Axillary nodal prognostic impact of two-dimensional tumor heterogeneity flux in breast cancer: evaluation via dynamic contrast-enhanced magnetic resonance imaging

Background: Breast cancer remains to have a high mortality toll in women worldwide. Several studies indicate benefit in identifying axillary nodal involvement towards effective patient risk stratification and treatment. Tumor heterogeneity recently emerged as a key factor impacting clinical outcomes. Voxel intensity gradient (VIG), a measure of contrast amongst radiological features of heterogeneity, harbors significance in determining intra-tumoral properties. Our project aims to apply the divergence theorem in correlating the 2-dimensional (2D) surface flux of this quantity to extra-tumoral axillary nodal involvement. Methods: A retrospective cohort of 47 patients with early stage breast cancer following surgery was accrued. Pathology information and preoperative dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) sequences were acquired. Tumor volumes were contoured and exported in slices for digital delineation, filtration, and computation. VIG and VIG divergence were approximated at every tumor pixel and divergence structurally summed. This measure of flux was normalized to tumor volume. Statistical analysis utilized Pearson and Spearman correlation coefficients with leave-one-out (LOO) cross validation. Results: Among the 47 patients analyzed, 33 had T1 tumors with size (1.02 +/- 0.48 cm) and 14 had T2 tumors (3.10 +/- 0.86 cm). Normalized heterogeneity flux demonstrated significant correlation with axillary nodal ratio of positive to number collected: for non-sentinel ratio r= 0.57 (P= 0.001), and total node ratio r= 0.50 (P< 0.001). In nodal-positive patients r= 0.72 (P= 0.001) and r= 0.58 (P= 0.002), respectively. All mean squared errors were < 0.05. Conclusions: In quantifying heterogeneity departing the surface, flux mechanistically exhibited correlation with axillary nodal involvement. This correlation is optimally displayed in patients with nodal positivity. This novel radiological variable capable of characterizing tumor environment may be incorporated into future prognostic indices (nomograms) aimed at helping clinicians with axillary risk assessment.