Synopsis

Keywords: Arterial spin labelling, Arterial spin labelling

The blood-brain barrier integrity can be reflected by the pre-exchange lifetime of water molecules, Tex, which can be measured using multi-TE multi-delay ASL. Nevertheless, the low SNR of ASL limits the detectability of subtle Tex changes within a feasible scan time for clinical applications. In this study, optimised protocols were evaluated for the theoretical detectability of 10% changes in haemodynamic parameters. Simulation shows that while changes in CBF and arterial transit time (ATT) could be detected on individual level in a five-minute scan, the same detectability of Tex would require a minimum of 6 subjects within ten minutes of scanning.

Introduction

The pre-exchange lifetime of water molecules across the blood-brain barrier (BBB), Tex, can be used as a surrogate measure for BBB integrity, where changes in the BBB permeability are associated with many cerebrovascular diseases^1-3. Multi-TE pseudo-continuous arterial spin labelling (pCASL) with multiple post-labelling delays (PLD) is a non-invasive MRI approach that could quantitatively measure cerebral haemodynamic parameters, such as CBF, arterial transit time (ATT) and Tex^4-7. However, the detection of subtle changes in such parameters (e.g., 10% change) within a clinically-desirable scan time has been challenging due to the intrinsically low SNR of the ASL technique. In this study, we obtained protocols with optimised PLD and TE timings aimed for improved estimation accuracy of the parameters, and evaluated the detectability of subtle changes in the parameters in an individual based on simulation.

Methods

Optimisation
Optimisation of PLDs and TEs was achieved using a general optimisation framework for ASL experiments, which is based on maximising the Fisher Information Matrix (FIM) to minimise the parameter variance specified by Cramer-Rao Lower Bound⁸. The parameters of interest in the optimisation were $$$\boldsymbol{\theta}=\{CBF,ATT,Tex\}$$$. The sensitivity function of each parameter was derived using a two-compartment kinetic model separating the IV and EV signal contributions⁹.
By changing the weightings on each parameter, four optimality criteria were developed: CBFopt, ATTopt, and Texopt, which were optimised for the estimation of a specific parameter while treating others as confounds, as well as ALLopt that was optimised for the average of all three parameters. To maintain the SNR of each PLD, the number of repeats of optimised protocols was fixed to 2. Under each optimality criterion, the optimisation was performed with numbers of PLDs ($$$nPLD$$$) ranging from 10 to 40, with higher $$$nPLD$$$ leading to longer total scan time, resulting in a total of 143 optimised protocols for evaluation.
Evaluation
The evaluation aimed to investigate the theoretical detectability of parameter changes by the optimised protocols. PCASL signals using the two-compartment model were simulated and added white noise to achieve a typical SNR of 5. The parameters used in optimisation and simulation are listed in Table 1. The signals were fitted with the same kinetic models used in optimisation by two methods: nlinfit function in MATLAB (The MathWorks, Natick, MA) in a non-linear least squares (NLLS) fashion, and FSL’s fabber_asl tool using Bayesian Inference (FABBER). Estimation standard deviation ($$$\sigma$$$) of CBF, ATT and Tex were obtained over 1000 simulations at each ground truth value. The detectability of each protocol was indicated by the subject sample size ($$$N$$$) required to detect a parameter change ($$$\Delta$$$)¹⁰, which was set to 10% of the ground truth values in this study. $$$N$$$ was calculated by the equation $$N=\frac{2\sigma^2(Z_{1-\alpha}+Z_{1-\beta})}{\Delta^2}$$ where $$$Z_{1-\alpha}$$$ and $$$Z_{1-\beta}$$$ are the z-score at confidence level ($$$1-\alpha$$$) and power $$$\beta$$$. At 95% confidence level and 80% power, $$$Z_{1-\alpha}=1.645$$$ and $$$Z_{1-\beta}=0.84$$$.

Results and Discussion

The relationship between $$$nPLD$$$ and the total scan time of each protocol under four optimality criteria is shown in Figure 1. When $$$nPLD$$$ was fixed, CBFopt had the longest scan time and ATTopt the shortest due to the distribution of longer and shorter PLDs required for optimal CBF and ATT estimation accuracy, respectively, consistent with previous findings⁸.
Figure 2 and 3 show the sample size ($$$N$$$) required to detect a 10% change in each ground truth CBF, ATT, and Tex value with 95% confidence and 80% power, when the signal is fitted with NLLS and FABBER models, respectively. For ATT and Tex, detectability improved with higher ground truth values, due to a larger change in absolute values. The ability to detect 10% changes in CBF and ATT across most of the ground truth values was down to individual level ($$$N\le{1}$$$) by CBFopt and ATTopt protocols, respectively, when $$$nPLD\gt{20}$$$, which was around 5 minutes of scanning. However, a minimum group of 6 subjects was needed to detect a 10% change in Tex within 10 minutes of scan time by Texopt protocols, when ground truth Tex was above 0.3s, a typical value for grey matter in literature⁹. This demonstrated the challenge of accurately estimating for and detecting subtle changes in Tex in an individual. Comparing the two fitting methods, NLLS appeared to have higher detectability (lower $$$N$$$) for ALLopt, CBFopt, and Texopt protocols, while FABBER had higher detectability for protocols under the ATTopt criterion.
Figure 4 shows the minimum sample size averaged over the ground truth ranges of CBF, ATT and Tex as a function of $$$nPLD$$$. Although CBFopt, ATTopt, and Texopt had the highest sensitivity to detect a change in the corresponding parameter, the trade-off of losing detectability on other parameters was high. Protocols under the ALLopt criterion, which balanced the estimation of all three parameters, could offer an intermediate level of detection.

Conclusion

Optimised pCASL protocols were obtained with variable numbers of PLDs, and were evaluated for their detectability of 10% change in three haemodynamic parameters. Simulation showed that while CBFopt and ATTopt protocols could achieve such detection in CBF and ATT in an individual with 95% confidence and 80% power in a five-minute scan, Texopt protocols would require at least 6 subjects with 10 minutes of scanning to have the same detectability of Tex changes.

Acknowledgements

This work received funding from the Engineering and Physical Sciences Research Council (EP/P012361/1).