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Due to its highly mechanical function, there is a tendency for people to think of bone as being inert or less biologically active than the soft tissues of the body. In fact, bone is a highly dynamic tissue that is constantly in a state of remodeling. Bone adapts its structure in response to the loads that it experiences, as described by Wolffs law. Remodeling of bone microstructure is a cell- driven process that occurs in response to microdamage (e.g., cracks) or elevated local strain. Osteocytes are the specialized cells that can sense strain levels in the bone and can initiate an osteogenic response. Osteoclasts begin the process by resorbing existing bone, and osteoblasts follow by forming new bone tissue. The figure below summarizes this process, as well as the lineages of osteoclasts and osteoblasts. Hematopoietic Stem Cels Siem Cells Cells Lining Cells Osteocytes Osteoclasts Resting Bone Resorption Reversal The femur provides an excellent example of the dynamic nature of bone remodeling. The shaft of the femur is somewhat curved, as depicted in the figures below, giving the bone a tendency to bend predominantly in one direction (with the curvature) when under axial loading. This creates higher stresses on the inside curvature of the bone than on the outside curvature, which stimulates a net deposition of bone on the inside curvature. The resulting bone structure becomes better aligned with the applied forces and consequently subjected to lower levels of stress. This process is summarized in the figure on the right, below. Hore force outside eurvature In a previous and less biologically accurate analysis, we considered that the femur of a person standing on one leg might be modeled using equations for centric axial loading. We used this assumption to compute the average normal stress that would occur in the femoral midsection. Due to the structure of the hip joint and the curvature of the femur, the assumption of centric loading is not accurate 400 N Consider a 400 N force applied axially to the femur, as depicted in the figure at the right. The force is applied on the head of the femur, at a distance of 50 mm from the axis that passes through the centroid of the 38 femur midsection. Dimensions of the femur are also depicted in the figure The shafts of long bones can be mechanically modeled as hollow sections of cortical bone, as the cancellous bone and bone marrow carry very little stress in comparison. Assume that femur midsection has a hollow circular cross-section with outer diameter of 22 mm and thickness of 5 mm. all dimensions in mm. (a) Calculate the average normal stress at the midsection of the femur, assuming that the 400 N force is centric (i.e., not how it is depicted), with respect to the cross-section of the femur midsection. (b) Now consider the 400 N force applied eccentrically (i.e., as depicted). Calculate the normal stresses that occur at the midsection of the femur on the outer surfaces of the bone corresponding to the inside and outside curvature. mickhess of 5 mm. all dimensions in mm (a) Calculate the average normal stress at the midsection of the femur, assuming that the 400 N force is centric (i.e., not how it is depicted), with respect to the cross-section of the femur midsection. (b) Now consider the 400 N force applied eccentrically (i.e., as depicted). Calculate the normal stresses that occur at the midsection of the femur on the outer surfaces of the bone corresponding to the inside and outside curvature. (c) Draw the cross-section of the femur midsection and sketch the normal stress distribution on this drawing. (d) It has been reported that a net bone deposition is stimulated when local strain levels exceed 1000 microstrain. Does our analysis agree with this reported value? Note that the elastic modulus (E) of cortical bone is approximately 20 GPa.

Answer 1

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