A multi-directional mass-spring-damper model for simulating nonlinear breast dynamics during physical activity

The biomechanics of breasts during dynamic activities exhibits complex nonlinear dynamics, which cannot be accurately captured by conventional one-dimensional models. To address this limitation, a three-dimensional (3D) nonlinear mass-spring-damper (MSD) model was developed to simulate breast dynamics. The proposed model integrates 16 elastic springs, 16 dampers, and 9 mass blocks to replicate tissue property heterogeneity and multi-directional displacements. Model parameters, including stiffness and damping coefficients, were optimized via iterative calibration against motion capture data from 5 km/h running, and validated using independent data from 10 km/h running. Results show that the simulated displacement trajectories are in good agreement with experimental data, achieving mean relative errors < 3% in all three directions. The proposed framework demonstrates that a computationally efficient MSD model, when coupled with data-driven parameter optimization, can reliably simulate complex breast biomechanics. This work provides a novel and practical modeling tool for breast biomechanical research, with promising utility in clinical and biomechanical areas.