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

Parameters	ER		p value	PR		p value	HER2		p value
Parameters	Negative	Positive	p value	Negative	Positive	p value	Negative	Positive	p value
Mono-ADC (x10^− 3 mm²/s)	1.07 ± 0.18	1.01 ± 0.15	0.152	1.11 ± 0.18	0.99 ± 0.14	0.028	1.01 ± 0.16	1.05 ± 0.15	0.387
IVIM-D (x10^− 3 mm²/s)	0.72 ± 0.11	0.65 ± 0.11	0.018	0.72 ± 0.12	0.64 ± 0.10	0.002	0.65 ± 0.12	0.70 ± 0.10	0.041
IVIM-D* (mm²/s)	0.02 ± 0.01	0.02 ± 0.01	0.715	0.02 ± 0.01	0.02 ± 0.01	0.192	0.02 ± 0.01	0.02 ± 0.01	0.031
IVIM-f	0.24 ± 0.05	0.25 ± 0.04	0.476	0.24 ± 0.04	0.25 ± 0.05	0.334	0.25 ± 0.04	0.23 ± 0.05	0.052
DKI-MD (x10^− 3 mm²/s)	1.20 ± 0.21	1.15 ± 0.18	0.211	1.21 ± 0.21	1.13 ± 0.17	0.047	1.16 ± 0.19	1.17 ± 0.19	0.883
DKI-MK	0.79 ± 0.11	0.86 ± 0.16	0.041	0.79 ± 0.12	0.87 ± 0.16	0.004	0.87 ± 0.16	0.79 ± 0.12	0.012
SEM-DDC (x10^− 3mm²/s)	0.99 ± 0.20	0.92 ± 0.19	0.111	1.01 ± 0.21	0.90 ± 0.18	0.022	0.93 ± 0.20	0.96 ± 0.19	0.549
SEM-α	0.75 ± 0.03	0.74 ± 0.04	0.465	0.75 ± 0.66	0.74 ± 0.04	0.478	0.74 ± 0.04	0.75 ± 0.03	0.159
CTRW-D_m (x10^− 3 mm²/s)	0.90 ± 0.14	0.84 ± 0.13	0.141	0.90 ± 0.14	0.83 ± 0.12	0.031	0.85 ± 0.14	0.87 ± 0.12	0.507
CTRW-α	0.97 ± 0.05	0.96 ± 0.04	0.060	0.97 ± 0.04	0.96 ± 0.04	0.043	0.96 ± 0.04	0.97 ± 0.04	0.116
CTRW-β	0.74 ± 0.04	0.75 ± 0.05	0.942	0.74 ± 0.04	0.75 ± 0.05	0.395	0.75 ± 0.05	0.75 ± 0.04	1.000

Parameters	Ki-67		p value	Histological grades		p value	ALNM		p value
Parameters	Low	High	p value	Low	High	p value	Negative	Positive	p value
Mono-ADC (x10^− 3 mm²/s)	1.05 ± 0.15	1.00 ± 0.16	0.054	1.03 ± 0.15	1.02 ± 0.18	0.740	1.03 ± 0.15	1.01 ± 0.17	0.520
IVIM-D (x10^− 3 mm²/s)	0.69 ± 0.11	0.65 ± 0.12	0.089	0.68 ± 0.11	0.66 ± 0.12	0.658	0.68 ± 0.11	0.64 ± 0.12	0.103
IVIM-D* (mm²/s)	0.02 ± 0.01	0.02 ± 0.01	0.192	0.02 ± 0.01	0.02 ± 0.01	0.345	0.02 ± 0.01	0.02 ± 0.01	0.574
IVIM-f	0.25 ± 0.04	0.24 ± 0.04	0.203	0.24 ± 0.05	0.25 ± 0.04	0.730	0.24 ± 0.04	0.25 ± 0.05	0.148
DKI-MD (x10^− 3 mm²/s)	1.21 ± 0.17	1.12 ± 0.19	0.009	1.17 ± 0.19	1.15 ± 0.18	0.712	1.17 ± 0.18	1.15 ± 0.20	0.501
DKI-MK	0.84 ± 0.14	0.84 ± 0.16	0.946	0.83 ± 0.15	0.86 ± 0.15	0.555	0.83 ± 0.16	0.86 ± 0.13	0.340
SEM-DDC (x10^− 3 mm²/s)	0.98 ± 0.19	0.90 ± 0.20	0.030	0.95 ± 0.20	0.93 ± 0.20	0.734	0.95 ± 0.19	0.93 ± 0.21	0.459
SEM-α	0.74 ± 0.04	0.75 ± 0.03	0.049	0.74 ± 0.04	0.74 ± 0.03	0.935	0.74 ± 0.04	0.75 ± 0.03	0.512
CTRW-D_m (x10^− 3 mm²/s)	0.88 ± 0.13	0.83 ± 0.13	0.067	0.87 ± 0.13	0.84 ± 0.13	0.496	0.86 ± 0.13	0.84 ± 0.13	0.469
CTRW-α	0.97 ± 0.03	0.96 ± 0.05	0.258	0.96 ± 0.04	0.96 ± 0.05	0.577	0.96 ± 0.05	0.97 ± 0.03	0.319
CTRW-β	0.74 ± 0.05	0.75 ± 0.05	0.036	0.74 ± 0.05	0.75 ± 0.04	0.354	0.74 ± 0.04	0.75 ± 0.05	0.287

Note: Data are presented as mean ± standard deviations. P values < 0.05 were considered statistically significant. Bolded text indicates statistical significance. ER = estrogen receptor; PR = progesterone receptor; HER2 = human epidermal growth factor receptor 2; ALNM = axillary lymph node metastasis.

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