Kin·e·mat·ics (kn-mtks) n: The branch of mechanics that deals with pure motion without reference to the masses or forces involved in it. From Greek knma, knmat-, movement.

As can be presumed from the derivation of the word kinematics, its essence revolves around motion. All injury is related to the interaction of the host and a moving object. That object may be commonplace and tangible, such as a moving vehicle or speeding bullet or more subtle as in the case of the moving particles and molecules involved in injury from heat, blasts, and ionizing radiation. Newtonian mechanics, the basic laws of physics, and the anatomic and material properties of the human body explain many of the injuries and injury patterns seen in blunt and penetrating trauma. Injury is related to the energy of the injuring element and the interaction between that element and the victim. Although most patients suffer a unique constellation of injuries with each incident, there are quite definable and understandable energy transfer patterns that result in certain predictable and specific injuries. Knowing the details of a traumatic event may aid the treating physician to further investigative efforts to uncover occult but predictable injuries.

BASIC PRINCIPLES

 Newton’s Laws, Impulse, Momentum, Energy and Work, Elastic and Inelastic Collisions

Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is the definition of inertia. Newton’s second law builds on the first and further defines a force (F) to be equal to the product of the mass (m) and acceleration (a).

The application of a force does not occur instantaneously, but over time. If we multiply both sides of the above equation by time

The product of force and time is known as impulse and multiplying acceleration by time yields velocity. Momentum (p) is defined to be the mass (m) of an object times its velocity (v).

hence impulse = change in momentum.

 Penetrating Trauma and Ballistics

The performance of the bullet and the injury sustained is reliant upon velocity, construction of the bullet, and composition of the target.  The energy and construction characteristics of the projectile will be discussed here while target properties will be reviewed in the section on biomaterials. The prominent 18th-century surgeon John Hunter stated, “If the velocity of the ball is small, then the mischief is less in all, there is not so great a chance of being compounded with fractures of bones etc.” As such, high-velocity missiles will generally cause more tissue destruction than their lower velocity counterparts.

 Blast Injury and Ionizing Radiation

The transfer of energy that results from explosions follows the previously stated rules of physics, but also has additional dimensions that deserve mention. The transmission of energy from an explosive blast is best understood in the context of wave mechanics. All conventional explosions have in common several characteristics in that they all involve a solid or liquid mixture that undergoes a rapid chemical reaction producing a gaseous by-product and a large amount of released energy. This release of energy pushes gaseous molecules from the explosion and within the atmosphere radially away from the explosion center producing a spherical wave of compressed gas, known as the blast wave, with increased density, pressure, and temperature when compared with the ambient air. The movement of these molecules creates what is known as a blast wind, and the compression of these molecules into a given space increases the density and pressure. This blast overpressure is defined as the wavefront pressure generated above ambient pressure. This peak overpressure is a function of the energy released from the blast and the distance from the point of detonation, and its decay is expressed as a scaling function

 Pedestrian Injuries

Pedestrian injuries frequently follow a well-described pattern of injury depending on the size of the vehicle and the victim. Nearly 80% of adults struck by a car will have injuries to the lower extremities. This is intuitively obvious as the level of a car’s bumper is at the height of the patient’s knee and this is the first contact point in this collision sequence. A victim struck by a truck or other vehicle with a higher center of mass will more frequently have serious injuries to the chest and abdomen because the initial force is applied to those regions. In the car–pedestrian interaction, the force applied to the knee region causes an acceleration of the lower portion of the body that is not shared by the victim’s trunk and head, which tend to stay at rest, by Newton’s first law. As the lower extremities are pushed forward they will act as a fulcrum bringing the trunk and head forcefully down on the hood of the car applying a secondary force to those regions, respectively. The typical injury pattern in this scenario is a tibia and fibula fracture or dislocation of the knee joint, injury to the trunk such as rib fractures or rupture of the spleen, and injury to the brain.

 Falls

Falls from height can result in a large amount of force transmitted to the victim. The energy absorbed by the victim at impact will be the kinetic energy at landing. This is related to the height from which the victim fell. The basic physics formula describing the conservation of energy in a falling body states that the product of mass, gravitational acceleration, and height, the potential energy prior to the fall, equals the kinetic energy as the object strikes the ground. With mass and gravitational acceleration being a constant for the falling body, velocity, and, therefore, momentum and kinetic energy are directly related to height. The greater the change in momentum upon impact the larger the load or force applied to the victim. Injury patterns will vary depending upon which portion of the victim strikes the ground first and, hence, how the load is distributed.

The typical patient with injuries sustained in a free fall has a mean fall height of just under 20 ft. One prospective study of injury patterns summarized the effects of falls from heights ranging between 5 and 70 ft. Fractures accounted for 76.2% of all injuries, with 19–22% of victims sustaining spinal fractures and 3.7% developing a neurological deficit. Nearly 6% of patients had intra-abdominal injuries, with the majority requiring operative management for injury to a solid organ. Bowel and bladder perforation were observed in less than 1% of injuries.