A Novel Method for Curvefitting the Stretched Exponential Function to Experimental Data

Area of Science:

• Biophysics
• Materials Science
• Computational Modeling

Background:

• The stretched exponential function is widely used for modeling experimental relaxation data.
• Standard fitting algorithms for this function can yield inconsistent results due to sensitivity to initial parameter values.
• This inconsistency poses challenges in accurately characterizing material properties from relaxation experiments.

Purpose of the Study:

• To develop a novel, robust algorithm for fitting the stretched exponential model to relaxation data.
• To address the limitations of existing methods, particularly their sensitivity to initial parameter guesses.
• To provide a more reliable tool for analyzing experimental relaxation data.

Main Methods:

• Development of a new fitting algorithm for the stretched exponential model.
• The algorithm requires only a single adjustable parameter and does not need initial parameter values.
• Validation using simulated datasets and experimental stress-relaxation data from bone and cartilage.

Main Results:

• The novel algorithm demonstrated strong correlations between simulated and fitted parameters for simulated data, indicating accurate parameter determination.
• High-quality fits were achieved for experimental stress-relaxation data from bone and cartilage.
• The new method significantly outperformed a commonly-used Quasi-Newton method in fitting accuracy for experimental data.

Conclusions:

• The developed algorithm offers a reliable and accurate method for fitting stretched exponential models to relaxation data.
• This approach mitigates issues associated with parameter initialization and sensitivity in traditional methods.
• The algorithm shows significant potential for applications in biophysics and materials science, particularly for analyzing biological tissue relaxation.