European Radiology

, Volume 28, Issue 7, pp 2812–2822 | Cite as

Liver fibrosis: stretched exponential model outperforms mono-exponential and bi-exponential models of diffusion-weighted MRI

  • Nieun Seo
  • Yong Eun ChungEmail author
  • Yung Nyun Park
  • Eunju Kim
  • Jinwoo Hwang
  • Myeong-Jin Kim
Magnetic Resonance



To compare the ability of diffusion-weighted imaging (DWI) parameters acquired from three different models for the diagnosis of hepatic fibrosis (HF).


Ninety-five patients underwent DWI using nine b values at 3 T magnetic resonance. The hepatic apparent diffusion coefficient (ADC) from a mono-exponential model, the true diffusion coefficient (D t ), pseudo-diffusion coefficient (D p ) and perfusion fraction (f) from a biexponential model, and the distributed diffusion coefficient (DDC) and intravoxel heterogeneity index (α) from a stretched exponential model were compared with the pathological HF stage. For the stretched exponential model, parameters were also obtained using a dataset of six b values (DDC#, α#). The diagnostic performances of the parameters for HF staging were evaluated with Obuchowski measures and receiver operating characteristics (ROC) analysis. The measurement variability of DWI parameters was evaluated using the coefficient of variation (CoV).


Diagnostic accuracy for HF staging was highest for DDC# (Obuchowski measures, 0.770 ± 0.03), and it was significantly higher than that of ADC (0.597 ± 0.05, p < 0.001), D t (0.575 ± 0.05, p < 0.001) and f (0.669 ± 0.04, p = 0.035). The parameters from stretched exponential DWI and D p showed higher areas under the ROC curve (AUCs) for determining significant fibrosis (≥F2) and cirrhosis (F = 4) than other parameters. However, D p showed significantly higher measurement variability (CoV, 74.6%) than DDC# (16.1%, p < 0.001) and α# (15.1%, p < 0.001).


Stretched exponential DWI is a promising method for HF staging with good diagnostic performance and fewer b-value acquisitions, allowing shorter acquisition time.

Key Points

• Stretched exponential DWI provides a precise and accurate model for HF staging.

• Stretched exponential DWI parameters are more reliable than D p from bi-exponential DWI model

• Acquisition of six b values is sufficient to obtain accurate DDC and α


Liver Fibrosis Liver cirrhosis Diffusion magnetic resonance imaging 



Alpha, Intravoxel heterogeneity index


α obtained using a six-b-value dataset (in this study)


Coefficient of variation


Distributed diffusion coefficient


DDC obtained using a six-b-value dataset (in this study)


Pseudo-diffusion coefficient


True diffusion coefficient


Perfusion fraction


Hepatic fibrosis


Intravoxel incoherent motion



The authors state that this work has not received any funding.

Compliance with ethical standards


The scientific guarantor of this publication is Yong Eun Chung.

Conflict of interest

The authors of this manuscript declare no relationships with any companies, whose products or services may be related to the subject matter of the article.

Statistics and biometry

Hyunsoo Yang in Yonsei University Health System performed statistical analysis, and he is not one of the authors.

Informed consent

Written informed consent was waived by the Institutional Review Board.

Ethical approval

Institutional Review Board approval was obtained.


• retrospective

• diagnostic study

• performed at one institution


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Copyright information

© European Society of Radiology 2018

Authors and Affiliations

  1. 1.Department of Radiology, Severance HospitalYonsei University College of MedicineSeodaemun-guKorea
  2. 2.BK21 PLUS Project for Medical ScienceYonsei University College of MedicineSeoulRepublic of Korea
  3. 3.Department of Pathology, Severance HospitalYonsei University College of MedicineSeodaemun-guKorea
  4. 4.Philips Healthcare KoreaSeoulKorea

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