Multi-TE ASL data offers the ability to distinguish blood and tissue compartments in the ASL signal based on transverse relaxation (T2), which differs significantly at 3 T. Utilizing this technique, an extended multi-TE two-compartment model was recently introduced [17]. This model separates exchange time (Tex)—the time taken by labeled water to move from blood into tissue—and intra-voxel transit time (ITT)—the time required for labeled water to traverse smaller vessels, such as arterioles, before reaching the site of capillary exchange. This addresses the limitation of assuming the instantaneous arrival of labeled water at the exchange site.

The extended model assumes that during the ITT, limited or no exchange occurs, and the signal decays with the T1 of blood only, resulting in a purely blood-based signal component. After ITT, when labeled blood reaches single-cell capillaries, exchange occurs between blood and tissue. The total ASL signal is modeled as a combination of all three components. Detailed model equations can be found in Mahroo et al. (2021).

Accurately estimating CBF and BBB permeability is crucial for understanding brain physiology and pathology. Simulations were conducted to evaluate the impact of one-stage and two-stage model fitting approaches for estimating physiological parameters, including CBF, arterial transit time (ATT), Tex, and ITT. By comparing these approaches, we aim to identify the approach that provides greater accuracy and reliability in parameter estimation, offering insights into the suitability and robustness of these approaches for BBB imaging.

Groundtruth data with a matrix size of 100×100x3 were simulated using the extended multi-TE two-compartment model [17] for two different protocols using MATLAB (MathWorks, Natick, US). Two datasets of multi-TI, single-TE ASL were generated with a sub-bolus duration (SBD) of 450 ms, post-labeling delays (PLD) of 600 ms and 800 ms, and TE of 13.2 ms, resulting in two sets with seven TIs each ranging from 1000 ms to 3400 ms and, 1200 ms to 3600 ms with an increment of 400 ms. A multi-TI, multi-TE ASL dataset was generated with SBD = 1050 ms, PLD = 500 ms, TIs = [1500, 2500, 3500] ms, and eight TEs ranging from 13.8 ms to 207 ms, with an increment of 27.6 ms. Other parameters included 500 ms < ATT < 2500 ms, 0 ms < Tex < 1000 ms, ITT = 200 ms, CBF = 60 ml/100 g/min. Fixed values from the literature [18] were taken for T1 blood = 1664 ms, T1 tissue = 1331 ms, T2 blood = 165 ms and T2 tissue = 85 ms.

For the one-stage approach, both datasets were concatenated, and all four parameters (CBF, ATT, Tex, and ITT) were estimated using the extended multi-TE two-compartment model. In the two-stage approach, CBF and ATT were first estimated using the multi-TI, single-TE data with the Buxton model [19]. These estimated values were then applied in the second stage with the multi-TI, multi-TE data to estimate Tex and ITT using the extended multi-TE two-compartment model. The workflow of the two fitting approaches is shown in Fig. 1. Model fitting was conducted using the Bayesian non-linear fitting framework of fabber [20] module in Oxford Centre for Functional MRI of the Brain (FMRIB)’s Software Library (FSL) [21].

Schematic representation of the one-stage and two-stage model fitting approaches used for parameter estimation. A In the one-stage approach, all ASL data (multi-TI and multi-TE) is concatenated and processed simultaneously using the extended two-compartment multi-TE model to estimate CBF, ATT, Tex, and ITT. B In the two-stage approach, CBF and ATT are first estimated from multi-TI, single-TE ASL data using the Buxton model. These estimates are then fixed as inputs in the second stage, where the multi-TI, multi-TE ASL data is used along with the extended two-compartment multi-TE model to estimate Tex and ITT

To compare the accuracy of the two approaches, relative errors against the ground truth data were calculated. Figures 2 and 3 show errors in fitted parameters resulting from one-stage approach and the two-stage approach, respectively. The one-stage estimation yielded robust results across all four parameters, with minimal interdependence between Tex and ITT. However, slight cross-talk was observed at lower Tex values (0–100 ms). In contrast, the two-stage approach showed a 2% error in ATT and up to 10% underestimation of CBF in the initial stage. This underestimation of CBF propagated into the second stage, causing a significant overestimation of ITT, while Tex estimation remained relatively stable, with errors at low values which seem to appear as interdependence with ITT.

Error maps for estimated parameters across a range of simulated ATT and Tex values using the one-stage approach. Each panel displays the error in a specific parameter: A ATT error, B CBF error, C ITT error, and D Tex error

Error maps for estimated parameters across a range of simulated ATT and Tex values using the two-stage approach. Each panel displays the error in a specific parameter: A ATT error, B CBF error, C ITT error, and D Tex error

The simulations suggest that the two-stage approach, which applies different models at each stage, is vulnerable to error propagation due to parameter cross-dependence. Specifically, the Buxton model led to up to a 10% underestimation of CBF. This underestimation can be attributed to the limitations of single-TE data and the single-TE-based Buxton model, which relies on a single time point to estimate signal decay. This approach may assume a slower decay rate because of only one TE time point, potentially leading to a lower intercept and, consequently, a lower CBF estimate. In contrast, multi-TE data and models that incorporate multiple TEs better capture the true signal decay, which may be faster in reality. This more accurate characterization of decay likely results in a higher intercept and explains the higher CBF estimates observed with the multi-TE approach.

These fixed estimates of CBF and ATT in the second step propagated errors into ITT, resulting in considerable overestimation, while Tex remained relatively stable as it is primarily dependent on T2 changes in tissue and blood. Moreover, these results highlight that the physiological fluctuations and errors tend to affect ITT, leaving Tex estimation stable, highlighting the importance of separating the phenomena of transit within the voxel and exchange time. Both approaches showed some interdependence between Tex and ITT at low Tex values, suggesting that additional signal weighting (such as diffusion weighting) is required to accurately separate Tex and ITT and minimize cross-talk. Nevertheless, with expected Tex values in the 200–500 ms range, both approaches produced relatively robust estimates for Tex with minimum error.

Both modeling approaches yielded stable Tex estimates; however, the one-stage approach minimized cross-dependence issues and provided more reliable CBF and ITT accuracy. Hence it was adopted for the in vivo data analysis.

Ten healthy volunteers (age 31 ± 9 years, 3 females) were examined at 3 T (MAGNETOM Vida Fit, Siemens Healthineers AG) using a 20-channel head coil. A written informed consent was provided by all volunteers before scanning. The study was conducted under a general protocol for pulse-sequence development approved by the ethical committee of the University of Bremen, Bremen, Germany. All volunteers were regular coffee drinkers, reporting an average consumption of two cups of coffee per day. Every volunteer was scanned in the morning in a fasting state and was instructed to avoid caffeine intake for at least 8 h prior to the scan.

Five sets of baseline pre-caffeine ASL and M0 scans, each 04:50 min long, were acquired to evaluate fluctuations in physiological parameters. After acquiring the baseline sets, the volunteers were taken out of the scanner and given a 200 mg caffeine tablet while remaining in the supine position, then immediately placed back into the scanner without any delay. Six sets of post-caffeine ASL and M0 scans were acquired, covering the post-caffeine dynamics for approximately 35 min. Figure 4 provides a visual representation of the study design.

Overview of study design. A BBB-ASL protocol was designed using a combination of single-TE and multi-TE Hadamard measurements aimed at estimating exchange time as a proxy measure of blood–brain barrier permeability. Five measurements were acquired as a baseline to observe fluctuations in physiological parameters before administering caffeine, represented here as ‘pre 1–5’. Six measurements were taken after administering a caffeine tablet (200 mg) to the volunteers, shown here as ‘post 1–6’

A combination of single-TE and multi-TE Hadamard pseudo-continuous arterial spin labeling (pCASL) sequence [22], implemented in the in-house developed vendor-independent MRI framework gammaSTAR [23, 24] with 3D GRASE readout [25] was used. Two measurements of multi-TI, single-TE data were acquired using Hadamard-8 (HAD-8) matrix with a sub-bolus duration (SBD) of 400 ms and a post-labeling delay (PLD) of 600 ms and 800 ms, respectively (TE = 13.2 ms, TR = 4000 ms, turbo factor = 12, and scan time = 02:15 min). The resulting two sets of seven inflow times (TI, where TI = SBD + PLD) ranged from 1000 to 3400 ms with an increment of 400 ms, and from 1200 to 3600 ms with an increment of 400 ms, respectively. A multi-TI, multi-TE data was acquired using Hadamard-4 (HAD-4) matrix with SBD of 1000 ms and PLD of 500 ms. The resulting three TIs were 1500 ms, 2500 ms and 3500 ms (TR = 4500 ms, turbo factor = 2, and scan time: 01:55 min) and each TI was acquired at eight different echo times ranging from 13.8 ms to 207 ms with an increment of 27.6 ms. Two FOCI pulses were used for background suppression of T1 values 700 ms and 1400 ms. All pCASL measurements were acquired with the in-plane field of view (FOV) = 320×160 mm2, matrix size = 64×32x32, nominal spatial resolution = 5×5x5 mm3, EPI factor = 16, bandwidth = 2300 Hz/Px, slice partial Fourier = 6/8, one pre-scan and an acceleration of 2 × 2 with CAIPIRINHA. M0 images were acquired in RL and LR phase encoding directions for distortion correction and to quantify perfusion (TE = 13.2 ms, TR = 5000 ms, TIs = 300, 1300, 2300 ms, scan time = 00:20 min). A T1 MPRAGE was acquired with the following parameters: TR = 2200 ms, TE = 2.98 ms, inversion time (TI) = 900 ms, flip angle = 9°, FOV = 256 mm2, voxel size = 1×1x1 mm3, matrix size = 224×256x256, sagittal orientation, and scan duration = 05:07 min.

Data were analyzed with an in-house developed pipeline using Oxford Centre for Functional MRI of the Brain (FMRIB)’s Software Library (FSL) [21]. Structural T1 MPRAGE images were preprocessed with fsl_anat. The ASL time series were corrected for motion using MCFLIRT, employing a six-parameter rigid transformation, and distortion corrected using M0 images acquired in phase-reversed directions (RL and LR) with the FSL TOPUP module [26]. ASL signal at each TI and TE was decoded by applying the respective Hadamard decoding matrix.

All ASL data were concatenated and fitted to estimate CBF, ATT, Tex, and ITT using the extended two-compartment multi-TE model incorporated into the Bayesian non-linear fitting framework of FSL FABBER [20]. Mean gray matter values were calculated using a 50% probability gray matter mask. The parameter maps were registered to structural and MNI 152 standard spaces to compare them within and across subjects.

A mixed-effect model was applied to investigate the time-dependent change in estimated parameters using R (RStudio 2024.04.2 + 764). Additionally, pre-caffeine measurements were averaged across subjects to create a baseline, which was compared with the last post-caffeine measurement using a two-tailed paired Student’s t-test.