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Biomed Eng Res. 2013 Dec 1;2(4):153-158.

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

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Department of Mechanical and Industrial Engineering, Montana State University, Bozeman, MT.
Department of Electrical Engineering, Stanford University, Stanford, CA.
Departments of Biomedical Engineering and Orthopaedics, University of California, Davis, Davis, CA.


The stretched exponential function has many applications in modeling numerous types of experimental relaxation data. However, problems arise when using standard algorithms to fit this function: we have observed that different initializations result in distinct fitted parameters. To avoid this problem, we developed a novel algorithm for fitting the stretched exponential model to relaxation data. This method is advantageous both because it requires only a single adjustable parameter and because it does not require initialization in the solution space. We tested this method on simulated data and experimental stress-relaxation data from bone and cartilage and found favorable results compared to a commonly-used Quasi-Newton method. For the simulated data, strong correlations were found between the simulated and fitted parameters suggesting that this method can accurately determine stretched exponential parameters. When this method was tested on experimental data, high quality fits were observed for both bone and cartilage stress-relaxation data that were significantly better than those determined with the Quasi-Newton algorithm.


Cartilage Biomechanics; Curvefitting; Optimization; Osteoarthritis; Polymer Dynamics

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