The rationale for proposing a magnetic resonance slow diffusion metric and its proof-of-concept testing showing spleen parenchyma and hepatocellular carcinoma have faster diffusion than liver parenchyma

Introduction

Diffusion weighted imaging (DWI) plays a pivotal role in magnetic resonance imaging (MRI) evaluation of a variety of pathologies. However, clinical application of the DWI derived quantitative metrics of apparent diffusion coefficient (ADC) and intravoxel incoherent motion (IVIM) parameters [perfusion fraction (PF), D_slow, D_fast] have not been very successful. ADC is indeed widely used, while it is generally regarded by physicians and radiologists that its role is only ‘supportive’ rather than ‘confirmative’. IVIM technique has largely remained in the research phase.

In the literature reported in vivo ADC results, there exists a ‘T2-ADC curve’, with ADC measure strongly affected by T2 relaxation time (T2) (1-6). T2 can be divided into short T2 band [<60 millisecond (ms)], intermediate T2 band (60–80 ms), and long T2 band (>80 ms, all 3T values). For the short T2 time band, there is a negative correlation between T2 and ADC. For the long T2 time band, there is a positive correlation between T2 and ADC. A tissue likely measures a low ADC if its T2 is close to 70 ms (such as the cases of lymphoma, abscess liquid, and the acute phase of brain ischemic stroke). The spleen (with T2 of around 60 ms) and parotid gland Warthin’ tumors (with T2 of around 80 ms) have a low ADC despite having rich blood perfusion. On the other hand, a tissue is likely to measure a high ADC if its T2 is far away from 70 ms, such as the cases of cartilage (with very short T2 and high ADC), myxoma and chondrosarcoma (both with very long T2 and very high ADC) (4). It appears to be unreasonable that the spleen has an ADC of only around 0.8×10⁻³ mm²/s while chondrosarcoma has an ADC of around 2.3×10⁻³ mm²/s (4). This ‘T2-ADC curve’ is graphically shown in Figure 1 (2,4,5,7). Uterine myometrium has T2 and ADC similar to that of skeletal muscles (5). A synthetic analysis based on the articles of DeMulder et al. (8), Bura et al. (9), and Barral et al. (10) shows that, relative to the myometrium T2 and ADC, myometrium tumors with shorter T2 are associated with higher ADC, myometrium tumors with longer T2 are associated with lower ADC, and myometrium tumors with very longer T2 (cystic degenerated leiomyoma and myxoid degenerated leiomyoma) are associated with high ADC, thus being very consistent with the ‘T2-ADC curve’ [see the supplementary figure in (5)]. This high dependency of ADC on T2 suggests that, though ADC can be contributed to a certain degree by tissue diffusion, it is overall not a good biomarker to reliably reflect true tissue diffusion (6).

Figure 1 Data show triphasic dependency of ADC on T2 relaxation time. (A) and (B) are all 3.0T data. Only the liver fibrosis models in (B) are animal study results; all others are human study results. In (B), model 1 is with a partial bile duct ligation cholestatic liver fibrosis rat model, and ADC was based on b-values =0, 800 s/mm², model 2A (ADC based on b-values=0, 200 s/mm²) and model 2B (ADC based on b-values =400, 500, 600, 800, 1,000 s/mm²) are with a carbon tetrachloride liver fibrosis rat model. (A) is reused with permission from (4), (B) is adapted with permission from (2). (C) Triphasic dependency of ADC on T2 for brain tissues [reused with permission from (5)]. The dotted blue arrow shows that, as brain tissue turns into abscess or lymphoma, T2 increases and ADC decreases. The dotted red arrow shows that, as glioma T2 increases, glioma ADC increases. Data sources for (A-C) were explained in (2,4,5). (D) is based on brain ischemic stroke results reported by Lutsep et al. (7). Y-axis is ADC (×10⁻³ mm²/s) or T2 signal ratio (ratio of stroke lesion signal intensity to normal brain signal intensity on T2-weighted image, and assumed to be 1 when without stroke). (D) indicates that, when T2 increases, ADC of the stroke lesion initially decreases and then increases, thus following a triphasic pattern. ADC, apparent diffusion coefficient; hrs, hours; mo, months; PA, pleomorphic adenoma.

We have recently proposed the metric of diffusion derived ‘vessel density’ (DDVD) (11-13), which is derived from the equation:

DDVDb0b1=S(b0)/ROIarea0−S(b1)/ROIarea1[unit:arbitraryunit(au)/pixel][1]

where ROIarea0 and ROIarea1 refer to the number of pixels in the selected region of interest (ROI) on b=0 and b=1 s/mm² diffusion weighted (DW) image, respectively. S(b₀) refers to the measured sum signal intensity within the ROI when b=0, and S(b₁) refers to the measured sum signal intensity within the ROI when b=1 s/mm², thus S(b)/ROIarea equates to the mean signal intensity within the ROI. S(b₁) and ROIarea1 can also be approximated by other low b-values (such as b=10 s/mm²) DW image. We have demonstrated that, for the liver and spleen DDVD measurement, when the time of echo (TE) is short or modest and time of repetition (TR) is long (such as TR >1,600 ms, TE =60 ms) and the 2^ndb-value is 1 or 2 mm²/s, DDVD_liver is approximately similar to DDVD_spleen which agrees with the known physiology that liver and spleen have similar amount of blood perfusion (14). According to the analysis in (14), a liver DDVD value of 11 au/pixel at 1.5T or 35 au/pixel at 3.0T will be approximately equivalent to computed tomography (CT) perfusion of blood volume of 18 mL/100 mL with a blood flood speed of around 1.2 mL/min/mL. This also correlates with the liver IVIM-PF measure of about 18% reported by us (15). In physiological studies, the hepatic blood volume including that of the large vessels is about 25 mL/100 g and blood flow is about 1.04 mL/min/mL (16). When a TE of 59 ms (TR =1,600 ms, free breathing acquisition) and b=0, 2 mm²/s were used for the DDVD calculation of 26 cases of hepatocellular carcinoma (HCC), we measured a mean DDVD_HCC/DDVD_liver ratio of 1.42. This value agrees well with the perfusion CT blood volume literature results median ratio of 1.38, while the perfusion CT blood flow literature results mean ratio is 1.92 (Figure 2) (17). Our study of parotid tumor DDVD also showed parotid tumor DDVD ratio measures were consistent with CT measured blood volume ratios (18). One of the initial goals of using DDVD was to minimize the T2 effect (which is defined as MRI signal differences contributed by T2 relaxation time difference). This is approximately achieved when TR is long and TE is short or modest (17). DDVD is less sensitive to TE selection and the ‘T2 effect’ compared to that of ADC and IVIM (17).

Figure 2 The DDVD_HCC/DDVD_liver ratio agrees well with the HCC/liver ratio of perfusion CT measured blood volume. (A,B) 1.5T liver diffusion weighted images with b-value of 0 (A), 2 s/mm² (B). The signal difference between b=0 s/mm² image and b=2 s/mm² images is dramatic, particularly the vessels show high signal when the motion probing gradient is ‘off’ while show dark signal when the motion probing gradient is ‘on’. The high intensity of the vasculature seen on b=0 s/mm² image, which is different from conventional T2-weighted image and suggests an ‘angiographic effect’, led to the naming of DDVD. (C,D) HCC measure to surround liver parenchyma measure ratios of perfusion CT measured blood volume (C) and blood flow speed (D). (C,D) are based on a random selection of 10 reports for blood volume and 9 reports for blood flow speed (each dot represents the result from one study, except the dots for median/mean value calculation). (E) is based on authors’ own data of 26 cases of HCC. DDVDr was measured at 3.0T, with a TE of 59 ms (TR =1,600 ms, free breathing acquisition) and b=0, 2 s/mm². This figure is reused with permission from (17). CT, computed tomography; DDVD, diffusion derived ‘vessel density’; DDVDr, DDVD ratio; HCC, hepatocellular carcinoma; SD, standard deviation; TR, time of repetition; TE, time of echo.

As in vivo diffusion metrics can be only measured with MRI thus external validation is not possible for diffusion metrics, it will be convenient and practical for us to consider liver/spleen parenchyma as the reference tissues. The spleen has been known to have a much lower ADC than the liver. However, the liver and spleen have similar amounts of blood perfusion per tissue volume per minute (14), and the spleen is waterier than the liver (the spleen has longer T1 and longer T2 than the liver, and the spleen has lower CT density than the liver). The magnetization transfer signal ratio (MTR) measure shows a higher proportion of water molecules in the liver are bound to other macro-molecules than the water molecules in the spleen (19), which supports that water molecules in the spleen have a greater extent of free diffusion. Free water molecules also allow longer T1 and T2 relaxation times than bounded water molecules. The spleen is also an organ with the function of storing blood (20). The spleen can respond to sympathetic stimulation by contracting its fibroelastic capsule and trabeculae to increase systemic blood supply. Recently, Yeung et al. (21) reported that spleen tissue had a higher contrast-enhanced CT extracellular volume fraction (ECV) than the liver, in healthy tissues and in tissues with systemic amyloid light-chain amyloidosis. We consider that it is unreasonable that spleen ADC is much lower than liver ADC. As HCCs are mostly associated with increased blood supply and increased proportion of arterial blood supply and higher water content (i.e., edema, as shown with higher signal on T2-weighted image and with lower density on X-ray CT), we consider that it is also unreasonable that HCC has a lower ADC than adjacent liver parenchyma. We argue that the lower ADC of the spleen and HCC relative to liver parenchyma is due to their longer T2 relative to liver parenchyma (6).

Another two entities with confusing ADC measures are liver hemangioma and simple liver cyst. Cysts are known to have a longer T2 and a higher ADC than hemangioma (Figure 3) (22-28). We also hypothesize that the higher ADC of liver simple cysts are due to their longer T2 (6). Due to the ‘flushing’ of blood flow inside the hemangioma, we hypothesize that actual diffusion of hemangioma liquid is faster than the more ‘static’ liquid of the cysts. Indeed, in a gadolinium-enhanced dynamic MRI study, Nam et al. (29) reported that ADC values were higher in the rapidly contrast enhancing hemangiomas than in the intermediately or the slowly contrast enhancing hemangiomas.

Figure 3 Compared to simple liver cyst, the liver HG has a substantially shorter T2 and a substantially lower ADC. Data are re-plotted from the reports of Yamada et al. (22), Parikh et al. (23), Tokgoz et al. (24), Erturk et al. (25), Fenlon et al. (26), Cittadini et al. (27), and Cieszanowski et al. (28). (A-F) Data in mean ± standard deviation; (G) data in mean and range. Y-axis: ADC in ×10⁻³ mm²/s or T2 in millisecond (ms). ADC, apparent diffusion coefficient; FNH, focal nodular hyperplasia; HCC, hepatocellular carcinoma; HG, hemangioma; Met, metastases; ML, malignant lesions.

During the course of our research activities and following the same concept as DDVD, we found that we can use a straightforward method to calculate a metric reflecting tissue slow diffusion, and we term this metric as ‘slow diffusion coefficient (SDC)’:

SDC=S(b1)−S(b2)b2−b1[unit:au/s][2]

where b₁ and b₂ refers to a high b-value (e.g., 400 mm²/s for the case of liver DWI) and a higher b-value respectively (e.g., 600 mm²/s for the case of liver DWI), where S(b₁) and S(b₂) denote the image signal intensity acquired at the high b-value and the higher b-value respectively (Figure 4). In this study, we explain the rationale of why we propose such a diffusion metric and attempt to conduct proof-of-concept testing with the liver, spleen, HCC, liver hemangioma, and simple liver cysts for such a metric. As ADC measure is heavily affected by T2 (6), we test whether SDC can minimize the T2 effect.

Figure 4 The images on the left are one liver IVIM series with various b-values. The graph on the right is the corresponding signal decay curve for the liver. As b-value increases, the liver signal intensity decreases on DW images, and the data are fitted with a bi-exponential decay model (blue curve line). We use the initial fast signal decay (e.g., b=0 and b=2 s/mm² data) to calculate DDVD and use the later part with high values (such as b=400 and b=600 s/mm² data) to calculate SDC. DDVD, diffusion derived vessel density; DW, diffusion weighted; IVIM, intravoxel incoherent motion; SDC, slow diffusion coefficient.

Methods

This is a retrospective analysis of previously prospectively acquired liver IVIM data. The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). All IVIM data were acquired with institutional ethical approval and with informed consent obtained from individual participants. 1.5T MRI was performed with a Philips scanner (Achieva, Philips Healthcare, Best, Netherlands). The IVIM diffusion imaging was based on a single-shot spin-echo type echo-planar sequence, with 15 b-values of 0, 1, 2, 15, 20, 30, 45, 50, 60, 80, 100, 200, 300, 600, and 800 s/mm². Number-of-excitation (NEX) was 2 for all image acquisition. The TR was 1,600 ms and the TE was 63 ms. SPIR technique (Spectral Pre-saturation with Inversion-Recovery) was used for fat suppression. Respiratory-gating was applied in all scan participants. Other parameters included slice thickness =7 mm and inter-slice gap 1 mm, matrix =124×97, field of view (FOV) =375 mm × 302 mm, number of slices =6. 3.0T MRI was performed with a Philips scanner (Ingenia, Philips Healthcare, Best, Netherlands). The IVIM diffusion imaging was based on a single-shot spin-echo type echo-planar sequence, with 16 b-values of 0 (NEX =5), 2 (NEX =5), 4 (NEX =1), 7 (NEX =1), 10 (NEX =1), 15 (NEX =1), 20 (NEX =1), 30 (NEX =1), 46 (NEX =1), 60 (NEX =3), 72(NEX =1), 100 (NEX =1), 150 (NEX =1), 200 (NEX =1), 400 (NEX =2), and 600 (NEX =2) s/mm². The default SPIR technique was used for fat suppression. The TR was 1,600 ms and the TE was 59 ms. Data was acquired with free breathing. Other parameters included slice thickness =7 mm and inter-slice gap =1.5 mm, matrix =123×124, FOV =372 mm × 341 mm, number of slices =20.

All image processing was implemented in a custom program developed on MATLAB (Mathworks, Natick, MA, USA). For the analysis of liver and spleen parenchyma, on each DW image for the liver/spleen, ROIs were drawn to cover a large portion of the right liver parenchyma and spleen parenchyma while avoiding large vessels and artifacts. Based on Eq. [1], for 1.5T data, DDVD_b0b1, DDVD_b0b2, DDVD_b0b15, DDVD_b0b20, and DDVD_b0b30, DDVD_b0b45, DDVD_b0b50, DDVD_b0b60, DDVD_b0b80, DDVD_b0b100, DDVD_b0b200, DDVD_b0b300, DDVD_b0b600, and DDVD_b0b800, were calculated from b=0 and b=1, b=0 and b=2, b=0 and b=15, b=0 and b=20, b=0 and b=30, b=0 and b=45, b=0 and b=50, b=0 and b=60, b=0 and b=80, b=0 and b=100, b=0 and b=200, b=0 and b=300, b=0 and b=600, and b=0 and b=800 s/mm² images, respectively. For 3.0T data, DDVD_b0b2, DDVD_b0b4, DDVD_b0b7, DDVDb_0b10, DDVD_b0b15, DDVD_b0b20, and DDVD_b0b30, DDVD_b0b46, DDVD_b0b60, DDVD_b0b72, DDVD_b0b100, DDVD_b0b150, DDVD_b0b200, DDVD_b0b400, and DDVD_b0b600, were calculated from b=0 and b=2, b=0 and b=4, b=0 and b=7, b=0 and b=10, b=0 and b=15, b=0 and b=20, b=0 and b=30, b=0 and b=46, b=0 and b=60, b=0 and b=72, b=0 and b=100, b=0 and b=150, b=0 and b=200, b=0 and b=400, and b=0 and b=600 s/mm² images, respectively.

For 1.5T data, SDC_b600b800 was calculated according to Eq. [2], where b₂ and b₁ refer to 800 and 600 s/mm², respectively, and S(b₂) and S(b₁) denote the signal intensity on b=800 and b=600 s/mm² images, respectively. For 3.0T data, SDC_b400b600 was calculated according to Eq. [2], where b₂ and b₁ refer to 600 and 400 s/mm², respectively, and S(b₂), and S(b₁) denote the signal intensity on b=600 and on b=400 s/mm² images, respectively. With 1.5T data, SDC_b600b800 was calculated for 10 healthy volunteer cases’ liver and spleen parenchyma, as well as two simple liver cysts and their corresponding liver parenchyma. With 3.0T data, SDC_b400b600 was calculated for 14 healthy volunteer cases’ liver and spleen parenchyma, as well as 13 HCC masses, 9 simple liver cysts, 13 hemangiomas and their corresponding liver parenchyma. These HCC, hemangioma, and cysts happened to exist in our datasets, and a random selection for these lesions was only based on that they were of reasonable sizes for measurement. Measurement of HCC excluded apparent necrotic areas whenever possible.

Based on the ROI drawn for DDVD analysis, conventional ADC was calculated according to:

ADC=ln(S(b1)/S(b2))b2−b1[unit:mm2/s][3]

where b₂ and b₁ refers to the high b-value and low b-value respectively, where S(b₂) and S(b₁) denote the image signal intensity acquired at the high b-value and low b-value respectively.

Based on Eq [3], for 1.5T data, ADC_b1b800, ADC_b2b800, ADC_b15b800, ADC_b20b800, and ADC_b30b800, ADC_b45b800, ADC_b50b800, ADC_b60b800, ADC_b80b800, AD_b100b800, ADC_b200b800, ADC_b300b800, and ADC_b600b800, were calculated from b=1 and b=800, b=2 and b=800, b=15 and b=800, b=20 and b=800, b=30 and b=800, b=45 and b=800, b=50 and b=800, b=60 and b=800, b=80 and b=800, b=100 and b=800, b=200 and b=800, b=300 and b=800, and b=600 and b=800 s/mm² images, respectively. For 3.0T, ADC_b2b600, ADC_b4b600, ADC_b7b600, ADC_b10b600, ADC_b15b600, ADC_b20b600, and ADC_b30b600, ADC_b46b600, ADC_b60b600, ADC_b72b600, ADC_b100b600, ADC_b150b600, ADC_b200b600, and ADC_b400b600, were calculated from b=2 and b=600, b=4 and b=600, b=7 and b=600, b=10 and b=600, b=15 and b=600, b=20 and b=600, b=30 and b=600, b=46 and b=800, b=60 and b=600, b=72 and b=600, b=100 and b=600, b=150 and b=600, b=200 and b=600, and b=400 and b=600 s/mm² images, respectively.

For each case, the mean signal intensity of each ROI was weighted by the number of pixels included in each ROI in different slices, then the average of the weighted DDVDs was calculated to obtain the value for each case. The measures of liver parenchyma were used to normalize the measures of spleen parenchyma, HCC, cysts, and hemangiomas. Data are presented graphically. For statistics, SDC values were tested by Mann-Whitney U test. A P value <0.05 was considered statistically significant, >0.1 as not significant, and between 0.05 and 0.1 as with a trend of significance.

Results

The DDVD_spleen/DDVD_liver ratio results with the 2^ndb-value started being very low and increased to 800 s/mm² for 1.5T data and 600 s/mm² for 3.0T are shown in Figure 5. For 1.5T’s DDVD_b0b1, the ratio of DDVD_spleen/DDVD_liver was 1.24; from DDVD_b0b15 to DDVD_b0b80, the ratio of DDVD_spleen/DDVD_liver stayed around or slightly below 1. For 3.0T, from DDVD_b0b2 to DDVD_b0b100, the ratio of DDVD_spleen/DDVD_liver stayed around or slightly below 1. From DDVD_b0b100 to DDVD_b0b800 for 1.5T and from DDVD_b0b150 to DDVD_b0b600 for 3.0T, DDVD_spleen/DDVD_liver ratio became increasingly higher.

Figure 5 DDVD_spleen/DDVD_liver ratio results from DDVD_b0b1 to DDVD_b0b800 for 1.5T and from DDVD_b0b2 to DDVD_b0b600 for healthy volunteers. The 2^ndb-value starts from 1 s/mm² for 1.5T and 2 s/mm² for 3.0T and then increases to 800 s/mm² for 1.5T and 600 s/mm² for 3.0T. There is an initial slight decrease and then followed by a substantial increase in DDVD_spleen/DDVD_liver ratio, and the changes in trend are more noticeable with 3.0T data than 1.5T data. See first paragraph in discussion for the explanation of the trends seen in this graph. Note that TE for was 63 ms for 1.5T acquisition and 59 ms for 3.0T acquisition. DDVD, diffusion derived vessel density.

The ratios of SDC_spleen/SDC_liver and SDC_cyst/SDC_liver for 1.5T data are shown in Figure 6A, and the ratios of SDC_spleen/SDC_liver, SDC_HCC/SDC_liver, SDC_cyst/SDC_liver, and SDC_hemangioma/SDC_liver for 3.0T data are shown in Figure 6B. For both 1.5T and 3.0T data, SDC_spleen/SDC_liver was >1, and a trend was noted with ‘SDC_hemangioma/SDC_liver’ > ‘SDC_cyst/SDC_liver’ > ‘SDC_HCC/SDC_liver’ > ‘SDC_spleen/SDC_liver’. Absolute SDC values of the above data are shown in Figure 7, with the hemangiomas having the highest median SDC value. Parametric visualizations of these results are shown in Figures 8-11.

Figure 6 SDC ratio results for spleen/liver (healthy volunteer), cyst/liver, HCC/liver, and HG/liver. (A) 1.5T results; (B) 3.0T results. All the ratios have a median value >1. The ratio values for liver lesions are scattered, partly due to some of the lesion sizes being small. HCC, hepatocellular carcinoma; HG, hemangioma; SDC, slow diffusion coefficient.

Figure 7 SDC absolute values (au/s, median and 95% confidence level) for the liver (healthy volunteer), spleen (healthy volunteer), cyst, HCC, and HG. (A) 1.5T results for SDC_b600b800; (B) 3.0T results for SDC_b400b600. The large 95% confidence level for liver lesions is partly due to some of the lesion sizes being small. HCC, hepatocellular carcinoma; HG, hemangioma; SDC, slow diffusion coefficient.

Figure 8 A SDC pixel map (calculated by b=400 and b=600 s/mm²) of upper abdomen showing the SDC value for spleen is higher than the SDC value for liver. Also note that the kidneys show very high SDC value. Data were acquired at 3.0T. SDC, slow diffusion coefficient.

Figure 9 HCC tumorous tissue shows higher SDC than adjacent liver parenchyma. (A) is a T2W image, where the HCC mass shows substantially higher signal compared with the surrounding liver tissue, indicating edema of the HCC. The spleen also shows higher signal compared to the liver, indicating that the water content of the spleen is higher. (B) is an ADC pixel map (calculated with b=0 and b=600 s/mm² images) showing that the ADC values of HCC and spleen are lower than that of liver parenchyma. (C) is an SDC pixel map (calculated with b=400 and b=600 s/mm² images) showing SDC values of HCC and spleen are higher than that of liver parenchyma. With tissues in the boxes measured (square for the HCC, large rectangle for liver parenchyma, and small rectangle for spleen parenchyma), the results are: ADC_HCC/ADC_liver =0.822, ADC_spleen/ADC_liver =0.811, SDC_HCC/SDC_liver =5.48, SDC_spleen/SDC_liver =6.11. Data were acquired at 3.0T. The color scale may differ among the images, as the goal of illustration is to use the liver parenchyma as reference. ADC, apparent diffusion coefficient; HCC, hepatocellular carcinoma; SDC, slow diffusion coefficient; T2W, T2-weighted.

Figure 10 HCC tumorous tissue (arrow) shows lower ADC and higher SDC than adjacent liver parenchyma. (A) ADC pixel map (calculated with b=0 and b=600 s/mm² images). (B) SDC pixel map (calculated with b=400 and b=600 s/mm² images). Data were acquired at 3.0T. The color scale may differ among the images, as the goal of illustration is to use the liver parenchyma as reference. ADC, apparent diffusion coefficient; HCC, hepatocellular carcinoma; SDC, slow diffusion coefficient.

Figure 11 Case examples show that SDC_hemangioma/SDC_liver ratio is higher than SDC_cyst/SDC_liver ratio. (A,B) A liver cyst (arrow); (C,D) a liver hemangioma (arrow). (A,C) ADC pixel map; (B,D) SDC pixel map. Compared with the background liver, the SDC of the cyst is also with high signal (B), but the relative signal is even higher on the ADC map (A). Compared with the background liver, the ADC of the hemangioma is also with high signal (C), but the relative signal is even higher on the SDC map (D). Cyst images (A,B) were acquired at 1.5T; hemangioma images (C,D) were acquired at 3.0T. The color scale may differ among the images, as the goal of illustration is to use the liver parenchyma as reference. ADC, apparent diffusion coefficient; SDC, slow diffusion coefficient.

ADC_spleen/ADC_liver ratio from ADC_b1b800 to ADC_b600b800 for 1.5T data and from ADC_b2b600 to ADC_b400b600 for 3.0T data are shown in Figure 12, with all the ratio values being <0.81.

Figure 12 ADC_spleen/ADC_liver ratio results from ADC_b1b800 to ADC_b600b800 for 1.5T and from ADC_b2b600 to ADC_b400b600 for 3.0T for healthy volunteers. The higher b-value is always 800 s/mm² for 1.5T data and 600 s/mm² for 3.0T data. The 1^stb-value starts from 1 s/mm² for 1.5T and 2 s/mm² for 3.0T and then increases to 600 s/mm² for 1.5T and 400 s/mm² for 3.0T. All the ratio values are <0.81. ADC, apparent diffusion coefficient.

Discussion

The results in Figure 5 show the change of DDVD values following the increase of the 2^ndb-value. Note that, an application of the diffusion gradients will lead to a decrease in observed T2 for tissues, which can be interpreted as an application of diffusion gradients is associated with a longer TE for data acquisition (30,31). Our modeling analysis shows that, when the 2^ndb-value is very low (such as 1 s/mm²), liver and spleen DDVD measures are contributed by both blood pool volume and blood flow speed; however, when the 2^ndb-value is only low (such as 10 or 20 s/mm²), then liver and spleen DDVD measures are more contributed by blood pool volume (13). It has been reviewed that the blood pool volume of the liver is slightly larger than that of the spleen, while the blood flow speed of the spleen is slightly faster than that of the liver [see Tab. 1 and Tab. 2 in (14)]. Figure 5 shows that, when the 2^ndb-value was 1 s/mm², DDVD_spleen/DDVD_liver was slightly larger than 1. When the 2^ndb-value was between >2 and 100 s/mm², a shorter T2 of the liver than that of the spleen (liver T2 =40 ms, spleen T2 =60 ms, 3.0T data) might have led to a faster initial signal decay during DWI signal acquisition and promotes ‘fast compartment’ measurement (6,31), and with these 2^ndb-value ranges, DDVD_spleen/DDVD_liver was around 0.9 (Figure 5). This remains also reasonable since liver blood pool volume is indeed slightly larger than that of the spleen. Following the 2^ndb-value being higher and higher, liver and spleen DDVD values were contributed more and more by slow diffusion (13). DDVD_spleen/DDVD_liver ratio returned to 1 when the 2^ndb-value was around 80 s/mm² for 1.5T and around 100 s/mm² for 3.0T. After the 2^ndb-value was ≥150 s/mm², the slow diffusion’s contribution to DDVD further built up, and the measure for spleen became higher than the measure for liver. According to the IVIM theory, the perfusion contribution would already have been very small at the stage when the 2^ndb-value is ≥150 s/mm². In addition, since liver and spleen have similar amounts of perfusion, data in Figure 5 show that when the 2^ndb-value was sufficiently large, slow diffusion started to dominate the DDVD value resulting in DDVD_spleen being measured higher than DDVD_liver. Such a DDVD observation suggests that it is possible to predominately measure the slow diffusion, and thus the conceiving of the SDC metric (Figure 4). In Figure 5, the changes of the trends were more ‘substantial’ for 3.0T data than for 1.5T data. This is likely due to that the T2 relaxation times were shorter at 3.0T than at 1.5T.

In this study, as shown in Figures 6,7, we confirmed that SDC_spleen was higher than SDC_liver. This is consistent with the fact that spleen has a higher extent of free water (thus likely with a faster slow diffusion than that of the liver). We also confirmed that SDC_HCC was higher than SDC_liver, and this agrees with the facts that HCC tumorous tissue has a higher water extent, being higher perfused and being perfused mainly with arterial blood (while liver parenchyma is perfused about 3/4 with venous blood). Another interesting observation is that SDC_hemangioma is higher than SDC_cyst. Earlier literature reported substantially higher ADCs for cysts than for hemangiomas (Figure 3). Due to the ‘flushing’ of blood flow inside the hemangioma, it is reasonable that the diffusion of hemangiomas liquid is faster than that of the more ‘static’ liquid of the cysts. Note that, the size of a water molecule is 280 picometers. If we consider that the size of a hepatocyte is 25 µm in diameter, then the size ratio of water molecule to hepatocyte is about 1/100,000. If we consider that the size of a spleen cell is 6.5 µm in diameter, then the size ratio of water molecule to spleen cell is about 1/26,000. Hepatic sinusoids (about 10–15 µm in diameter) are also quite ‘big’ considering the size of a water molecule. Water molecules may be freer to move inside in vivo tissue than we anticipated.

As ADC measure is heavily affected by T2 (6), in addition to minimizing the perfusion information, one of the goals of using SDC is also to minimize the T2 effect. For tissues with T2 less than 70 ms (such as spleen and HCC), the advantage of SDC over ADC has been demonstrated (Figures 6,7). For these tissues’ ADC, we consider them to be ‘fast diffusion compartment dominant’, and longer T2 depresses the measure for ADC’s ‘fast diffusion compartment’ (6). By focusing on the ‘slow diffusion compartment’, SDC measured higher values for the spleen and HCC than for the liver. This is likely to reflect truly faster ‘slow diffusion’ of the spleen and HCC than that of the liver. For tissues with T2 of more than 80 ms (such as cyst), longer T2 promotes the measure for ADC’s ‘slow diffusion compartment’ (6). For SDC, despite cysts having longer T2 than hemangiomas (Figure 3), SDC_hemangioma was higher than SDC_cyst, thus SDC is not dominated by the T2 effect. The T2 effect would ever exist, but this might be further mitigated by only using a small to moderate interval between the high b-value and the higher b-value for SDC calculation. Note that liver hemangiomas have a very high DDVD measure while the DDVD of liver cysts is close to zero when properly measured (14,32).

As the liver has a rather short T2, DW images of the liver with higher b-values are commonly associated with a low signal-to-noise ratio. This study used historical liver IVIM data, and we did not purposely try to optimize image quality with high b-values. For the absolute SDC values, the 95% confidence intervals as shown in Figure 7 were overall large. This is partly due to some of the lesion sizes being small. Figure 7 also shows absolute SDC values from different scanners/different magnetic fields may not be directly comparable. In our study, TE for 1.5T acquisition (=63 ms) and for 3.0T acquisition (=59 ms) are slightly different. A small but anticipated difference in Δ (time interval between the two motion probing pulses) and δ (time duration of the motion probing pulses) among different scanner models might also have contributed to the absolute SDC value difference between 1.5T results and 3.0T results. Our earlier experience with DDVD is that the ratio results were more comparable (14), and this is also tentatively shown in Figure 6. For DDVD-based differential diagnosis with the same MRI scanner, DDVD ratio results have been shown to be ‘somewhat’ better, but not massively better, than absolute DDVD values at a group level (33-35).

In this study, we tested whether ADC values calculated using Eq. [3] but with various combinations of high b-values could play a similar role as SDC. However, with all the combinations of liver DWI clinically applicable b-values as shown in Figure 12, spleen ADCs were all lower than liver ADCs. Therefore, ADC value calculated with a combination of high b-values cannot replace SDC. The literature results of IVIM-D_slow also differ from SDC. IVIM-D_slow and IVIM-PF for the spleen have been consistently measured much lower than that of the liver (15). In most literature reports, IVIM-D_slow for HCC has been measured lower than that of the surrounding liver parenchyma (36-38). Therefore, IVIM-D_slow also cannot replace SDC. Note that, though in principle SDC and IVIM-D_slow measure the same phenomenon, the actual calculation approaches are different. In its most simplified term, IVIM-D_slow is calculated according to:

IVIM-Dslow=S(b200)/S(b0)−S(b600)/S(b0)b600−b200[unit:mm2/s][4]

S(b₀) is affected by T2 of the target tissues. Therefore, the compounding factor of S(b₀) is introduced. Though histology and imaging data such as those of perfusion CT and DDVD show HCCs tend to be hypervascular, in most IVIM literature, PF for HCC has been reported to be lower than PF of the adjacent liver (33,36,38). For IVIM analysis excluding b=0 s/mm² data, as such when curving fitting starts from b=2 s/mm², IVIM results are still heavily affected T2 (39). It has also been described that IVIM analysis poorly characterizes liver hemangioma (40).

There are many limitations to this study. The assumptions of: (I) the spleen has a faster diffusion than the liver; (II) HCC has a faster diffusion than the surrounding liver parenchyma; and (III) liver hemangioma has a faster diffusion than liver cyst, are all based on theorization, rather than actual experimental validation. While MRI perfusion measures can be validated such as the results in Figure 2 and the liver IVIM-PF being approximately 20% (15,36), diffusion measures cannot be validated (41). This study aimed only to prove the principle that the spleen and HCC have a faster diffusion than liver parenchyma, and hemangiomas have a faster diffusion than the simple liver cysts, while we did not pre-calculate the statistical power for significance of among various entities’ SDC. For the 3.0T data ratio difference of SDC_hemangioma/SDC_liver and SDC_cyst/SDC_liver, the P value was only 0.096. However, we highly anticipate that, given sufficient sample size, the observed trend will be statistically significant. For the patient studies with HCC, potential variability such as liver fibrosis will affect ratios. The primary goal of this study was not to recommend the wider adoption of the diffusion metric SDC, which will require more testing with various organs and with different pathological entities. Data acquisition optimization for SDC also remains to be further explored. How SDC is sensitive to the TE parameter, as compared with that of ADC, should be explored in future studies. We also anticipate that further improvement of DWI data acquisition techniques will enhance the stability of DDVD and SDC measurement.

Conclusions

In conclusion, with the diffusion metrics SDC, in this study we achieved our primary goal of confirming that, the spleen has a faster diffusion than the liver, HCC tumorous tissues on average have a faster diffusion than the surrounding liver parenchyma, and hemangiomas have a faster diffusion than the simple liver cysts. There is a possibility that SDC will be a useful diffusion metric in clinical practice. Theoretically, an application of four DWI b-values, such as b=0, 10, 600, 800 s/mm², will allow the generation of three parameters, i.e., DDVD, SDC, and ADC, with ADC considered a composite biomarker commonly dominated by T2 effect and with its features in various disease entities well characterized. This may further improve disease classifications.

Acknowledgments

None.

Footnote

Funding: This study received funding from a Hong Kong GRF Project (No. 14112521).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-537/coif). Y.X.J.W. serves as the Editor-in-Chief of Quantitative Imaging in Medicine and Surgery. Y.X.J.W. is the founder of Yingran Medicals Ltd., which develops medical image-based diagnostics software. B.H.X. contributed to the development of Yingran Medicals Ltd. The other author has no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. This is a retrospective analysis of previously prospectively acquired liver IVIM data. The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). All IVIM data were acquired with institutional ethical approval and with informed consent obtained from individual participants.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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