Biomechanics of Bone

Introduction

Bone is a living tissue capable of altering its shape and mechanical behaviour by changing its structure to withstand the stresses to which it is subjected. Bones form the body's hard, strong skeletal framework. Each bone has a hard, compact exterior surrounding a spongy, lighter interior. Long bone has a central cavity containing bone marrow. Bone is composed chiefly of calcium, phosphorous and a fibrous substance collagen. Like other connective tissues, it has cells fibres and ground substance (for more details refer chapter1). It has also inorganic substances in the form of mineral salts which contribute about two third of its weight. As explained earlier, bone is developed by two methods viz membranous and endochondral. Bone is the primary structural element of the human body. Bones form the building blocks of the skeletal system (see the figure) which protects the internal organs, provides kinematic links, provides muscle attachment sites, and facilitates muscle actions and body movements. Bone is hard due to presence of inorganic substances, but it has a degree of elasticity due to the presence of organic fibres. Since bone is a living tissue, it can repair itself if it is properly aligned after fracture. The major factors that decides the stress bearing capacities of bone are:

1. The composition of bone.

2. The mechanical properties of the tissues comprising the bone.

3. The size and geometry of the bone,

4. The rate of applied loads with magnitude and direction.

Classification Of Bones

1. The skeleton is made of 206 bones. Although individual bones are rigid, but the skeleton is flexible and allows the human body a huge range of movement. Bones can be classified as per their shapes as :

· long and short bones

· irregular bones

· flat bones and

· sesamoid bones

The locations of these types of bones are:

(a) Long and short bones: They are in the limbs. For examples, humerus in upper arm, radius and ulna in forearm; femur, tibia and fibula in lower limb are long bones while metacarpal and metatarsal bones of hand and foot respectively are small bones (refer to figure of skeleton)

(b) Flat and irregular bones are in the skull, back bone and the limb girdles.

(1) to reduce friction when it rubs over bony surface,

(2) to alter the pull of tendon to which it is attached. The largest sesamoid bone is ‘patella’ of the knee joint.

Composition Of Bone

1.All organs of the body are formed of tissues. A tissue is a collection of similar type of cells which are associated with some intercellular matrix (ground substance) governed by some laws of growth & development. Bone is made of connective tissue. Bone binds together various structures of the body. Bone is a composite material with various solid and fluid substances, besides cells, an organic mineral matrix of fibres and a ground substance, it has inorganic substances in the form of mineral salts which make it hard and relatively rigid. However, organic components provide flexibility and resilience. The density and composition of bone varies with age and disease which results into degrading of mechanical properties.

2. The bones consist of two types of tissues as shown in ‘cut section view’. The compact bone tissue is a dense material forming the outer shell of bones and the diaphyseal region of long bones. The outer shell is called cortical. The other tissue consists of thin plates (trabeculae) in a loose mesh which is enclosed by the cortical bone tissue. This is called cancellous, trabecular or spongy bone tissue. A dense fibrous membrane surrounds the bone and it is called periosteum (epithelium tissue as explained in chapter 1) the periosteum membrane covers the entire bone except the joint surfaces which are covered with articular cartilage. It is the most sensitive part of the bone.

Mechanical Properties Of Bone

1. Material can be homogeneous or nonhomogeneous. Homogenous material has same composition in all directions. Bone is a non-homogeneous material as it has different compositions in different directions as it consists of various cells, organic and inorganic substances laid in uniform manner. Material can be isotropic having mechanical properties same in all directions or anisotropic with mechanical properties different in different directions. Bone is anisotropic material as its mechanical response depends upon the direction of the applied load. For example compressive strength is more than tensile strength and tensile load capacity is more than transverse load capacity of the bone. Bone has both liquid and solid constituent, hence it has viscoelastic properties which is time dependent i.e., the mechanical response of the bone is dependent on the rate of loading of the bone. Bone can stand rapidly applied loads much better than gradually applied loads.

2. Mechanical properties of metals, concrete and polymers are found out by testing the specimen under tensile, compression and bending load by universal testing machine and torsional load by torsion testing machine. Similar tests can be performed on bone specimen for bulk properties. It can also be performed separately for cortical and cancellous part of the bone.

3. The stress and strain diagram for the cortical bone under tensile loading is shown in the figure. The stress and strain diagram has three distinct regions. The part ‘OA’ is elastic region and the slope of this line is equal to the elastic modulus (E) of the bone which is 17 GPa (109 pascal). In the intermediate region (AB), the bone exhibits non-linear elasto-plastic material behaviour. Now the bone does not retains its original length on removal of load (possible in region OA) and a permanent yielding takes place.

On removal of load, the specimen follows path BO’ instead BAO and there is a permanent strain of OO′. On loading the specimen will now follow path O′B which amounts to higher strength. This is known as strain hardening. The bone exhibits a linearly plastic material behaviour in region BC after yield strength (Point B). The bone fractures when tensile stress is about 128 MPa (106 Pascal) for which the tensile strain is about 0.020. The stress and strain diagram of the cortical bone depends upon strain rate and the diagram is drawn for the strain rate of 0.05 per second. It has been seen that a specimen of bone which is loaded rapidly, has a greater elastic modulus and ultimate strength than a specimen which is loaded slowly. This has been shown in the figure. We also know that resilience energy is the area under the stress and strain diagram. Hence absorbed energy increases with rapidly loading. It has been seen that bone tissues are subjected to a strain rate of about 0.01 per sec during normal activities.

4. Bone is an anisotropic material. Hence its stress-strain behaviour depends upon the orientation of bone with respect to the direction of loading. Bone is stronger (larger ultimate strength) and stiffer (larger elastic modulus) in longitudinal direction (along long axis) than transverse direction (vertical to long axis).

Bone fails in brittle manner at lower load during transverse loading as compared to the longitudinal loading. Stress and strain diagram for these loadings is given in the figure. The values of ultimate strength and elastic modulus are given in the table.

ULTIMATE STRENGTH, E AND G OF BONE

5.Cancellous bone: The distinguishing characteristics of the cancellous bone is its porosity. Hence cancellous bone has lower density depending upon porosity. The stress-strain of cancellous bone depends upon porosity and the mode of loading. In compressive loading, stress and strain in elastic region varies linearly up to a strain about 0.05 and after this yielding occurs when the trabeculae’s begin to fracture. Yielding occurs at constant stress until fracture, showing a ductile material behaviour. However on tensile loading, cancellous bone fractures abruptly, showing a brittle material behaviour. The capacity to absorb energy is higher in compressive loading than in tensile loading

6.Factors affecting strength: Factors affecting the strength or structural integrity of bone are:

(a) Area: Larger is the bone, the larger is area upon which the internal forces are distributed and the smaller is the intensity of stresses.

or Force = σ × Area of bone Hence, bone with larger area can withstand more force for a given value of maximum permissible stress.

(b) Geometry of bone: The bone can be solid or hollow tube. The moment of inertia & polar moment of inertia of solid and hollow tube are:

Hence for equal cross-sectional area

According to bending moment equation, applied bending moment

which shows that hollow bone can take more bending load for given σ permissible. Similarly, applied torsion

which shows that hollow bone can take more torsion load for given τ permissible as compared to solid bone.

(C)Reduction in Density: The strength of bone decreases with reduction of density which may result due to skeletal conditions such as osteoporosis, with ageing or after period of disease. Certain surgical treatments may alter the geometry of the normal bone which may reduce the strength of the bone. Screw holes or other defects in the bone also reduce the load bearing capacity of the bone as stress concentration at these locations of defects increases loading to failure.