T2 relaxation time elongation of hepatocellular carcinoma relative to native liver tissue leads to an underestimation of perfusion fraction measured by standard intravoxel incoherent motion magnetic resonance imaging
Letter to the Editor

T2 relaxation time elongation of hepatocellular carcinoma relative to native liver tissue leads to an underestimation of perfusion fraction measured by standard intravoxel incoherent motion magnetic resonance imaging

Fu-Zhao Ma, Yì Xiáng J. Wáng

Department of Imaging and Interventional Radiology, Faculty of Medicine, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China

Correspondence to: Yì Xiáng J. Wáng, PhD. Department of Imaging and Interventional Radiology, Faculty of Medicine, The Chinese University of Hong Kong, 30-32 Ngan Shing Street, Shatin, New Territories, Hong Kong SAR, China. Email: yixiang_wang@cuhk.edu.hk.

Submitted Oct 13, 2023. Accepted for publication Nov 14, 2023. Published online Nov 29, 2023.

doi: 10.21037/qims-23-1437

Hepatocellular carcinomas (HCCs) mostly show higher perfusion compared with adjacent normal liver tissue, reflecting their hypervascular nature (1,2). With computed tomography (CT) perfusion, Sahani et al. (3) measured blood flow (mL/100 g/min), blood volume (mL/100 g), and mean transit time (second) to be 92.8±88.6, 4.9±3.5, and 8.1±3.1 for HCC, whereas 14.9±2.8, 2.6±0.9, and 14.9±2.3 for background liver (with or without liver cirrhosis). With perfusion magnetic resonance imaging (MRI), Abdullah et al. (4) reported normalized total perfusion (mL/100 g/min) of HCC to corresponding tumor free liver to be 4.0 (range, 0.5–16.5). With perfusion MRI, Pahwa et al. (5) reported contrast distribution value was 49.0%±20.5% for HCC and 29.4%±8.3% for liver tissue. With perfusion CT, Ippolito et al. (6) reported median tissue blood volume (mL/100 g) was 20.4 for HCC and 10.9 for cirrhotic liver parenchyma. Using diffusion derived vessel density (DDVD) parameter (7,8) measuring the diffusion-weighted imaging (DWI) signal difference between b=0 and b=2 s/mm2 data of 72 HCC patients, we found HCC had a higher DDVD measure than the background liver, with the median ratio of HCC DDVD to background liver DDVD being around 3.0 (authors’ unpublished results).

Intravoxel incoherent motion (IVIM) theory in MRI was proposed by Le Bihan et al. to account for the effect of vessel/capillary perfusion on the aggregate magnetic resonance (MR) DWI signal. The fast component of diffusion is related to micro-perfusion, whereas the slow component is linked to molecular diffusion. Three parameters can be computed. Dslow (Ds, or D) is the diffusion coefficient representing the slow molecular diffusion (unaffected by perfusion). The perfusion fraction (PF, or f) 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 (Df, or D*) is the perfusion-related diffusion coefficient representing speed. IVIM has been applied to evaluate perfusion component of HCC. Paradoxically, most authors, such as Penner et al. (9), Zhu et al. (10), Woo et al. (11), Shan et al. (12), and Hectors et al. (13), reported a decreased PF of HCC relative to adjacent liver. In the meantime, with perfusion MRI, Hectors et al. (13) also reported a higher total blood flow of HCC than the adjacent liver.

In this letter, we propose that PFm (measured PF with IVIM imaging) is underestimated in the cases of HCC and this underestimation phenomenon is at least partially caused by the HCC’s T2 relaxation time (T2) elongation relative to adjacent liver tissue. If the tissue diffusion component and the tissue perfusion component have separate T2 relaxation times of T2t(T2of the tissue diffusion component) and T2p (T2 of the perfusion component, i.e., blood) respectively, to count for T2 dependency the standard IVIM model can be modified as [see Jerome et al. (14) and Lemke et al. (15)]:

S(b,TE)=S0((1−PF)⋅e−TE/T2te−bDs+PF⋅e−TE/T2pe−bDf)

where S0 is a scaling term independent of both diffusion and ‘T2 effect’ (which is defined as 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. Considering T2 does not have a linear relationship with DWI signal intensity and T2effect cannot be eliminated by normalizing with the signal intensity at b=0, we can divide Eq. [1] by (1−PF)e−TE/T2t+(PF)e−TE/T2p, and Eq. [1] can also be written as [see Jerome et al. (14)]:

S(b,TE)=S0((1−PF)⋅e−TE/T2t+PF⋅e−TE/T2p)      ⋅((1−PFm)e−bDs+PFm e−bDf)

Where PFm is the DWI measured PF which can be obtained by fitting the signal intensity of different b-values:

PFm(TE)=PF⋅e−TE/T2p(1−PF)⋅e−TE/T2t+PF⋅e−TE/T2p

Thus, PFm is PF taking into consideration its T2 dependency as shown with Eq. [3], and which is a parameter we actually measure. Eq. [3] can be simplified as:

PFm(TE)=1η⋅e−α⋅TE+1

Where η=1−PFPF, α=1T2t−1T2p.

Parameters PFm, T2t and T2p can be obtained by DWI data points with various time of echo (TE) and b-values by Eq. [4].

When b-value is sufficiently large, the perfusion component will decay to be minimal, and the signal intensity will be:

S(b,TE)=S0⋅(1−PF)⋅e−TE/T2te−bDs

If we take logarithm, then:

Log[S(b,TE)]=−TET2t+log(S0⋅(1−PF)e−bDs)

For the data points with same b value and various TE, logarithm of signal intensity is linear to the TE and the slope will be 1/T2t. Using data with identical b-value and various TEs, the value of T2t can be directly fitted by the least square method. After obtaining the specific value of η and T2t, we then know the result of T2p.

For the standard DWI sequence with given TE, PFm can be regarded as a function of T2t,T2pand actual PF as below:

PFm(PF,T2t,T2p)=11−PFPF⋅e−TET2t⋅e−TET2p+1

With the methods discussed above and assuming TE could be very short (i.e., close to zero) so to eliminate the T2 effect, Jerome et al. (14) estimated liver PF (PFm when TE =0) to be 0.08 (Figure 1). This would suggest that PF in normal liver is routinely overestimated with the standard IVIM assessment when TE of around 60 ms is commonly applied. In experimental physiology studies, it was suggested that the hepatic blood volume including that of the large vessels is about 25 mL/100 g (16,17). That PF of 0.08 is notably lower than the results obtained by other methods also suggests that PF may not be straightforwardly interpreted as a physiological perfusion volume fraction. We commonly estimated healthy liver PFm to be 0.18 (excluding large vessels) (18,19) when a TE of around 60 ms was applied. Note that PFm calculated with bi-exponential IVIM model is assumed to reflect fast diffusion contributed by both arteries and veins (13,20). In the study of Jerome et al. (14), the estimation of T2tand T2p of healthy liver at 1.5 Tesla (T) was around 38 ms (Figure 2) and around 80 ms respectively. T2t is close to the T2a (T2a refers to the measured T2 contributed by both T2tand T2p) of liver reported by other authors (21-23) while T2p is notably different to the literature value (24-26). Two possibilities may explain why the measurement of T2p was less stable. In the study of Jerome et al., T2t and α were estimated initially with two separate least square fittings, and T2p was calculated later. The bias of each fitting would have accumulated for the calculation of T2p. Moreover, 1/T2p was obtained prior to its reciprocal. Given that T2p is around 100 ms, slight disturbance at fitting would influence the value of 1/T2p substantially.

Figure 1 Five volunteer liver results from Jerome et al. (14). (A) Measured signal with various TE and b-values acquired at 1.5 Tesla. b-values (s/mm2) included 0, 50, 100, 150, 200, 250; and TE (ms) included 62, 72, 82, 92, 102. Standard IVIM model was used to fit the results of each TE individually. It can be seen that the signal decay pattern following increasing b-values differs according to different TEs. (B) The curve is the fitting result of PFm with T2 extended IVIM model. Points with 95% standard error bar represent the PFm values for a given TE with the standard model (color labeling is the same as in A), with a shorter TE associated with a smaller PFm. Note if TE =0, the curve intersects Y-axis at the value of around 8% (arrow). The figures are reproduced with permission [Jerome et al. (14)]. PFm, measured perfusion fraction; TE, time of echo; IVIM, intravoxel incoherent motion.
Figure 2 A high repeatability of the T2t measurement is shown. Measured signal with various TE and a specific b-value were used to obtain T2t according to Eq. [6], with the slope indicating −1/T2t. The high level of similarity of the slopes of lines suggests a high repeatability of T2t regardless of the choice of b-values. Data from Jerome et al. (14). TE, time of echo; T2t, T2 of the tissue diffusion component.

In this letter, the liver’s T2p as 80 ms from the model estimation of Jerome et al. (14) and 180 ms of measured results in literature (24-26) are tested for the analysis of HCC PFm dependency of its T2avalue. We demonstrate the PFm dependence of T2p and T2t with actual PF =0.08 and TE =55 ms. A number of authors reported that the T2a of HCC is around 60 ms with adjacent liver tissue’s T2abeing around 40 ms (27-29). If HCC occurred at the background of liver fibrosis, the differences between liver fibrotic tissue and HCC are assumed already considered (27-29). Higher HCC T2ahave also been reported (HCC and metastasis have approximately similar T2a) (30,31), which could be related to the differentiation of the HCC. Poorly differentiated HCCs may have deviated more from native liver tissue with longer T2a. Note that T2does not change much over the range of field strengths used for routine clinical MRI (0.2 to 3.0 T) (32). Considering that blood flow contribution to each tissue voxel’s T2a is small, T2a of HCC can be assumed to be same as its T2t. T2p of HCC has not been measured with T2 extended IVIM model. However, T2p of HCC will be longer than liver tissue as HCC contains a larger portion of arterial blood. Figures 3,4 show the estimated result of PFm based on modeling results of the study of Jerome et al. (14) and measured T2p/T2t results in literature, respectively. In Figure 3, the PFm of liver tissue is 0.157. PFm of HCC varies from 0.099 to 0.118 when T2p changes from the value equals to liver venous blood 180 ms to the value of arterial blood 250 ms. Increase of HCC’s T2p will slightly mitigate the PFm underestimation relative to liver tissue but the underestimation caused by T2 effect is always observable. In Figure 4, the same phenomenon is observed. PFm of liver tissue is 0.202 while PFm of HCC may vary from 0.138 to 0.149 depending on the T2p values assumed.

Figure 3 Change of PFm following the deviation of HCC T2t and T2p from native liver values [values based on modeling results of Jerome et al. (14)], showing an elongation of T2tof HCC leading to an underestimation of PFm. The estimation of PFm is based on Eq. [7] with assumed PF =0.08 and TE =55 ms. Liver parenchyma (green ball) is assumed to have T2t of 38 ms and T2p of 80 ms (14), then PFm will be 0.157. If an HCC has T2t of 60 ms (27-29) and its T2p remains the same as liver, then PFm will decrease to 0.099 (red ball). T2p of arterial blood is reported to be around 250 ms, while that of venous blood is 180 ms (22). HCC contains a much greater proportion of arterial blood (than the liver) which means HCC would have a higher T2p. If HCC is mostly supplied with arterial blood, and assuming liver is mostly supplied with venous blood, thus we assume an HCC has T2t and T2p of 60 ms and 112 ms [i.e., considering (180/250) = (80/112)], then PFm will be 0.118 (pink ball). Therefore, underestimation of HCC PFm will always exist even if HCC T2p increases dramatically relative to liver T2p. More likely HCC PFm will be between the result of red ball and the result of pink ball. HCC, hepatocellular carcinoma; PFm, measured perfusion fraction; T2t, T2 of the tissue diffusion component; T2p, T2 of the perfusion component; TE, time of echo.
Figure 4 Change of PFm following the deviation of HCC T2t and T2p from native liver values (values based on literature), showing an elongation of T2t of HCC leading to an underestimation of PFm. The estimation of PFm is based on Eq. [7] with assumed PF =0.08 and TE =55 ms. T2p of arterial blood is reported to be around 250 ms, while that of venous blood is 180 ms (24-26). If liver T2pof 180 ms is assumed to be close to that of venous blood, and liver T2t is 40 ms (19-21), then PFm is 0.202 (green ball). If an HCC has T2t of 60 ms (25-27) and its T2p remains the same as liver (180 ms), then PFm will decrease to 0.138 (red ball). HCC contains a greater proportion of arterial blood which will measure higher T2p. If HCC is mostly supplied with arterial blood, we assume an HCC has T2t of 60 ms and T2p of 250 ms, then PFm will be 0.149 (pink ball). Note that liver T2p is likely to be higher than 180 ms due to its 25% arterial blood supply and HCC T2p is likely to be lower than 250 ms with some extent of venous blood supply. Under these conditions, liver PFm will be higher and HCC PFm will be lower than the values indicated above, therefore the underestimation of HCC PFm relative to liver will be even greater. HCC, hepatocellular carcinoma; PFm, measured perfusion fraction; T2t, T2 of the tissue diffusion component; T2p, T2 of the perfusion component; TE, time of echo.

In conclusion, underestimation of HCC PFm caused by T2effect due to the elongation of T2a time of HCC relative to the liver is present during the standard IVIM measurement. The analysis in this letter can help to explain the much lower PFm observed for the spleen than for the liver (0.09 vs. 0.18) as spleen has a longer T2avalue than liver (18,33). The analysis in this letter may partially help to explain the recent observation that for tissue with T2a <60 ms, a negative correlation is noted with T2a time and apparent diffusion coefficient (ADC) (33). The analysis in this letter may also partially help to explain the paradoxical observation of Schmid-Tannwald et al. (34) that hypervascular liver metastases demonstrate significantly lower ADC values compared to hypovascular metastases, as hypervascular lesion will have a longer T2athan hypovascular lesion. Liver fibrosis has been consistently shown to have a reduced PFm by IVIM measure even at an early stage (35,36). Liver fibrosis is also noted to be associated with an increased T2a (37,38). Though pathophysiologically liver fibrosis is indeed associated with perfusion reduction (39-41), the PFm measured by standard IVIM could also have overestimated the extent of its reduction (or it could be a false positivity for the early-stage liver fibrosis cases). In the opposite direction, we noted that a higher liver iron content, and thus the associated shortening of T2a/T2*, may be associated with a higher liver PFm (42). In a healthy volunteer liver DWI study, it was noted that older subjects with higher liver iron content and thus shorter T2* and T2a demonstrated higher PFm relative to younger subjects (43). Based on empirical observations, it has been suggested that, for standard modeling, IVIM PFm and Ds are ‘mutually constrained’ (43-45). If one parameter changes toward one direction (e.g., decreasing), then the other changes toward to the opposite direction (e.g., increasing). A reduction of PFm of brain tissue has been noted to be associated with an increase of Ds(45). Considering T2 change is a major contributor to ADC change (33), and on the other hand for the standard IVIM modeling it does not appear that there is a mathematical reason that PFm and Dshave to be ‘mutually constrained’, we may hypothesize that the ‘mutually constraining’ of PFm and Ds are moderated by T2.

Acknowledgments

The authors thank Mr. Ben-Heng Xiao, at the Chinese University of Hong Kong, for helpful discussions during the manuscript preparation.

Funding: This work was supported by Hong Kong GRF Project (No. 14112521).

Footnote

Conflicts of Interest: Both authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-23-1437/coif). Y.X.J.W. serves as the Editor-in-Chief of Quantitative Imaging in Medicine and Surgery. 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.

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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Cite this article as: Ma FZ, Wáng YXJ. T2 relaxation time elongation of hepatocellular carcinoma relative to native liver tissue leads to an underestimation of perfusion fraction measured by standard intravoxel incoherent motion magnetic resonance imaging. Quant Imaging Med Surg 2024;14(1):1316-1322. doi: 10.21037/qims-23-1437

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