A total of 126 patients diagnosed with breast carcinoma, confirmed through pathological examination from January 2021 to December 2023, were recruited retrospectively. The adopted inclusion criteria involved: a) Subjects were all examined via conventional MRI, IVIM, and DKI, b) no contraindications for MRI examination, and c) complete clinicopathological data were obtained. The following exclusion criteria were implemented: a) patients who had undergone any prior treatment including core needle biopsy, radiotherapy, chemotherapy, or surgery before MRI examination, b) cases where MRI image quality was poor (defined as images with severe motion artifacts or insufficient signal-to-noise ratio for reliable ROI placement) or examination dates were incomplete, c) patients that had not undergone tumor resection within one week following MRI, and d) cases where the tumor did not present as a mass type. Ultimately, 104 patients who met the specified inclusion and exclusion parameters were enrolled for study ( Figure 1 ). Additionally, 91 breast carcinoma patients were concurrently enrolled from another tertiary medical center, applying the same inclusion and exclusion criteria, to form an external validation cohort for assessing the model’s generalizability.

A GE Discovery 750W 3.0T MR scanner was utilized, featuring a dedicated 8-channel phased-array coil designed to encompass both breasts of all patients in a prone position. The MRI sequences included DKI, fast spin-echo T1-weighted imaging (FSE-T1WI), fat-suppressed fast-recovery fast spin-echo T2-weighted imaging (FRFSE-T2WI), DWI, and IVIM. The parameters employed to acquire FSE-T1WI images were as follows: echo time (TE)=10 ms, repetition time (TR)=420 ms, number of excitations (NEX)=1, and matrix = 320×288. The following sequences were employed to obtain FRFSE-T2WI images: TR = 6000 ms, TE = 88 ms, NEX = 2, matrix = 320×288. The DWI parameters were NEX = 2, TR = 3600 ms, matrix=320×288, TE = 73 ms, b-values=0, and 1000 s/mm². The IVIM parameters were defined as follows: TE = 90 ms, thirteen b-values of 0, 20, 30, 50, 70, 100, 150, 200, 500, 700, 1000, 1500, 2000 s/mm², matrix=128×128, NEX increased from 1 to 6, and TR = 2500 ms. DKI was acquired using the following sequence: NEX = 2, matrix=128×128, b-values at 0, 1000, 2000 s/mm². TE = 90 ms, field of view (FOV)=35 cm×35 mm, TR = 5000 ms, slice thickness=4 mm, and slice spacing= 0.4mm. The above sequence layers are all slice thickness=4mm, FOV = 35 cm×35 mm, and slice spacing=0.4mm.

Processing of resulting data on DWI, IVIM, and DKI was completed by virtue of the Function tool MADC and DKI software (GE Healthcare, USA) to acquire parametric maps.

For DWI, ADC maps were generated using a mono-exponential model: S_b/S₀ = exp (-b·ADC), where b denotes the diffusion factor, specifically, b=0 s/mm² for one volume and b=1000 s/mm² for the other (18).

The fitting equation reported previously was employed to calculate IVIM-derived parameters: S_b/S₀ = (1 - f) × exp (-b × D) + f × exp[-b × (D* + D)], where S_b represents the intensity of the MRI signal possessing diffusion weighting b, S₀ the intensity of non-diffusion-weighted signal, and ADC the apparent diffusion coefficient. D signifies the true diffusion coefficient for water molecules concerning the pure diffusion. The pseudo-diffusion coefficient D* corresponds to incoherent microcirculation related to perfusion and the microvascular volume fraction is denoted by the perfusion fraction f (18).

The parameters derived from DKI were obtained using the equation: S_b = S₀·exp(-b²·D² + b·D²·K/6), where S_b and S₀ correspond to signal intensities at different b-values (0 s/mm² and others, respectively). MD denotes the diffusion coefficient under normal conditions, adjusted for the non-Gaussian effects, while MK denotes non-Gaussian diffusion behavior (18).

Two radiologists (ZW with 5 years of experience together with WW having 8-year experience in breast MRI) who were blinded to all pathological results and clinical data, drew the ROIs independently. Since IVIM and DKI images displayed a low signal-to-noise ratio, the tumor’s most enormous layers were selected to determine the ROI as per the DWI and T2WI images in the axial direction (b = 1000 s/mm²). Three ROIs, each with 50~150 mm2 area, were drawn on the tumor’s solid part, excluding the regions of cystic degeneration, bleeding, and necrosis as much as possible, and then copied the ROI onto the D, D *, f, MD, and MK pseudocolor images. The average values of the quantitative parameters from both radiologists were calculated for final analysis. In cases of significant discrepancy in ROI placement (defined as a > 10% difference in measured value for any parameter), the images were jointly re-reviewed to reach a consensus. This approach, which focused on solid components, was chosen to minimize the confounding effects of necrosis and hemorrhage on parameter calculation, even though it may not fully capture the entire tumor’s heterogeneity.

All participating patients underwent surgical interventions, specifically, radical mastectomy, modified radical mastectomy, and breast-conserving surgery in 68, 24, and 12 cases, respectively. The clinical database was utilized to extract multiple pathologic characteristics, such as histologic type, tumor size, ER/PR/HER-2/HIF-1α/VEGF/Ki-67 status, histologic grade, tumor subtype, and patient age. All immunohistochemical evaluations of HIF-1α, Ki-67, and VEGF were performed on postoperative surgical specimens obtained from the resected tumor mass. All surgically resected specimens were carried out by two independent pathologists (with working experience of 6 and 15 years), depending on levels of either estrogen receptor (ER), ki-67, human epidermal growth factor-2 (Her-2), as well as progesterone receptor (PR). Positivity for PR and ER was determined in cases where 10% or more nuclei exhibited positive staining. Ki-67 expression ≥14% was considered positive, while levels below this threshold were considered negative. Her-2 staining intensity was semiquantitatively scored 0 points for negative, 1+ point for weak, 2+ points for moderate or 3+ points for strong. The score of 0 or 1+ point meant Her-2 negative, while 3+ score was classified Her-2-positive. For tumors with a score of 2+ points, fluorescence in situ hybridization was conducted for further evaluation of gene amplification (19). Four distinct molecular subtypes of breast cancer were identified, namely, Her-2-positive (negative for ER and PR, Her-2-positive), luminal A (Her-2-negative, positive for ER or PR, ki-67≥14%), triple-negative (negative for ER, PR and Her-2), and luminal B (negative for Her-2, positive for ER or PR, Ki-67<14%). Assessment of HIF-1α was conducted by calculating the ratio of cells with positive HIF-1α to the total number of cells and scored as follows: 0 points (0–25%), 1 point (25–50%), 2 points (50–75%), 3 points (75–100%) and 4 points (100%). The intensity of staining was rated on a scale of 0 (no color), 1 (light yellow), 2 (brown), and 3 (dark brown) points. Low expression was defined by staining intensity <2 points alongside cells with positive HIF-1α <2 points. In contrast, a high expression was defined (20). The scoring system was applied to evaluate VEGF immunostaining based on the computed percentage of positive cells (0, no positive cells; 1, ≤25% positive cells; 2, 25%< positive cells ≤50%; 3, >50% positive cells) in addition to staining intensity (0=negative; 1=weak; 2=moderate; 3=high). The grading of these parameters yielded combined scores of 0–2, 3–4, and 5–6 corresponding to negative, positive, and strongly positive results, respectively (21).

MedCalc 19.5.1 (Ostend, Belgium), R version 4.0.0 (http://www.r-project.org/), and SPSS 25.0 (IBM Corporation, Armonk, NY, USA) were employed for statistical analyses. The statistical analysis was performed under the supervision of a professional statistician (Juntao Zhang, GE Healthcare PDX GMS medical affairs, Senior Data Scientist). Interclass correlation coefficients (ICCs) were utilized to assess interobserver reproducibility. The criteria adopted for interpretation of ICC agreement were as follows: ICC ≤ 0.20, poor; 0.21<ICC ≤ 0.40, fair; 0.40<ICC ≤ 0.60, moderate; 0.60<ICC ≤ 0.80, good; 0.80<ICC ≤ 1.00, excellent (22). Two quantitative data samples were subjected to the Kolnogorov-Smirnov normality test to evaluate their distribution patterns. Data that followed normal and non-normal distribution were expressed as mean ± standard deviation and median plus interquartile range, respectively. The independent samples t-test was used for normally distributed data, and the Mann-Whitney U test was applied for non-normally distributed data. Different groups were compared using the independent-sample chi-square test. The binary logistic regression analysis was used to identify independent factors. Receiver operating characteristic (ROI) curves were performed to evaluate the diagnostic efficacy of each parameter or model. The Delong test analyzed the values of area under different groups’ ROC curve (AUC). A nomogram was subsequently constructed and validated using decision curve analysis (DCA), together with calibration techniques. The Spearman rank was employed to describe the correlation of each parameter with HIF-1α, VEGF, and Ki-67, respectively. A correlation coefficient (r) of 0.75-1.00 was considered to indicate a good correlation, 0.50-0.74 a moderate correlation, 0.25-0.49 a mild correlation, and 0.24 or lower little or no correlation, p <0.05 denoted a difference of statistical significance (23).

The 104 participants in the study had a mean age of 52.99 ± 9.58 years, with an range from 29 to 71. Within this cohort of 104 cases of breast cancer, 95 (91.3%) were classified as invasive ductal carcinoma and 9 (8.7%) as non-invasive ductal carcinoma. Among the 104 patients, 11 (11%) were categorized as luminal A subtype, 19 (18%) as HER-2-positive subtype, 51 (49%) as luminal B subtype, and 23 (22%) as triple-negative subtype ( Table 1 ). In the training set, no statistically significant differences were found in tumor genotypes between the high- and low-expression groups of HIF-1α, VEGF, and Ki-67 (P = 0.42, 0.24, and 0.55, respectively). This lack of significant association was consistently observed in the external validation cohort, with corresponding P values of 0.22, 0.14, and 0.22.

The two radiologists reported ICCs of 0.887 [95% CI: 0.837–0.922], 0.917 [95% CI: 0.880–0.943], 0.860 [95% CI: 0.800–0.903], 0.880 [95% CI: 0.828–0.917], 0.909 [95% CI: 0.868–0.937], and 0.863 [95% CI: 0.805–0.905] for ADC, D, D*, f, MD, and MK, respectively. These results reflect a significant level of agreement between observers.

In the training set, the D and MD values were significantly lower in tumors in the high-expression than the low-expression HIF-1α group (p < 0.05). Additionally, the high-expression group was observed with increased values of D*, f, and MK compared with the low-expression group (p < 0.05). D [odds ratio(OR) = 0.001, P <0.001], D* (OR = 1.805, P = 0.018), MD (OR = 0.168, P = 0.011), and MK (OR = 2034.665, P = 0.015) as significant predictive factors of HIF-1α. ROC curve analysis showed that among the individual parameters, the D value exhibited the highest predictive efficacy (AUC = 0.724). A D value ≤ 0.88×10^-3 mm²/s should strongly suggest high HIF-1α expression. The AUC of the combined model incorporating MD, D, MK, and D* was 0.860 with an accuracy of 77.9%, representing a modest but statistically significant improvement (Z=2.878~3.881, all P<0.05). A similar trend was observed in the external validation set. The combined model demonstrated comparable performance in the external validation set, achieving an AUC of 0.841, which was not significantly different from that in the training set (DeLong’s test, Z = 0.262, P = 0.794). This indicates that the combined model provides a more reliable non-invasive assessment of tumor hypoxia ( Tables 2 , 3 ; Figures 2 , 3 ).

In the training set, comparative analyses revealed that relative to the low-expression group, the high-expression VEGF group had lower ADC, D, and MD values, along with higher D*, MK, and f values (P<0.05). Furthermore, D (OR = 1.805, p = 0.018), f (OR = 1.805, p = 0.018), and MD (OR = 1.805, p = 0.018) served as independent predictors for assessing VEGF expression status. ROC curve analysis revealed that the f parameter was the most powerful single indicator for predicting VEGF expression (AUC = 0.882). The parameter f exhibited a significantly larger AUC than D and MD (Z = 2.036, P = 0.042; Z = 2.375, P = 0.018). In clinical practice, an f value ≥ 29.82% can serve as a key imaging biomarker suggesting high VEGF expression, i.e., active tumor angiogenesis. The combined model that incorporated D, f, and MD produced an AUC of 0.923, achieving an accuracy of 87.5%, demonstrating improved performance compared to the use of D or MD alone (Z = 3.357, P<0.001; Z = 3.927, P<0.001). Notably, however, the combined model did not significantly outperform f alone in terms of AUC (Z = 1.837, P = 0.066). A similar trend was observed in the external validation set. The generalizability of the combined model was further supported by the external validation results, which showed a consistently high AUC of 0.918. No statistically significant difference was found compared to the training set performance (DeLong’s test, Z = 0.089, P = 0.929). This suggests that the f parameter may play a central role in assessing angiogenesis ( Tables 3 , 4 ; Figures 2 , 3 ).

In the training set, the high-expression Ki-67 group exhibited significantly decreased ADC, D, and MD values, along with increased D* and f values, compared to the low-expression group (P < 0.05). The parameters D (OR = 0.007, P = 0.002), D* (OR = 1.080, p = 0.005), and MD (OR = 0.120, p = 0.002) emerged as predictors that could independently assess the status of Ki-67 expression. ROC curve analysis indicated MD as the most predictive single parameter for Ki-67 expression (AUC = 0.762), showing significantly greater efficacy than D* (Z = 2.022, P = 0.043). Thus, an MD value ≤ 2.21×10^-3 mm²/s strongly suggests high tumor proliferative activity. Furthermore, the combined model of D, D*, and MD achieved an AUC of 0.852, with an accuracy of 77.9%, which was superior to that of the D, D*, and MD parameters (Z=2.368~4.199, all P<0.05). A similar trend was observed in the external validation set. However, no statistically significant difference was found for the D*parameter. No statistically significant difference was observed in the AUC values between the training set and the external validation set (AUC = 0.847) as assessed by DeLong’s test (Z = 0.073, P = 0.942). This demonstrates the model’s strong and generalizable predictive performance. This result indicates that integrating diffusion and perfusion information provides a more comprehensive perspective for the non-invasive assessment of tumor proliferation ( Tables 3 , 5 ; Figures 2 , 3 ).

Based on the final regression analysis, we incorporated independent factors demonstrating significant associations with the diagnostic efficacy of parameters from DWI, IVIM, and DKI for expression of HIF-1α, VEGF, and Ki-67 into multivariate regression analysis, subsequently leading to the development of three nomograms ( Figures 4A–C ). Next, we evaluated the performance of the model by establishing internal calibration curves ( Figures 4D–F ). The probability of HIF-1α, VEGF, and ki-67 expression, as predicted via the nomogram, was set as the X-axis, with the actual probability represented on the Y-axis. The results showed that the ideal dotted line was more approximated by the solid line, suggesting higher predictive accuracy of the nomograms (p = 0.59, 0.40, and 0.08).The decision curve analysis (DCA) described in Figures 4G–I highlights the excellent net clinical benefit of the predictive model.

HIF-1α showed mild positive correlations with D*, f, and MK, respectively (r = 0.292, 0.267, 0.276, p<0.05). HIF-1α was mildly correlated with D and MD, respectively (r = -0.375, -0.302, p<0.05). VEGF showed mild and moderate positive correlations with D* and f, respectively (r = 0.390, 0.644, p<0.05). VEGF was mildly correlated with D and MD, respectively (r = -0.425, -0.411, p<0.05). Ki-67 showed mild positive correlations with D* and f (r = 0.242, 0.308, p<0.05). Ki-67 was mildly correlated with D and MD, respectively (r = -0.422, -0.445, p<0.05).