Annals of Biomedical Engineering

, Volume 21, Issue 6, pp 621–631

SENSOP: A derivative-free solver for nonlinear least squares with sensitivity scaling


  • I. S. Chan
    • Center for BioengineeringUniversity of Washington
  • A. A. Goldstein
    • Center for BioengineeringUniversity of Washington
  • J. B. Bassingthwaighte
    • Center for BioengineeringUniversity of Washington

DOI: 10.1007/BF02368642

Cite this article as:
Chan, I.S., Goldstein, A.A. & Bassingthwaighte, J.B. Ann Biomed Eng (1993) 21: 621. doi:10.1007/BF02368642


Nonlinear least squares optimization is used most often in fitting a complex model to a set of data. An ordinary nonlinear least squares optimizer assumes a constant variance for all the data points. This paper presents SENSOP, a weighted nonlinear least squares optimizer, which is designed for fitting a model to a set of data where the variance may or may not be constant. It uses a variant of the Levenberg-Marquardt method to calculate the direction and the length of the step change in the parameter vector. The method for estimating appropriate weighting functions applies generally to 1-dimensional signals and can be used for higher dimensional signals. Sets of multiple tracer outflow dilution curves present special problems because the data encompass three to four orders of magnitude; a fractional power function provides appropriate weighting giving success in parameter estimation despite the wide range.


Optimization Curve fitting Indicator dilution Probability density function Sensitivity function Model identifiability Weighting function

Copyright information

© Pergamon Press Ltd. 1993