Diffusion Kurtosis Breast Imaging model – Which should be the highest b-value?
Filipa Borlinhas1, Luísa Nogueira2, Sofia Brandão3, Rita G. Nunes1, Raquel Conceição1,4, Joana Loureiro3, Isabel Ramos3, and Hugo A. Ferreira1

1Instituto de Biofísica e Engenharia Biomédica, Faculdade de Ciências da Universidade de Lisboa, Lisboa, Portugal, 2Escola Superior de Tecnologia da Saúde fo Porto, ESTSP/IPP, Porto, Portugal, 3Hospital de São João, Porto, Porto, Portugal, 4Institute of Biomedical Engineering, University of Oxford, United Kingdom, Oxford, United Kingdom


For the application of the Diffusion Kurtosis Imaging (DKI) model, the use of higher b values is advised. Here, the diagnostic performance of the DKI model in the differentiation of benign and malignant breast tumors was studied for the first time regarding the most suitable higher b-value (2000, and 3000 s/mm2). In this study were included 36 benign and 75 malignant lesions, assessed using combinations of b-values 50 to 2000, and to 3000s/mm2. The b-value range 50 to 3000 s/mm2 showed the best results regarding diagnostic performance and so this range is suggested for use in future DKI breast cancer studies.


Diffusion Kurtosis Imaging (DKI) can be used to model Diffusion Weighted MRI data so as to estimate how much the distribution probability of water displacement deviates from a Gaussian function; this is due to the presence of tissue barriers. This model includes the Mean Diffusivity (MD) parameter, which corresponds to the Apparent Diffusion Coefficient when the water displacement distribution probability is Gaussian, and the Mean Kurtosis (MK), which reflects the deviation from Gaussianity1,2. Recently, it has been stated that these parameters can be used to differentiate benign and malignant breast lesions3,4. In DKI studies, the use of high b-values is recommended1 but the optimal highest b-value in breast DKI remains uncertain.

The purpose of this study was to assess which high b-value, 3000 or 2000s/mm2, for calculating the DKI parameters so as to differentiate benign and malignant breast lesions.


This study included 111 breast lesions: 36 benign and 75 malignant lesions confirmed histologically. Informed consent was obtained from all patients. Data were acquired using a 3T MRI scanner with a dedicated breast coil and a spin-echo single-shot echo-planar imaging sequence with 3 orthogonal diffusion gradient directions and b-values 0, 50, 200, 400, 600, 800, 1000, 2000 and 3000s/mm2. The MD and MK parameters were obtained from fitting the DKI model to the data, considering 2 ranges: 50 to 2000s/mm2, and 50 to 3000s/mm2. Comparisons between the 2 methods regarding their performance in the differentiation between benign and malignant lesions were made. Non-parametric statistic tests, and ROC curve analysis were performed, and the root-mean-square errors (RMSE) associated to the measurements were determined.

Results and Discussion

When higher b values are used MD and MK mean values are lower, considering both lesion types (Table 1). Considering any of the b-value combinations under study, both DKI parameters can differentiate between benign and malignant breast lesions (p=0.000) (Table 1). The Wilcoxon Signed-Rank test indicates (Table 2) that there are no significant differences between b-value groups in benign tumors, but significant differences are present considering the malignant ones. This means that the choice of used b-values range is very important.

Considering the ROC curve analysis (Figure 1), the b-value range with the best performances is b=50 to 3000s/mm2, for both MD and MK parameter. Moreover, for that b-value range, higher sensitivity was obtained (0.77 and 0.79 for MD and MK, respectively) (Table 3), indicating a stronger potential to identify the presence of malignant lesions. Likewise, the highest specificity was obtained for the same b-value range with the MD parameter (0.89).

Using the b=50 to 3000s/mm2, the highest accuracies were obtained for both parameters (0.81 for MD and 0.80 for MK) (Table 3), the higher values for Negative Predictive Value (NPV) were obtained for both DKI parameters (0.65), and the higher Positive Predictive Value (PPV) was obtained for MD parameter (0.94). These results indicate that these b-values are more suitable when applying the DKI model.

Furthermore, as shown in Table 3, the lower False Negative Rate (FNR) was obtained for MK (0.21), and the lower False Positive Rate (FPR) was obtained for MD parameter (0.11), in both cases using the 50 to 3000s/mm2 b-value range. Consistently, the risk of having a False Negative or a False Positive result is higher for the b-value group ranging from 50 to 2000s/mm2. The RMSE associated to model fitting resulted in similar values for the two methods considered (2.04 for b=3000s/mm2, and 1.96 for b=2000 s/mm2).

These experiments may indicate the need for using b-values as high as 3000s/mm2 in breast DKI. However, since using 2000s/mm2 as the highest b-value, also enables distinguishing breast lesions, and as the high b-value images are noisier, care is needed when interpreting these results.


The two b-value ranges under study enabled the differentiation of benign and malignant breast lesions. The majority of the statistical tests performed suggest that the b-value range from 50 to 3000s/mm2 is the best one for breast DKI from those tested. Further tests are needed to evaluate if the same result would be observed when considering the differentiation between malignant lesions subtypes.

Future studies applying DKI to breast imaging should take this result into consideration and include a high b-value of 3000s/mm2.


Research supported by Fundação para a Ciência e Tecnologia (FCT) and Ministério da Ciência e Educação (MCE) Portugal (PIDDAC) under grants UID/BIO/00645/2013, and FCT Investigator Program, grant IF/00364/2013.


1. Jensen JH, Helpern JA, et al. Diffusional kurtosis imaging: the quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med. 2005 Jun;53(6):1432–40.

2. Jensen JH, Helpern J. MRI quantification of non-Gaussian water diffusion by kurtosis analysis. NMR Biomed. 2010;23(7):698–710.

3. Nogueira L, Brandão S, et al. Application of the diffusion kurtosis model for the study of breast lesions. Eur Radiol. 2014 Jun;24(6):1197–203.

4. Wu D, Li G, et al. Characterization of breast tumors using diffusion kurtosis imaging (DKI). PLoS One. 2014;9(11):e113240.


Figure 1 - On the left, the ROC curves for MD are represented, and on the right the ROC curves for MK, considering the 2 b-value ranges. The pink and the yellow curves are the ones with the best performances, which correspond to the 50 to 3000s/mm2 b-value range.

Table 1 – Mean±SD, maximum and minimum values for benign and malignant breast tumors, obtained for DKI parameters estimated using the 2 combinations of b-values (b=50 to 2000s/mm2, b=50 to 3000s/mm2). b-values - s/mm2, SD - Standard Deviation, MD - Mean Diffusivity (×10-3mm2/s), MK – Mean Kurtosis (dimensionless measure), *-significant differences.

Table 2 – Results for Wilcoxon Sign Test and the respective p-values, for the different b-value groups considered in this study. MD - Mean Diffusivity (×10-3mm2/s), MK – Mean Kurtosis, * - statistical significant differences.

Table 3 – Statistical parameters extracted for each range of b-value in study. b-values - s/mm2, MD - Mean Diffusivity(×10-3mm2/s), MK – Mean Kurtosis, Area Under the Curve (AUC), Confidence Intervals (CI), Positive Predictive Value (PPV), Negative Predictive Value (NPV), False Negative (FN) rate , False Positive (FP) rate, * - significant differences.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)