Biomechanics

Biomechanics Overview   Torsion   Bending   Compression   Fracture  

Overview

Determining the physical behaviour of bone is important to the study of its mechanical function. This information is also used to assess the changes in the physical properties of bone as a result of age or disease as well as to determine the effectiveness of drug therapies to counteract these changes.

When a force is applied to a bone, the bone will deform according to the specific material and structural relationships of that particular bone. The force-deformation relationship of bone (shown on the right) has certain characteristics. First, it can be divided into two sections: (i) elastic and (ii) plastic regions. In the elastic region, the deformations produced are reversible, so once the force is removed the bone returns to its original shape. Within this region, there is typically a linear relationship between force and deformation. The slope of the elastic curve represents the extrinsic stiffness or elastic rigidity of bone. If deformation continues beyond the yield point, the bone will behave plastically and a portion of the applied deformation becomes permanent. If deformation continues, the bone will eventually fail. The energy required to break the bone is called the toughness, which can determined from the area under the force-deformation curve.

It is import to remember that the force-deformation relationship of a bone reflects both its material behaviour and geometry. For example, a larger bone will break at higher forces than a smaller bone made of the same material. Thus, to determine the material properties of bone, the parameters determined from the force-deformation relationship are normalized to remove the geometric effects on its observed behaviour. For example, the rigidity of the bone reflects the stiffness of the bone material as well as its geometry whereas the modulus of elasticity (the normalized equivalent of rigidity) only reflects the stiffness of the bone material.

The direction of force application also is very important since a material can behave differently when subjected to different loading conditions. For example, bone is much weaker in tension than compression. For this reason specific experiments are performed to determine the mechanical properties of bone under different loading conditions, such as: torsion, bending and compression (shown on the left).

Torsion

Torsion tests are performed to measure the shear properties of the cortical bone of long bones or cores samples of cancellous bone from the femoral head. The ends of the bone are fixed within a custom-built torsion device and a torque is applied one end of the bone with a servomotor. The resulting rotation of the bone shaft is measured using a rotational linear voltage displacement transformer (LVDT) and the applied torque is measured with a torque-cell. The test is typically conducted until the torque is great enough that the bone's integrity is compromised and it shatters.

From the information obtained from this test, the maiximum shear stress, torsional stiffness (rigidity), shear modulus (elasticity) and maximum shear strain of the bone can be calculated.

Three & Four Point Bending

Bending tests are performed to measure the bending properties of the cortical bone of long bones. Bending causes tensile forces on the lower side of the bone and compressive forces on the upper side of the bone, where the deformation is applied. The bone is loaded until failure and since bone mineral is weaker in tension than compression, the side in tension fails first leading to catastrophic failure. Two different types on bending tests can be conducted on bone: (i) three-point (image on the left) and (ii) four-point bending (diagram on the right). In three-point bending, although a simple test to conduct, the bone has a higher chance of fracture due to the large shear stresses developed at the mid-section of the bone. In four-point bending, however, these transverse shear stresses are minimized, but this test is more complicated to perform. In both tests, the bone is placed on two supports and is bent by lowering an another support(s) in the mid-shaft of the bone using a material testing system (Instron™). The applied force is measured by a load-cell located at the top of the device. The resulting deformation is measured with a LVDT attached to the crosshead that is lowered to induce bending.

Compression

Vertebral compression tests are conducted to determine the mechanical properties of cancellous bone that make up the majority of the vertebra

The vertebra is compressed between two parallel plates until failure using a material testing system (Instron™)

Failure usually occurs internally rather than by catastrophic failure as observed in bending. As many of the trabeculae (or struts) of cancellous bone break, the entire structure cannot support the applied force, which in the test is observed as a drop in force, and consequently the functional failure of the vertebra.

As in the bending experiments, the applied force is measured using a load-cell and the resulting deformation is measured using a LVDT

Fracture

The purpose of this experiment is to determine the mechanical properties of the femoral neck due to the high incidence of neck fracture in the elderly and in disease states such as osteoporosis. Typically, the femur is immobilized and a high velocity, short duration force is applied to the femoral head using a servohydraulic material testing system (Instron™) used for high-speed force applications. The applied force is measured by a load-cell located at one end of the immobilized femur. Failure usually occurs at the femoral neck due to the combined bending and compressive forces that act on the neck. Although it is difficult to normalize the results to determine the specific material properties of the femoral neck, the structural properties obtained during this experiment provide very useful information.