Dynamic Behavior of Anisotropic Protein Microtubules Immersed in Cytosol Via Cooper–Naghdi Thick Shell Theory

In the present research, vibrational behavior of anisotropic protein microtubules (MTs) immersed in cytosol via Cooper–Naghdi shell model is investigated. MTs are hollow cylindrical structures in the eukaryotic cytoskeleton which surrounded by filament network. The temperature effect on vibration frequency is also taken into account by assuming temperature-dependent material properties for MTs. To enhance the accuracy of results, strain gradient theory is utilized and the motion equations are derived based on Hamilton’s principle. Effects of various parameters such as environmental conditions by considering the surface traction of cytosol, length scale, thickness and aspect ratio on vibration characteristics of anisotropic MTs are studied. Results indicate that vibrational behavior of anisotropic MTs is strongly dependent on longitudinal Young’s modulus and length scale parameters. The results of this investigation can be utilized in the ultrasonic examine of MT organization in medical applications particularly in the treatment of cancers.                 

Keywords:

Anisotropic protein MT , Cooper–Naghdi thick shell model , Strain gradient theory , Visco-elastic bio-medium