MSB estimation of bound fraction: bias from binding energy uncertainty

Abstract

Magnetic spectroscopy of nanoparticle Brownian motion, MSB, uses the magnetization produced by magnetic nanoparticles in a sinusoidal magnetic field, which can be observed remotely at low enough concentrations to enable it to be used for "molecular imaging". The MSB signal is sensitive to chemical binding, temperature and viscosity. If the MSB signals from nanoparticles in multiple bound states are known, a mixture model can be used to find the concentration of nanoparticles in each bound state. The accuracy has been shown to be high for two and three bound states. However, if the bound states are not accurately known, as is often the case in vivo, the model is perturbed significantly. Using simulations of two bound states based on the effective field approximation to the Fokker-Planck equations, we show that the error in the bound fraction is roughly proportional to the error in the bound state relaxation time. The errors in bound fraction were roughly proportional to the error in the relaxation time for the bound state used in the mixture model. The largest errors occurred for short relaxation time bound states. But for all bound state relaxation times, 10% errors in the relaxation time of the bound state resulted in errors in the bound fraction of less than 10%. Introduction: