Characterization of focal liver lesions using the stretched exponential model: comparison with monoexponential and biexponential diffusion-weighted magnetic resonance imaging

  • Hyung Cheol Kim
  • Nieun SeoEmail author
  • Yong Eun Chung
  • Mi-Suk Park
  • Jin-Young Choi
  • Myeong-Jin Kim



To compare the stretched exponential model of diffusion-weighted imaging (DWI) with monoexponential and biexponential models in terms of the ability to characterize focal liver lesions (FLLs).


This retrospective study included 180 patients with FLLs who underwent magnetic resonance imaging including DWI with nine b values at 3.0 T. The distributed diffusion coefficient (DDC) and intravoxel diffusion heterogeneity index (α) from a stretched exponential model; true diffusion coefficient (Dt), pseudo-diffusion coefficient (Dp), and perfusion fraction (f) from a biexponential model; and apparent diffusion coefficient (ADC) were calculated for each lesion. Diagnostic performances of the parameters were assessed through receiver operating characteristic (ROC) analysis. For 20 patients with treated hepatic metastases, the correlation between the DWI parameters and the percentage of tumor necrosis on pathology was evaluated using the Spearman correlation coefficient.


DDC had the highest area under the ROC curve (AUC, 0.905) for differentiating malignant from benign lesions, followed by Dt (0.903) and ADC (0.866), without significant differences among them (DDC vs. Dt, p = 0.946; DDC vs. ADC, p = 0.157). For distinguishing hypovascular from hypervascular lesions, and hepatocellular carcinoma from metastasis, f  had a significantly higher AUC than the other DWI parameters (p < 0.05). The α had the strongest correlation with the degree of tumor necrosis (ρ = 0.655, p = 0.002).


The DDC from stretched exponential model of DWI demonstrated excellent diagnostic performance for differentiating malignant from benign FLLs. The α is promising for evaluating the degree of necrosis in treated metastases.

Key Points

• The stretched exponential DWI model is valuable for characterizing focal liver lesions.

• The DDC from stretched exponential model shows excellent performance for differentiating malignant from benign focal liver lesions.

• The α from stretched exponential model is promising for evaluating the degree of necrosis in hepatic metastases after chemotherapy.


Liver Hepatocellular carcinoma Metastasis Diffusion magnetic resonance imaging Comparative study 



Apparent diffusion coefficient


Area under the ROC curve


Confidence interval


Distributed diffusion coefficient


Diffusion-weighted imaging


Epithelioid hemangioendothelioma


Focal liver lesion


Focal nodular hyperplasia


Hepatocellular carcinoma


Intrahepatic cholangiocarcinoma


Intravoxel incoherent motion


Magnetic resonance imaging


Receiver operating characteristic


Region of interest


T2-weighted imaging



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

Compliance with ethical standards


The scientific guarantor of this publication is Nieun Seo.

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

Nieun Seo performed statistical analysis, who is one of the coauthors.

Informed consent

Written informed consent was waived by the Institutional Review Board.

Ethical approval

Institutional Review Board approval was obtained.


• retrospective

• diagnostic or prognostic study

• performed at one institution


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Copyright information

© European Society of Radiology 2019

Authors and Affiliations

  1. 1.Department of Radiology, Severance HospitalYonsei University College of MedicineSeoulSouth Korea

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