A spline-enhanced non-negative least squares inversion approach for estimating magnetic nanoparticle size distribution from magnetization curves

Abstract Accurate determination of magnetic nanoparticle (MNP) core size distribution is critical for optimizing their performance in biomedical applications. In this work, we present a Spline-Enhanced Non-Negative Least Squares (SNNLS) inversion technique for reconstructing nanoparticle size distributions from static magnetization measurements. The proposed method employs B-spline basis functions to achieve a flexible, smooth representation of size distributions without imposing strong parametric assumptions, enabling the resolution of complex, potentially multimodal particle populations. We validate the approach using simulated magnetization data and apply it to experimental measurements of Resovist, a clinically relevant iron oxide nanoparticle formulation. Comparative analysis with conventional NNLS and Kaczmarz inversion methods demonstrates that SNNLS achieves superior reconstruction accuracy, as measured by Jensen-Shannon divergence, while also exhibiting lower computational cost. Residual analysis further confirms the stability and regularization quality of the inversion. The extracted core size distribution shows strong agreement with transmission electron microscopy (TEM) data, confirming the physical validity of the results. The combination of mathematical robustness, computational efficiency, and experimental agreement positions the SNNLS technique as a powerful tool for high-fidelity magnetic nanoparticle characterization.