The Solid-Liquid Two-Phase Theory Of Cancellous Bone And It's Application

The physiological structure of cancellous bone is composed of the trabeculae architecture and the tissue fluid which is full of the porous skeleton. Therefore, the microscopic structure of cancellous bone is a typical solid-liquid two-phase body. In this paper, the compressive experiment to the specimens of cancellous bone with the tissue fluid was conducted first, and a simple analysis on the two-phase mechanical behavior during the compressive process was also provided. The analytical results were used to fit the experimental results. The experiment on the viscosity of tissue fluid was also completed. The viscosities under the different shear strain rates were obtained in a certain range of shear strain rate. The experimental results showed that the tissue fluid had the outstanding non-linear mechanical properties.According to the geometrical structure of trabecular in the cancellous bone and the above experimental results, the necessity of establishing the solid-liquid two-phase model of cancellous bone was pointed out. Then, with a kind of constitutive equation of the anisotropy poroelasticity (Biot's theory), the controlled equations of the solid-liquid two-phase theory of cancellous bone were obtained. In the equations, the remodeling behavior of cancellous bone under the non-equilibrium state was considered. And the Wolffs law of trabecular architecture in the cancellous bone as a solid-liquid two-phase body was given under the equilibrium state. Furthermore, the solid-liquid two-phase theory of cancellous bone was also studied from the view of the mesomechanics, which showed the relations between some parameters in the theory and the mechanical properties, geometrical structure and deformation form of trabecular and the mechanical properties of tissue fluid in the cancellous bone.For analyzing the effect of the tissue fluid on the load-bearing of cancellous bone, taking the cranium, the costal bone and the vertebrae as the examples, the mechanicalbehaviors of cancellous bone as a solid-liquid two-phased body were analyzed. First,according to the geometrical structure of the skull and the composition of the cranium, the shell model of the cranium was provided in this paper. And, with the membrane theory, the controlled equations of this model were derived. The analytical results on this model showed that the pressure in the tissue fluid of the cancellous bone in the cranium was about 11 times the internal cranial pressure at the initial time when the internal cranial pressure increased. Second, according to the geometrical structure and the composition of the costal bone, the cured beam model of rib was provided, and the controlled equations of this model were derived. The analytical results on the model of rib showed that the point of maximum moment in the rib was far from the costal head since there was the tissue liquid in the cancellous bone of rib. For the vertebrae, it and the discs were as a typical system. Under considering the flow of tissue fluid between the cancellous bone in the vertebrae and the nucleus in discs, the mechanical model of this system was establishedx The research results on this system showed that it had the same constitutive equations with the viscoelasticity. And, at the initial time of loading on this system, the pressure in the nucleus was higher than one in the cancellous bone in the vertebrae. So, under the pressure difference, the tissue fluid would flow between the vertebrae and the nucleus.In the end, with some assumptions in the theory of mixtures, the further discussion was completed on the two-phase structure of cancellous bone. The applied range of the constitutive equations in this paper was discussed. And, some new constitutive relations were also derived, which were the basis for further researching the two-phase mechanical behaviors of cancellous bone.