Over the last few years, some novel researches in the field of medical science made a tendency to have therapy without any complications or side-effects of the disease with the aid of prognosis about the behaviors of the microtubules. Regarding this issue, the stability/instability analysis of curved microtubule-associated protein in axons with attention to different size effect parameters based on an exact continuum method is presented. The real property of the living biological cells is presented as the Kelvin-Voight viscoelastic properties. Considering length scale parameter (l/R = 0.2) in modified couple stress theory (MCST) leads to a better agreement with experimental results in comparison by other theories that in the results section is presented, in detail. Based on presented exact results, the effect of parameter on the relative frequency changes of the microtubules is hardly depended to the value of the external forced load that should be attention to this value. Another important consequence is that the influence of the microtubule curvature parameter on the relative frequency changes of the living substructure is hardly depended on the value of the time-dependent viscoelastic property, that researchers in the analysis of the microtubule should be attention to this important issue.Communicated by Ramaswamy H. Sarma.
Keywords: Dynamic modelling; biscoelastic properties; living biological cells; protein; telative frequency.