It is well known that breast cancer is a heterogeneous disease, and its heterogeneity is driven by both the intrinsic factors of tumor cells and the surrounding microenvironment, which suggests that a single tumor may have different molecular subtypes [1,2]. The biopsy cannot indicate the heterogeneity of the entire tumor since it does not accurately reflect its real composition, although it is a relatively reliable method of identifying breast cancer [3]. The assessment level of tumor heterogeneity has risen as a result of advances in imaging technologies. Breast magnetic resonance imaging (MRI) is a high-sensitivity technology for the detection of breast disease, and diffusion-weighted imaging (DWI) may offer information related to biological characteristics, such as the cellularity of tissue and the integrity of the cell membrane [4]. Many scholars have studied the assessment of different diffuse models for breast cancer identification and management, some of which have been limited to calculating and comparing average parameters in the regions of interest (ROIs), not fully reflecting the tumor heterogeneity [5,6]. The histogram of diffusion parameters is a tool used to describe the distribution in the image. Typically, histogram analyses and other pixel-by-pixel analyses are used to measure and compare the spatial distribution of tumor biomarkers to learn more about heterogeneity [7]. Many kinds of tumor investigations have made extensive use of MRI histogram analysis [[8], [9], [10]].

Lots of scholars have found that the histogram analysis of the diffusion model has good diagnostic efficiency in the differentiation of benign and malignant breast lesions [11,12], but there is little research on the correlation of prognostic factors. The associations between breast cancer prognostic factors and the histogram characteristics of the apparent diffusion coefficient (ADC) have been studied in some studies [6,13,14]. The intravoxel incoherent motion (IVIM) model can differentiate between the microcirculation and diffusion of water molecules and reflect perfusion through microvessels, a pseudo-diffusion motion related to tumor micro-vascular flow. So, the goal of the research is to explore the extent of correlation between the histogram metrics of DWI and IVIM parameters and breast cancer molecular subtypes and prognostic factors.