An explanation for the triphasic dependency of apparent diffusion coefficient (ADC) on T2 relaxation time: the multiple T2 compartments model
For in vivo diffusion weighted imaging (DWI), the apparent diffusion coefficient (ADC) has been considered to reflect tissue diffusion. ADC is calculated according to:
where b2 and b1 refers to a high b-value and a 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. When the low b-value is 0, ADC is calculated according to
where b2 and b0 refers to the high b-value and b=0 s/mm2 respectively, where S(b0) and S(b2) denote the image signal-intensity acquired at the b-factor value of b=0 and the high b-value, respectively.
ADC can also be calculated using the three b-values (such as b=0, 50, 800 s/mm2), according to the formula:
Where bi is the ith b value (unit: s/mm2), S(bi) is the signal intensity at bi.
Recently, we proposed that in vivo ADC measure is strongly associated with T2 relaxation time (T2) (1-5). T2 can be divided into short T2 band [<60 milliseconds (ms)], intermediate T2 band (60–80 ms), and long T2 band (>80 ms, all 3-T 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. On the other hand, a tissue is likely to measure a high ADC if its T2 is far away from 70 ms (Figures 1-3) (1-10). This observation initially appears to be puzzling. However, from Eq. [2], it can be seen that ADC value is high when the DWI signal difference between the b=0 image and the high b-value image is large. Thus, this phenomenon can be ‘simplistically remembered’ that, ADC value is high when: (I) the signal decay between b=0 image and high b-value image is fast such as the case for tissues with short T2, or (II) tissue has a very long T2 and appear high signal on b=0 image so that there is large amounts of signal to decay between b=0 image and high b-value image. ADC will measure a low value when tissue T2 is in the intermediate range of 60–80 ms. 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 time of echo (TE) for data acquisition (11).



In this letter, we attempt to explain the T2 dependency of ADC with the concept of the Intravoxel Incoherent Motion (IVIM) model. The IVIM model considering the T2 effect is expressed as (11-14):
where S0 is considered a scaling term independent of both diffusion and ‘T2 effect’ [which is defined as magnetic resonance imaging (MRI) signal differences contributed by T2 difference], and it is implicitly assumed that repetition time is long enough to ensure no significant modulation of the signal from incomplete T1 relaxation. Dslow is the diffusion coefficient representing the slow ‘pure’ molecular diffusion (unaffected by perfusion). The perfusion fraction (PF) represents the fraction of the compartment related to (micro)circulation, which can be understood as the proportional ‘incoherently flowing fluid’ (i.e., blood) volume. Dfast is the perfusion-related diffusion coefficient representing the incoherent microcirculation within the voxel, which holds information for blood perfusion’s speed.
A number of IVIM studies have shown that, if the TE is increased for DWI data acquisition, which can be seen as a shortening of T2 in MRI signal measurement in the transverse plane (i.e., faster signal decay, see Eq. [4]), there is an associated increase of PF (Figure 4) (12,13,15). Note that Dfast and PF are most commonly positively correlated (16). We can take it that, within a region-of-interest (ROI) or within a voxel, the T2 is not homogeneous, instead within a ROI or within a voxel there are multiple T2 elements (including T2 of arterial blood and T2 of venous blood). These T2 elements can be conceptually classified into shorter T2 elements (together referred to as ’shorter T2 compartment’ in this letter) and longer T2 elements (together referred to as ‘longer T2 compartment’ in this letter). In in vivo tissues, there are likely multiple T2 compartments. There are very short T2 compartments and very long T2 compartments. For simplicity, in this letter, we only summarily consider the ‘shorter T2 compartment’ and ‘longer T2 compartment’. From the measurement of MRI signal, shorter T2 compartment can be considered equivalent to perfusion (fast diffusion) compartment (fast initial signal decay in the IVIM model), and longer T2 compartment can be considered equivalent to diffusion compartment (Figure 5). For IVIM modeling, the initial fast signal decay at lower b-values can be due to either perfusion or due to shorter T2 elopements. Therefore, longer TE or shorter T2 is associated with increased PF (increased initial signal decay in the IVIM model). Hereby shorter T2 can be due to a higher portion of shorter T2 elements or the T2 relaxation times are actually shorter or a combination of both. On the other hand, an increase of T2 is associated with an increase of Dslow and decreased measure of the fast component [Figure 6 (13,15,17-20), Figure 7 (20-22), Figure 8 (23), Figure 9 (24-29), Figure 10 (28,30-32)]. Similarly, in a mouse study at 7.0 T with implanted tumors, an increase of the diffusion gradient separation time was associated with an increase of PF and a decrease of a Dslow variant which considered the non-Gaussian diffusion kurtosis model (Figure 11) (33). A mouse brain tissue study at 11.7 T with a triexponential model also showed similar results (Figure 12) (34). Thus, Eq. [4] can be re-written as:









Where Ffast reflects the compartment portion associated with shorter T2 and Fslow reflects the compartment portion associated with longer T2, and (Ffast + Fslow) =1. For Ffast, to be consistent with existing literature, we continue to use the abbreviation PF. Thus, PF in this letter may also represent the fast signal decay fraction associated with shorter T2 rather than the actual PF. It can be seen that, if all other variables can be fixed, then a decrease in shorter T2 corresponds to an increase in PF (if only shorter T2 and PF are the variables), and an increase in longer T2 corresponds to an increase in Dslow (if only longer T2 and Dslow are the variables). However, since a change in shorter T2 or longer T2 can affect other variables such as S0 and S(b), only experimental studies can further confirm the changes of IVIM parameters caused by T2 change. Note that, during IVIM analysis, we observed that the perfusion compartment and the diffusion compartment are mutually constrained (35-40). For example, the iron deposition and the resulting shorter T2 lead to lower Dslow and artificially higher PF and Dfast in older subjects’ liver and spleen than in younger subjects’ liver and spleen (35,40). And this may explain younger men’s liver has lower Dslow and higher PF than younger women’s liver. Due to the menstrual cycle, pre-menopausal women have lower liver iron level than men. The mutually constrained fast component measure and slow component measure suggests the ratio S(b)/S0 is indeed at least to a degree ‘stable’. If S(b)/S0 is ‘more stable’ or ‘with lesser change’, then Eq. [5] suggests fast component measure and slow component measure can be negatively correlated (such as an increase of PF can be compensated by a decrease of Dslow so that S(b)/S0 will be stable).
ADC is the composite of perfusion metrics (PF and Dfast) and diffusion metric (Fslow and Dslow). If the 1st b-value is 0, and b2 is the 2nd b-value, then from Eq. [2] and Eq. [4], ADC calculation can be approximated according to (ignoring the difference between T2shorter and T2longer):
Eq. [6] shows ADC is positively correlated with Dslow and Dfast, and negatively correlated with Fslow (thus, positively correlated with PF).
Figure 5 illustrates that, for tissues with aggregate T2 value <60 ms, if T2 increases from 40 to 60 ms, fast compartment measure decreases while slow compartment measure increases (if we do not consider other contributing factors); however, the decreased measure of fast compartment dominates and the net effect for the composite ADC is a decreased measure. Despite the pathohistological evidence of groupwise higher vasculature in hepatocellular carcinoma (HCC), HCC has been measured paradoxically with a lower PF by IVIM (14). For tissues with aggregated T2 value >80 ms, if T2 decreases from 170 to 90 ms, fast compartment measure increases while slow compartment measure decreases (if we do not consider other contributing factors); however, the decrease of the slow compartment dominates and the net effect for the composite ADC is a decreased measure. The observation as shown in Figure 5 can explain many of the apparently paradoxical observations for ADC measures. For example, articular cartilage has a high ADC of around 1.5×10−3 mm2/s and a T2 of around 37 ms at 3.0 T [see discussion in (4)], thus its high ADC is likely due to its dominant shorter T2 compartment. Chondrosarcoma has a high ADC of around 2.3×10−3 mm2 and a T2 of around 120 ms [see discussion in (4)], its high ADC measure is likely due to its dominant longer T2 compartment. In the cases of liver lesions, HCC ADC has been noted to have restricted diffusion relative to the liver. However, 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 computed tomography), it is unlikely that HCC has true lower diffusion, instead the lower HCC ADC is due to the longer T2 of HCC relative to the liver. Schmid-Tannwald et al. (41) reported that the mean ADC value of hypervascular liver metastases was paradoxically lower than the mean ADC value of hypovascular metastases. This could be due to the fact that hypervascular liver metastases have a higher proportion of the longer blood T2 contributed to the lower ADC measure [blood has longer T2 than that of liver metastases, see discussion in (14)].
In addition to T2 (which is often dominant), ‘true tissue diffusion’ indeed contributes to ADC (2). This is also evidenced by the success of the diffusion tensor imaging technique. When a cluster of voxels has a homogeneous T2 value, then their dominant diffusion direction can still be measured. In addition to the proportions of shorter T2 compartment and longer T2 compartment and ‘true tissue diffusion’, other factors such as ‘true vessel volume’ and macroscopic motion also contribute to the composite ADC measure. In an IVIM study of uterine fibroid, after continuous intravenous infusion of oxytocin which is known to decrease uterine fibroid blood flow, Sainio et al. (42) reported that all three IVIM parameters (i.e., PF, Dslow, Dfast) of the uterine fibroid decreased. In the case of kidney, kidney ADC is higher than can be predicted by T2, this could be due to the kidney being associated with higher true diffusion and higher true vessel volume [see discussion in (2)]. Kidney medulla and cortex have a long T2 of around 138 and 121 ms respectively at 3 T (2,43). Recently, Stabinska et al. (44) reported that, by increasing the diffusion gradient separation time, the measured kidney medulla and cortex PF both increased, while the measured kidney medulla and cortex Dslow both decreased, and the net ADC increased (Figure 13). In the case of liver aging, there is a shortening of liver T2 (45), a decrease of liver Dslow (35), and an artificial increase of liver PF and Dfast (35). However, the net liver ADC still decreases (46). There could be a decrease of liver true diffusion with aging, and note that there is also a decrease of true vessel volume with aging as measured by histology (47) and by the perfusion metric diffusion derived vessel density (DDVD) (35).

This explanation as shown in Figure 5 may not apply to in vitro studies with phantoms. For example, in a study with phantom, which might have a homogeneous T2 value, Laubach et al. (48) did not show a very low ADC measure for the solution with T2 of around 70 ms. Moreover, body fluids also have no perfusion element and their T2 may be ‘more homogeneously long’. For the case of gallbladder fluid, ADC is measured higher than can be predicted from T2 (Figure 1). Liver cysts are noted to have a higher ADC value than liver hemangioma, though liver hemangiomas are associated with blood flow inside the lesion [for T2 and ADC values see Figure 14 in (49), also see (50-52)]. Note that liver hemangiomas have a very high DDVD measure while the DDVD of liver cysts is close to zero when properly measured (49,53).

In this letter, we discuss as if ADC is calculated with two b-values with the low b-value being 0. However, regardless of whether ADC is calculated with b=0 or without b=0 (such as using b=50 and b=800 s/mm2), or with three b-values (such as using b=0, b=50, and b=800 s/mm2), the pattern of triphasic relationship between T2 and ADC always exists (2,4), and the same is true for the relationship between T2 and IVIM parameters (Figure 14) (37). If the first b-value to calculate the ADC is high, then ADC will be more equivalent to IVIM-Dslow. However, Dslow values do not appear to be reasonable as well. For example, in a review article by Englund et al. (54), it was noted that skeletal muscle has a Dslow of 1.46±0.30 mm2/s which is much higher than the liver Dslow of 1.1 mm2/s (20,22). We would think that the Dslow of skeletal muscles will not be higher than that of liver with the liver more richly perfused by hepatic artery and portal vein and with lots of sinusoids and space of Disse. Majority of literature reported a lower Dslow in HCC tissue than in liver parenchyma (22,55). However, HCC is associated with faster blood transit time and higher free water content than liver parenchyma. Liver fibrosis is associated with longer T2 (2,56), and this longer T2 may depressed PF measure and promote Dslow measure. We have commented that IVIM measured liver Dslow may be too high for severe liver fibrosis patients (39). Both the ‘shorter T2 compartment’ and ‘the longer T2 compartment’ consist of a spectrum of varying T2 elements. Though we describe a triphasic dependency of ADC on T2 relaxation time, it is possible that it is actually a biphasic relationship (2). However, due to the ever-existing measurement imprecision and other factors contributing to the ADC, the exact valley bottom of T2 cannot be located. When T2 is around 70 ms, we can assume that the PF is very low due to the slower signal decay compared to that when T2 is shorter (such as 30 ms), on the other hand the Dslow is also sufficiently low when T2 is 70 ms.
Note that this letter is not a systematic review. Associated with various data processing approaches, the current IVIM literature is highly heterogeneous with varying degrees of data quality. For the fast compartment, the discussion in this letter has been mainly on PF, rather than Dfast, as Dfast is generally more difficult to quantify reliably (16,22). Note that, Fslow = (1 − PF), and Fslow is mostly >0.80 in perfusion/diffusion IVIM observations. In the case of liver, which is richly perfused, its PF is around 20% (22). Another point is the discussions on T2 relaxation time in this letter are mostly based on 3-T data.
Diffusion concepts developed from in vitro studies may not be applicable to in vivo phenomena with heterogeneous T1 and T2 elements. As shown in Figures 1-3, in vivo ADC measure is more contributed by T2 than by true tissue diffusion, thus we suggest that we do not routinely use the term ‘diffusion restriction’ when interpreting clinical high b-value DW images and ADC maps. Instead, we may choose to use the term ‘high signal’ on high b-value DW image and ‘low signal’ on ADC map.
Acknowledgments
None.
Footnote
Funding: This work was supported by Hong Kong GRF Project (No. 14112521).
Conflicts of Interest: The author has completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-2025-195/coif). Y.X.J.W. serves as the Editor-in-Chief of Quantitative Imaging in Medicine and Surgery. The author has no other conflicts of interest to declare.
Ethical Statement: The author is 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.
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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