Eunju Kim^{1,2}, Jinwoo Hwang^{1}, Jae-Hun Kim^{3}, and Marc Van Cauteren^{4}

We propose a new approach to IVIM analysis using computed DWI (cDWI) based on stretched exponential model. IVIM analysis is widely studied clinically to evaluate tissue perfusion and diffusivity using a range of low and high b values. However, signal attenuation curves of different b values are heterogeneous because of biological effects from multiple components and patient’s motion during the acquisition. So we generated cDWI first using stretched exponential model which can better fit for signal attenuation curve and analyse IVIM parametric maps using cDWI. The proposed approach can fit more robustly the IVIM model parameters.

Introduction

Recently, Intravoxel incoherent motion (IVIM) parameters have been widely used as quantitative imaging biomarkers. But reliable estimation of IVIM parameters is difficult because of the non-linearity of the model, the limited number of low b-values and the low SNR in high b-values [1,2,3]. In this study, we proposed a new approach to estimate IVIM parameters using computed DWI (cDWI) based on the stretched exponential model, having no assumption of the number of intravoxel components. From the cDWI, IVIM parameters could be reliably obtained by increasing the number of b-values and SNR of DWI in low and high b-value.Methods

Acquisition of DWI

Five healthy subjects underwent 3.0T magnetic resonance imaging (Ingenia CX, Philips Healthcare, The Best, Netherlands) using an anterior-posterior coil for single shot-EPI DWI sequence with 10 b-values. (b values = 0, 25, 50, 75, 100, 200, 300, 500, 800, and 1000 s/mm2, TR/TE = 2700ms/67ms, slice thickness = 7mm, matrix size = 128x126, FOV = 40x40cm2, the number of slices = 29, and total scan time = 2.5 minutes).

MRI data analysis

cDWI using Stretched exponential model

For cDW images, the stretched-exponential model [4] was used.

$$$\frac{S(b)}{S_{0}}=\exp(-{(bDDC)^\alpha)}$$$, where $$$\alpha$$$ is the stretching parameter, which characterizes the deviation of the signal attenuation from the mono-exponential model. A value of $$$\alpha$$$ that is near one indicates high homogeneity in apparent diffusion, whereas a low value of $$$\alpha$$$ result from non-exponential model caused by the addition of multiple components. The DDC is the distributed diffusion coefficient, which is similar to D parameter in mono-exponential model. For each voxel, the value of $$$\frac{S(b)}{S_{0}}$$$ was computed using estimated DDC and $$$\alpha$$$ values, and then the cDWI data (S(b)) were estimated.

IVIM parameters

For estimating IVIM parameters, the bi-exponential model was used.

$$$\frac{S(b)}{S_{0}}=f\times\exp(-bD*)+(1-f)\times\exp(-bD)$$$

, where f is the perfusion fraction, D is the diffusion coefficient and D* is the pseudo-diffusion coefficient. To obtain the IVIM parameters, the IVIM signal equation above was calculated by means of the Luciani simplified method [2,5] using home-built SW (Diffusion analysis software, EXPRESS 2.0, Philips Healthcare, Korea). To estimate D parameters, first, the curve was fitted for b>200 s/mm2 (D* is significantly greater than D). And then the curve was fitted for f and D* over all values of b, while keeping D constant. This simplified two-step method was used to increase robustness under biological conditions. For comparison, we compared the IVIM parameters estimated from raw DWI and the cDWI calculated by the stretched exponential model.

**Discussion and conclusion**

1. Le Bihan D, MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders.Radiology. 1986 Nov; 161(2):401-7.

2. Luciani A, Vignaud A, Cavet M, et al. Liver cirrhosis: intravoxel incoherent motion MR imaging pilot study. Radiology 2008;249(3):891– 899.

3.Dow-Mu Koh, David J. Collins, Matthew R. Orton et al. Intravoxel Incoherent Motion in Body Diffusion-Weighted MRI: Reality and Challenges. AJR:196, June 2011

4.Bennett KM, Schmainda KM, Bennett RT et al. Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model. Magn Reson Med. 2003 Oct;50(4):727-34.

5. Seber GA, Wild CJ. Nonlinear regression. Hoboken, NJ: Wiley-Interscience; 2003.

6. Sigmund et al. Intravoxel incoherent motion and diffusion-tensor imaging in renal tissue under hydration and furosemide flow challenges. Radiology. 2012 Jun;263(3):758-69

Figure 1: Diagram of IVIM analysis using cDWI based on stretched
exponential model. cDWI is calculated from DDC and α using stretched
exponential fitting (a, b). IVIM parameters (f, D* and D) is calculated from
the cDWI using bi-exponential model (c,d).

Figure 2: Raw multiple b-value DWI (a) and multiple b-value
cDWI calculated from stretched exponential model (b).

Figure 3: IVIM parametric maps and fitting
curve using bi-exponential model. f, D* and D parametric maps,
exponential and logarithm(log) decay curve from raw DWI (a) and cDWI (b).

Figure 4: The comparison of IVIM
parameters (f, D* and D) calculated from raw DWI (blue) and cDWI (orange). Box plots for f, D*, and D parameters estimated
from raw DWI and cDWI data, and their 3D scatter plot.