Background

The liver longitudinal water proton relaxation rate R₁ is important for several reasons. It is a biomarker of liver pathology, and baseline R₁ is essential for the derivation of several other biomarkers. However, measurements of R₁ in individual livers or liver regions suffer from both systematic errors and random errors. Systematic errors (bias) arise because methods of measurement are suboptimal. Other systematic deviations occur when methods depend differently on liver composition and physiology. Random (repeatability) errors arise from physiologic and instrument noise, and can be high particularly when regions are small. In addition, even in the absence of bias and noise, there may be, in each study, genuine between-subject differences in R₁ due to between-subject variation in physiology or subclinical pathology. The aim of this study is to survey published values for native liver R₁ in order to help investigators ascertain whether the liver R₁ or T₁ values and variabilities they measure are broadly consistent with, or discordant from, prior literature.

Methods

Literature was searched using "Ovid Medline". Liberal inclusion criteria were employed. Human and rodent subjects were included if they were normal controls, if the study reported normal parts of livers with focal disease, or if they were patients in whom no liver abnormality had been found. Ex vivo studies were excluded. The mean and variance of R₁ across all subjects in each study was estimated from the publications, with the coefficient of variation given by $$$CoV=\frac{\sqrt{variance}}{mean}$$$. Any R₁ measurement method was allowed, as long as T₁/s or R₁/s^-1 was reported. To aggregate the data, individual studies were weighted by the inverse of their inter-subject variance in R₁. Two methods of representing B₀ dependence were used: a heuristic log-log relationship, and a biophysically-based model developed by Diakova et al[1]. R₁ was fitted to B₀ using the weighted non-linear least squares function in “R”. The fitted parameters in the heuristic log-log fit (Eq.1) were M and C: $$log(R_{1})=Mlog(B_{0})+C$$ The fitted parameters in the biophysically-based model (Eq.2) were A and B: $$R_{1}=A\omega^{-0.6}+B\tau_{D}[\ln(1+(\omega\tau_{D})^{-2})+4\ln(1+(2\omega\tau_{D})^{-2})]+R_{1,\inf}$$ where R_1,inf is the high-frequency asymptote, set here to 0.213 s^-1 at 310K; τ_D is the translational correlation time from Diakova et al. adjusted for temperature to 1.43×10^-11 s; and $$$\omega=2\pi\times42.58\times10^{6}\times B_{0}$$$ s^-1.

Results

After exclusions, 106 publications remained, with publication dates between 1981 and 2020. These represented 3122 humans, 109 mice and 233 rats. Sixteen field strengths were included between 0.04T to 9.4T. Figs.1 and 2 plot R₁ against B₀. Fig 3 plots inter-subject CoV against year of publication. R₁ showed the expected decrease with increasing field. The fit to Eq.1 gave M=-0.3649±0.0126 and C=0.2809±0.0059. The fit to Eq.2 gave A=(8.994±0.725)×10⁴ and B=(1.197±0.077)×10⁹. In studies published since 1992 (Fig.3), the median inter-subject CoV was 7.4% (lower quartile 5.1%, upper quartile 10.9%). In half of the studies, the measured R₁ deviated from Eq.2 by 9.0% or less (lower quartile 4.0%, upper quartile 19.1%).

Discussion

Fits from the heuristic and biophysical models were very similar. The major difference is that the heuristic model forces R₁ to zero at infinite field, while the biophysical model forces R₁ to asymptote. This difference might be important above 7T. In this study, following Diakova et al., we set the asymptote R_1,inf to 1/4.7 s^-1, the R₁ of pure deoxygenated water at high field, although a slightly higher value of might be appropriate if liver R₁ does not fully converge with water R₁ as illustrated by the dotted curve in Fig.1. The within-study between-subject CoV (median 7.4%) reflects not only repeatability, but also the expected between-subject variation. Between-study variation also includes between-population variation, together with bias from interactions between each study’s measurement method and its livers’ variation in flow, motion, fat, oedema, collagen, glycogen and iron. There are some limitations. Some literature may have been missed because suitable keywords were not included in their abstracts. Few reports validated their liver R₁ by means of a phantom, so accuracy is unknown. It was difficult to explore the effect of methodology on R₁, because some studies used methodology which was poorly described or did not appear robust, and because of correlation between field strength and methodology (old studies used old methodology and lower fields). Likewise, there was correlation between field strength and species (humans at low-medium fields, rats at medium-high fields and mice at high fields).

Conclusion

Quantitative relaxometry requires validation with phantoms and analysis of propagation of errors. However, it is also good scientific practice to compare one’s own findings with prior literature. An investigator who finds their average liver R₁ to be within 9% of Eq.2 with between-subject CoV <8%, can conclude that their measurements are consistent majority of the literature: measurements far outside these limits should be justified on physiological or methodological grounds.

Acknowledgements

The research leading to these results received funding from the Innovative Medicines Initiatives 2 Joint Undertaking under grant agreement No 116106 (IB4SD-TRISTAN). This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and EFPIA.

References

1. Diakova G, Korb J-P, Bryant RG. The Magnetic Field Dependence of Water T1 in Tissues. Magn. Reson. Med. (2012) 68:272–277.