TITLE:
Estimation of the Parameters of the Reiber’s Hyperbolic Function with the Levenberg-Marquardt Algorithm
AUTHORS:
Piotr Lewczuk
KEYWORDS:
Cerebrospinal Fluid, Blood-CSF Barrier, Numerical Optimization, Levenberg-Marquardt Algorithm
JOURNAL NAME:
Open Journal of Statistics,
Vol.15 No.5,
September
28,
2025
ABSTRACT: A hyperbolic model for the diffusion of proteins through the blood-cerebrospinal fluid (CSF) barrier revolutionized clinical neurochemistry thirty years ago. The regression curves were informally parametrized based on physiologically-driven constraints. The current paper readdresses this issue with numerical optimization for unconstrained non-linear regression, implementing the Levenberg-Marquardt Algorithm (LMA). Astonishingly similar estimates are obtained, which reconfirms the concepts of H. Reiber proposed in 1990s. The LMA is discussed in the context of other optimization algorithms.