Vastly accelerated linear least-squares fitting with numerical optimization for dual-input delay-compensated quantitative liver perfusion mapping

Fig. S1. Simulation results for a healthy liver (AF=30%, ECV=30 ml/100ml, MTT=30 s) comparing performance of voxel-wise LLS vs. voxel-wise NLLS as a function of CNR. Shown are relative errors (%) for ECV (Extracellular volume), AF (Arterial Fraction), MTT (Mean Transit Time) and errors (s) for AIF (Arterial Input Function) delay and PVIF (Portal Venous Input Function) delay a) without delay b) with AIF delay=12 s, PVIF delay=0 s.

Fig. S2. Comparison of voxel-wise LLS (a) and voxel-wise NLLS (b) methods for a simulated healthy liver (AF=30%, ECV=30 ml/100ml, MTT=30 s) including delays at CNR = 50. The horizontal and vertical axes indicate the true PVIF and AIF delays, respectively. Shown are the mean relative error (%) for the perfusion parameters and corresponding mean error (s) in the estimated AIF and PVIF delays.

Fig. S3. Comparison of whole-field LLS and voxel-by-voxel LLS in estimating perfusion parameters and associated input function delays for a healthy liver (AF=30%, ECV=30 ml/100ml, MTT=30 s) as a function of CNR. Note that for each CNR, the results are averaged over a range of AIF and PVIF delays (see text for details).

Fig. S4. Comparison of perfusion parameters using whole-field LLS (a) and voxel-wise NLLS (b) methods in the liver donor subject (see Table 1). Perfusion parameters in both methods are similar to that of a normal liver and consistent with reported values in the literature (1) including an average of 20 ml/100ml in extracellular volume, an arterial fraction, ranging between 15%-25% and an average of 20 s for mean transit time. Good agreement was found between whole-field LLS and voxel-wise NLLS in perfusion and delay maps.

Fig. S5. Dependency of voxel-wise LLS and voxel-wise NLLS on temporal resolution in calculating perfusion parameters for a simulated healthy liver (AF=30%, ECV=30 ml/100ml, MTT=30 s) shown in (a) and a simulated tumor (AF=90%, ECV=80 ml/100ml, MTT=10 s) shown in (b). Original noiseless enhancement curves were generated with 4 frames per second temporal resolution and duration of 67 seconds and downsampled to simulated lower temporal resolution.

Fig. S6. Input curves (aorta and portal vein) used in dual-input single compartment model to generate synthetic tissues including a healthy liver (AF=30%, ECV=30 ml/100ml, MTT=30 s) and a hypervascular tumor (AF=90%, ECV=80 ml/100ml, MTT=10 s) and corresponding tissue enhancement curves.