Considering convenience for routine practice, the authors suggest that the mean ADC apparent diffusion coefficient of the conventional method would be practical to use for estimating the Ki-67 labeling index.

• Tumour ADC was significantly lower in LVI-positive than LVI-negative breast cancer. • Peritumoral maximum-ADC was significantly higher in LVI-positive than LVI-negative breast cancer. • Peritumour-tumour ADC ratio was significantly higher in LVI-positive breast cancer. • Diagnostic performance of the peritumour-tumour ADC ratio was highest for positive LVI. • Peritumour-tumour ADC ratio showed higher diagnostic ability in postmenopausal than premenopausal patients.

• Identification of invasive components in DCIS before treatment is clinically important. • Diffusion-weighted MR imaging can help lesion assessment in breast cancer. • The minimum ADC value may suggest the presence of an invasive component in DCIS. • The ADC difference value also suggests the presence of an invasive component in DCIS. • Preoperative evaluation of diffusion-weighted MR imaging may help surgical planning for DCIS.

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Rationale and Objectives: To evaluate whether parameters from empirical mathematical model (EMM) for ultrafast dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) correlate with histological microvessel density (MVD) in invasive breast cancer.Materials and Methods: Ninety-eight consecutive patients with invasive breast cancer underwent an institutional review board-approved ultrafast DCE-MRI including a pre-and 18 postcontrast whole breast ultrafast scans (3 seconds) followed by four standard scans (60 seconds) using a 3T system. Region of interest was placed within each lesion where the highest signal increase was observed on ultrafast DCE-MRI, and the increase rate of enhancement was calculated as follows: ΔS = (Slpost -SIpre)/SIpre. The kinetic curve obtained from ultrafast DCE-MRI was analyzed using a truncated EMM: ΔS(t)=A(1 -e −αt ), where A is the upper limit of the signal intensity, α (min −1 ) is the rate of signal increase. The initial slope of the kinetic curve is given by Address correspondence to: N.M. naokomori7127@gmail.com. CONFLICTS OF INTERESTWe wish to draw the attention of the Editor to the following facts that may be considered as potential conflicts of interest and to significant financial contributions to this work. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing, we confirm that we have followed the regulations of our institutions concerning intellectual property. We further confirm that any aspect of the work covered in this manuscript that has involved has been conducted with the ethical approval of all relevant bodies and that such approvals are acknowledged within the manuscript.

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