Experimental Verification of Viscoelastic Properties of Compact Bone

M. Petrtýl, L. Melzerová, J. Danešová, and A. Wohlmuthová (Czech Republic)

Keywords

compact bone, constants viscoelastic properties, rheological

Abstract

This research work has been aimed at the experimental and analytical determination of the coefficient of viscosity , and the modulus of elasticity of the time-dependent viscoelastic strain E in the compact bone of human femurs. It is Poynting-Thompson model that belongs to the most relevant mechanical models which enable us to determine the material rheological constants in the compact bone tissue as precisely as possible. The experimental measuring has shown that the increase in load above the physiological level results in the decrease in values of the moduli of elasticity of the time-dependent viscoelastic strain, the same fact being identified at coefficients of viscosity. The influence of viscoelasticity on the value of relative strains of the compact bone tissue of the femur diaphyses is a comparatively small. After a five-minute loading of the bone tissue through a physiological load, the strains increase by about 5-6%. modulus of elasticity of the time-dependent viscoelastic = 1 + 2 = E *t E * 1 t E *t + e ( )* e d + 0 0 e 0 E0 0 0 strain E in the compact bone of human femurs. The viscoelastic properties of the compact bone tissue are influenced by the biopolymers of collagen and protheoglycans; they are dependent on the presence of elastin, on the stage of tissue mineralization, on the fluids in extracellular spaces of osteocytes, and on some other factors. 2. METHODS It is Poynting-Thompson model that belongs to the most relevant mechanical models which enable us to determine the material rheological constants in the compact bone tissue as precisely as possible. This model is made up of an elastic element characterized by the modulus of elasticity E0, and of the Kelvin-Voight viscoelastic member that consists of an elastic element of the time-dependent viscoelastic strain E and the coefficient of viscosity . For the resultant bone tissue relative strain, the following equation applies: in witch E0 is the modulus of elasticity given by the stress ratio and the immediate elastic strain , E is the modulus of elasticity of the time-dependent viscoelastic strain, is the coefficient of viscosity, 0, 0 are stresses and strains in the initiate time t0. In the order to determine the rheological constants, the total number of 15 male femurs and 15 female femurs were used. The miniature beams of 5 x 5 x 60 mm were taken out of the medial parts of their diaphyses from the anterior, posterior, medial and lateral side. The strain gauges of 3 mm base made by the company HBM were attached with glue onto each of these miniature beams. Then the beams were placed into a loading device and exposed to tension in bending. Strains in the damp bone tissue (that was extracted from human beings not later

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