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.


OptimizationCurve fittingIndicator dilutionProbability density functionSensitivity functionModel identifiabilityWeighting function

Copyright information

© Pergamon Press Ltd. 1993