A multiscale computational framework for predictive modeling of HER2-targeted PEGylated SPION magnetic relaxation biosensing

Breast cancer remains a major global health challenge, where early detection of biomarkers such as human epidermal growth factor receptor 2 (HER2) plays a decisive role in diagnosis and therapeutic decision-making. In this study, a multiscale computational framework is presented to predict the magnetic relaxation behavior of HER2-targeted superparamagnetic iron oxide nanoparticles (SPIONs) under physiologically relevant conditions. The model integrates nanoscale superparamagnetic behavior described by the Langevin theory, mesoscale Brownian–Néel relaxation dynamics, molecular ligand-receptor binding kinetics, and a simplified macroscale biodistribution model following systemic administration. Simulations under physiological conditions suggest that four-arm branched polyethylene glycol (PEG) functionalization, antibody conjugation, and HER2 binding do not alter the intrinsic magnetic properties of the SPION core. Nevertheless, these interactions modify hydrodynamic volume, increasing the effective relaxation time from approximately \(12.6 \mu s\) $12.6\mu s$ in the unbound state (HER2-) to \(32.84 \mu s\) $32.84\mu s$ in the bound state (HER2+). Operating in an intermediate dynamic regime \((\omega \tau \approx 1)\) $(\omega \tau \approx 1)$ , the model predicts reductions in magnetization amplitude, increased phase lag, susceptibility peak displacement, and attenuation of harmonic voltage response. The proposed framework provides a predictive computational approach for exploring how molecular recognition events may influence measurable magnetic relaxation signals in HER2-targeted SPION systems.