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Estimation of the Parameters of the Reiber’s Hyperbolic Function with the Levenberg-Marquardt Algorithm
Lab for Clinical Neurochemistry, Department of Psychiatry, Universitätsklinikum Erlangen, Erlangen, Germany
- 1 Lab for Clinical Neurochemistry, Department of Psychiatry, Universitätsklinikum Erlangen, Erlangen, Germany
Open Journal of Statistics·Volume 15 (2025)·Pages 391–396·Published 28 September 2025·DOI10.4236/ojs.2025.155021
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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.
KeywordsCerebrospinal FluidBlood-CSF BarrierNumerical OptimizationLevenberg-Marquardt Algorithm
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