Fundamentals of Musculoskeletal Biomechanics

Abstract

Biomechanics is the field of study which applies fundamental principles of mechanics to biological problems. Mass, time, and length are the basic variables of the biomechanics, and they are scalar quantities which can be described by a magnitude. Force and moment are vector quantities that take direction (or line) of action into account in addition to the magnitude. Time rate of change of position is velocity, and time rate of change of velocity is acceleration. Force and moment (torque) are the two important concepts at the basis of biomechanics which give forth to linear and rotational motion, respectively. The magnitude of the forces is equal to mass times acceleration. The magnitude of the moment is equal to the force times its moment arm.

The analyses in biomechanics are based on two broad branches of the mechanics: rigid body mechanics and deformable body mechanics. Statics and dynamics are two sub-branches of rigid body mechanics. When the sum of all the forces and moments acting on a body is zero, the body is said to be in static equilibrium. The equations of static equilibrium are often used to calculate unknown forces and moments acting on a rigid body. Dynamics is divided into two subfields: kinematics and kinetics where kinematics explains the motion in linear (meters) or angular (radians, degrees) units. Kinetics is the analysis of forces and moments which give forth to the motion. Newton’s laws, the work–energy relationship, and the principle of energy conservation can be used to document the relationship between force and motion. Motion in the concept of deformable body mechanics is considered as local changes of the shape within a body (internal movement of the body), called deformations. The focus of deformable body mechanics is to analyze experimentally determined relationships between forces and deformations. Forces and deformations apply to structures such as whole bones or implants. At the material level, load and deformation are required to be normalized by cross-sectional area and length, respectively, to obtain stress and strain. Stress–strain relations reveal material properties such as elastic modulus, resilience, ultimate strength, and toughness. Stress–strain curves provide information about the resistance of the material to fracture at a single loading episode, such as trauma. On the other hand, repeated low level of stress results in failure by fatigue. Material properties of materials are dependent on several factors: their composition, environmental and test conditions, and loading schemes. Biological tissues are viscoelastic materials meaning that their deformation depends on the rate and time of loading. Musculoskeletal tissues are also considered as composite materials meaning that they are composed of at least two different materials. The bone is an example where mineral crystals reinforce a ductile collagen matrix. These tissues are also anisotropic materials meaning that their material properties depend on loading direction. For instance, tendon is the strongest when pulled along its longer axis. Finally, it is essential to determine a safe stress level for a structure in order to account for possible uncertainties in its environment.