Non-Gaussian Diffusion Imaging with a Fractional Order Calculus Model to predict response to neoadjuvant chemoradiotherapy in local advanced rectal cancer
Yanfen Cui1, Zhizheng Zhuo2, and Xiaotang Yang1

1Shanxi Province Cancer Hospital, Taiyuan, China, 2MR Clinical Sciences, Philips Healthcare Greater China, Beijing, China


A novel non-Gaussian diffusion model based on fractional order calculus (FROC) were successfully applied to diffusion MRI of rectal cancer. Statistically significant differences in △D and △β values are observed between the responder group and non- responder group (p < 0.01), indicating that FROC-derived parameters from the FROC diffusion model may be useful as imaging biomarkers in predicting the biological properties of rectal cancer in clinical practice.


Water molecular diffusion in vivo tissue is much more complicated. Over the past decades, many non-Gaussian diffusion model has been increasingly used for rectal cancer characterization and treatment evaluations, including intravoxel incoherent motion (IVIM)[1], stretched-exponential model (SEM)[2],diffusion kurtosis model(DKI) [3], and others. Taking into account of anomalous diffusion in locally heterogeneous tissue structures and environment, a novel non-Gaussian diffusion model based on fractional order calculus (FROC) had been successfully applied to diffusion MRI of pediatric brain tumors and prostate cancer [4-5], The goal of our present study was to determine the diagnostic accuracy of FROC model-derived parameters to assess the response to CRT in patients with local advanced rectal cancer.


This retrospective study was approved by our institutional review board and written informed consent was waived. 43 patients with local advanced rectal cancer (LARC) underwent neoadjuvant chemoradiotherapy (CRT) and subsequent surgery, were enrolled in this study. All patients underwent pre- and post-CRT MRI at 3.0 T scanner(Achieva; Philips Healthcare, Best, The Netherlands) with 8-channel phased array torso coils, including T2-weighted imaging (T2WI), diffusion-weighted imaging (DWI) and contrast enhanced T1-weighted imaging. DWI was performed using a single-shot EPI sequence with multiple b-values (b = 0, 700, 1400, and 2100 s/mm2). Key acquisition parameters for DWI were as follows: TR/TE = 4,000/80 ms; flip angle= 90°; parallel imaging acceleration factor = 2; slice thickness = 3 mm, no slice gap; field of view (FOV) = 25 cm × 25 cm; matrix = 256 ×256; Total imaging time for DWI = 3 min 51 s. The FROC diffusion model was applied to fitting the multi-b-value diffusion dataset on a pixel-by-pixel basis using the following equation: S/S0=exp{-Dμ2(β-1)(γGdδ)2β[Δ-(2β-1) δ/(2β+1)]} [4], where the spatial fractional order β (dimensionless) is correlated to the degree of tissue heterogeneity and the spatial quantity μ (in units of μm) is related to the diffusion mean free length[4-5]. In data fitting, the initial D value was estimated by a mono-exponential fitting model using data acquired at b-values ≤ 1000 sec/mm2, allowing a direct comparison with ADC value. All image processing and analysis were performed using customized software developed in Matlab (Mathworks Inc, MA). For each patient, Regions of interests (ROIs) were manually drew on DWI maps with b= 1400 or 2100 sec/mm2 along the border of the tumor, and excluded the cystic, necrosis and hemorrhage areas by referring to the conventional MR images, by one experienced radiologists who were both blinded to all the clinical information. Mean values and standard deviations of D, β and μ were calculated from the tumor ROIs for each patient. Since a strong correlation between D and μ has been reported previously[4], our analysis was limited to D and β. Student’s t-test and receiver operating characteristic(ROC) curves were used to evaluate the diagnostic performance of FROC-derived parameters before and after CRT for prediction of histopathological response. All statistical analyses were performed using SPSS 19.0(IBM, New York, NY, USA) and MedCalc 15.8 (MedCalc,Mariakerke, Belgium).


Eleven patients (25.6 %) were classified as responders, while 32 subjects (74.4 %) were considered as non-responders. Before CRT, none of the mean D and β values correlated with subsequent tumor response (P>0 .05). While post-CRT, both the percentage difference between pre- and post-CRT D and β in the responder group was significantly higher than that in the non-responder group (P=0.005) (Figure1). ROC analysis showed that △β had a higher diagnostic performance, with the AUC of 0.912, and the specificity was improved compared with the mean △D(Figure2).

Discussion and Conclusion:

Our results demonstrate that there are significant difference in both the percentage difference between pre- and post-CRT D and β values between the responder group and non- responder group. △β yield greater accuracy in discrimination between good and poor responders, especially in improving the specificity, compared with the △D values. This may allow for personalized treatment-options in rectal cancer patients.


This study was supported by the Science and Technology Project of Shanxi Province (Grant No. 20150313007-5).


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Figure 1 A set of images from one representative patient with pre-CRT MRI for good responder (A-C) and non-responder(D-F). (A/D) DWI with b=1400 sec/mm2: (B/E): D map; (C/F): β map.

Figure 2 Diagnostic Performance of FROC-derived parameters △D and △β in assessing good response.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)