A multiscale finite model of a stress fracture

Abstract: Stress fractures are problematic type of fractures as they are prone to delayed and nonunions. In order to achieve healing and restore the bones mechanical aspects, invasive treatments such as attaching plates, nails and screws are sometimes needed to stabilize the bone and facilitate healing. These surgical treatments often cause discomfort and pain to the patient. Therefore different options need to be considered, in order to reach better result. The purpose of this study is to improve understanding of why stress fractures do not heal during daily activity, through the use of a multiscale finite element model. The presented study is also the first to use finite element modelling and analyses of the stress and strain concentration in a patient with atypical fracture at the femur. With the use of clinical CT- and µCT images, finite element models of the whole femur and the stress fracture were established. The contact force generated by different daily activities is applied at the conjunction of the hip and the femoral head. An inhomogeneous isotropic material model with poroelastic features is implemented where the Young's modulus is based on a set of densitometric relations. The displacements of the organ model at the location of the boarder of the micro model is registered and then applied to the micro model. A comparative study of the stresses, principal strains, octahedral shear strains and uid velocities both pre- and post-surgery is done. These parameters are of significant matter as they describe the deformation of the tissue and may provide some insight into the tissue differentiation. The predicted stress and strain state in the granulation tissue of the micro model and post-surgery organ model is studied and compared with different tissue differentiation theories. The results indicate that the stress and strain concentration within the bony material of the micro model correlated well with the presurgery organ model. Each studied load case, representing normal activity, predicted that certain areas of the crack are under the influence of high values of principal strain in tension, octahedral shear strains and uid velocities. They are of such magnitude that the soft tissue undergo large deformation, which describes the stress fractures poor ability to heal. The predicted values of the principal strain, octahedral strain and uid velocity between the studied activities were almost equally large, this suggest that there is no specific type of activity that is more strenuous on the crack.