variables ($K_w$ and $ATT$) if we trace the model back to Eqs. (2) and (3). In the DW ASL protocol, $ATT$ is measured separately so that, ultimately, the equation for $A_1$ is solved for the primary imaging measure of interest: $K_w$, defined as the capillary permeability surface-area product of water ($P{S}_w$) divided by distribution volume of water tracer in the capillary space ($V_c$).

FIGURE 1.

(A) Arterial spin labeling kinetic signal split into the total, blood, and tissue components through the two-compartment model. A downward-facing arrow denotes bolus arrival time at 1.2 s, whereas an upward-facing arrow denotes the kinetic curve peak. The labeling duration of 1.5 s is the distance between the two arrows. Water exchange rate (Kw) was set at 140 min⁻¹. Gray vertical lines represent the three postlabel delays. (B) A1 signal fraction curve representing the blood signal divided by the total signal.

Furthermore, these terms, which are functions of time, will change in magnitude depending on the PLD. In this study, the $\Delta M$ data are acquired at two $b$ values: zero ($b_0$) and a larger value ($b_{\text{DW}}$) at a sufficient strength to suppress the vascular signal but with minimum effect on the tissue signal. In this case, $A_1$ and $A_2$ are defined as follows:

$$A_1(t)=1-\frac{\Delta M\left(b_{DW}\right)}{\Delta M\left(b_0\right)}$$ (7)

and

$$A_2(t)=\frac{\Delta M\left(b_{DW}\right)}{\Delta M\left(b_0\right)}$$ (8)

3 |. METHODS

3.1 |. Numerical simulation

Figure 1A is a plot of the simulated ASL kinetic signal showing the total signal (blue) and its intravascular (red) and extravascular (green) components from the two-compartment model. The ATT and the peak of the kinetic curve are both labeled as well as representative schematic of where PLDs of 1500 ms, 1800 ms, and 2100 ms sample the ASL kinetic signal to calculate the blood signal fraction, $A_1\left(t\right)$, from which Kw is extracted. Figure 1B shows the theoretical $A_1\left(t\right)$ curve as a function of time. Here, it is evident that the $A_1$ amplitude is dependent on the Kw and PLD in addition to the set ATT of that voxel. Figure S1 shows the A₁ distributions for each PLD and Kw with added white Gaussian noise, as described subsequently.

To investigate the robustness of the Kw fitting protocol to Gaussian noise, simulations in MATLAB were performed at PLDs of 1500 ms, 1800 ms, and 2100 ms; Kws of 80 min⁻¹, 140 min⁻¹, and 200 min⁻¹; and a range of ATTs from 500 ms to [3000 ms, 3300 ms, 3600 ms] corresponding to the PLD and spaced by 100 ms. These values reflect the in vivo acquisition parameters as well as expected and extreme physiological Kw^{16 26} and ATT,²⁹ respectively. Using the two-compartment model theory,²² fractional DW ASL signals ($A_1$ and $A_2$), with, $\Delta M\left(b_{DW}\right)$, and without, $\Delta M\left(b_0\right)$, diffusion weighting, which crushes the intravascular blood signal, were simulated for a single voxel. Simulation parameters include CBF = 60 mL/100 g/min, labeling efficiency $\alpha =0.77$,²⁶ blood-water partition coefficient $\lambda =0.9$, labeling duration = 1.5 s, R1_bl = 0.6 s⁻¹,³⁰ and R1_ex = 0.77 s⁻¹.³¹

Monte Carlo simulations were performed in which random white Gaussian noise was added to the simulated ASL signal before estimating Kw. The value of $M_{0,bl}$ was first estimated from an in vivo brain-tissue reference acquired at PLD = 2000 ms without background suppression. For each combination of underlying Kw, ATT and PLD, $A_1\left(t\right)$ was calculated by simulating $\Delta M\left(b_{DW}\right)$ and $\Delta M\left(b_0\right)$ using the theoretical equations at a specific PLD time. For each iteration, noise was then added to the corresponding $A_1$ using a standard deviation of 0.2% of $M_{0,bl}=1200$ a.u. for ASL according to the method described by Woods et al.³² Noise was added separately to the $A_1$ numerator and denominator (Eq. [5]) at an SNR that varies with the blood and tissue signal strengths, which in turn is dependent on the PLD, ATT, and Kw. Kw was then estimated from simulated noisy $A_1$ using the fzero function in MATLAB, and the percent error from the known ground-truth Kw was calculated. This process was repeated 1000 times per ATT at three different PLDs and three different Kw values.

3.2 |. Imaging protocol

Ten young, healthy adults (aged 23–30y, 5 females) were scanned on a 3T Magnetom Skyra (Siemens Healthineers, Erlangen, Germany) MRI with a 32-channel head coil (Figure 3). All participants gave informed consent under a protocol approved by the Institutional Review Board at the University of California, Davis. T₁-weighted magnetization-prepared rapid gradient-echo sequence structural images³³ were acquired at resolution = 1.0 × 1.0 × 1.0 mm³, followed by three 3D gradient-and-spin-echo DW ASL scans, representing Measurement 1 (M1), to assess Kw at PLDs of 1500 ms, 1800 ms, and 2100 ms. These three DW ASL scans were then repeated within the same scan session for Measurement 2(M2) to assess the intrasession repeatability at each PLD. In half (or 5) of the participants, the PLD order was reversed to minimize ordinal bias. The flow-encoding arterial spin tagging (FEAST)³⁴ acquisition to measure ATT was incorporated into each DW ASL scan and was kept identical (with PLD of 900 ms) across all repetitions.

FIGURE 3.

(A) Scanning protocol of the 10 participants. Separate diffusion-weighted (DW) arterial spin labeling (ASL) MRI scans were acquired at DW postlabel delays (PLDs) of 1500, 1800, and 2100 ms. (B,C) Structural T₁ image and FreeSurfer gray and white -matter masks. (D-F) Water Exchange Quantification Toolbox generated cerebral blood flow (CBF), arterial transit time (ATT), and water exchange rate (Kw) maps.

The DW ASL sequence was acquired at repetition time = 4 s, echo time = 36.5 ms, field of view = 224 mm, matrix size = 64 × 64, 12 slices (10% oversampling), resolution = 3.5 × 3.5 × 8 mm³, label/control duration = 1500 ms, and centric ordering.^19,26 DW ASL scans included 20 repetitions with diffusion weightings ($b$-value) at 0 and 50 s/mm² to measure Kw, which lasted 6 min. Each DW ASL scan also included a FEAST acquisition with 15 repetitions at a diffusion weighting ($b$-value) of 0 and 14 s/mm² with a total acquisition time of 4 min to estimate ATT. Therefore, the total time for each scan was 10 min. The slice prescription was aligned with the top of the brain so that as much of the superior cortical structures could be covered as possible.

3.3 |. Postprocessing

The DW ASL raw scan data were processed with the Water Exchange Quantification (WEQ) Toolbox to generate whole-brain ATT, CBF, and Kw maps, as well as global averages.³⁵ A two-stage single-pass approximation model was used to measure ATT and Kw.²³ We used FreeSurfer³⁶ to segment the structural T₁ into 35 gray-matter ROIs in each hemisphere using the recon-all function. The output parametric maps were then linearly registered and resampled to the skull-stripped FreeSurfer structural T₁ images in FSL FLIRT using the nearest neighbor option. In MATLAB, the FreeSurfer masks were overlayed onto the registered ATT, CBF, and Kw maps to extract the average parameter in each gray-matter ROI. Furthermore, for each ROI, we calculated the percent voxel coverage and excluded regions with less than 60% coverage. Our in vivo analysis was performed by averaging the values within each FreeSurfer ROI across all participants who meet the 60% voxel coverage threshold criterion. Analysis with participant-specific values of gray-matter ROIs is provided in Figure S2.

Furthermore, 3D cortical maps showing Kw averaged across the 10 participants were created by overlaying the 35 FreeSurfer ROIs onto a structural brain image in MNI space as seen in Figure 4. We also included individual Kw maps in MNI space for 3 participants at DW PLDs of 1500, 1800, and 2100 ms, which is presented in Figures S3–S5. All cortical renderings were performed using MRIcroGL.³⁷

FIGURE 4.

Cortical water exchange rate (Kw) representation at a postlabel delay (PLD) of 1500 ms (A), 1800 ms (B), and 2100 ms (C) between Measurements 1 (M1) and 2 (M2). Each FreeSurfer brain region represents the average across all participants with at least 60% voxel coverage. The underlying structural image is in MNI space.

3.4 |. Statistical methods

Mixed-effect linear regression with FreeSurfer ROIs set as the random effect was used to assess the repeatability of M1 and M2 ATT, CBF, and Kw measurements. The average within-subject coefficient of variation (CV) between M1 and M2 was calculated for the four major brain lobes and reported to assess the variability of the measurements between scans. We focused on within-subject CV, because it assesses the precision of the repeated measures within a participant, without being biased by the values of the rest of the group. The slope ($\beta$) and $p$-value were reported along with the line of best fit. An F-test and T-test to compare the variances and mean, respectively, of two samples was performed to assess the difference between the FreeSurfer gray-matter Kw distribution between M1 and M2. Normal distribution was assumed.

4 |. RESULTS

4.1 |. Numerical simulation

Figure 2 shows the simulation results that test the accuracy of the model fits in the presence of white Gaussian noise at three different Kw and PLD values and at a range of physiologic and extreme ATTs. Panels (A)–(F) show the two-compartment model’s fitting performance at Kw of 80 and 140 min⁻¹, values reflective of typical physiological states, and suggests that the fitting protocol had sufficient performance (error < 10%) at ATT range of about 1000–2000 ms in healthy adults.³⁸ Panels (G)–(I) extend the simulation to examine fitting protocol at a faster Kw of 200 min⁻¹. Here, the error rates increased beyond 10% at extremely long ATTs, and there was prominent bias at lower ATTs at a PLD of 2100 ms.

FIGURE 2.

Single-voxel Monte Carlo simulation showing percent error of fit at a range of arterial transit times (ATT). The vertical line depicts the postlabel delay time (PLD) and separates sampling at the descending (left) and ascending portions (right) of the kinetic curve. DW, diffusion-weighted.

4.2 |. In vivo analysis

Table 1 displays the whole-brain average value for ATT, CBF, and Kw. For whole-brain Kw, the PLDs of 1800 ms and 2100 ms showed the most consistent measurement at M1 (128 ± 17 min⁻¹) versus M2 (133 ± 11 min¹) and M1 (127 ± 13 min⁻¹) versusM2 (132 ± 17 min⁻¹), respectively. Table 2 displays the within-subject CV between Kw M1 and M2, where DW PLD of 1500 ms exhibited the highest CV of 0.15 as compared with DW PLDs of 1800 ms and 2100 ms that had CVs of 0.10 and 0.08, respectively, across the four major brain lobes.

TABLE 1.

Whole-brain averages of arterial transit time (ATT), cerebral blood flow (CBF), and water exchange rate (Kw) measurements across 10 young, healthy participants.

FEAST PLD	900 ms		900 ms		900 ms
ATT (s)	M1	1.20 ± 0.10	M1	1.19 ± 0.07	M1	1.18 ± 0.06
	M2	1.18 ± 0.11	M2	1.20 ± 0.09	M2	1.16 ± 0.08
DW PLD	1500 ms		1800 ms		2100 ms
CBF (mL/100 g/min)	M1	58.2 ± 13	M1	59.9 ± 13	M1	59.9 ± 10
	M2	55.7 ± 12	M2	57.8 ± 12	M2	58.1 ± 14
Kw (min−1)	M1	115 ± 24	M1	128 ± 17	M1	127 ± 13
	M2	129 ± 19	M2	133 ± 11	M2	132 ± 17

Abbreviations: DW, diffusion weighted; FEAST, flow-encoding arterial spin tagging; PLD, postlabel delay.

TABLE 2.

Within-subject coefficient of variation (CV) between water exchange rate (Kw) Measurements 1 (M1) and 2 (M2) for the four major lobes of the brain averaged across 10 participants.

	Frontal	Parietal	Temporal	Occipital	Average
1500 ms	0.14	0.15	0.16	0.15	0.15
1800 ms	0.07	0.09	0.10	0.13	0.10
2100 ms	0.06	0.09	0.08	0.09	0.08

Figure 4 shows cortical representations of FreeSurfer regional gray-matter Kw values. Each region contains the mean Kw across all participants for regions that meet the 60% or greater voxel coverage criterion. Across PLDs, a consistent pattern of Kw distribution was apparent, with consistently low Kw values at the posterior end of the brain and the occipital lobe showing the lowest Kw at all PLDs. Specifically, at a PLD of 1800 ms, voxels associated with the right and left frontal, parietal, and temporal lobes had average Kw values of 133.4 ± 14.2 min⁻¹, 128.1 ± 16.2 min⁻¹, and 130.4 ± 18.5 min⁻¹, respectively, compared with an average Kw of 115.4 ± 18.5 min⁻¹ $(p<0.001)$ in voxels of the occipital lobe. Visual consistency between intrasession measurements (M1 and M2) was strongest at PLD of 1800 ms, and the Kw maps appeared most similar between 1800 ms and 2100 ms across PLDs. Averaged Kw values for each FreeSurfer region between M1 and M2 are provided in Table S1.

Figure 5 depicts scatterplots of mixed-effect linear regression between M1 and M2, with each point representing the average Kw within a FreeSurfer ROI across all participants that meet the 60% threshold coverage. Figure 5A–C shows three runs of ATT measurements that were all acquired at a FEAST PLD of 900 ms. As expected, all three FEAST ATT measurements showed intrasession consistency with $\beta =0.68$ $(p<0.001)$, $\beta =0.84$ $(p<0.001)$, and $\beta =0.71$ $(p<0.001)$. CBF also showed very high intrasession repeatability at PLD 1500, 1800, and 2100 ms with $\beta =0.89$ $(p<0.001)$, $\beta =0.94$ $(p<0.001)$, and $\beta =0.90$ $(p<0.001)$, respectively, whereas Kw only showed significant strong positive correlation at PLD of 1800 ms with $\beta =0.33$ $(p<0.001)$.

FIGURE 5.

Gray-matter FreeSurfer region of interest (ROI) analysis of cerebral blood flow (CBF), arterial transit time (ATT), and water exchange rate (Kw) between Measurement 1 (M1) and Measurement 2 (M2). Only regions with 60% or greater voxel coverage were included. Mixed-effect linear regression was performed with the participant as the random effect. Each point represents an ROI in the right or left hemisphere of the brain averaged across all 10 participants. Coefficient of variation (CV) is reported as the within-subject CV (between the two repeat scans), averaged across participants and regions.

Figure 6 shows the histograms of average Kw of all bilateral 35 FreeSurfer gray-matter ROIs averaged across participants that meet the 60% voxel coverage threshold. $F$-tests and $T$-tests to assess differences in standard deviation and mean of the distributions, respectively, showed a PLD of 1800 ms ($F$-test: $p=0.09,T$-test: $p=0.49$) and 2100 ms (F-test: $p=0.16$, T-test: $p=0.01$) to produce the most similar Kw distribution between M1 and M2.

FIGURE 6.

Gray-matter water exchange rate (Kw) distribution for Measurements 1 (M1) and 2 (M2) for 10 individuals. Each count represents a gray-matter region of interest. Only regions with 60% or greater voxel coverage were included. DW, diffusion-weighted; PLD, postlabel delay.

Figure 7 contains scatterplots of M2 results displaying Kw against Figure 7A–C ATT and Figure 7D–F CBF, with each point representing a FreeSurfer gray-matter ROI in the right or left hemisphere. For PLDs of 1500 ms and 2100 ms, a significant positive correlation was observed when a mixed-effect linear regression model taking each FreeSurfer ROI as a random effect is fitted between Kw and CBF: $(\beta =0.26,p=0.005)$ and $(\beta =0.39,p<0.006)$, respectively. Additionally, a significant negative correlation was observed between Kw and ATT in PLDs of 1500 ms $(\beta =-0.04,p=0.006)$ and 2100 ms $(\beta =-0.05,p=0.006)$.

FIGURE 7.

Correlation between water exchange rate (Kw) and arterial transit time (ATT) and cerebral blood flow (CBF) for all FreeSurfer regions of interest (ROIs) in both brain hemispheres averaged across all participants for Measurement 2 (M2). A mixed-effect linear regression model was performed between Kw and ATT (A–C) and CBF (D–F) with the participant as the random effect. Only regions with 60% or greater voxel coverage were included.

5 |. DISCUSSION

Our findings confirmed that Kw was most stable between intrasession measurements at a DW PLD of 1800 ms (Figure 5H). Furthermore, there exists a significant positive correlation between CBF and Kw at DW PLDs of 1500 ms (Figure 7D) and 1800 ms (Figure 7F). Finally, regional Kw distribution (Figure 4) showed the occipital lobe having the lowest Kw at 115.4 min⁻¹ compared with the other three major brain lobes, which collectively has an average Kw value of 130.6 min⁻¹.

5.1 |. Numerical simulations

In this work, we used simulations with Gaussian noise to investigate the effect that different PLDs has on Kw fitting error within a single voxel at a range of ATTs. Simulation results (Figure 2) showed that there is reasonable fitting error (< 10%) under physiological ATTs (1000–2000 ms) at a Kw of 80 min⁻¹ and 140 min⁻¹ and PLD of 1500 ms and 1800 ms. Kw of 200 min⁻¹ at PLD of 1500 ms also fell within the normal error range. However, as the PLD and Kw increased to 2100 ms and 200 min⁻¹, respectively, the error increased beyond 10% at ATTs outside the physiological range. As a reference, Shao et al.³⁹ reported normal whole-brain average Kw in males to be 120.7 ± 17.4 min⁻¹ in young, healthy male participants (age 8–35) and 97.9 ± 31.4 min⁻¹ in an elderly male cohort (age 62–92). These results affirmed the robustness of the two-compartment model to estimate Kw under normal physiologic conditions but suggested that changes to the sequence parameters may be necessary for extreme cases where ATT is prolonged, such as in the elderly or certain patient populations.^12,29

In Figure 2, the Kw error was highest at an ATT of 500 ms and then gradually decreased with increasing ATT. At shorter ATTs, sampling occurs along the descending portion of the ASL kinetic curve, and more time has passed before the prescribed PLD, leading to signal relaxation decay and lower SNR of the Kw measures (Figure 1A). This signal decay was exacerbated at high underlying Kw values (such as our simulations for Kw = 200 min⁻¹ due to fast exchange, which results in low blood signal fraction ($A_1$) values. For high Kw rates, adding noise also causes $A_1$ to become negative (Figure S1) in some instances, leading to poor or unreasonable model fits.

For ATTs longer than the PLD, the sampling occurs at the ascending portion of the kinetic curve, such that the sampled signal was lower, and the simulated corresponding error also increases dramatically. In these scenarios, Kw estimates may face challenges, considering that the diffusion-weighting gradient will not necessarily crush all the blood signal at a given PLD.^25,26 A previous optimization study showed that a sufficient fraction of the labeled spins needs to travel across the BBB into the tissue compartment so that, ideally, only about 15% of the signal originates from the blood component, $\Delta M_{bl}$. In participants with prolonged ATTs, such as the elderly or those with vascular abnormalities, it may be beneficial to choose a longer PLD more consistent with the lengthened ATTs, even though the overall signal amplitude would have decayed more when assessing BBB Kw.^29,40

5.2 |. In vivo findings

In our in vivo analysis between M1 and M2 of the average Kw in FreeSurfer gray-matter ROIs, the PLD of 1800 ms generated the most repeatable and consistent Kw measurements in young, healthy individuals compared with PLDs of 1500 ms or 2100 ms. Linear regression results (Figure 5) showed that Kw measurements at PLD of 1800 ms had the best overall consistency between M1 and M2 $(\beta =0.33,p<0.001)$, although at PLDs of 1500 ms $(\beta =0.20,p=0.05)$ and 2100 ms $(\beta =0.18,p=0.13)$, the correlation was also positive yet not significant. It should be noted that M1 of PLD = 1500 ms appears to be particularly low compared with M2, the latter of which is more consistent with the Kw cortical maps of the other PLDs. This may be due to an inherent limitation of selecting such a short PLD relative to estimated ATT of 1.3–1.4 s in our cohort, such that some labeled water molecules may have remained in the large arteries, thereby violating the assumption of pseudo-random orientation of spins flowing in the capillary space. It should also be noted that the lower M1 distribution at PLD of 1500 ms is largely driven by 2 participants in the study who had unusually low Kw values throughout the brain.

Our results are an extension of the initial test–retest repeatability study performed by Shao et al.,²⁶ in which 19 subjects were scanned approximately 6 weeks apart. In this work, we focused on the within-subject CV to assess the precision of the DW ASL sequence at different DW PLDs within the same participants. Our results showed within-subject CV to be highest at a PLD of 1500 ms (CV = 0.15) compared with a PLD of 1800 ms (CV = 0.10) and 2100 ms (CV = 0.08). This higher CV in the 1500 ms case is due in part to 2 participants in the M1 acquisition who exhibited diffusely low Kw values throughout the brain. Despite these two anomalies, we decided to include these subjects in our analysis to highlight a potential limitation of choosing a relatively shorter PLD. In Shao et al., the authors assessed the ICC of whole-brain measurements to be 0.74 as well as in eight different brain ROIs of varying sizes with ICC as high as 0.72 in the frontal lobe to ICC as low as 0.17 in smaller structures such as the parahippocampal gyrus. Although ICC was not our primary metric of reproducibility, we also observed variable ICC across regions, with higher ICCs in the parietal lobe (for PLDs of 1500 ms and 2100 ms) and occipital lobe (for PLD of 1500 ms).

Moreover, the diffusely low Kw exhibited in 2 subjects at PLD of 1500 ms could suggest that a PLD of 1500 ms may not be long enough to obtain consistent Kw measurements across individuals. To summarize, distribution of bilateral FreeSurfer ROIs (Figure 6) exhibited the highest consistency at PLDs of 1800 ms (within-subject CV = 0.10) and 2100 ms (within-subject CV = 0.08), consistent with the PLD used by the primary developer of the sequence,^16,26 although two studies,^1,17 one in participants with obstructive sleep apnea and the other with schizophrenia, chose 1500 ms as their PLD for studies performed on relatively younger subjects. Our results for PLD of 1500 ms indicate that it is possible that at lower PLD times, the Kw maps may be erroneously low due to SNR limitations with the acquisition rather than the actual underlying BBB physiology. Choosing the appropriate DW PLD for a subject group is therefore a critical component of ensuring reliable and repeatable Kw maps. In future studies, it may be valuable to apply this repeatability study on a group of elderly participants and assess the performance of this sequence at a PLD of 2100 ms.

In cortical map representations (Figure 4), PLDs of 1800 ms and 2100 ms also showed the most consistent intrasession Kw measurements as well as the most consistency between the PLD measurements. These Kw values are mostly consistent with the healthy participants of a recent study that found Kw declines diffusely across the brain with age.³⁹ However, we saw a relatively low Kw average in the occipital lobe in both hemispheres compared with the global brain average. At an average value of 115.4 min⁻¹, this corresponds more to Kw values seen in typical older, middle age cohorts^16,18 and may be the result of other contributions such as relatively longer transit time of the occipital lobe, which is supplied primarily by the relatively thin cortical branches of the posterior cerebral artery.⁴¹ Additionally, we show in Figure 7 that Kw and ATT are negatively correlated to each other (i.e., longer ATT lower Kw). This is reasonable, because perfusion has been shown to decrease with increased transit time.²⁹ Thus, regions with longer transit times are less perfused and do not possess the high enough systolic pressure to drive water out across the BBB. Furthermore, we observed overall lower Kw for a lower PLD of 1500 ms in Table 1 and Figure 4, which is analogous to a scenario when ATT increases for the same PLD. This finding was also reinforced in our sensitivity analysis—where we scanned 4 participants at an extremely low PLD value of 500 ms and an extremely high value of 3000 ms–presented in Table S2 with the caveat that model fits were not reliable at very short PLDs when the labeled spins have not sufficiently crossed the BBB. Additionally, the 130.6-min⁻¹ average Kw value of the frontal, parietal, and temporal lobes is slightly higher than the 120.7-min⁻¹ and 121.7-min⁻¹ whole-brain Kw averages reported in males and females, respectively by Shao et al.³⁹ This slight discrepancy could be due to a number of factors including the different tissue types being compared, scanner variability, and sample-size differences.

Furthermore, our sensitivity analysis showed that for the short PLD of 500 ms, which is significantly lower than the average ATT, there was insufficient amount of signal in the brain to adequately fit CBF and Kw in most individuals. The Kw maps in 3 participants resulted in Kw values at the upper limit of the fitting toolbox and the low corresponding perfusion estimates suggest that inadequate fraction of arterial labeled spins reached and exchanged with the capillary bed. However, in the other extreme, a PLD of 3000 ms produced reliable CBF and Kw values. This observation suggests that despite the reduced vascular signal contribution expected at very long PLD, the two-compartment model is suitable to measure a consistent “equilibrium” Kw. This is an important finding, because it implies that the use of longer PLDs to account for longer physiological ATTs is a practical option with this DW ASL sequence.

A significant positive relationship exists between CBF and Kw at a DW PLD of 1500 ms $(\beta =0.26,p=0.005)$ (Figure 7D) and 2100 ms $(\beta =0.39,p=0.006)$ (Figure 7F). This observation is physiologically reasonable, because CBF is positively correlated with cerebral perfusion pressure, which is the difference between mean arterial blood pressure and intracranial pressure.⁴² In other words, brain regions with high CBF also possess high systolic pressure that forms the pressure gradient which is responsible for increased blood flow. This high systolic pressure, also referred to as hydrostatic pressure in the Starling principle, is the driving force that pushes water and solutes out of the capillary into the interstitial fluid of the brain tissue.^43,44 A recent 2025 study by Padrela et al.⁴⁵ applied a general linear model on time of exchange, as measured with multi-echo ASL, and CBF, and also found a significant positive correlation. Recall that time of exchange is the multiplicative inverse of Kw. Given that the direction of change in water exchange rate with age is opposite between DW and multi-echo ASL,²⁰ it may not be surprising that the relationship between water exchange rate and CBF is also opposite. Additionally, in our young cohort, there was a significant negative relationship between Kw and ATT at DW PLDs of 1500 ms $(\beta =-0.04,\text{p}=0.006)$ and 1800 ms $(\beta =-0.04,p=0.008)$. This is reasonable, because it makes sense physiologically that longer ATTs correspond to lower CBF measurements, which further corresponds with lower Kw values.

In addition, multi-echo ASL is another noninvasive MRI method that takes advantage of the different transverse relaxation times (T₂) between the blood and tissue to separate the overall signal into a blood and tissue component from which Kw can be estimated using the two-compartment model.^21,22 Currently, there are few comparison studies in the literature that characterize the differences between these methods. Morgan et al.²⁰ recently compared DW and multi-echo ASL Kw in two cohorts: one greater than age 55 years and another between 45 and 65 years. In this study, the authors found a nearly 3-fold discrepancy between Kw values for DW and multi-echo ASL at 106.6 ± 19.7 min⁻¹ and 306.8 ± 71.7 min⁻¹, respectively. These averages are consistent with what has been reported in the literature thus far for each sequence. We note that the DW ASL estimate of 106.6 ± 19.7 min⁻¹ from Morgan et al. derives from a cohort of 30 participants (63.8 ± 10.4 years) and is much lower than the average value of 122.6 ± 15 min⁻¹ we observed in our younger cohort of 10 participants (26.2 ± 2.3 years). This Kw difference between our studies may reflect age-related decrease in Kw, especially after the age of 62 years.¹⁶ Moreover, a significant negative correlation was observed between the Kw measured with DW and multi-echo ASL across participants, which points out an opposing direction of water exchange in aging. This is surprising, given that these two methods are purportedly measuring the same physiological metric of Kw across the BBB. This discrepancy between the ASL techniques may reflect differences in modeling approach, such as how T₂ relaxation effects (and potential oxygenation-related changes in aging that alter T₂) and intercompartment exchange are considered in each method.²⁰ For DW ASL, the efficacy of vascular crushers—not used in the current multi-echo ASL sequence—may also change with lower perfusion and aging, also contributing to discrepancy between the two approaches. Future comparison studies are warranted to study the performance of these two BBB ASL sequences in the same participants.

5.3 |. Limitations

Our study has several limitations. First, given the difference in resolution between the FreeSurfer masks (1 × 1 × 1 mm³) and the BBB Kw maps (3.5 × 3.5 × 8 mm³), there is significant partial volume effect contributing to each ROI. This makes individual exploration, especially of small regions, challenging. To minimize noise, we also performed our main regional analysis on a group level for each FreeSurfer gray-matter ROI. This approach allowed us to evaluate the relationship of regional Kw values to local CBF and ATT but did not provide information on an individual participant level (as in Figure S2). Second, our simulation did not apply the total generalized variation regularization to Kw map fitting. This means that our voxel-level Kw fitting simulation does not fully reflect how the in vivo Kw maps were calculated through the Water Exchange Quantification Toolbox, which likely improved SNR of in vivo fits through shared ASL signal information from adjacent voxels but also may indirectly smooth the Kw maps. Third, our pilot study to test out this sequence involved a small sample size of 10 young healthy adults within the same session, with a Kw range from about 100 min⁻¹ to 150 min⁻¹. In future studies, it may be impactful to investigate the performance of DW ASL in a cohort with longer ATTs and across a more prolonged time to see if the repeatability of this sequence still holds at PLD of 1800 ms. Fourth, the DW ASL scan FOV fails to capture the entirety of the brain. In this study, we aligned the top of the prescription window with the superior part of the brain, meaning that inferior structures such as parts of the temporal lobe may have been excluded in larger brains. Finally, the two-compartment model may not be sufficient in estimating Kw, as the bipolar gradients used to crush the intravascular signal are velocity-sensitive, and blood within the microvessels move at such a slow speed that their signal may not be entirely crushed. This would affect the tissue fraction $\left(A_1\right)$, thereby skewing the estimated Kw.

6 |. CONCLUSION

To conclude, DW ASL MRI showed good intrasession repeatability in assessing BBB Kw across different brain regions in young healthy adults at a PLD of 1800 ms compared with 1500 ms and 2100 ms. Furthermore, our study suggests that there could be a positive correlation between CBF and Kw and a negative relationship between ATT and Kw. Cortical representations of different brain regions showed consistent, reproducible Kw measurements in major lobes of the brain between intrasession measurements, with the occipital lobe having significantly lower Kw compared with the frontal, temporal, and parietal lobes. Simulation analysis demonstrated that the Kw fitting algorithm is robust to Gaussian noise at physiologic ATTs and Kw values. Future studies would explore the effects of different PLDs in cohorts with prolonged ATTs to examine this sequence’s performance in elderly and diseased populations.

Supplementary Material

Supplementary Material

Figure S1. A1 blood signal fraction at three postlabel delays (PLDs) with added random Gaussian white noise for water exchange rate (Kw) value of 80 min⁻¹ (A), 140 min⁻¹ (B), and 200 min⁻¹ (C).

Figure S2. Individual participant-level gray-matter FreeSurfer region of interest (ROI) analysis of cerebral blood flow (CBF), arterial transit time (ATT), and water exchange rate (Kw) between Measurement 1 (M1) and Measurement 2 (M2). Only regions with 60% or greater voxel coverage were included. Mixed-effect linear regression was performed with the participant as the random effect. Each point represents a ROI in the right or left hemisphere of the brain.

Figure S3. Cortical water exchange rate (Kw) representation at a postlabel delay (PLD) of 1500 ms between Measurements 1 (M1) and 2 (M2) for 3 individuals. The underlying structural image is in MNI space.

Figure S4. Cortical water exchange rate (Kw) representation at a postlabel delay (PLD) of 1800 ms between Measurements 1 (M1) and 2 (M2) for 3 individuals. The underlying structural image is in MNI space.

Figure S5. Cortical water exchange rate (Kw) representation at a postlabel delay (PLD) of 2100 ms between Measurements 1 (M1) and 2 (M2) for 3 individuals. The underlying structural image is in MNI space.

Table S1. Average water exchange rate (Kw) values between Measurement 1 (M1) and Measurement 2 (M2) for left hemisphere (LH) and right hemisphere (RH) in 35 FreeSurfer gray-matter regions. (T), (F), (O), and (P) signify the temporal, frontal, occipital, and parietal lobes of the brain. Not a number (NaN) values result from insufficient coverage, and that the corpus callosum region (4) was omitted because it is white matter.

Table S2. Sensitivity analysis performed on 4 subjects at two extreme postlabel delays (PLDs) of 500 ms and 3000 ms along with the original three PLDs of 1500, 1800, and 2100 ms analyzed at a single measurement.

Additional supporting information may be found in the online version of the article at the publisher’s website.

APPENDIX A

If we assume labeled blood arrive in a voxel at time $ATT$, and that bolus is saturated for a labeling duration of $LD$, the inflow function $c$ can be defined by

$$c(t)=\left\{\begin{array}{c}0\\ \alpha \cdot e^{-tR{1}_{bl}}\\ 0\end{array}\text{for}\left\{\begin{array}{c}t<ATT\\ ATT<t<ATT+LD\\ t>ATT+LD\end{array}\right.\right.$$ (A1)

where $\alpha$ is the labeling efficiency, and $R{1}_{bl}$ is the longitudinal blood relaxation rate. The residue function governing the water exchange can be modeled as

$$r_{\mathit{\text{exch}}}\left(t\right)=e^{-t{K}_w}$$ (A2)

where $K_w$ is the water exchange rate. The magnetization relaxation functions are defined as

$$m_{bl}\left(t\right)=e^{-t\cdot R{1}_{bl}}$$ (A3)

$$\begin{array}{rr}& \\ & m_{ex}\left(t\right)=e^{-t\cdot R{1}_{ex}}\end{array}$$ (A4)

where $R{1}_{ex}$ represents the longitudinal relaxation rate of the tissue. In this model, we can neglect outflow based on the assumptions that the extracellular compartment is much larger than the blood compartment and that the image acquisition time is on an order that is much shorter than the vascular transit time. Therefore:

$$r_{bl,out}\left(t\right)\equiv r_{ex,out}\left(t\right)\equiv 1$$ (A5)

DATA AVAILABILITY STATEMENT

Anonymized scan images and MATLAB simulation scripts are available on our lab GitHub website (https://github.com/fanlab-ucdavis). Please contact the corresponding author, YDZ, with any issues.