Magnetic Levitation of Intact Tumor Biopsies Reveals Multivariate Biophysical Signatures of Breast Cancer Aggressiveness

Diagnostic assessment of breast cancer biopsies remains reliant on resource-intensive histopathology and molecular profiling, which often lack real-time physiological readouts. Magnetic levitation (MagLev) enables label-free density profiling of single cells, yet its application to intact tissue biopsies has been precluded by size-dependent geometric artifacts and the absence of analytical frameworks for biopsy-scale samples. Here, we report the first application of MagLev to intact invasive breast carcinoma biopsies (200-600 m) for biophysical profiling, generating multivariate biophysical signatures from 203 samples across 17 patients. We developed a physics-based size-correction algorithm (xmc) that isolates biological density from geometric artifact, and demonstrate that tissue viability is predicted not by average levitation height, but by spatial heterogeneity across replicate samples, reflecting the microenvironmental complexity of metabolically active tumors. Multivariate integration using Partial Least Squares (PLS) regression and Factor Analysis of Mixed Data (FAMD) identified nodal status (N) as the strongest biophysical predictor, suggesting that lymphatic dissemination capacity leaves a measurable signature in the primary tumor density profile. Unsupervised patient clustering in PLS-derived latent space recovered three clinically coherent subgroups aligned with molecular subtypes. This 30-minute, low-cost assay provides exploratory biophysical stratification complementary to existing diagnostics, particularly in resource-limited settings.