Kinematics
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.1
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.
This chapter has been organized in a stepwise fashion. First, the basic laws of physics and materials that dictate the interaction between the victim and the injuring element are reviewed. This is followed by a more detailed examination of penetrating and blunt trauma and a synopsis of mechanisms specific to organs and body regions. It is hoped that this will offer the reader a better understanding of specific injury patterns, how they occur, and which injuries may result.
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.
The important fact is that a force or impulse will cause a change in momentum and, likewise, a change in momentum will generate a force.2 This folds into Newton’s third law, which states that for every action or force there is an equal and opposite reaction.3 For instance, when two objects of equal velocity and mass strike each other, there velocities are reduced to zero (at the moment of impact). This change in velocity and, hence, momentum was caused by each object applying a force to the other. During impact the forces are equal and opposite. Recalling Newton’s second law, a force is associated with a change in momentum. In this system, the net force is zero and, therefore, the change in momentum is zero. This illustrates the law of conservation of momentum. The total momentum of a system will remain constant unless acted upon by an external force. The momentum of this two object system is the same after a collision as it was prior to impact.4
The next important basic principles are those of work and energy. Work (W) is defined as a force exerted over a distance and is frequently written as
with 
and 
which after integration yields the familiar formula for kinetic energy: 1/2mv2
Therefore, the work being done by a moving object, which interacts with a second object, equals the kinetic energy of the first object prior to doing work minus the kinetic energy after the interaction. In other words, the work done is equal to the change in kinetic energy of the first object.5 When this interaction sets the other body in motion, the second body now has kinetic energy of its own, equal to the work done. James Joule described the first law of thermodynamics in 1840, which simply states that energy can be neither created nor destroyed.6 Interactions in which both momentum and energy are conserved are termed elastic.
In trauma most collisions are inelastic. Inelastic collisions conserve momentum, but not kinetic energy. In these instances the kinetic energy “does work” in the deformation of materials even to the point where objects can conglomerate and form a single object. This is the hallmark of the inelastic collision. This energy transfer or work done is what is typically responsible for the injury sustained by the host.
Energy transfer and momentum conservation can be illustrated in the collision of two cars. Fig. 1-1(A) represents a head-on collision of two cars with equal mass and velocity and, thus, equal kinetic energy and momentum. The momentums are equal, but in opposite directions. Thus, the total momentum for the system is 0 prior to the crash and, by the law of conservation of momentum, must be 0 after the crash. Upon impact, both cars will come to rest. It is as if one of the cars struck an immovable wall. Recalling Newton’s second and third laws, this sudden change in momentum represents a force, which is equally applied to both cars. Because the final velocity is 0, the final kinetic energy is 0, meaning that all the kinetic energy has been converted to work that stops the other car and causes deformation such as breaking glass, bending metal, and causing physical intrusion into the passenger compartment. If the momentum of car A was greater than that of car B by having a greater mass or velocity, the resultant mass C will have momentum in the previous direction in which car A was traveling.
FIGURE 1-1 Energy and momentum available in various motor vehicle crash scenarios. (A) Frontal collisions have the greatest change in momentum over the shortest amount of time and hence the highest forces generated. (B) T-bone collision. When cars A and B collide their resultant momentum directs them toward their final position C; the individual momentums in the x and y axis are dissipated over a greater time resulting in smaller forces then head-on collision. (C) Rear-end collision. Since these vehicles move in the same direction the change in momentum and forces generated are smaller.
In T-bone type crashes the directions of the momentum of cars A and B are perpendicular. Therefore, in the momentum axis of car A, car B has 0 momentum and, in the momentum axis of car B, car A has no momentum. The conglomerate C conserves momentum in both the A and B axes with the resultant direction as shown in Fig. 1-1(B). As a consequence, the changes in momentum and force generated are far less than that of a head-on collision. Also, C continues to have a velocity and, as such, kinetic energy. This means that some of the initial kinetic energy was not converted to work, and less damage to the automobiles will occur. In general, the closer to a head-on collision the greater the change in momentum and, thus, the greater the force generated.
In rear-end collisions the momentum of both cars is typically in the same direction, Fig. 1-1(C). Therefore, the changes in momentum and resultant forces generated are typically small as is the conversion of kinetic energy to work. These principles apply to all collisions whether they are a bullet penetrating a victim, a car hitting a pedestrian, or a driver impacting the windshield.
Penetrating Trauma and Ballistics
Although the above principles were elaborated in the setting of blunt trauma, they are equally applicable to penetrating trauma. The study of ballistics details the energy of projectiles as they leave the firearm and the energy transfer once the bullet strikes the victim. Theodore Kocher first proposed that the kinetic energy possessed by the bullet was dissipated in the four following ways: namely, heat, energy used to move tissue radially outward, energy used to form a primary path by direct crush of the tissue, and energy expended in deforming the projectile.7 Despite limited techniques for studying ballistics, Kocher was for the most part correct. Our more extensive knowledge of the behavior of projectiles in a host comes from the observed performance of bullets in gelatin, which has properties similar to that of muscle and is thought to reflect the way in which energy is transferred through tissue. From such experiments several characteristics of a projectile piercing tissue have been described. These include the following: (a) penetration (the distance the projectile passes through tissue is reflected in the distance from the cut edge of the gelatin block to where the projectile comes to rest); (b) fragmentation (the pattern is assessed by biplaner x-rays and the degree reflected in the difference of the weight of the prefired projectile minus the weight of the collected fragments); (c) permanent cavity (the tissue disintegrated by direct contact with the missile and preserved in the gelatin); and (d) temporary cavity (the amount of “stretch” caused by the passing projectile). This is reflected by the distance from the edge of the permanent cavity to the outer perimeter of the cracks within the gelatin.8
The performance of the bullet and the injury sustained is reliant upon velocity, construction of the bullet, and composition of the target.9 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.”10 This astute observation reflects the exponential importance of velocity in determining the amount of kinetic energy that a particular projectile is capable of transmitting to a given target (kinetic energy = 1/2mv2). As such, high-velocity missiles will generally cause more tissue destruction than their lower velocity counterparts. The velocities and kinetic energies11,12 of common handguns and rifles are listed in Table 1-1.
TABLE 1-1 Velocity and Kinetic Energy Characteristics of Various Guns
The amount of energy imparted (or work) to the tissue by a projectile is equal to the kinetic energy of the missile as it enters the tissue minus the kinetic energy as it leaves the tissue. Bullets are extremely aerodynamic, causing little disturbance while passing through the air. To some extent, this is similar in tissue (i.e., if the projectile moves with the point forward and passes in and out of the tissue, only a small portion of its kinetic energy will be transferred to the target). The characteristics of damage created along the track of a bullet are divided into two components, the temporary and the permanent cavities. The temporary cavity is the momentary stretch or movement of tissue away from the path of the bullet. This could be construed as an area of blunt trauma surrounding the tract of the projectile. The temporary cavity increases in size with increasing velocity. The largest portion of the temporary cavity is on the surface where the velocity of the striking missile is the greatest.12 The concept of the temporary cavity has been used to advocate excessive tissue debridement in high-velocity wounds. In truth, postinjury observation of wound healing and animal experiments involving microscopic examination of tissue in the temporary cavity demonstrate that the momentary stretch produced does not usually cause cell death or tissue destruction.13 As such, debridement of high-velocity injuries should be confined to obviously devitalized tissue. Bullets can be constructed to alter their performance and increase the permanent cavity after they strike their target. This can be enhanced in four ways that all work by increasing the surface area of the projectile–tissue interface that facilitates the transfer of kinetic energy to the target. These include the following: (a) yaw, the deviation of the projectile in its longitudinal axis from the straight line of flight; (b) tumbling, the forward rotation around the center of mass; (c) deformation, a mushrooming of the projectile that increases the diameter of the projectile, usually by a factor of 2, increases the surface area, and, hence, the tissue contact area by four times; hollow point, soft nose, and dum–dum bullets all promote deformation; and (d) fragmentation, in which multiple projectiles can weaken the tissue in multiple places and enhance the damage rendered by cavitation. This usually occurs in high-velocity missiles. Nonfragmenting bullets will have a deeper penetration, whereas a fragmented projectile will not penetrate as deeply, but will affect a larger cross-sectional area.14–16 If the bullet deforms, yaws, tumbles, or fragments, it will cause more tissue destruction. This occurs in deeper structures, not at the surface (Fig. 1-2). Wounds caused by knives are of very low energy and cause only a permanent cavity. With little energy transferred to the tissue, serious injury is caused by directly striking vital structures such as the heart, major vessels, lung, or abdominal organs.
FIGURE 1-2 Yaw, tumble, deformation, and fragmentation. (A) Yaw describes deviation from flight path along the longitudinal axis. (B) Tumble is deviation in a “head over heels” manner. (C) Deformation occurs on impact and increases the actual surface area of the projectile. (D) Fragmentation involves the bullet scattering. All of these increase surface area of the projectile/tissue interface.
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 function17
where W/W1 is a ratio of weights of a given explosive and D/D1 a ratio of distances from the epicenter. A compilation of experimental results showed that if a peak overpressure for one weight of explosive occurred at one distance, the same overpressure could be produced with a smaller weight of explosive at a shorter distance and for a larger weight of explosives at a longer distance (Fig. 1-3A). This relationship is known as the cube root rule or Hopkinson’s rule, and has been demonstrated to hold true for numerous modern-day explosive materials.18
FIGURE 1-3 Physical characteristics of an explosive blast. (A) The Scaling Laws relate the overpressure at specific distances to the ratio of distances from the epicenter of a blast and the cube root of the ratios of corresponding weights of the charges. (B) The Pressure–time relationship at any given distance from the epicenter—the peak overpressure represents the passing wave front with a subsequent decrease in pressure until ambient pressure is reached. This is known as the positive phase. The passing wave will then cause a decrease in pressure below baseline resulting in a relative vacuum, or negative pressure phase.
At any given distance from the explosion there will be a distinct pressure–time curve with an abrupt increase in overpressure. Peak overpressure is dictated by the cube root rule and a decay in pressure that varies with the particular explosive compound and the time past the initial blast wavefront. As the wave moves past a given point, this positive pressure phase will be followed by a negative pressure phase19 (Fig. 1-3B). Pressure is a force applied per unit area. When a force is applied over a given time, an impulse is present and has the ability to change momentum. This force when applied across a distance has the ability to transfer energy and do work.
Nuclear blast waves have a similar pressure–time relationship, but their positive phase may last several seconds as compared to the milliseconds of conventional munitions.20 The energy released from a nuclear explosion is on the order of thousands of times greater than conventional explosives with a corresponding increase in overpressure. The energy available is dictated by Einstein’s mass–energy equivalency formula:21
A large portion of this energy is released in the form of kinetic energy that dictates the wave characteristics of the blast. Also, there is the production of high-energy subatomic particles, such as gamma radiation, which has the ability to cause destruction at the cellular level. Where h = Planck’s constant, the energy of these particles is directly related to their frequency (v).22
They can be released at the time of the blast, but also for a period of time after the explosion as unstable products of a nuclear reaction undergo radioactive decay. Therefore, a nuclear explosion has the ability to transfer energy to a victim and do damage long after the initial blast.
PROPERTIES OF BIOMATERIALS
Stress, Strain, Elasticity, and Young’s modulus
When a force is applied to a particular material, it is typically referred to as a stress, which is a load or force per unit area. This stress will cause deformation of a given material. Strain is the distance of the deformation caused by the stress, divided by the length of the material to which the stress was applied.23
Strain can be tensile, shear, compressive, or overpressure (a relative of compressive strain) (Fig. 1-4). Tensile strain of a particular structure or organ occurs as opposing forces are applied to the same region. The forces are opposite and concentrated upon a particular point. This essentially interrupts the integrity of the structure by pulling it apart. Shear strain occurs as opposing forces are applied to a particular structure, but at different points within that structure. This can be caused by an application of opposing external forces or can arise from a relative differential in the change of momentum within a single structure or between structures that are attached to one another.24
FIGURE 1-4 Biomechanical mechanisms of injury. (A) Tensile strain—Opposite forces stretching along the same axis. (B) Shear strain—Opposite forces compress or stretch in opposite direction but not along the same axis. (C) Compressive strain—Stress applied to a structure usually causing simple deformation. (D) Overpressure—A compressive force increases the pressure within the viscus passing the “breaking point” of the wall.
Compressive strain is the direct deformation that occurs as a result of impact. The energy involved with a particular force does work on the structure causing a crushing-type injury resulting in deformation and interruption of the structural integrity of the injured organ. Overpressure is a type of compressive strain that is applied to a gas- or fluid-filled cavity. The energy applied to a gas- or fluid-filled viscus can deform that structure and cause a decrease in the volume of the structure. Following Boyle’s law:
The product of the pressure and the volume prior to an applied force must be equal to the product afterward.4 Therefore, a decrease in its original volume will increase the pressure inside that viscus. If the rise in pressure, which is a force, overcomes the tensile strength of the viscus, it will rupture.25
When stress is plotted on the same graph as strain, there are several clear and distinct aspects to the curve. The elastic modulus is that part of the curve in which the force does not cause permanent deformation, and a material is said to be more elastic if it restores itself more precisely to its original configuration.26 The portion of the curve beyond this is called the plastic modulus and denotes when an applied stress will cause permanent deformation.27 The tensile, compressive, or shear strength is the level of stress at which a fracture or tearing occurs.28 This is also known as the “failure point.” The area under the curve is the amount of energy that was applied to achieve the given stress and strain (Fig. 1-5).29
FIGURE 1-5 The concept of stress, strain, elastic modulus, plastic modulus, tensile strength and energy as demonstrated by a tensile stress applied to a given structure. The tensile strain is the change in length under a stress divided by the original length. This concept is applicable to compressive and shear strain. In the stress/strain relationship the elastic modulus is the portion of the curve where permanent deformation does not occur as opposed to the plastic modulus where it does fracture or tearing occurs at the tensile strength. The energy applied is the area under the curve.
How well tissue tolerates a specific insult varies with the type of force applied and the tissue in question. In blunt and penetrating trauma, the higher the density of a particular tissue, the less elastic it is and the more energy is transferred to it in a collision. Lung is air-filled and extremely elastic. In lower velocity blunt trauma, energy tends to be dissipated across the lung easily, while in penetrating trauma the actual destruction of the permanent cavity and stretch caused by the temporary cavity are better tolerated because of the elasticity of the lung. In contrast, solid organs such as spleen, liver, or bone tend to absorb energy and will have greater tissue destruction as a consequence.30 In blast injury it is the air-filled structures of the lung and bowel that tend to be injured because of their ability to transmit the blast wave and cause localized pressure increases that overcome the structural failure point of the organ.20
BLUNT TRAUMA MECHANISMS AND PATTERNS OF INJURY
The transfer of energy and application of forces in blunt trauma is often much more complex than that of penetrating trauma. The most frequent mechanisms of blunt trauma include motor vehicle crashes, auto–pedestrian crashes, and falls from a significant height. In these instances there are typically varying energies and forces in both the victim and the striking object. Other variables that complicate care include the larger surface area over which the energy is dispersed as compared to penetrating trauma and the multiple areas of contact that can disperse energy to different regions of the victim’s body. The interactions and directions of these lines of force and energy dispersion are often instrumental in causing specific kinds of injury.
Motor Vehicle Crashes
Although there are frequently confusing vectors for energy transfer and force in a victim of a motor vehicle crash, mortality is directly related to the total amount of energy and force available. Mortality from motor vehicle crashes is accounted for in large part by head-on collisions with mortality rates up to 60%. Side impact collisions (20–35%) and rollovers (8–15%) have progressively lower mortality rates with rear-end collisions (3–5%) having the lowest.31–32 Rollover crashes have a lower than expected mortality because the momentum is dissipated, and forces generated and projected to the passenger compartment are in a random pattern that frequently involves many different parts of the car. Although there are certain forces and patterns of energy exchange that occur in a motor vehicle crash, the vehicle itself does offer some degree of protection from the direct force generated by a collision. Patients who are ejected from their vehicle have the velocity of the vehicle as they are ejected and a significant momentum. They typically strike a relatively immobile object or the ground and undergo serious loads. Trauma victims who were ejected from the vehicle were four times more likely to require admission to an intensive care unit, had a 5-fold increase in the average Injury Severity Score, were three times more likely to sustain a significant injury to the brain, and were five times more likely to expire secondary to their injuries in one study.33
Understanding the changes in momentum, forces generated, and patterns of energy transfer between colliding vehicles is important. For example, the principal direction of force in a head-on collision is affected by the degree of overlap of the vehicles.34 Yet, the behavior of the occupants of the passenger compartment in response to this is what helps identify specific patterns of injury. In frontal collisions the front of the vehicle decelerates as unrestrained front-seat passengers continue to move forward in keeping with Newton’s first law. Lower extremity loads, particularly those to the feet and knees, occur early in the crash sequence and are caused by the floorboard and dashboard that are still moving forward. Therefore, relative contact velocity and change in momentum are still low. Contact of the chest and head with the steering column and windshield occurs later in the crash sequence; therefore, contact velocities and deceleration, change in momentum, and contact force are higher.31,35
Types of injuries are dependent on the path the patient takes. The patient may slide down and under the steering wheel and dashboard. This may result in the knee first impacting the dashboard causing a posterior dislocation and subsequent injury to the popliteal artery. The next point of impact is the upper abdomen or chest. Compression and continued movement of solid organs results in lacerations to the liver or spleen.
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