Influence of Muscle Forces on Stresses in the Human Femur

Abstract: Bone growth and development is highly sensitive to the mechanical loading to which it is subjected. Due to its adaptive ability, abnormal loading can cause the bone to develop in an abnormal way. The mechanical loading both comes from external forces which depend on the physical activity and internal forces which come from the muscles that are attached to the bones. Motion disorders, such as cerebral palsy, often involve spastic muscle tone in the lower limbs which both causes altered internal loading and external loading in how it contributes to altered gait pattern. Several bone deformities are seen in patients with cerebral palsy in which two commonly occur at the femur neck. These are increased neck shaft angle (coxa valga) and increased femoral anteversion angle. Studies investigating femoral deformation in patients with cerebral palsy have been made in regards of using mechanobiological principles (the osteogenic index), to predict these previously mentioned deformities by using gait data from typically developing children and children with cerebral palsy. The osteogenic index is calculated from stresses acting in the octahedral plane; the hydrostatic stress and octahedral shear stress. The hypothesis is that octahedral shear stresses in growth plates induce growth while compressive hydrostatic stresses in the growth plates prohibit growth. The objectives of this study were to determine how muscle forces contribute to the stress state in the proximal femur and to use the osteogenic index to predict their effect on growth. The focus was on the femoral neck as it was of interest to see how individual muscles groups contributed to the development of the femoral anteversion angle and the neck shaft angle. This was performed by evaluating gait data from one typically developing child and two children with cerebral palsy by using musculoskeletal modelling and finite element modelling of the femur. Magnitudes of the muscle forces were obtained by importing data from gait analysis into musculoskeletal modelling software. The muscle activity, net moment arms and forces were obtained by inverse dynamics and the magnitudes of each muscle force acquired through static optimization which used the muscle activity as an optimization criteria. The hip contact force was then found taking into account optimized muscle activity. The muscle forces and the hip contact force were then transferred into a finite element model of the femur where they were applied as point forces, and stress analysis of the femur neck was carried out. Muscle forces were then both applied all at the same time and successively applied one at a time. Finally were changes in the calculated osteogenic index at the estimated growth plate observed. The results showed that the effects of the muscle forces could be seen when comparing load case where all of the muscle forces were applied at the same time to the load case where only the hip contact force was applied. In all three children a tendency for increase of femoral anteversion angle was indicated. A decrease in the neck shaft angle was predicted for the typical developing child and one of the children with cerebral palsy, whereas inclination of the neck shaft angle was predicted for the other child with cerebral palsy. The trend of the change in the calculated osteogenic index was similar throughout the different muscle groups. The hip abductors were however the muscle group that deviated significantly from the trend both in terms of magnitude and contribution to the increase in femoral anteversion angle whereas other muscle groups contributed to the decrease in the femoral anteversion angle. It should be noted that the stress analysis was highly sensitive to the choice of boundary conditions, which should be investigated further in future studies. Introducing both subject-specific musculoskeletal models and subject-specific finite element models would also help improve the reliability and accuracy of the results. Better understanding of how muscle forces contribute to bone development can be beneficiary to help developing treatment plans for patients with motion disorders to improve function and gait kinematics and to minimize abnormal bone development.