Associations between angiogenic factors and intravoxel incoherent motion-derived parameters in diffusion-weighted magnetic resonance imaging of breast cancer

Abstract

Intravoxel incoherent motion (IVIM) diffusion-weighted magnetic resonance imaging (MRI) can be used to estimate perfusion-related parameters, but these parameters may differ, based on the curve-fitting algorithm used for IVIM. Microvessel density (MVD) and vascular endothelial growth factor (VEGF) status are used as angiogenic factors in breast cancer. We aimed to investigate the relationship between MVD, VEGF, and intravoxel incoherent motion (IVIM)-derived parameters, obtained by 4 curve-fitting algorithms, in patients with invasive breast cancers.

This retrospective study investigated IVIM-derived parameters, D (ie, tissue diffusivity), D^∗ (ie, pseudodiffusivity), and f (ie, perfusion fraction), of 55 breast cancers, using 10 b values (range, 0–800 s/mm²) and 4 curve-fitting algorithms: algorithm 1, linear fitting of D and f first, followed by D^∗; algorithm 2, linear fitting of D and f and nonlinear fitting of D^∗; algorithm 3, linear fitting of D and f, linear fitting of D^∗, and ignoring D contribution for low b values; and algorithm 4, full nonlinear fitting of D, f, and D^∗. We evaluated whole-tumor histograms of D, f, and D^∗ for their association with MVD and VEGF.

D^∗₁₀, D^∗₂₅, D^∗₅₀, D^∗_mean, D^∗₇₅, D^∗₉₀, f₁₀, and f₂₅, derived using algorithm 3, were associated with VEGF expression (P = .043, P = 0.012, P = .019, P = .024, P = .044, P = .041, P = .010, and P = .005, respectively). However, no correlation existed between MVD and IVIM-derived parameters.

Perfusion-related IVIM parameters obtained by curve-fitting algorithm 3 may reflect VEGF expression.

1. Introduction

Breast cancer is the most frequently diagnosed cancer in women worldwide. Owing to its strong invasiveness and metastasis ability, breast cancer is the leading cause of cancer-related deaths among women.^[1,2] Angiogenesis is a well-known critical factor that stimulates tumor growth and the development of metastases.^[3–5] Microvascular density (MVD) and vascular endothelial growth factor (VEGF) status are commonly used as angiogenic markers and have been proven to be the prognostic factors associated with treatment response and the relapse-free and overall survival of cancer patients.^[6–8]

Diffusion-weighted imaging (DWI) has been extensively explored in oncologic imaging. Most such studies have relied on the apparent diffusion coefficient (ADC), a robust and easy-to-calculate parameter.^[9] To date, many studies have attempted to demonstrate a correlation between ADC and angiogenic markers; however, these studies yielded variable results, which range from no correlation in head and neck cancer^[10] to a positive correlation in cervical and pancreatic cancer.^[11] Intravoxel incoherent motion (IVIM), an advanced DWI technique, has received increased interest because it can be used to estimate perfusion-related parameters, including pseudodiffusivity (D^∗), which is indicative of blood flow, and the perfusion fraction (f), which is indicative of the fractional volume of active capillaries in a tumor.^[12,13] We hypothesized that IVIM may be more sensitive for predicting angiogenic markers. Moreover, IVIM can provide perfusion-related parameters without the need for contrast agents, which is important, considering the recent finding of gadolinium deposition in the brain after repeated contrast injections.^[14] If MVD and VEGF can be evaluated using IVIM, then IVIM could become a noninvasive tool to monitor the effects of vascular targeting agents in the routine follow-up of cancer patients.

However, IVIM values are computed with multistep postprocessing, based on the fitting algorithm used, and limited interalgorithm agreement and quantification of vascular diffusion effects impose a significant challenge.^[15–18] In addition, previous IVIM algorithm studies have used a single section of a tumor as a representation of the whole tumor by contouring the tumor or placing regions-of-interest on one representative section of the tumor. However, considering the heterogeneity of tumors, the subjective choice of the measurement section by a researcher may result in measurement deviations.^[19] More sophisticated methods such as histogram analysis have recently been applied to these maps and have yielded additional biomarkers and more information in patients with breast cancer.^[20] Therefore, we investigated the associations between MVD, VEGF, and IVIM MRI parameters, using 4 different curve-fitting algorithms and whole-tumor histogram analysis in patients with invasive breast carcinomas.

2. Materials and methods

This retrospective study was approved by the ethics committee of our hospital (IRB KC19RESI0706), and the requirement for obtaining informed patient consent was waived owing to the nature of the study.

2.1. Patients and IVIM acquisition

Seventy-eight patients with invasive breast carcinomas, which were diagnosed between 2014 and 2016, were considered for enrollment in our study, based on the following criteria: invasive ductal carcinoma was confirmed by percutaneous biopsy and IVIM DWI with 10 b values on a 3-T system were acquired for the preoperative evaluation. Exclusion criteria were a lack of consent by the patient for immunohistochemical staining (n = 10), failure of the acquisition of IVIM parameters because of artifact (n = 2), systemic therapy with distant metastasis (n = 3), neoadjuvant chemotherapy (n = 8). Fifty-five patients were included in the analysis of the IVIM parameters and angiogenic markers. All patients included in this study underwent surgery. Histopathologic information was obtained from the pathology reports in the patients’ medical records. For each patient, the single largest lesion located in the breast on one side was selected.

For the IVIM sequence, the patients were examined in a 3.0-T MRI imaging system (Magnetom Verio; Siemens Healthcare, Erlangen, Germany) with a dedicated bilateral breast surface coil. The patients were placed in the prone position. IVIM was obtained with single-shot echo-planar imaging, using 10 b values (0 s/mm², 25 s/mm², 50 s/mm², 75 s/mm², 100 s/mm², 150 s/mm², 200 s/mm², 300 s/mm², 500 s/mm², and 800 s/mm²) with the following parameters: repetition time/echo time, 5600/55 ms; field of view, 340 mm × 170 mm; matrix size, 192 × 192; slice thickness, 4 mm; and acquisition time, approximately 4 minutes.

2.2. IVIM analysis and four fitting algorithms for IVIM-derived parameters

The IVIM data were retrospectively evaluated with consensus of 2 radiologists with >15 years and 5 years of experience, respectively, in breast MRI. DICOM images from the IVIM sequence were postprocessed using the prototype software MR Body Diffusion Toolbox, v1.3.3 (Siemens Healthcare) to extract the ADC and IVIM parameters. In the IVIM model, the relationship between signal variation and b factor is expressed as

$${\text{S}}_{\text{b}}/{\text{S}}_0=(1-\text{f})\times \exp (-\text{b}\cdot \text{D})+\text{f}\times \exp (-\text{b}{\text{D}}^{*})$$

where S is the signal intensity; f is the perfusion fraction representing the volume fraction of microcirculation; D^∗ is the pseudodiffusion coefficient related to perfusion-related diffusion; and D is the true diffusion coefficient that reflects the pure molecular diffusion.

In this study, we proposed 4 curve-fitting algorithms for IVIM analysis. Algorithm 1 involves linear regression to determine D and f from high b values, and linear regression to determine D^∗ from low b values, as proposed in method 3 by Suo et al.^[15] Algorithm 2 involves linear regression to determine D and f from high b values, and nonlinear fitting to determine D^∗ from low b values, as proposed by Sigmund et al.^[21] Algorithm 3 involves linear regression to determine D and f from high b values (by neglecting D^∗ effects), and linear regression to determine D^∗ from b values ≤50 s/mm² (by neglecting D effects). Algorithm 4 involves full nonlinear fitting, based on the Nelder–Mead simplex optimization technique.

The prototype software MR Multiparametric Analysis, v 1.0.0 (Siemens Healthcare), was used for histogram analysis on a personal computer running Windows (Microsoft Corporation, Redmond, WA). The radiologist manually marked the seed points for the target tumor on axial and multiplanar reconstruction images and then ran the segmentation (Fig. 1   ). The results of segmentation could be corrected by adjusting the seed points. Finally, voxel-based histogram data were generated for the whole tumor volume, and the following parameters were calculated: the 10th percentile, 25th percentile, 50th percentile (ie, median), mean, 75th percentile, 90th percentile, skewness (describes asymmetry), and kurtosis (describes peakedness).

Figure 1.

MR images of a 52-year-old woman with a 3.3-cm surgically verified right invasive ductal breast cancer and high vascular endothelial growth factor (VEGF) expression. (A) Regions of interest were manually traced along the margin of the cancer on axial and multiplanar reconstruction images. (B–D) The D^∗ (B), D (C), and f (D) parameter maps calculated from each of the four curve-fitting algorithms are displayed with histograms for the whole tumor. The values, obtained using algorithm 3, are as follows: D^∗₁₀ 113 × 10⁻⁴ mm²/s, D^∗₂₅ 201 × 10⁻⁴ mm²/s, D^∗_median 267 × 10⁻⁴ mm²/s, D^∗_mean 270 × 10⁻⁴ mm²/s, D^∗₇₅ 334 × 10⁻⁴ mm²/s, D^∗₉₀ 416 × 10⁻⁴ mm²/s, f₁₀ 58%, f₂₅ 76%.

Figure 1 (Continued).

MR images of a 52-year-old woman with a 3.3-cm surgically verified right invasive ductal breast cancer and high vascular endothelial growth factor (VEGF) expression. (A) Regions of interest were manually traced along the margin of the cancer on axial and multiplanar reconstruction images. (B–D) The D^∗ (B), D (C), and f (D) parameter maps calculated from each of the four curve-fitting algorithms are displayed with histograms for the whole tumor. The values, obtained using algorithm 3, are as follows: D^∗₁₀ 113 × 10⁻⁴ mm²/s, D^∗₂₅ 201 × 10⁻⁴ mm²/s, D^∗_median 267 × 10⁻⁴ mm²/s, D^∗_mean 270 × 10⁻⁴ mm²/s, D^∗₇₅ 334 × 10⁻⁴ mm²/s, D^∗₉₀ 416 × 10⁻⁴ mm²/s, f₁₀ 58%, f₂₅ 76%.

2.3. Pathologic analysis

Tumor angiogenesis was evaluated based on MVD and VEGF expression. A pathologist with 15 years of experience in oncologic pathology, analyzed immunohistochemical staining for CD34 (clone QB End 10, 1:100; DAKO, Carpinteria, CA) and VEGF (clone A-20, 1:200; Santa Cruz, Heidelberg, Germany). Any positively stained endothelial cells that were separate from adjacent microvessels or tumor cells were considered to be countable vessels. CD34-immunostained sections were examined under a microscope at 40-magnification for the area containing the greatest number of microvessels. Five high-power fields were manually counted, and the average counts of the 5 fields were recorded. As previous methods have shown,^[22] VEGF immunostaining was assessed using the scoring system, which is based on the percentage of positive tumor cells (0, 0% immunopositive cells; 1, <25% positive cells; 2, 26%–50% positive cells; 3, >50% positive cells; 4, 67%–100% positive cells) and staining intensity (0, negative; 1, weak; 2, moderate; and 3, strong). In terms of the level of VEGF expression, 2 groups were classified (ie, low vs high VEGF expression).

2.4. Statistical analysis

All statistical analyses were conducted using the SAS Enterprise Guide 5.1 software package (SAS Institute, Cary, NC), SPSS software (version 26.0; SPSS, Inc., Chicago, IL) IBM SPSS Statistics Grad Pack 26.0. P values <.05 were considered to be statistically significant. Intraclass correlation coefficient (ICC) and analysis of variance (ANOVA) were calculated to assess the agreements between IVIM parameters derived using the different fitting algorithms. ICC values close to 1 indicated good interalgorithm reliability. We calculated the precision of the parameter estimates by means of their coefficients of variation (CVs).^[23,24] Spearman correlation was applied to determine the association between IVIM-derived parameters and MVD. Differences in IVIM-derived parameters between the low and high expression of VEGF were calculated using the Mann–Whitney U test.

3. Results

3.1. Histopathological characteristics

The mean tumor size of 55 invasive breast cancers was 2.5 ± 0.9 cm (range, 1.1–5.4 cm). The mean patient age was 52.6 ± 10.7 years (range, 36–74 years). The mean MVD was 41.2 ± 18.4. VEGF expression was low in 29.1% (16/55) of the tumors and high in 70.9% (39/55) of the tumors.

3.2. Interalgorithm agreement between IVIM-derived parameters

Table 1 presents the histogram analysis of each D^∗ value, calculated from the four different algorithms, and the results of the ANOVA. Significant difference (P < .001) was observed for all D^∗ parameters calculated from each algorithm. All f parameters, except for the 10^th percentile, skewness, and kurtosis, also showed significant differences among the algorithms (P < .005). However, all D values calculated from each of the 4 algorithms, except for the 10^th and 25^th percentiles and skewness values, revealed no significant difference (P > .005).

Table 1.

Interalgorithm agreement of D^∗ parameters with histogram analysis.

	IVIM D∗ (10−4 mm2/s) parameter
	Algorithm 1	Algorithm 2	Algorithm 3	Algorithm 4	P
10th percentile					<.0001
Mean ± SD	27.7 ± 13	31.3 ± 21.2	8.9 ± 2.7	48.3 ± 49.4
Median (IQR)	26.5 (18.5–34.5)	23.5 (17.5–40.5)	8.5 (7–10.5)	39 (0–70.2)
25th percentile					<.0001
Mean ± SD	52.4 ± 19.5	63.8 ± 26.4	16.2 ± 4.8	134.7 ± 74.9
Median (IQR)	50 (40–62.5)	59.5 (45.5–74.5)	15.5 (12.5–19.5)	130.5 (80–209)
50th percentile					<.0001
Mean ± SD	86.8 ± 25.9	106.3 ± 32	27.9 ± 11	238.5 ± 60.7
Median (IQR)	78.5 (70–94.5)	100.5 (87.5–117.5)	24.5 (20.5–32.5)	238 (203.5–278)
Mean					<.0001
Mean ± SD	94.2 ± 23.3	123.6 ± 33.8	34.9 ± 14.3	251.3 ± 55.3
Median (IQR)	88.9 (81–99.2)	117.3 (103.7–134.5)	31.5 (23.3–43.1)	249.9 (214.1–290.3)
75th percentile					<.0001
Mean ± SD	126.6 ± 31.5	160.1 ± 43.3	45 ± 20.9	339.5 ± 69.2
Median (IQR)	119.5 (105.5–133)	152.5 (133.5–179.5)	40 (29.5–53.5)	334 (291–386)
90th percentile					<.0001
Mean ± SD	170.3 ± 38.2	234.8 ± 70.5	68.8 ± 34.5	461.2 ± 103.7
Median (IQR)	158.5 (143–188)	217.5 (196.5–261.5)	62.5 (41.5–87.5)	436 (400–505.6)
Skewness					<.0001
Mean ± SD	0.9 ± 0.5	1.6 ± 0.8	2.3 ± 1.2	0.7 ± 0.4
Median (IQR)	0.8 (0.6–1.2)	1.5 (1.1–2.1)	2 (1.6–3)	0.7 (0.5–1)
Kurtosis					<.0001
Mean ± SD	1.6 ± 2.4	4.9 ± 5.5	10.6 ± 13.5	1.1 ± 1
Median (IQR)	0.9 (0.1–2.1)	3.5 (1.6–7.5)	6.3 (2.8–14.8)	0.9 (0.4–1.5)

With regard to the ICC test for interalgorithm agreement of IVIM-derived parameters calculated from the four algorithms, all D^∗ values also showed poor to slight agreement (ICC < 0.1), which was similar to the results obtained with ANOVA. Examples of IVIM-derived parameter maps of breast cancer derived by the 4 algorithms are shown in Figures 1    and 2   .

Figure 1 (Continued).

MR images of a 52-year-old woman with a 3.3-cm surgically verified right invasive ductal breast cancer and high vascular endothelial growth factor (VEGF) expression. (A) Regions of interest were manually traced along the margin of the cancer on axial and multiplanar reconstruction images. (B–D) The D^∗ (B), D (C), and f (D) parameter maps calculated from each of the four curve-fitting algorithms are displayed with histograms for the whole tumor. The values, obtained using algorithm 3, are as follows: D^∗₁₀ 113 × 10⁻⁴ mm²/s, D^∗₂₅ 201 × 10⁻⁴ mm²/s, D^∗_median 267 × 10⁻⁴ mm²/s, D^∗_mean 270 × 10⁻⁴ mm²/s, D^∗₇₅ 334 × 10⁻⁴ mm²/s, D^∗₉₀ 416 × 10⁻⁴ mm²/s, f₁₀ 58%, f₂₅ 76%.

Figure 2.

MR images of a 67-year-old woman with a 4.5-cm surgically verified right invasive ductal breast cancer and low vascular endothelial growth factor (VEGF) expression. (A) Regions of interest were drawn along the tumor boundary on axial and multiplanar reconstruction images. (b-d) The D^∗ (B), D (C), and f (D) parameter maps calculated from each of the four curve-fitting algorithms are displayed with histograms for the entire tumor. The values, obtained using algorithm 3, are as follows: D^∗₁₀ 39 × 10⁻⁴ mm²/s, D^∗₂₅ 116 × 10⁻⁴ mm²/s, D^∗_median 226 × 10⁻⁴ mm²/s, D^∗_mean 227 × 10⁻⁴ mm²/s, D^∗₇₅ 319 × 10⁻⁴ mm²/s, D^∗₉₀ 410 × 10⁻⁴ mm²/s, f₁₀ 27%, f₂₅ 54%.

Figure 2 (Continued).

MR images of a 67-year-old woman with a 4.5-cm surgically verified right invasive ductal breast cancer and low vascular endothelial growth factor (VEGF) expression. (A) Regions of interest were drawn along the tumor boundary on axial and multiplanar reconstruction images. (b-d) The D^∗ (B), D (C), and f (D) parameter maps calculated from each of the four curve-fitting algorithms are displayed with histograms for the entire tumor. The values, obtained using algorithm 3, are as follows: D^∗₁₀ 39 × 10⁻⁴ mm²/s, D^∗₂₅ 116 × 10⁻⁴ mm²/s, D^∗_median 226 × 10⁻⁴ mm²/s, D^∗_mean 227 × 10⁻⁴ mm²/s, D^∗₇₅ 319 × 10⁻⁴ mm²/s, D^∗₉₀ 410 × 10⁻⁴ mm²/s, f₁₀ 27%, f₂₅ 54%.

Figure 2 (Continued).

MR images of a 67-year-old woman with a 4.5-cm surgically verified right invasive ductal breast cancer and low vascular endothelial growth factor (VEGF) expression. (A) Regions of interest were drawn along the tumor boundary on axial and multiplanar reconstruction images. (b-d) The D^∗ (B), D (C), and f (D) parameter maps calculated from each of the four curve-fitting algorithms are displayed with histograms for the entire tumor. The values, obtained using algorithm 3, are as follows: D^∗₁₀ 39 × 10⁻⁴ mm²/s, D^∗₂₅ 116 × 10⁻⁴ mm²/s, D^∗_median 226 × 10⁻⁴ mm²/s, D^∗_mean 227 × 10⁻⁴ mm²/s, D^∗₇₅ 319 × 10⁻⁴ mm²/s, D^∗₉₀ 410 × 10⁻⁴ mm²/s, f₁₀ 27%, f₂₅ 54%.

Figure 2 (Continued).

MR images of a 67-year-old woman with a 4.5-cm surgically verified right invasive ductal breast cancer and low vascular endothelial growth factor (VEGF) expression. (A) Regions of interest were drawn along the tumor boundary on axial and multiplanar reconstruction images. (b-d) The D^∗ (B), D (C), and f (D) parameter maps calculated from each of the four curve-fitting algorithms are displayed with histograms for the entire tumor. The values, obtained using algorithm 3, are as follows: D^∗₁₀ 39 × 10⁻⁴ mm²/s, D^∗₂₅ 116 × 10⁻⁴ mm²/s, D^∗_median 226 × 10⁻⁴ mm²/s, D^∗_mean 227 × 10⁻⁴ mm²/s, D^∗₇₅ 319 × 10⁻⁴ mm²/s, D^∗₉₀ 410 × 10⁻⁴ mm²/s, f₁₀ 27%, f₂₅ 54%.

3.3. IVIM-derived parameter precision

We assessed the quality of an IVIM-derived parameter using the CV as the quantitative precision measure. Figure 3 shows the bar plots of the CVs for the IVIM-derived parameters calculated from the 4 different algorithms. The CV of D^∗ calculated from algorithm 4 (22%) was lower than that obtained from algorithms 1 (24.8%), 2 (27.3%), and 3 (40.9%). The CV calculated from algorithm 4 (33.9%) was also lower than that obtained from algorithms 1 (39.6%), 2 (44.7%), and 3 (48.4%).

Figure 1 (Continued).

MR images of a 52-year-old woman with a 3.3-cm surgically verified right invasive ductal breast cancer and high vascular endothelial growth factor (VEGF) expression. (A) Regions of interest were manually traced along the margin of the cancer on axial and multiplanar reconstruction images. (B–D) The D^∗ (B), D (C), and f (D) parameter maps calculated from each of the four curve-fitting algorithms are displayed with histograms for the whole tumor. The values, obtained using algorithm 3, are as follows: D^∗₁₀ 113 × 10⁻⁴ mm²/s, D^∗₂₅ 201 × 10⁻⁴ mm²/s, D^∗_median 267 × 10⁻⁴ mm²/s, D^∗_mean 270 × 10⁻⁴ mm²/s, D^∗₇₅ 334 × 10⁻⁴ mm²/s, D^∗₉₀ 416 × 10⁻⁴ mm²/s, f₁₀ 58%, f₂₅ 76%.

Figure 3.

The bar graphs of the coefficients of variance for the intravoxel incoherent motion parameters obtained using four different curve-fitting algorithms.

3.4. Correlations between IVIM-derived parameters and tumor angiogenesis

In Table 2, lower D^∗₁₀, D^∗₂₅, D^∗₅₀, D^∗_mean, D^∗₇₅, D^∗₉₀, f₁₀, and f₂₅ values, obtained using algorithm 3, and D^∗₉₀ values, obtained using algorithm 2, were significantly associated with low VEGF expression (P < .05). However, the other IVIM-derived parameters, which were obtained using curve-fitting algorithm 1, 2, and 4, showed no statistically significant correlation with VEGF expression. With regard to MVD, we did not find statistically significant correlations with IVIM-derived parameters, calculated from the four different algorithms (P > .05).

Table 2.

Summary of correlation analysis between intravoxel incoherent motion parameters and VEGF expression.

IVIM curve-fitting algorithm	IVIM-derived parameter	Low VEGF expression	High VEGF expression	P
Algorithm 3	D∗10	8.27 (10−4 mm2/sec)	9.78 (10−4 mm2/s)	.043
	D∗25	15.01	17.84	.012
	D∗50	25.22	31.25	.019
	D∗mean	31.44	40.62	.024
	D∗75	40.03	51.97	.044
	D∗90	61.42	82.16	.041
Algorithm 3	f10	35.19 (%)	44.09 (%)	.010
	f25	68.67	86.47	.005
Algorithm 2	D∗90	220.45 (10−4 mm2/s)	275.03 (10−4 mm2/s)	.031

4. Discussion

In this study, we investigated the relationship between MVD, VEGF, and IVIM-derived parameters, obtained by 4 curve-fitting algorithms, in patients with invasive breast cancers. We found significant associations between VEGF expression and perfusion-related IVIM parameters, which were obtained using curve-fitting algorithm 3, in invasive breast cancer. In our histogram analysis, higher D^∗₁₀, D^∗₂₅, D^∗_median, D^∗_mean, D^∗₇₅, D^∗₉₀, f₁₀, and f₂₅ values, calculated using fitting algorithm 3, were associated with high VEGF expression. IVIM may aid in the evaluation of treatment response to VEGF-targeted therapy in breast cancer. Previous studies have reported this finding. For example, in a murine embryonal rhabdomyosarcoma model, Yuan et al^[25] also showed a positive correlation between the D^∗ value and VEGF expression. Togao et al^[26] exhibited excellent agreement between the f value and the histological vascular density in meningiomas. Klau et al^[27] reported a good correlation between MVD and IVIM perfusion parameters in pancreatic cancer. However, some reports indicate that IVIM may not be sensitive in this regard. In the study by Yang et al^[28] using a hepatocellular carcinoma mouse model, MVD was not correlated with IVIM perfusion parameters. We also failed to reveal any significant association between IVIM-derived parameters and MVD. The correlation between IVIM parameters and microvascular histology is not entirely clear. Further studies are needed to validate the correlation.

We evaluated whole-tumor histograms to assess interalgorithm agreements between IVIM-derived parameters calculated using four different curve-fitting algorithms in breast cancer. In this study, D^∗ histogram parameters differed significantly, depending on which of the four algorithms was used, whereas the 50th, 75th, and 90th percentiles, mean, and kurtosis of the D parameters revealed no significant interalgorithm differences. Barbieri et al^[16] used 6 calculation methods for an IVIM model in upper abdominal organs and showed that the variability of D^∗ value was higher than that of f values, which was higher than the variability of D values. Suo et al^[15] also showed significant differences for each IVIM-derived parameter obtained using 3 different methods in 30 patients with breast cancer. This finding was in accordance with that of existing reports.^[17,18] However, in their studies, the authors measured the mean pixel value within a single-slice map, which did not encompass the entire tumor volume. By contrast, our histogram analysis showed heterogeneous intratumoral signal intensity and the whole tumor volume. Other histogram analysis by Song et al^[29] obtained similar results in that their histogram parameters, derived from true diffusion coefficient maps, were more reproducible than those derived from pseudodiffusion coefficients and perfusion fraction maps. However, they investigated rat breast carcinomas and did not assess interalgorithm agreement in vivo.

By means of the CV in our IVIM data, D had higher precision than did D^∗ or f. This result was consistent with reports by Freiman et al.^[23] The IVIM-derived parameter, f represents an “incoherently flowing” blood volume, whereas D^∗ is related to blood speed. D^∗ is primarily determined at the range of lower b values (typically < 100 s/mm²), so multiple data sampling in the lower b value range and an higher signal-to-noise ratio than is available with most clinical DWI methods, are needed for the precise estimation of D^∗, as shown by Pekar et al.^[30] Many different curve-fitting algorithms have been developed to obtain more reliable estimates of perfusion-related IVIM parameters. Thus, the variations between IVIM-derived parameters from different algorithms may be the natural consequence of the complex mathematical approaches. In addition, IVIM is sensitive to any fluid flow. Besides microcapillary perfusion, active transport, resulting from secretion of the breast ducts, may be explored in the breast.

We found good results with D^∗ parameters obtained using algorithm 3. However, some limitations in this study should be noted. First, our study was retrospective. Also, we were unable to evaluate optimized b-value selection for biexponential IVIM analysis. Previous literatures have shown that the choice of b-values affects IVIM-derived parameter calculation.^[13] Lastly, the sample size was small. Larger, prospective studies may be needed for a further investigation to validate the correlation of IVIM parameters and angiogenic factors.

In conclusion, the D^∗ and f IVIM parameters, obtained using curve-fitting algorithm 3, were significantly correlated with VEGF expression in breast cancer. Thus, IVIM may be used as a noninvasive tool to reflect VEGF expression. Perfusion-related IVIM parameters should be more widely investigated in clinical studies in the future.

Author contributions

Conceptualization: Sung Hun Kim

Data curation: Youn Joo Lee, Bong Joo Kang, Sung Hun Kim.

Formal analysis: Youn Joo Lee, Yo Han Son.

Investigation: Youn Joo Lee

Methodology: Yo Han Son, Sung Hun Kim

Project administration: Sung Hun Kim.

Software: Yo Han Son, Robert Grimm.

Supervision: Sung Hun Kim

Validation: Bong Joo Kang

Writing – original draft: Youn Joo Lee.

Writing – review & editing: Sung Hun Kim, Robert Grimm