Journal of Biomedical Engineering Research (대한의용생체공학회:의공학회지)

The Korean Society of Medical and Biological Engineering (대한의용생체공학회)
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Estimation of Suitable Methodology for Determining Weibull Parameters for the Vortex Shedding Analysis of Synovial Fluid

  • Singh, Nishant Kumar (School of Biomedical Engineering, Indian Institute of Technology, (Banaras Hindu University)) ;
  • Sarkar, A. (Department of Mechanical Engineering, Indian Institute of Technology, (Banaras Hindu University)) ;
  • Deo, Anandita (School of Biomedical Engineering, Indian Institute of Technology, (Banaras Hindu University)) ;
  • Gautam, Kirti (School of Biomedical Engineering, Indian Institute of Technology, (Banaras Hindu University)) ;
  • Rai, S.K. (School of Biomedical Engineering, Indian Institute of Technology, (Banaras Hindu University))
  • Received : 2015.11.18
  • Accepted : 2015.12.29
  • Published : 2016.02.29
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Abstract

Weibull distribution with two parameters, shape (k) and scale (s) parameters are used to model the fatigue failure analysis due to periodic vortex shedding of the synovial fluid in knee joints. In order to determine the later parameter, a suitable statistical model is required for velocity distribution of synovial fluid flow. Hence, wide applicability of Weibull distribution in life testing and reliability analysis can be applied to describe the probability distribution of synovial fluid flow velocity. In this work, comparisons of three most widely used methods for estimating Weibull parameters are carried out; i.e. the least square estimation method (LSEM), maximum likelihood estimator (MLE) and the method of moment (MOM), to study fatigue failure of bone joint due to periodic vortex shedding of synovial fluid. The performances of these methods are compared through the analysis of computer generated synovial fluidflow velocity distribution in the physiological range. Significant values for the (k) and (s) parameters are obtained by comparing these methods. The criterions such as root mean square error (RMSE), coefficient of determination ($R^2$), maximum error between the cumulative distribution functions (CDFs) or Kolmogorov-Smirnov (K-S) and the chi square tests are used for the comparison of the suitability of these methods. The results show that maximum likelihood method performs well for most of the cases studied and hence recommended.

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References

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