Yoshifumi Noda^{1}, Satoshi Goshima^{1}, Kimihiro Kajta^{1}, Yuta Akamine^{2}, Masatoshi Honda^{2}, Tomoyuki Okuaki^{2}, Hiroshi Kadohara^{2}, Nobuyuki Kawai^{1}, Hiroshi Kawada^{1}, Yukichi Tanahashi^{1}, and Masayuki Matsuo^{1}

Intravoxel incoherent motion, a bi-exponential model of diffusion-weighted imaging with multiple b values, can represent pure molecular diffusion and perfusion, and be used in characterizing focal hepatic lesions. Recently, stretched exponential model has been used in glioblastoma and prostate cancer. In this study, we evaluated the feasibility of stretched exponential model for differentiating benign and malignant hepatic lesions. Our results showed that DDC value from a stretched exponential model was the highest diagnostic potential, so it could be a quantitative imaging biomarker for differentiating benign and malignant hepatic lesions.

This prospective study was
approved by our institutional review board and written informed consent was obtained.
Eighteen patients with suspected liver disease underwent magnetic resonance
(MR) imaging. Twenty-three focal liver lesions were identified in 18 patients.
Fifteen lesions were benign, composed of simple cyst (*n* = 10), hemangioma (*n* = 3),
complicated cyst (*n* = 1), and focal
nodular hyperplasia (*n* = 1). Eight
lesions were malignant included hepatocellular carcinoma (*n* = 6) and metastasis (*n*
= 2).

MR imaging was performed using 3-T MR system (Ingenia 3.0T CX, Philips Healthcare). DWI was obtained using free-breathing two-dimensional fat-suppressed single-shot echo-planar sequence (repetition time/echo time, 5,000/57 msec; matrix, 96 × 96; field of view, 40 × 32 cm; parallel imaging factor, 2.0; b factors, 0, 10, 25, 50, 75, 100, 200, 500 and 800 s/mm2; section thickness, 6 mm with 1-mm intersection gap; acquisition time for 30 sections, 4 min 15 s).

A radiologist measured the DWI parameters of hepatic lesions greater than 10 mm in maximum diameter using home-built SW (Diffusion analysis software, EXPRESS 2.0, Philips Healthcare, Korea), including the apparent diffusion coefficient (ADC) from a mono-exponential model, the true diffusion coefficient (D), pseudo-diffusion coefficient (D*) and perfusion fraction (f) from a bi-exponential model, and the distributed diffusion coefficient (DDC) and water molecular diffusion heterogeneity index (α) from a stretched exponential model.

The Mann-Whitney U test was conducted to compare all DWI parameters between benign and malignant hepatic lesions. Areas under the receiver-operating-characteristic (ROC) curve (AUC) were compared to assess the diagnostic values in differentiating benign and malignant hepatic lesions. A P value of less than 0.05 was considered to be significant.

This study demonstrated that the DDC value from a stretched exponential model had the highest diagnostic potential and showed comparable with ADC value for differentiating benign and malignant hepatic lesions.

A stretched exponential model characterizes non-Gaussian behavior of molecular diffusion and reflects the degree of intravoxel heterogeneity of biological tissue 1. The DDC value reflects a continuous distribution of diffusion coefficients from each diffusion compartment. In our study, DDC value was significantly lower in malignant hepatic lesions than in benign lesions. The reduction of DDC value represents the destruction of a higher density of cells and stroma, resulting in the restriction of the water in the tissue.

The ADC value was lower than DDC in normal tissue, on the other hand, higher than DDC in cancer 2. Thus, the gap of ADC values between normal and cancer tissue would be smaller than DDC. Actually, in our data, the gap of DDC value between benign and malignant hepatic lesions was larger than that of ADC value (2.18 × 10-3 mm2/s in DDC vs 1.57 × 10-3 mm2/s in ADC). The AUCs for differentiating benign and malignant hepatic lesions were comparable between DDC and ADC values at this time. We could confirm the above phenomenon, however, we believe that DDC value may have more potential to distinguish benign and malignant hepatic lesions than ADC value in larger cases.

In conclusion, ADC and DDC values provided by bi-exponential and stretched exponential models could be a quantitative imaging biomarker for differentiating benign and malignant hepatic lesions.

[1] Bennett KM, Schmainda KM, Bennett RT, Rowe DB, Lu H, Hyde JS. Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine 2003;50(4):727-34.

[2] Liu X, Zhou L, Peng W, Wang H, Zhang Y. Comparison of stretched-Exponential and monoexponential model diffusion-Weighted imaging in prostate cancer and normal tissues. J Magn Reson Imaging 2015;42(4):1078-85.