Optimization of intra‐voxel incoherent motion measurement in diffusion‐weighted imaging of breast cancer

Abstract Purpose The purpose of this study was to optimize intra‐voxel incoherent motion (IVIM) measurement in diffusion‐weighted imaging (DWI) of breast cancer by separating perfusion and diffusion effects through the determination of an optimal threshold b‐value, thus benign and cancerous breast tissues can be accurately differentiated using IVIM‐derived diffusion and perfusion parameters. Materials and Methods Twenty‐eight patients, with biopsy‐confirmed breast cancers, were studied with a 3T MRI scanner, using T1‐weighted dynamic contrast‐enhanced MRI images, and diffusion‐weighted images with nine b‐values, ranging from 0 to 1000 s/mm². IVIM‐derived parameter maps for tissue diffusion coefficients D, perfusion fraction f, and pseudo‐diffusion coefficients D* were computed using the segmented fitting method with optimized threshold b‐value, and the sum of squared residuals (SSR) were calculated for IVIM‐derived parameters in different breast lesions. Results The IVIM analysis method developed in this work can separate perfusion and diffusion effects with the optimal threshold b‐value of 300 s/mm², and the results of diffusion and perfusion parameters from IVIM analysis can be used to differentiate pathological changes in breast tissues. It was found that the averages and standard deviations of the diffusion and perfusion parameters, D, f, D*, are the following, for malignant, benign and normal breast tissues respectively: D (0.813 ± 0.225 × 10−3 mm2/s, 1.437 ± 0.538 × 10−3 mm2/s, 1.838 ± 0.213 × 10−3 mm2/s), f (10.73 ± 3.44%, 7.86 ± 3.70%, 8.92 ± 3.72%), D* (15.23 ± 12.17×10−3 mm²/s, 12.02 ± 3.19 × 10−3 mm2/s, 12.03 ± 7.21 × 10−3 mm2/s). Conclusion IVIM‐derived diffusion and perfusion parameter maps depend highly on the choice of threshold b‐value. Using the methodology developed in this work, and with the optimized threshold b‐value, the diffusion and perfusion parameters of breast tissues can be accurately assessed, making IVIM MRI a technique of choice for differential diagnosis of breast cancer.


| INTRODUCTION
Breast cancer is one of the most common malignant tumors in females, and is the second leading cause of cancer death in women. 1 Magnetic resonance imaging (MRI) has been used more and more widely for the detection and diagnosis of breast cancers. 2 As a functional MRI technique, diffusion, and perfusion imaging are two of the most popular methods in breast cancer imaging. 3 Diffusion imaging or diffusion-weighted MRI (DWI) utilizes the Brownian motion effects of water molecules in the tissue intra-and extracellular spaces, has the potential to provide biological information on tumor blood micro-vasculature at the cellular levels. 4,5 Conventional DWI uses diffusion-weighting factors, the so called b-values, to derive the diffusion parameters. Based on MRI water signal attenuation model, the apparent diffusion coefficients (ADC) can be computed and images of diffusion parameters such as ADC maps can be reconstructed. 6 Due to active tumor cell growth pattern, diffusion of water molecules in malignant tissues is usually restricted by more tightened cellular membrane microstructure, and the ADC values in tumors thus are reduced. However in DWI images, malignant tissues show higher signal intensities. DWI therefore can be used to detect, monitor, and predict the tumor growth. 2,3 DWI measurement may be affected by contributions from perfusion phenomena. [7][8][9] Due to random distribution of capillary network in tissue, at the single voxel level, measured ADC values are typically higher than actual values, because of the contribution from blood flow perfusion effects from intra-voxel incoherent motion. DWI measurement thus reflect contribution also from tissue perfusion effects, as the microscopic blood flow in a randomly oriented capillary network produce a pseudo-diffusion contribution to the overall diffusion-weighted (DW) MR signal.
Le Bihan et al. 7,8 demonstrated that blood microcirculation in capillary network (perfusion) was able to change DW signal intensities at low b-values, and the intra-voxel incoherent motion (IVIM) theory was proposed to account for the molecular diffusion contribution driven by thermal energy as well as perfusion-based pseudodiffusion contribution. In IVIM theory, diffusion measurement contribution has two parts: true diffusion part and pseudo-diffusion part from perfusion. The selection of b-values in DWI measurement was considered to have strong effects for IVIM analysis and its derived diffusion parameters. 10 In recent years, IVIM measurement in the imaging of different organs has gained more attention, for example, in normal livers and liver cirrhosis, [11][12][13][14] in kidney, [15][16][17] and in the prostate. 10 proposed a computation method to evaluate IVIM parameters by optimal selection of b-value thresholds for the separation of perfusion and diffusion effects. 24 In diffusion-weighted imaging studies of breast tissue with multiple b-values, the benefit of using IVIM MRI is that it can result in information of tissue perfusion without the use of the "traditional" intravenously injected MR contrast agents, in additional to the diffusion parameters. IVIM analysis can extract detailed information about tissue diffusion and perfusion simultaneously, and has the potential to evaluate tissue perfusion noninvasively. There are previous studies indicating the clinical diagnosis potential of IVIM MRI for breast cancers. [21][22][23]25,26 However, currently published studies used different parameters and methods for IVIM analysis, limited data showed that the IVIM-derived parameters were very different with large errors, especially for parameters f and D*. 22 The purpose of this study is therefore to optimize IVIM measurement and analysis for breast cancer patients, specifically, an optimized threshold bvalue will be sought out so that diffusion and perfusion effects in three types of breast tissues and lesions can be separated.

2.A | Study population
This study was approved by our institutions' review boards (IRB), consents to participate in the study were obtained from each patient before MRI examination were performed. In total, 28 women who were diagnosed with breast tumors were recruited for this study, among them, 18 tumor lesions were diagnosed as malignant (invasive ductal carcinoma, IDC), and 11 tumors were benign lesions (one of them has two benign lesions) . The mean age of the patients was 47 years old, ranging from 15 to 62 years old.

2.C | IVIM analysis
Parametric maps of diffusion and perfusion with IVIM image analysis were all reconstructed with MATLAB program (Mathworks, Natick, MA, USA). In IVIM model, the signal intensity curves from multiple bvalue DWI experiments were expressed with the following formula: Where S(b) and S 0 denote the diffusion-weighted signal intensities of the pixels with and without diffusion-encoding gradients (indicated by the b-value), respectively. D is the apparent diffusion coefficient as reflected by pure molecular diffusion. f denotes the perfusion fraction. D* denotes the pseudo-diffusion coefficient.
The computation of D used the "traditional" mono-exponential diffusion model from diffusion-weighted images at multiple b-values, with the use of Eq. (2): To separate diffusion and perfusion in the presence of IVIM effects, a segmented bi-exponential analysis method was used. [21][22][23] Since perfusion contribution is negligible in high b-values DWI measurements, D maps were first computed with the polynomial fitting Secondly, the perfusion fraction (f) is calculated according to Where S int denotes the intercept pixel signal intensity when b-value extrapolates to 0 from the fitting curves. To calculate the pseudo-  The selection of ROI for IVIM analysis from a slice in a patient case study is shown in Fig. 3. Figure 3(a) shows an example of T1weighted dynamic contrast-enhanced breast images; Fig. 3   T A B L E 2 Numbers of patient cases that yield the optimal threshold b-value with the smallest residuals for malignant and benign tissues from all patients; there is a maximum number of patients (9 + 7, 16) whose IVIM analysis results indicated the optimal threshold b-value is 300. To determine the optimal threshold b-value for IVIM analysis of breast tissue at 3T, minimum SSR for each patient was used to extract the optimal threshold, the results are shown in Table 2 10 À3 mm 2 /s, 12.03 AE 7.21 9 10 À3 mm 2 /s).

Intra-voxel incoherent motion (IVIM) diffusion-weighted imaging has
recently gained an increasingly interest due to its potential to insight tissue microenvironment with both tissue diffusion and perfusion information. Several studies 23,25,26,28,29 have shown that using differ- As with other recent studies, [30][31][32] segmented fitting method has been used in the present work to derive the parameters through multiple fitting steps. Segmented fitting method is known to prevent over-fitting, and computation errors can be reduced. [33][34][35] There are typically two methods of segmented fitting [11][12][13]18,21,23 : two-step fitting and three-step fitting, and the most important step is the calculation of D maps with higher b-value images using Eq. (2). A twostep segmented fitting method uses high b-value DWIs to calculate the D maps with a simplified linear-fitting Equation [see Eq. (2)], then f and D* are calculated using a nonlinear-fitting algorithm for all b-value DWIs. 23 In general, due to limited data sampling and small perfusion fraction, two-step segmented fitting process ill-conditioned, thus may produce large errors. A three-step segmented fitting method is used in this work due to its fitting robustness and computation stability.
The determination of optimal threshold b-value is the most important step in segmented fitting procedure. If no optimal threshold b-value is chosen for the first step of D map computation, the estimation of IVIM perfusion fraction and pseudo-diffusion parameters will generate large errors, since diffusion and perfusion effects are not well separated in the IVIM analysis.
In some recent studies with breast cancer patients, 28  In this current study, we have determined that the optimal threshold b-value to separate diffusion and perfusion effects for accurate IVIM analysis is 300 s/mm 2 , as showed in the Results section. Our selection came from the detailed three-step analysis by comparing seven groups of IVIM-derived parameters, and nonlinear curve fitting was performed with experimental data (Fig. 1). Through quantitative SSR analysis (Fig. 2(d)) for all three tissue types, it was found that the optimal threshold b-value for malignant and benign lesions were 300 s/mm 2 , while normal breast tissue was 400 s/mm 2 .
For differential diagnosis, and in comparing with our experimental results, it was determined that the optimal threshold b-value of IVIM breast tissue imaging and analysis is 300 s/mm 2 (Table 2).
Finally, the following IVIM parameters were obtained in this study for malignant, benign and normal breast tissues, respectively:

CONFLI CT OF INTEREST
No conflict of interest.