The multi-color relaxation wall: fundamental limits of spectral separation in physics-based MPI

Multi-color Magnetic Particle Imaging (MPI) differentiates biological processes by exploiting particle-specific relaxation times, but conventional approaches require extensive calibration. We extend Sanders' physics-based framework with particle-specific Debye operators, enabling calibration-free multi-color reconstruction. Simulations with Momentum scanner parameters separate free-circulating (tau1 = 1 microsecond) and tissue-bound (tau2 = 20 microseconds) particles, achieving 95.9% and 78.4% purity and quantifying a frequency-domain trade-off: long-tau responses suffer attenuation when omega*tau >> 1, yielding approximately 15 dB difference at 45 kHz relative to short-tau particles. The formulation links tau-ratios to spectral separability (S = 0.375, rho = 0.625) and provides practical guidance for selecting particles and protocols without particle-specific calibration, applicable to preclinical and clinical MPI studies.