Prostate Perfusion Mapping using Fourier-Transform based Velocity-Selective Arterial Spin Labeling: Choice of Cutoff Velocity and Comparison with Brain

Abstract

Purpose:

To develop velocity selective arterial spin labeling (VSASL) protocols for prostate blood flow (PBF) and prostate blood volume (PBV) mapping.

Methods:

Fourier-transform based velocity-selective inversion and saturation pulse trains were utilized in VSASL sequences to obtain blood flow and blood volume weighted perfusion signal, respectively. Here four cutoff velocities (V_cut = 0.25, 0.50, 1.00 and 1.50 cm/s) for PBF and PBV mapping sequences were evaluated with a parallel implementation in brain for measuring cerebral blood flow (CBF) and cerebral blood volume (CBV) with identical 3D readout. This study was performed at 3T on eight young and middle-aged healthy subjects comparing both perfusion weighted signal (PWS) and temporal SNR (tSNR).

Results:

In contrast to CBF and CBV, the PWS of PBF and PBV were rather unobservable at V_cut of 1.00 or 1.50 cm/s and both PWS and tSNR of PBF and PBV considerably increased at the lower V_cut, indicating that blood moves much slower in prostate than in brain. Similar to the brain results, the tSNR of PBV-weighted signal was about 2-4 times over the corresponding values of PBF-weighted signal. The results also suggested a trend of reduced vascularity within prostate during aging.

Conclusion:

For prostate, a low V_cut of 0.25-0.50 cm/s seemed necessary for both PBF and PBV measurements to obtain adequate perfusion signal. As in brain, PBV mapping yielded a higher tSNR than PBF.

Introduction

Prostate cancer is the most commonly occurring malignancy among American men, accounting for 27% of newly diagnosed cancers, and is the second leading cause male cancer mortality, accounting for 11% of cancer related death (1). Angiogenesis plays important roles for invasive proliferation of prostate carcinoma (2), which has been pathologically demonstrated by microvessel density counts (3-5). Tumor vascularity is an important radiologic biomarker utilized in prostate cancer detection, staging, and evaluation of therapeutic effect. The most well-established MRI methodology for quantitative perfusion and permeability measurements of prostate cancer is dynamic contrast-enhanced (DCE) MRI (6-8).

Arterial spin labeling (ASL) offers the ability to assess perfusion without injection of an exogenous contrast agent, potentially reducing imaging time and cost, and obviating risks related to cumulative gadolinium deposition. ASL is ideal for frequent non-invasive longitudinal monitoring and may serve as a viable alternative to commonly utilized DCE-MRI techniques. During the last decade, only the pulsed ASL (PASL) with 2D acquisition was explored for measuring prostate blood flow (PBF) (9-11).The pseudo-continuous ASL technique (12), which may offer higher perfusion sensitivity, has not been evaluated for prostate perfusion mapping, likely due to the requirement of manual positioning of the labeling plane and the susceptibility to long transit time delay.

To circumvent these restrictions, velocity-selective ASL (VSASL) was proposed to label all the blood in the vascular tree that is flowing faster than a certain cutoff velocity (V_cut) (13,14). The emerging Fourier-transfer based velocity-selective (FT-VS) pulse trains are able to saturate (FT-VSS) or invert (FT-VSI) static tissue while preserving spins flowing above a V_cut. FT-VSI has been applied for mapping cerebral blood flow (CBF) (15-19), as well as myocardial (20) and renal (21) blood flow. Additionally, by employing FT-VSS and removing the labeling delay in the VSASL sequence, cerebral blood volume (CBV) could be measured quantitatively with lower V_cut (22-24). Furthermore, the effectiveness of FT-VS labeling has also been demonstrated in cerebral (25,26), abdominal (27), and peripheral (28,29) MR angiography, along with a flowing phantom (30).

As the choice of V_cut determines the sensitivity to perfusion signal, the optimization of the VSASL labeling module for prostate perfusion mapping needs to be investigated first. In previous brain applications, V_cut = 2.0 cm/s was recommended for CBF mapping (14) and V_cut = 0.5 cm/s has been applied for CBV mapping (23,24); for prostate VSASL, lower V_cut values might be needed as slower blood movement in the prostate is expected. Here FT-VS prepared PBF and prostate blood volume (PBV) mapping sequences employing different V_cut and identical 3D acquisition were performed with a parallel implementation in brain for measuring CBF and CBV. This study aims to demonstrate the feasibility of mapping the PBF and PBV by comparing both perfusion weighted signal (PWS) and temporal SNR (tSNR) among different V_cut implementations.

Methods

Subjects

Four young males (26-40 years old) and four middle-aged males (59-66 years old) were included in this study after providing informed consent following the local Institutional Review Board guidelines. One middle-aged subject participated in the prostate experiment only, while all the other seven subjects participated in both brain and prostate experiments.

Scanner and sequences

Experiments were performed on a 3T scanner (Prisma, Siemens Healthineers, Erlangen, Germany) with a 20-channel head/neck receiving coil for brain scans and an 18-channel body receiving coil for prostate scans.

Both blood flow and blood volume mapping utilized 96 ms FT-VS label/control modules shown in Figure 1A. Nine excitation pulses (hard pulse, 0.06 ms duration each) with a flip angle of 20° (FT-VSI) or of 10° (FT-VSS) were interleaved with eight velocity encoding steps. Each step contained paired and phase-cycled composite refocusing pulses (90_x-180_y-90_-x,1.0 ms duration), surrounded by four velocity-encoding triangular gradient lobes (1.2 ms duration, 0.6 ms ramp time each). Bipolar gradients were used for label, while unipolar gradients were used for control. Two young subjects participated in initial prostate scans comparing velocity encoding along superior-inferior and left-right directions with V_cut of 0.25 and 1.00 cm/s by varying the strength of gradients. For both brain and prostate scans in all subjects, four V_cut values (0.25, 0.50, 1.00 and 1.50 cm/s) were compared along superior-inferior direction. Note that here V_cut followed the definition in the first VSASL review paper (14).

Figure 1.

(A) Diagram of Fourier-Transform based velocity-selective saturation (FT-VSS, 10° excitation) or inversion (FT-VSI, 20° excitation) pulse trains with bipolar gradients for label and unipolar gradients for control modules. Sequence diagrams of (B) FT-VSI based blood flow mapping and (C) FT-VSS based blood volume mapping. Both methods include slab-selective saturation with a post saturation delay, FT-VSI or FT-VSS label/control modules, regular fat saturation (not shown) followed by 3D single-shot GRASE readout with reduced FOV. (B) In blood flow mapping, post labeling delay with embedded background suppression pulses and a vascular crushing module were added between the label/control modules and readouts. (B) and (C) For prostate, a slab-selective saturation was added before the readout to eliminate the bladder's signal.

As previously described (16), the sequence for measuring blood flow consists five blocks (Figure 1B): a slab-selective saturation with 3.0 s post saturation delay (PSD), a FT-VSI based label/control module with 1.2 s post labeling delay (PLD), three background suppression pulses at 515/910/1075 ms after the labeling, a vascular crushing module with matched V_cut, and a 3D readout. The sequence for measuring blood volume consists of three blocks (Figure 1C): a slab-selective saturation with 3.5 s PSD, a FT-VSS based label/control module with PLD = 0 s, and a 3D readout. Product fat saturation module was applied before readout for both methods. For prostate, a slab-selective saturation was added before the readout to eliminate the bladder's signal (Figure 1B,C).

For both brain and prostate scans, the identical 3D gradient- and spin-echo (GRASE) readout was used with an imaging volume of 82×82×40 mm³ and resolution of 3.4×3.4×4.0 mm³, with a total of 10 slices. Note that this FOV was enough to cover the whole prostate gland, but only the size for the brain’s superior posterior portion. Inner-volume-excitation (31) was used to achieve a single-shot acquisition: slice oversampling = 20%, fast spin echo (FSE) factor = 12, echo planar imaging (EPI) factor = 13, bandwidth = 2894 Hz, echo time (TE) = 11.8 ms, echo spacing = 11.8 ms, and echo length = 142 ms. TR was set as 4.6 s for blood flow imaging and 3.9 s for blood volume imaging. Acquisition of 20 pairs of dynamics took 3.3 min for blood flow imaging and 2.8 min for blood volume imaging. If severe motion was observed during the scans, the affected sequences were repeated to double the number of dynamics acquired.

Proton density-weighted image (M0) was acquired with the same readout and TR of 10 s. For brain scans, a double inversion recovery (DIR) gray matter (GM) weighted image with two inversion pulses (TR = 10 s; TI₁ = 3.58 s; TI₂ = 0.48 s) to suppress both CSF and WM was also acquired. For prostate scans, a FSE sequence was performed in the axial orientation to get a structural T₂ weighted image with the FOV of 200×200×105 mm³ and a resolution of 0.6×0.6×3.5 mm³: echo spacing = 11.2 ms, TE = 101 ms, TR = 8.7 s; the refocusing flip angles were 160°. With a GRAPPA (GeneRalized Autocalibrating Partial Parallel Acquisition) acceleration factor of 2, the scan time was 4 min.

Data Analysis

Data-processing was performed using Matlab (The Mathworks, Nantick, USA) and ImageJ (Rasband W., National Institute of Health, USA, version 1.51s) (32). To mitigate contamination from motion, subtractions of each label/control pairs were manually investigated. If a sudden, abnormal, and large-scale signal change was observed, this label/control pair would be identified as with motion artifacts and excluded from averaging. PWS were analyzed as (label-control)/M0 and tSNR were computed as the ratio of the mean to standard deviation values.

For brain imaging, the GM ROIs were generated by applying an empirical threshold on DIR images. White matter (WM) ROIs were manually drawn on DIR images. Large vessel signal was excluded from those ROIs using blood volume images with the lowest V_cut (0.25 cm/s) as references. CSF signal was also manually excluded based on M0 images.

For prostate imaging, ROIs were first manually drawn on the M0 images to include the prostate tissue without further specifying different regions. Large vessels were manually excluded according to blood volume images with the lowest V_cut (0.25 cm/s).

Results

The PBF and PBV based PWS images at one slice of two subjects indicated markedly higher perfusion signal at V_cut of 0.25 cm/s along superior-inferior velocity-encoding direction compared to results along left-right direction or at V_cut of 1.00 cm/s along either direction (Figure 2). Results of more slices are arrayed in Supporting Information Figure S1. The superior-inferior direction was used as default for the rest of the experiments.

Figure 2.

The proton density-weighted images (M0) of prostate and the perfusion weighted signal (PWS) of prostate blood flow (PBF) and prostate blood volume (PBV) with V_cut of 0.25 and 1.00 cm/s along superior-inferior (S-I) and left-right (L-R) velocity-encoding directions at one axial slice of (A) subject 2 and (B) subject 4 from the young group, both showing higher perfusion signal at V_cut of 0.25 cm/s along S-I direction than the other three conditions.

Among both young and middle-aged groups, the numbers of dynamics excluded in each subject due to motion artifacts are listed in Supporting Information Table S1. Most exclusions were applied on the PBF weighted images with V_cut = 0.25 cm/s, with 14, 6, 5, 4 out of 40 dynamics for the four young subjects (the only four scans requiring repetition due to visible local motion during the scanning) and 2, 7, 6, 3 out of 20 dynamics for the four middle-aged subjects, respectively. All dynamics in PBV weighted images with different V_cut were included in the final analysis as no large motion artifacts were observed.

The CBF and CBV as well as PBF and PBV based PWS and tSNR images from one middle-aged subject are arrayed with four different V_cut at a single slice in Figure 3 as well as 4 out of 10 slices in Supporting Information Figure S2. The corresponding results at 4 slices of a young subject are displayed in Supporting Information Figure S3. One-slice examples of all young and middle-aged subjects are shown in Supporting Information Figures S4 and S5, respectively. As expected, PWS of blood flow and blood volume increased with lower V_cut for both brain GM, WM, and prostate tissues. tSNR showed a similar trend in PBF, PBV, and CBV, except that CBF’s tSNR decreased with reduced V_cut, indicating that FT-VSI labeled signal at very low V_cut was sensitive to physiological noise in the brain. Supplying arteries and draining veins appeared with hyperintensity in PWS images of both brain and prostate but presented rather low tSNR in prostate. In addition, there was also CSF signal visible through the middle of the brain in CBV weighted images, probably because the slow-flowing CSF got unintentionally labeled under lower V_cut.

Figure 3.

M0, anatomical images (DIR: double inversion recovery), as well as blood flow and blood volume weighted perfusion weighted signal (PWS) and temporal SNR (tSNR) at different V_cut of (A) brain and (B) prostate of one axial slice of one subject (sub 2) from the middle-aged group. CBF: cerebral blood flow; CBV: cerebral blood volume; PBF: prostate blood flow; PBV: prostate blood volume.

The blood flow and blood volume based PWS and tSNR of GM, WM, and prostate tissues at different V_cut are shown in Figure 4 and listed in Table 1. 1) With V_cut increasing from 0.25 to 1.50 cm/s and within young/middle-aged groups: for brain, the CBF based PWS were relatively stable for GM and WM; the CBF based tSNR increased about 77% for GM and 19/80% for WM; the CBV based PWS decreased around 58% for GM and WM; the CBV based tSNR decreased around 44% for GM and around 52% for WM; for prostate, PWS decreased 69-82% for PBF, 78-83% for PBV, and tSNR decreased 58-68% for PBF, 72-75% for PBV. 2) Comparing blood volume to blood flow across different V_cut of both young and middle-aged groups, the enhanced PWS and tSNR were 1.4-3.4 and 1.7-7.3 times higher for GM, 2.7-8.4 and 2.6-13.0 times higher for WM, 2.0-3.4 and 2.1-4.3 times higher for prostate, respectively. 3) At V_cut of 0.25 cm/s: the PBF and PBV based PWS were 3.1 and 2.3 times of CBF and CBV based PWS in WM for the young-age group, and 2.5 and 1.2 times for the middle-aged group; the ratios of the middle-aged over young group of PWS of blood flow and blood volume were 0.87 and 1.19 times in GM, 0.93 and 1.12 times in WM, 0.73 and 0.60 times in prostate, respectively.

Figure 4.

Averages of blood flow and blood volume perfusion weighted signal (PWS) and temporal SNR (tSNR) of gray matter (GM), white matter (WM) and prostate tissues for both young and middle-aged groups at different V_cut. The error bars are the standard deviation within the groups.

Table 1.

Mean and standard deviation of blood flow and blood volume perfusion weighted signal (PWS) and temporal SNR (tSNR) of gray matter (GM), white matter (WM) and prostate tissues for both young and middle-aged groups at different V_cut.

		GM				WM				Prostate
		Young group		Middle-age group		Young group		Middle-age group		Young group		Middle-age group
	Vcut (cm/s)	PWS (%)	tSNR	PWS (%)	tSNR	PWS (%)	tSNR	PWS (%)	tSNR	PWS (%)	tSNR	PWS (%)	tSNR
Blood flow	0.25	0.39±0.14	0.56±0.11	0.34±0.12	0.44±0.24	0.14±0.10	0.27±0.12	0.13±0.11	0.15±0.08	0.44±0.10	0.25±0.07	0.32±0.11	0.24±0.18
	0.50	0.30±0.03	0.78±0.12	0.28±0.05	0.67±0.34	0.10±0.05	0.36±0.21	0.06±0.02	0.17±0.08	0.18±0.06	0.15±0.07	0.16±0.08	0.12±0.11
	1.00	0.30±0.03	1.00±0.24	0.29±0.05	0.70±0.38	0.10±0.02	0.42±0.13	0.10±0.02	0.29±0.13	0.07±0.04	0.07±0.05	0.10±0.09	0.12±0.13
	1.50	0.29±0.02	0.99±0.22	0.28±0.05	0.78±0.41	0.07±0.02	0.32±0.15	0.07±0.05	0.27±0.17	0.08±0.06	0.08±0.06	0.10±0.04	0.07±0.05
Blood volume	0.25	0.96±0.09	2.90±0.68	1.14±0.20	3.23±0.64	0.59±0.10	2 25±0.51	0.66±0.13	1.90±0.10	1.33±0.57	1.00±0.29	0.80±0.52	0.85±0.75
	0.50	0.72±0.09	2.54±0.58	0.86±0.12	2.94±0.46	0.39±0.07	1.59±0.43	0.48±0.11	1.52±0.15	0.49±0.18	0.49±0.16	0.35±0.20	0.41±0.39
	1.00	0.50±0.11	1.83±0.52	0.61±0.04	2.28±0.47	0.27±0.02	1.10±0.10	0.33±0.01	1.11±0.20	0.23±0.07	0.30±0.09	0.18±0.12	0.25±0.21
	1.50	0.41±0.08	1.65±0.38	0.49±0.01	1.78±0.53	0.25±0.01	1.08±0.15	0.28±0.01	0.93±0.21	0.22±0.06	0.28±0.08	0.18±0.04	0.21±0.15

Discussion

This is the first work systematically investigating the blood flow and blood volume weighted perfusion mapping using FT-VS based ASL techniques in prostate and comparing them with the results in brain. The dependence on both the direction (Figure 2) and V_cut (Figures 3, 4, Supporting Information Figure S1-S3, Table 1) indicated that blood moves much slower in prostate than in brain. Cerebral applications of VSASL were previously shown to be insensitive to the direction of velocity encoding at V_cut of 1-2 cm/s for CBF (13) and of 0.5 cm/s for CBV (23). For CBF, when V_cut was lower than 1.00-1.50 cm/s, the PWS gain was minimum while tSNR dropped and CSF contamination increased (Figure 3). This is consistent with the current recommendation of 2 cm/s V_cut in the brain (14). For CBV, there was improvement in both PWS and tSNR with lower V_cut (Figures 3,4, Information Figure S1-S3, Table 1). However, the CBV with higher V_cut still preserved GM-to-WM contrast (Figure 3) and may have the benefit of less sensitivity to physiological motion. In contrast, for prostate VSASL, velocity encoding direction even at V_cut of 0.25 cm/s still showed some degree of anisotropy in labeling efficiency (Figure 2). The PWS of PBF and PBV were rather unobservable at V_cut of 1.00-1.50 cm/s and both PWS and tSNR of PBF and PBV considerably increased at the lower V_cut (Figures 3,4, Supporting Information Figure S1-S3, Table 1). Therefore, a V_cut around 0.25-0.50 cm/s along superior-inferior direction was necessary for VS based prostate perfusion imaging.

For both brain and prostate, blood volume weighted signal yielded much higher PWS and tSNR than blood flow weighted results (Figure 4). The tSNR of PBV-weighted signal was about 2-4 times over the corresponding values of PBF-weighted signal (Table 1). This was largely because that blood signal was acquired right after labeling without experiencing any T₁ relaxation. With blood T₁ for males as about 1.8 s at 3T (33), the labeled blood magnetization would exponentially decay ~50% during 1.2 s PLD employed in the VSASL sequence for blood flow estimation (Figure 1b). Given the inherently low SNR suffered by ASL methods, the markedly enhanced tSNR by blood volume based VSASL could be especially advantageous for cancer detection in brain, prostate, or any other tissue organs. One challenge though was the differentiation between large vessels and tumor in PWS images, especially in organs such as prostate, where the local vasculature anatomy is not routinely imaged and thus may not be familiar to radiologists. This could potentially be resolved by comparing with the corresponding tSNR images (Figure 3, Supporting Information Figure S1-S3) as tSNR of large vessels were much lower than that of the static tissue, likely due to the effect of pulsation. By all accounts the spatially connecting features of vessels would also help correct characterizations.

Note that absolute quantification of PBF and PBV were not conducted in this work due to still limited knowledge of labeling efficiency at various vessel segments at different V_cut and lack of literature values for comparison. However, as identical VSASL sequences were performed in both brain and prostate, their PWS could be compared among different tissues within the same subject or between young and middle-age groups. In this preliminary analysis, the PWS of normal prostate among middle-aged subjects had about 2.5 times higher blood flow and 1.2 times higher blood volume than normal white matter, and about 27-40% lower blood flow and blood volume than younger subjects, indicating a trend of reduced vascularity within prostate during aging.

As the diffusion weighting between the pair of velocity-selective labeling and velocity-compensated control modules was only partially matched (Figure 1a), the effect of diffusion-imbalance on the subtracted perfusion signal needs to be estimated. Based on the b-values of a single velocity-encoding step of the label and control modules for each V_cut (Supporting Information Table S2) and the normal T₁, T₂, and ADC values of GM, WM, and prostate (Supporting Information Table S3), the diffusion-induced signal bias among various cerebral and prostate PBS results (Table 1) were compared in Supporting Information Table S4. Considering the lowest V_cut of 0.25 cm/s bearing the highest unbalanced diffusion weighting, as the employed b-values were quite small for a single velocity-encoding step (label: 1.45 s/mm²; control: 0.56 s/mm²), their diffusion effects contributed relatively 14-18% of blood flow based PWS and 9-11% of blood volume based PWS in GM, 17-23% of blood flow based PWS and 14-15% of blood volume based PWS in WM, as well as 20-30% of blood flow based PWS and 10-17% of blood volume based PWS in prostate. This bias of overestimation reduced considerably with the increasing V_cut. It is worth noting that this diffusion-related bias for the absolute perfusion quantification is not going to affect the perfusion contrast of prostate tumors at such low b-values (< 2 s/mm²), as b-values higher than 600 s/mm² are typically required to detect significant ADC differences between benign tissue and prostate cancer (34)

Another problem from low V_cut is the higher susceptibility to motion near prostate, which required manual inspection and abandoning failed acquisitions. The much less motion-related artifacts in PBV images (Supporting Information Table S1) may be partly due to its higher PWS and better suppressed tissue signal. For PBF, more aggressive background suppression may be needed to improve its robustness to motion.

In addition, a low resolution of 3.4×3.4×4.0 mm³, which is typical for brain, was used in this study for optimizing the V_cut with a single-shot readout. Such a resolution may not be sufficient for clinical applications on a small organ like prostate. Increasing the resolution without being blurred will require more undersampled readout. The reproducibility of VSASL based perfusion mapping for prostate will need to be established as having been done for brain recently (35).

Conclusion

Compared to in brain, blood moves much slower in prostate and a low V_cut of 0.25-0.50 cm/s along superior-inferior direction seemed necessary to obtain adequate perfusion signal for both PBF and PBV measurements. As in brain, PBV mapping yielded a higher tSNR than PBF. Both methods need to be evaluated in patients to demonstrate their clinical utilities for characterizing prostate cancer.

Supplementary Material

supporting information

Table S1: Number of excluded/acquired pairs of label and control dynamics of each subject by the VSASL sequences applied for brain and prostate blood flow and volume, respectively.

Figure S1: The proton density-weighted images (M0) of prostate and the perfusion weighted signal (PWS) of prostate blood flow (PBF) and prostate blood volume (PBV) with Vcut of 0.25 and 1.00 cm/s along superior-inferior (S-I) and left-right (L-R) velocity-encoding directions at 4 out of 10 axial slices of (A) subject 2 and (B) subject 4 from the young group, both showing higher perfusion signal at Vcut of 0.25 cm/s along S-I direction than the other three conditions.

Figure S2: M0, anatomical images (DIR: double inversion recovery), as well as blood flow and blood volume weighted perfusion weighted signal (PWS) and temporal SNR (tSNR) at different V_cut of (A) brain and (B) prostate of 4 out of 10 axial slices of one subject (sub 2) from the young group. CBF: cerebral blood flow; CBV: cerebral blood volume; PBF: prostate blood flow; PBV: prostate blood volume.

Figure S3: M0, anatomical images (DIR: double inversion recovery), as well as blood flow and blood volume weighted perfusion weighted signal (PWS) and temporal SNR (tSNR) at different V_cut of (A) brain and (B) prostate of 4 out of 10 axial slices of one subject (sub 2) from the middle-age group. CBF: cerebral blood flow; CBV: cerebral blood volume; PBF: prostate blood flow; PBV: prostate blood volume.

Figure S4: M0, anatomical images (DIR: double inversion recovery), as well as blood flow and blood volume weighted perfusion weighted signal (PWS) and temporal SNR (tSNR) at different V_cut of (A) brain and (B) prostate of all subjects from the young group. Slice 9 was shown for brains and slice 6 was shown for prostate. CBF: cerebral blood flow; CBV: cerebral blood volume; PBF: prostate blood flow; PBV: prostate blood volume.

Figure S5: M0, anatomical images (DIR: double inversion recovery), as well as blood flow and blood volume weighted perfusion weighted signal (PWS) and temporal SNR (tSNR) at different V_cut of (A) brain and (B) prostate of all subjects from the middle-aged group. Slice 9 was shown for brains and slice 6 was shown for prostate. CBF: cerebral blood flow; CBV: cerebral blood volume; PBF: prostate blood flow; PBV: prostate blood volume.

Figure S6: Fitted relationship between (T_seg/T₂+b·ADC) and M_z. Dots are M_z calculated from Equation [S5] with matrix form. Solid lines are the fitted Equation [S6] with empirical four-parameter models. Dotted lines are (T_seg/T₂+b·ADC) and M_z of the label module of V_cut = 0.25 cm/s calculated from the empirical four-parameter models.

Table S2: The b-values of single velocity-encoding steps (Figure 1a) in this study calculated using the original integration equation for arbitrary gradient waveforms (Eq. [9.7] of Bernstein MA, King KF, Zhou ZJ. Handbook of MRI pulse sequences. Amsterdam; Boston: Academic Press; 2004.) and assuming perfect 180° refocusing pulses.

Table S3: Parameters used for estimating the diffusion bias.

Table S4: Estimation of diffusion bias for gray matter, white matter, and prostate following Equations [S1-S8]. The factor (T_seg/T2+b·ADC) with T_seg of 12 ms used in this study, the corresponding M_zl of label and control modules for FT-VSS and FT-VSI respectively (Equation [S6]), their difference M_{zl_diff} (Equation [S7]), the final M_{zf_diff} (Equation [S8], PSD = 3.0, 3.5 s for blood flow, blood volume estimation as used in this study), and the diffusion-induced bias relative to the blood flow or blood volume based perfusion weighted signal (PWS) results among both the young and middle aged groups listed in Table 1.