QUASAR ASL is a multi-delay ASL sequence that encodes both tissue and arterial blood information, allowing the bias from arterial blood component to be controlled in CBF quantification [1]. However, partial volume (PV) effects remain an issue to be fully addressed [2]. A linear regression (LR) approach has been proposed, but it typically blurs spatial details in the perfusion image [3]. Alternatively a method using adaptive spatial priors has been developed, but currently it relies upon a model of kinetics different from that seen in QUASAR [4]. Since model-based perfusion estimation for QUASAR ASL has been shown to be reliable [5], here we propose a spatially regularised PV effects correction method for QUASAR ASL and compare it with the LR approach.

A three-component model describes the ASL signal at time t from arterial blood, GM, and WM:

$$\Delta M(t)=ABV \cdot \Delta M_{A}(t) + P_{GM} \cdot \Delta M_{GM}(t) + P_{WM} \cdot \Delta M_{WM}(t),$$

where the $$$\Delta M$$$ are the longitudinal magnetisation differences between ASL tag and control images, P are the percentage of contribution of each type of tissue, and ABV is the arterial blood volume. Each of the magnetisation functions was expressed by the general kinetic model [5].

PV maps were estimated from a T1-weighted image using FSL FAST. The structural image was registered to a calculated T1 image, which was obtained by fitting a saturation recovery curve to the ASL control data. PV maps were then transformed to ASL image resolution.

Perfusion was estimated by model-fitting using spatial VB methods [6]. PV correction was performed by both LR and spatially regularised approaches. The LR method was implemented in two ways (both using regression size of $$$5^{2}\times 1$$$): (1) application of LR on ASL difference data prior to perfusion estimation; (2) application of LR on estimated CBF maps. The spatially regualarised approach used 200 iterations to ensure convergence.

Six QUASAR ASL data were collected from healthy individuals using the parameters of QUASAR Reproducibility Study except for matrix 80$$$\times $$$80, gap 2mm, TE 22ms [1]. A T1-weighted structural image was also obtained in each subject. An ROI analysis of mean estimated GM CBF was conducted with nine ROIs defined based on the signal intensity of estimated PV maps, each covering a 10% range of PV, values less than 10% were omitted.

Simulated ASL difference datasets at six SNR levels were generated using the three-component model (parameters listed in Table 1) and applying the PV estimate (PVE) map and ABV mask of Subject 1. The ABV map was estimated using model-fitting [5]. Clusters were formed at ABV of 1.2%, and the top four clusters with the largest spatial dimension were chosen and combined to give an ABV mask. PV correction was investigated on simulated data generated by both homogeneous and spatially varying GM CBF input (Figure 1). The root-mean-squared-error (RMSE) was computed for each PV correction method at each noise level.

Figure 1 shows the estimated GM CBF map from simulated data at SNR = 10. All three PV correction methods recovered the regions of hypo/hyper perfusion, but the boundary was more accurately preserved by the spatially regularized method.

Figure 2 shows the RMSE of the three PV correction methods. The LR method had lower error for homogenous GM perfusion simulations while the spatially regularised method was more accurate when spatial variation was introduced.

Figure 3 shows the estimated GM perfusion maps of two selected subjects. Similar to the simulations, the LR method introduced more smoothness than the spatially regularised method.

Figure 4 shows the ROI analysis for mean GM CBF in two subjects. Apparent overestimation of GM CBF at low PVE was exhibited by the spatially regularized method that was not seen in simulations.

In simulated data, the spatially regularised method has recovered higher heterogeneity than LR methods in the boundary between normal and hypo/hyper perfusion regions, which indicates that the spatially regularised method has preserved more spatial details. Although the two LR methods demonstrate similar effects in simulations, the ROI analysis shows differences of mean GM CBF, which implies that ASL signal is altered when LR method is implemented before CBF quantification. The overestimation of spatially regularised method in low PVE regions may be due to arterial blood signal affecting the PV estimation.