Introduction

Breast cancer characterized by significant tumor heterogeneity1, which necessitates highly individualized treatment strategies and survival prognosis based on molecular subtypes2. Clinically, breast cancer is classified into four intrinsic subtypes according to key prognostic factors, including the expression of estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2), and Ki-67 proliferation index3. Additionally, the assessment of histological grades and axillary lymph node metastasis (ALNM) is crucial for accurate staging and therapeutic planning4. However, the identification of these clinic prognostic factors generally relies on invasive histopathological examination5.

Dynamic contrast-enhanced MRI (DCE-MRI) is recognized for its high sensitivity in detecting breast cancer and plays a vital role in clinical practice6,7. However, it often suffers from variable specificity and raises concerns regarding the use of gadolinium contrast agents8,9,10. In contrast, diffusion-weighted imaging (DWI) is a non-invasive technique that exploits the diffusion of water molecules as an endogenous contrast, and it has been extensively investigated as an important complementary approach for detecting and characterizing breast cancer11,12,13,14,15. The apparent diffusion coefficient (ADC), a commonly used metric derived from the mono-exponential (Mono) model, is limited by its reliance on the simple Gaussian diffusion assumption, which may not be accurately reflect water diffusion in the presence of microperfusion and biological complexity16.

To address these limitations, more advanced diffusion models have been developed to better correlate diffusion parameters with biologically relevant microstructures17,18,19,20,21. The intravoxel incoherent motion (IVIM) model distinguishes between microcirculatory perfusion and water molecule diffusion, yielding quantitative parameters such as tissue diffusion coefficient (D), pseudo diffusion coefficient (D*) and perfusion fraction (f)22. The diffusion kurtosis imaging (DKI) model enhances our understanding of tissue heterogeneity and complexity through the calculation of the mean diffusion coefficient (MD) and dimensionless kurtosis coefficient (MK)23. The stretched exponential model (SEM) accounts for intravoxel heterogeneity and distributed diffusion, providing metrics such as the distributed diffusion coefficient (DDC) and heterogeneity index (α)24. The continuous-time random-walk (CTRW) model, a novel diffusion framework, captures intravoxel heterogeneity in both time and space dimensions, offering parameters α and β, alongside a derived metric Dm that is sensitive to tissue cellularity25.

While preliminary research has highlighted the potential of these diffusion models in providing valuable insights into breast lesions, a systematic comparison of these diverse diffusion imaging approaches regarding their ability to identify breast lesion pathology, prognostic biomarkers, and molecular subtypes is lacking. The purpose of this study is to comprehensively compare and evaluate the clinical value of various diffusion parameters derived from the Mono, IVIM, DKI, SEM, and CTRW models, with the goal of determining which metrics are most effective for the preoperative prediction of breast lesion pathology, prognostic biomarkers, and molecular subtypes.

Materials and methods

Patients

The institutional review board of Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology approved this retrospective clinical study and written informed consent was waived. All methods were performed in accordance with the relevant guidelines and regulations. From July 2021 through November 2022, one hundred and sixty-three consecutive female patients who underwent a complete breast MRI examination at our institution for suspicious breast lesions detected by mammography or ultrasonography were preliminarily recruited. The inclusion criteria were as follows: (1) mass lesion greater than 1 cm; (2) no biopsy, surgery, radiotherapy or chemotherapy before the MRI scanning; and (3) histopathological confirmation of either malignant or benign breast lesions following the initial MRI examination within 2 weeks. Thirty-one patients were excluded for the following reasons: (1) insufficient quality of DWI images for further processing (n = 6); (2) lesion diameter smaller than 10 mm (n = 9); (3) presence of nonmass-like enhancing lesion on DCE-MRI (n = 12); and (4) incomplete immunohistochemical results after scanning (n = 4). Only the largest tumor was included when multifocal or multicentric mass was present in either breast. Consequently, a total of 132 patients were included in this study.

MRI protocol

A 3T MR scanner (uMR 790; United Imaging Healthcare, Shanghai, China) equipped with a dedicated bilateral breast array coil consisting of 10 channels was used for all MRI examinations. The imaging protocol involved the sequential acquisition of T2-weighted, DWI, and DCE-MRI. The multi b value DWI data were acquired using echo-planar imaging (EPI) technique with the following parameters: repetition time (TR), 2000 ms; echo time (TE), 61.5 ms; field of view (FOV), 320 × 160 mm2; flip angle (FA), 90°; matrix size, 192 × 192; slice thickness, 5 mm; pixel bandwidth, 1500 Hz/Px; b-values, 0, 50, 100, 250, 500, 750, 1000, 1500, and 2000 s/mm2; gradient directions, 3 orthogonal directions; acquisition time, 5min33s.

Image analysis

All DWI data were analyzed using the Mono, IVIM, DKI, SEM, and CTRW models. Parametric maps derived from the five diffusion models were all reconstructed with MATLAB R2018b (MathWorks Inc., Natick, MA, USA).

  1. 1.

    The ADC value was obtained using the Mono model26:

    $$\:Sb/{S0}=exp(-bADC)$$
  2. 2.

    Maps of the pure diffusion coefficient (D), perfusion-related incoherent microcirculation (D*), and microvascular volume fraction (f) were derived using the IVIM model22:

    $$\:Sb/S0=(1-f)\:exp\:(-bD)\:+\:f\:exp\:[-b\:(D^{*}+D\left)\right]$$
  3. 3.

    Mean kurtosis (MK, which quantifies the deviation of water diffusion distribution from a Gaussian pattern) and mean diffusivity (MD, similar to ADC) maps were calculated based on the DKI model23:

    $$\:Sb/S0=exp\:(-bMD\:+\:1/6\:\times\:\:{b}^{2}\:\times\:\:{MD}^{2}\:\times\:\:MK)$$
  4. 4.

    Maps of the diffusion coefficient (DDC) and empirical heterogeneity index (α) were fitted using the SEM model24:

    $$\:Sb/S0=\text{e}\text{x}\text{p}[-{\left(bDDC\right)}^{\alpha\:}]$$
  5. 5.

    The CTRW model provided maps of temporal diffusion heterogeneity (α), spatial diffusion heterogeneity (β), and diffusion coefficient (Dm)21:

    $$\:Sb/S0={E}_{\alpha\:}\:[-{\left(bD_{m}\right)}^{\beta\:}]$$

S0 represents the signal intensity when b-values of 0 s/mm2, and Sb is the signal intensity at a certain b-value on the DWI image. The Mono model was calculated using b-values of 0 and 750 s/mm2 as utilized by Pereira et al. previously, whose study demonstrated that the ADC calculated from b = 0 and 750 s/mm2 was slightly better than the other b value combinations27. The IVIM model utilized b-values of 0, 50, 100, 250, 500, 750, and 1000 s/mm2 due to low b-value region particularly sensitive to tissue vascularity28. The DKI, SEM, and CTRW models were calculated using all available b-values. The Mittag-Leffler function is denoted by Eα. In the fitting process, Dm was first estimated using diffusion images with all b-values. After determining Dm, α, and β were subsequently obtained from all DWI images (b-values ranging from 0 to 2000 s/mm2) using an iterative Levenberg-Marquardt method, as detailed in Karaman et al.21

Two readers, with 11 years (T.A.) and 5 years (Y.Q.H.) of experience in breast MRI respectively, independently interpreted and performed volume of interest (VOI) measurements encompassing the entire tumor (including necrotic or cystic areas). Both readers were blinded to the pathological results. The VOIs were drawn on DWI images (b = 750 s/mm2) using ITK snape (version 3.8.0; http://www.itksnap.org), guided by the T2WI and DCE-MRI images. The VOI was then copied onto all five model parameter maps for each patient. Finally, the parametric values calculated by two radiologists were averaged as the final results for quantitative statistical analyses in our study.

Histopathologic analysis

Within 2 weeks after the MRI scan, histopathologic analyses were performed by two pathologists (with 5 and 13 years of experience) independently. Malignant tumors were confirmed by the excised specimens through surgery, while benign lesions were evaluated by surgery or core needle biopsy. Histopathologic information was obtained from detailed pathological reports. The negativity status of estrogen receptor (ER) or progesterone receptor (PR) was indicated by stained nuclei in < 1% of cancer cells29. Human epidermal growth factor receptor 2 (HER2) negativity was defined when membrane immunostaining was scored 0, 1+, or when there was no HER2 gene amplification in fluorescence in situ hybridization (FISH)30. The threshold value to discriminate low/high expression of Ki-67 was set at 20%31. Histological grades were categorized according to the World Health Organization (WHO) classification as low (WHO I and II) and high (WHO III)32. Positive axillary lymph node metastasis (ALNM) was confirmed by biopsy or surgery33. Molecular subtypes were defined as follows: Luminal A, Luminal B, HER2-positive, and Triple-negative (TN)34.

Statistical analysis

All statistical analyses were conducted with SPSS (version 26; SPSS, Inc., Chicago, IL, USA) and MedCalc (version 15.0; MedCalc, Mariakerke, Belgium). The inter-reader reliability of all diffusion parameters was evaluated using the intra-class correlation coefficient (ICC), which is considered excellent agreement if greater than 0.8. The diffusion parameters of lesion types (benign vs. malignant), ER/PR/HER2 expressions (negative vs. positive), Ki-67/histological grades (low vs. high), and ALNM status (negative vs. positive) were compared using Mann–Whitney U-tests. Among the molecular subtypes, the Kruskal-Wallis test was used, followed by post-hoc Bonferroni test. Sensitivities and specificities between lesion types were calculated using receiver operating characteristic (ROC) curves, and the threshold values were determined using the Youden Index. The IVIM model (D + D* + f), DKI model (MK + MD), SEM model (DDC + α), and CTRW model (Dm + α + β) were combined using logistical analysis. The area under the ROC curve (AUC) comparisons among different parameters and models were also performed using the Delong test. A p-value < 0.05 was considered statistically significant.

Results

Clinical characteristics

Among the 132 breast lesions confirmed by histopathologic analysis, 41 were classified as benign, while 91 were determined to be malignant. The benign lesions consisted of 23 fibroadenomas, 16 adenoses, and 2 intraductal papillomas. Among the malignant lesions, 13 patients were diagnosed with ductal carcinoma in situ (3 low-grade, 6 intermediate-grade, and 4 high-grade), and 78 had invasive ductal carcinomas. The age of patients with malignant lesions was found to be significantly higher than that of patients with benign lesions (p = 0.018). More detailed clinical characteristics of the breast lesions are presented in Table 1.

Table 1 Characteristics of patients and lesions.
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Comparisons of different parameters and models between Benign and malignant breast lesions

The inter-observer agreement was excellent for all quantitative parameters (ICC range: 0.969–0.998). The results of the Mann–Whitney U-test are presented in Table 2; Fig. 1, indicating that, apart from IVIM-D*, all diffusion parameters exhibited significant differences in distinguishing benign and malignant breast lesions. Specifically, Mono-ADC, IVIM-D, IVIM-f, DKI-MD, SEM-DDC, SEM-α, CTRW-Dm, CTRW-α, and CTRW-β values were significantly higher in benign lesions compared to malignant ones (all p < 0.005), whereas the DKI-MK value was significantly lower in benign lesions than in malignant ones (p < 0.001). Figures 2 and 3 depict a case of a malignant lesion and a benign lesion, respectively.

Table 2 Diagnostic performance of Multiparameter in differentiating Benign and malignant breast lesions.
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Fig. 1
figure 1

Violin graphs showing the significant quantitative metrics from Mono (a), IVIM (b-d), DKI (e-f), SEM (g-h), and CTRW (i-k) diffusion models between malignant and benign lesions. IVIM-f, DKI-MK, SEM-α, CTRW-α, and CTRW-β are dimensionless. The units for Mono-ADC, IVIM-D, IVIM-D*, DKI-MD, SEM-DDC, and CTRW-Dm are mm2/s. * = P < 0.01, ** = P value < 0.001.

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Fig. 2
figure 2

Invasive breast cancer in the right breast of a 26-year-old woman. Maps (a-k) showing Mono-ADC, IVIM-D, IVIM-D*, IVIM-f, DKI-MD, DKI-MK, SEM-DDC, SEM-α, CTRW-Dm, CTRW-α, and CTRW-β values calculated from multi-b-values DWI. The mean values for the malignant lesion were 0.99 × 10− 3 mm2/s, 0.49 × 10− 3 mm2/s, 0.02 mm2/s, 0.38, 1.07 × 10− 3 mm2/s, 0.94, 0.82 × 10− 3 mm2/s, 0.75, 0.78 × 10− 3 s/mm2, 0.97, and 0.79, respectively.

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Fig. 3
figure 3

Benign fibroadenoma in the left breast of a 29-year-old woman. Maps (a-k) showing Mono-ADC, IVIM-D, IVIM-D*, IVIM-f, DKI-MD, DKI-MK, SEM-DDC, SEM-α, CTRW-Dm, CTRW-α, and CTRW-β values calculated from multi-b-values DWI. The mean values for the benign lesion were 2.17 × 10− 3 mm2/s, 1.62 × 10− 3 mm2/s, 0.02 mm2/s, 0.21, 2.14 × 10− 3 mm2/s, 0.18, 2.09 × 10− 3 mm2/s, 0.92, 1.90 × 10− 3 mm2/s, 0.99, and 0.95, respectively.

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The results of ROC analyses for individual diffusion parameters and each model are listed in Table 2 and displayed in Fig. 4. Among these individual parameters, CTRW-Dm exhibited the highest AUC in the differentiation (AUC = 0.93; Table S1). In addition, the CTRW model demonstrated significantly higher AUC for the classifications, compared to either Mono or IVIM models (AUCs = 0.93, 0.88, and 0.87, respectively; Table S2).

Fig. 4
figure 4

Receiver Operating Characteristic curves for Mono, IVIM, DKI, SEM, and CTRW models used to differentiate benign lesions from malignant lesions.

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As shown in Fig. 5, strong correlations were found between Mono-ADC, IVIM-D, DKI-MD, DKI-MK, SEM-DDC, CTRW-Dm, and CTRW-α (all p < 0.01). Particularly, a strong positive correlation was observed between SEM-DDC and CTRW-Dm (r = 0.969, p < 0.01).

Fig. 5
figure 5

Matrix plot showing the significant correlation coefficients between all diffusion parameters. Colored entries indicate significant correlations (p < 0.05) with positive (blue) or negative (red) associations.

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Multiple parameters among different prognostic factor subgroups of breast Cancer

Table 3 presents the results of the analysis of various diffusion parameters among different molecular prognostic factors of breast cancer. It was observed that ER-positive lesions exhibited significantly lower IVIM-D values and higher DKI-MK values compared to ER-negative lesions (p = 0.018 and p = 0.041, respectively). PR-positive lesions showed significantly lower values of Mono-ADC, IVIM-D, DKI-MD, SEM-DDC, CTRW-Dm, and CTRW-α, while demonstrating higher DKI-MK values in comparison to PR-negative lesions (all p < 0.05). Additionally, HER2-positive lesions demonstrated significantly higher IVIM-D and IVIM-D* values, along with a lower DKI-MK value compared to HER2-negative lesions (p = 0.041, p = 0.031, and 0.012, respectively). Furthermore, the DKI-MD, SEM-DDC, SEM-α and CTRW-β values showed significant differences between lesions with low and high Ki-67 expression (all p < 0.05). However, no significant differences were observed in multiple diffusion parameters among breast cancers with different histological grades and ALNM subgroups (all p > 0.05).

Table 3 Comparison of diffusion parameters among different prognostic biomarker subgroups of breast cancers.
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Multiple parameters among different molecular subtypes of breast cancers

The analysis results of the association between quantitative diffusion parameters and different molecular subtypes are presented in Table 4; Fig. 6. The Kruskal-Wallis test indicated that Mono-ADC, IVIM-D, DKI-MD, SEM-DDC, CTRW-Dm, and CTRW-α exhibited significant differences among the four aforementioned subtypes (all p < 0.05; Table 4). Further analysis using post-hoc Bonferroni correction revealed that TN had significantly higher values of IVIM-D, DKI-MD, SEM-DDC, CTRW-Dm, and CTRW-α compared to Luminal B (all p < 0.05; Fig. 6). Luminal A exhibited higher values of Mono-ADC, IVIM-D, DKI-MD, SEM-DDC, and CTRW-Dm compared to Luminal B (all p < 0.05; Fig. 6).

Table 4 Parameters derived from multiple models for breast cancer molecular subtypes.
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Fig. 6
figure 6

Box plots illustrating significant differences in parameters observed among all subtypes (p < 0.05). *p < 0,05 and **p < 0.01 for post hoc comparisons.

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Discussion

In this study, we utilized the Mono, IVIM, DKI, SEM, and CTRW models to characterize the diffusion signal attenuation behavior in the tissue microenvironment of breast lesions and evaluate the effectiveness of the functional diffusion parameters in the preoperative prediction of breast lesion pathology, prognostic biomarkers, and molecular subtypes. From a quantitative perspective, different parameters provide distinct biological information related to cellularity, perfusion, and tissue heterogeneity. Specifically, Mono-ADC, IVIM-D, DKI-MD, SEM-DDC, and CTRW-Dm provide insights into cellularity, while IVIM-D* and IVIM-f offer information about perfusion. Furthermore, DKI-MK, SEM-α, CTRW-α, and CTRW-β provide insights into tissue heterogeneity. All parameters derived from the five models exhibited higher inter-observer agreement, indicating reliable and objective tumor analysis.

Differential diagnosis of breast lesions

Previous studies have extensively investigated the use of multiple diffusion-weighted imaging (DWI) models for the differential diagnosis of breast lesions24,35,36,37. Our findings revealed that malignant lesions had lower diffusion parameters, including Mono-ADC, IVIM-D, DKI-MD, SEM-DDC, and CTRW-Dm. These values decrease when there is limited space for the diffusion of free water molecules and increased cellularity in malignant tumors38. Huang et al. demonstrated decreased ADC values in malignant lesions30; and Suo et al. showed lower values for Mono-ADC, IVIM-D, DKI-MD, and SEM-DDC in malignant lesions39, which align with our results. In addition, Ji et al. observed lower CTRW-Dm values in malignant groups compared to benign ones, consistent with our study40.

The values derived from various diffusion-weighted imaging (DWI) models, such as DKI-MK, SEM-α, CTRW-α, and CTRW-β, reflect microstructure heterogeneity in distinct ways. Previous studies have established DKI-MK as an indicator of tissue heterogeneity26. Consistent with these findings, our study demonstrated higher DKI-MK values in malignant lesions compared to benign lesions, which is in line with previous research26,39,41. An elevated DKI-MK value in malignant breast lesions suggests a greater deviation from Gaussian distribution due to dense cellularity and high heterogeneity, leading to altered water diffusion characteristics30. The empirical heterogeneity index SEM-α enables the assessment of intravoxel water diffusion heterogeneity19. Previous studies have shown that the α value can effectively differentiate between breast lesions, which is consistent with our study results39. Our study found lower CTRW-α and CTRW-β values in malignant breast lesions. Breast cancers exhibit complex pathological heterogeneity compared to benign lesions due to the presence of cancer nests, necrosis, intraductal components, and other factors42. The lower values of CTRW-α and CTRW-β in malignant lesions indicate that water molecules diffuse through a more heterogeneous environment in both time and space43.

Although multiple parameters derived from the five models are interrelated, they offer distinct information. In our study, the area under the curve (AUC) for heterogeneity parameters (SEM-α, CTRW-α, and CTRW-β) was lower than that of diffusion parameters (Mono-ADC, IVIM-D, DKI-MD, SEM-DDC, and CTRW-Dm). This suggests that the heterogeneity between malignant and benign lesions is not as significant as the difference in diffusion coefficient. Logistic analysis demonstrated that all five models exhibited good sensitivity and specificity, with the CTRW model displaying a higher AUC compared to the other four models, although the difference was not statistically significant.

Classification of prognostic biomarker status

Regarding prognostic factors, our study revealed that ER-positive tumors exhibited lower IVIM-D values compared to ER-negative tumors. This finding is consistent with the results reported by Suo et al., suggesting that overexpression of ER inhibits angiogenesis and restricts water diffusion39. Similarly, PR-positive tumors also demonstrated lower IVIM-D values, likely due to similar effects of hormone receptors. Additionally, PR-positive tumors displayed lower Mono-ADC, DKI-MD, SEM-DDC, and CTRW-Dm values, which could be attributed to higher cellularity and increased cell membrane permeability15. Yang et al. identified significant differences in DKI-derived parameters based on ER and PR status26. Our results indicated that both ER- and PR-positive tumors had higher DKI-MK values, consistent with the findings of Kang et al.23. While a CTRW-α value was able to differentiate PR status, it failed to discriminate ER status, which is partially in line with our previous study. The discrepancy may be due to variations in the numbers and selection of b-values used to calculate the CTRW model. HER2-positive tumors, characterized by increased cell density, may exhibit higher IVIM-D values. Zhao et al. reported higher IVIM-D* values in HER2-positive tumors44, while Yang et al. found lower DKI-MK values in HER2-positive tumors26, which aligns with our study. These findings suggest that HER2-positive lesions tend to display more proliferation and angiogenesis. Furthermore, our study demonstrated lower DKI-MD values in tumors with high Ki-67 expression compared to those with lower Ki-67 expression, aligning with the study conducted by Sun et al.41. This observation may be attributed to enhanced cellularity in tumors with high Ki-67 expression30.

Classification of molecular subtypes

Although the role of various noninvasive parameters should not be overlooked when evaluating breast cancer, extensive research has focused on DCE-MRI parameters in molecular subtypes. Our study revealed that IVIM-D, DKI-MD, SEM-DDC, CTRW-Dm, and CTRW-α exhibited higher values in triple-negative (TN) subtypes compared to Luminal B subtypes. TN subtypes are known to exhibit higher levels of VEGF, promoting angiogenesis and resulting in increased microvessel density, which could explain the observed elevation in diffusion parameters (IVIM-D, DKI-MD, SEM-DDC, and CTRW-Dm) and the heterogeneity parameter (CTRW-α) in TN subtypes34. Notably, our study also demonstrated significantly lower values of Mono-ADC, IVIM-D, DKI-MD, SEM-DDC, and CTRW-Dm in Luminal B subtypes compared to Luminal A subtypes. This suggests a higher cellular density in Luminal B subtypes as supported by previous studies45,46, albeit with potential variations in specific values.

Several limitations of this study should be noted. Firstly, this is a single-center study with relatively small sample size and unbalanced data distribution. Our findings need to be validated in future multicenter large cohort with a prior sample size calculation. Secondly, further investigation is required to determine the optimal number and selection of b-values for all diffusion models. Thirdly, while our results indicate statistically significant differences in the diffusion parameters between benign and malignant lesions, it is important to note that there is also substantial overlap in the measured values between the two groups, which limits the clinical use of the proposed threshold value. Future efforts to standardize the acquisition protocols and data postprocessing and larger multiple institutions studies are vital for the widespread implementation of quantitative breast DWI. Lastly, in this study, we solely relied on mean values to evaluate breast lesions. However, histogram analysis can offer additional insights into tumor heterogeneity. Therefore, future studies comparing multiple diffusion models of breast lesions using histogram analysis are warranted.

In conclusion, the results of this study showed that multiple diffusion parameters derived from these five models differed between malignant and benign breast lesions and are promising as supplementary imaging biomarkers for improving the diagnostic accuracy of breast lesions. Additionally, the functional parameters might be of use in the prediction of the prognostic factors and molecular subtypes of breast cancer, which would be helpful in the prognostic estimation and the formulation of personalized treatment strategies in clinical practice.