Kinematics (kn-mtks) n: The science of pure motion, considered without reference to the matter or objects moved or to the force producing or changing the motion. From the Greek, suffix.¹

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. Studying kinematics in relation to trauma uses Newtonian mechanics, the basic laws of physics, and the anatomic and material properties of the human body to 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 lead the treating physician to further diagnostic 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 with an effort to dispel some of the common myths about these injury mechanisms. Finally, a synopsis of mechanisms specific to organs and body regions is examined. It is hoped that this will offer the reader a better understanding of specific injury patterns, how they occur, and which injuries may result.

The goal of studying kinematics in trauma is to help us understand how injuries occur. Understanding the biomechanics of injury may help us prevent and treat these injuries in order to optimize outcomes. It is tempting to believe in the finiteness of the understanding of physics and biomechanics, the sense that all there is to know is already known; however, ever-improving technology is making the experimental study and computer modeling of such phenomena more effective. Therefore, continual reassessment is critical in order to continue to maintain relevance in an ever-changing world. Nevertheless, much of the basis of current understanding has been laid down by the great minds of the past whose insight and understanding, though it might have come from rather humble or mundane observances, has absolute relevance as we examine biomechanics today.

James Prescott Joule, a 19th century English brewer and amateur physicist seeking to optimize the energy needs of his brewing operations, stumbled upon what is now known as the first law of thermodynamics or the law of conservation of energy. It states that, in a closed system, energy can be neither created nor destroyed, only transformed from one state to another.² This is in line with Newton’s first law, which states that an object in motion or at rest will tend to remain in this state unless acted upon by an external force. Thus, kinetic energy, or the energy of motion will be conserved until it is transformed by an external force. When this transformation occurs in the form of transference of energy from one object to another, it can lead to alteration of one or both objects. This is the fundamental principle of traumatic injury.

In order to understand this principle, one must first consider the basic principles of physics. One can divide these principles into two broad groups as follows: principles that describe motion of objects and their interactions, and those that describe the effects of these interactions on the objects themselves. The key principles that describe the former are force, momentum, and impulse. The key elements that describe the latter are stress, strain, and elasticity. First, let us consider momentum (p), which is defined as the product of mass (m) of an object and its speed or velocity (v).

Intuitively, we understand that in order to change an object’s momentum, we must typically introduce a force, which will cause the object to either speed up or slow down. When a force causes a change in momentum, it is referred to as impulse. This is a bidirectional exchange, however, where a force causes a change in momentum and, concomitantly, a change in momentum will generate a force.³

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, we get:

The product of force and time is known as impulse and multiplying acceleration by time yields velocity. This leads us to Newton’s third law, which states that for every action there is an equal and opposite reaction.⁴ For instance, when two objects of equal velocity and mass strike each other, their velocities are reduced to zero at the moment of impact. Each exerts its force on the other and, because these forces are exactly equal and opposite, the net force is zero. Therefore, the net change in momentum is zero. This means that these two objects would change their direction and “bounce” in opposite directions if each was traveling at the exact same velocity, but in the opposite direction. This occurs only if 100% of the energy could be transferred into changing velocity and none into altering mass.

Interactions in which both momentum and energy are conserved are termed elastic. In real trauma scenarios, 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 to structures that are deformed in response to a change in their momentum, such as organs and bones, is responsible for the injury sustained by the host.

We can understand the simple basics of these complex interactions using the example of two cars colliding. Figure 1-1A represents a head-on collision of two vehicles with equal mass and velocity and, thus, equal kinetic energy and momentum 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. Because both cars are traveling in exact opposite directions at exactly the same speed, their momentums will cancel each other out. If the cars were made of a perfectly nondeformable material, all kinetic energy would be exchanged and the cars would bounce in opposite directions at the exact same speed. In reality, however, these vehicles will be deformed by this interaction relative to their velocity on impact. Assuming that both cars come to rest as a single mass of entangled metal (referred to as object C), this 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 the direction of car A prior to impact. As such, the kinetic energy transferred to the occupants of vehicle A will be relatively less than that transferred to car B. This is intuitively accepted as we consider the effects of collisions between a compact car and an SUV with predictable consequences.

In T-bone type crashes the directions of the momentum of cars A and B are perpendicular and momentum is conserved in a third direction, C, Fig. 1-1B. Because kinetic energy is partly conserved in this new momentum, less energy was transferred to the vehicles (or their occupants) and less deformity occurs. In rear-end collisions, the energy exchange is a function of the net difference in momentum, not absolute momentum. The more momentum the conglomerate of the two vehicles (mass C) can conserve, the less energy is transferred into deforming the vehicles A and B and their occupants. In biomechanics as in life, the key to avoiding destruction when two forces meet is to maintain harmony in motion. If such an ideal is impossible to ensure, the next best thing is to protect the essential core of an object by focusing the deformity on nonessential parts. Modern automobile design, taking the lead from automobile racing engineers whose subjects are exposed to extraordinary speeds, involves building impact zones that deform easily on impact and absorb more of the energy transfer in the periphery of the vehicle. As the old saying goes, “something has to give.”

The deformation of the vehicle (and its occupants, perhaps) can best be described as work done and is an important concept in biomechanics. Work (W) is defined as a force exerted over a distance and is frequently written as

with F = ma and a = vdv/dx

which after integration yields the familiar formula for kinetic energy: 1/2mv²

Therefore, the work being done by one object in motion on another equals the kinetic energy of the 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, assuming no deformation occurred. The greater the momentum of the first object, the greater the magnitude of the work it can do on the second. A bowling ball in motion is a perfect example of this principle. Although moving at relatively low speed, its mass and non-deformable composition allow it to do more work on objects in its path, such as bowling pins. An object of far less mass, such as a baseball, would have to make up in speed what it lacked in mass, in order to be equally effective.

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.⁶ Likewise, for an object to have the same momentum as another of greater mass, it must be traveling at a commensurately greater velocity.

Ballistics is the study of objects in flight. Internal ballistics is the study of the objects themselves, such as shape, mass and velocity. External ballistics is the study of the effects of wind speed, drag, and gravity. What happens when projectiles reach their target is the science of terminal ballistics.⁷ Although this has been a particular obsession of humankind when the first hunter hurled the first stone at the unsuspecting prey, its application is forever and irrevocably changing. Col. Louis A. Lagarde wrote “…the wounds by firearms of fifty years ago and the results of the treatment then in vogue form no guide for a study of the subject today.” This was 100 years ago from the writing of this chapter, when the Western powers were engaged in a war whose savagery had never before been seen.⁸ It was the improvement in ballistics and weapons technology in the turn of the century that brought about a completely new and more gruesome way to fight wars. Although weapons technology has not made such a significant leap in the recent decades as it did between 1870 and 1914, the appearance of military-grade weapons in urban America has made treatment of ballistic injuries in civilian trauma centers a common reality.⁹

First to consider is that the motion of a projectile has three forces acting upon it as follows: the force of the propellant, such as a discharge or the force of a bowstring being released; the force of gravity pulling it down; and the resistance of the medium—air, water, or tissue—impeding or altering its flight. The performance of a bullet in producing injury is reliant upon velocity, construction of the bullet, and the composition of the target.¹⁰ Thus, if one knows all of the variables in the equation, projectiles have predictable trajectories and effects. The problem, of course, is that one rarely knows all of the variables. What follows is an attempt at summarizing current understanding of some of these variables and their clinical relevance in traumatic injury (Table 1-1).

Cavitation

The first concept to consider is the space that a bullet creates in tissue, which is termed cavitation. There are two main forms of cavitation. First, a permanent cavitation caused by the projectile by crushing and displacing the tissue before its leading edge, commonly referred to as the “bullet track” (Fig. 1-2).¹¹ Then there is the temporary cavity caused by the hydrostatic pressure wave generated by the bullet as it moves through the tissue, which induces stretching of the tissue adjacent to the bullet track. It is this temporary cavity and the injury it may produce that is most often misunderstood. The nature of the temporary cavity and, hence, its potential to cause injury, is a function of several factors.

Velocity

One of the most widely misconceived notions regarding ballistics is the idea that a projectile’s destructive power is directly determined by its velocity. It is true that the kinetic energy carried by a projectile is mainly determined by its velocity, if one considers the formula for kinetic energy (E _k):

While an increase in velocity will have an exponential effect on the energy of the system and the energy to be released, the determining factor for tissue destruction is not the kinetic energy of the projectile, but how much of that energy can be transferred to the host tissues.¹² This depends on several factors, chief among them is sectional density.

Sectional Density

The delivery of kinetic energy to a medium depends on the interaction of the projectile and the medium through which it travels. This interaction is described in the formula for drag, which is the degree to which a medium affects the motion of a projectile:

where CD is coefficient of drag for the projectile, d is the density of the medium through which it moves, v is the velocity of the projectile, M is the mass, and A is the cross-sectional area of the projectile. The coefficient of drag is difficult to measure, however, and the ballistic coefficient (BC) is more often used in reports.

where I is a coefficient of form, SD is the sectional density, or the ratio of the surface area of its leading edge (the arrow, bullet, or fragment tip) relative to its overall mass and can be summarized in the following formula¹³:

where diameter (D) is the diameter of the frontal surface area presented to the target and mass (m) is the overall mass of the entire projectile. The higher the sectional density, the higher the ballistic coefficient, and the less relative impedance that projectile will undergo through a medium. In other words, projectiles with low sectional density will be subject to relatively greater drag that retards their movement, thus losing their kinetic energy to the environment.

Recalling that the energy of a system will be conserved, we must accept that some or all of the kinetic energy of a projectile will be transferred to the medium in which it is moving as it loses momentum. It is the transfer of this kinetic energy that results in disruption of the medium through which it passes, its potential destructive force. The destructive force is influenced by a corollary to this equation, namely that the shape (and thus the sectional density) of a bullet is subject to change within the tissue through which it passes in three ways including tumbling, mushrooming, and fragmentation.

The degree to which a projectile’s tip deviates from its flight path is its yaw (Fig. 1-2).¹ An arrow is an extreme example of a projectile with a very high sectional density that remains stable as it traverses the host tissue, whereas the relatively short bullet is much more prone to extreme yaw and flip on its axis as it slows, which is termed “tumbling.” This will produce an immediate decrease in the sectional density, increasing drag and thus releasing more kinetic energy into the surrounding tissue. Given that the displacement of tissue occurs not gradually but instantaneously and that force is a function of both mass and the change in speed over time (acceleration), the destruction of tissue occurs not just because it is displaced, but because it is displaced extremely rapidly. The point of both maximal velocity and lowest sectional density corresponds with the site of greatest temporary cavitation (Fig. 1-2).

The most extreme form of change in sectional density is fragmentation, where the bullet breaks up into smaller pieces that will each produce separate injury tracks and patterns. In their experimental model, Fackler et al. noted that fragmentation of a bullet caused far greater tissue injury than did temporary cavitation in striated muscle.¹⁴ The greater injury was due to the greater number of “projectiles” lacerating and crushing tissue that might otherwise be only slightly affected by being subjected to temporary cavitation.

Tissue Characteristics: Density and Elasticity

Sir William MacCormack’s experiments with ballistics showed that, when fired through a metal can filled with water, a bullet will leave an exit hole of approximate size to its own; however, the hydrostatic pressure wave it carried resulted in a final exit hole that was larger and more irregular.^7,14 When reapproximating the pieces of the metal can together, it was obvious that the bullet exited first, creating a small hole, and then the hydrostatic pressure wave impacted the wall of the can tearing it asunder. The transfer of energy is far more perfect in an incompressible liquid like water and the hydrostatic wave more destructive. In the human body, differences in density, elasticity, compliance, and water content of various tissues along the path of a bullet make the precise nature of the hydrostatic wave less predictable. Nevertheless, this experiment served to illustrate the overall nature of the kinetic energy transfer of a projectile through tissue.

Some of the characteristics of wounds inflicted by bullets have been studied in real-time by the use of high-speed photography and so-called ordinance gelatin. Dr Martin Fackler, as head of the Wound Ballistics Laboratory at the Letterman Army Institute of Research in the 1980s, showed that 10% gelatin was an ideal medium for the purposes of studying ballistics in tissue.¹¹ He has also been its most vocal critic, stating that “with the advent of the high-speed movie camera … emphasis in wound ballistics has shifted from sound scientific method to spectacular cinematography—a triumph of high technology over common sense.”¹¹ Nevertheless, several key observations have been made using this method of ballistic testing and analysis of what he coined the wound profile, or the visual composite of trajectory characteristics in the medium (Fig. 1-1).

In this medium he recognized that, although the gelatin’s high elasticity allowed it to be displaced by the projectile and return to its original shape, radial lacerations occurred that correlated directly with the size of the temporary cavity. Unlike ordinance gelatin, the variance in tissue characteristics through which a projectile can pass makes accurate predictions of cavitation injury far more challenging.

Tissue with low density such as fat and lung may not impart much resistance to a projectile and not cause it to fragment or yaw significantly. Indeed, Kocher’s visit to Prussian field hospitals in the latter years of World War I confirmed many of his predictions regarding ballistic injuries of the newer forms introduced at the turn of the century. For example, he noted that a fine-tipped, smaller, harder projectile produced such minimal cavitation that through-and-through injuries of the thorax through lung resulted in mere weeks of convalescence prior to soldiers returning to the front in stark contrast to what he had seen in the prior decades when broad-tipped, soft lead bullets resulted in far more destructive injury patterns.¹⁵ Furthermore, each tissue has unique thresholds of stress and strain and a recoverable limit beyond which permanent destruction occurs.¹¹ In the case of hepatic tissue, which is very inelastic, the temporary cavity will result in tissue destruction comparable to the size of the temporary cavity, as anyone who has treated these injuries can attest.

Stopping Power

The image of gunshot wound victims being hurled bodily by the impact of bullets is a factual misrepresentation. If momentum of an object is mass × velocity, the maximum momentum transferred from any small arms projectile including an assault rifle or shotgun results in a backward motion of an 80 kg target body of under 0.2 m/s, which is negligible compared to the momentum of an adult even at a slow walk.¹⁶ The effect of the momentum transferred from the missile is virtually zero and there is no backward motion. The only injury that causes instant “stoppage” is a direct one to the brain or spinal cord inducing instantaneous paralysis. The remainder of injuries relies on exsanguination to produce the same effect by reducing blood flow to the central nervous system to below critical levels. In theory, greater cavitation effects are more likely to produce an exsanguinating injury, and a larger vascular defect will produce this effect more quickly; however, the stopping power of the weapon is mainly a function of its ability to produce rapid hemorrhagic shock and not any sort of physical counteraction in the target’s momentum.^16,17 As LaGarde concluded from his experiments, “We are not acquainted with any bullet fired from a hand weapon that will stop a determined enemy when the projectile traverses soft parts alone.”⁸

As we have discussed, there are many factors that influence the destructive force of a bullet, not the least of which are the intrinsic characteristics of the bullet itself. British soldiers noted that their new hard-jacketed, sharp bullets were not as effective at stopping the advancing enemy. They discovered that, by cutting off the tip, they exposed the soft lead core, and the bullets were predictably more effective at halting the enemy. The arsenal where these first bullets were produced was in Dumdum, India, so the term for an expanding or mushrooming bullet is dum-dum. These were effective enough that the 1899 International Convention at the Hague banned their use in warfare, although this ban did little to curb their use then or thereafter.^7,11

Contact Shots

Gunshot wounds where the muzzle is in contact with the skin are termed “contact shots” and have a very different wound profile. The muzzle blast releases expanding gases contained by the skin and subcutaneous tissue and directed inward with devastating effects.¹⁸ The result is a contained explosion that is more destructive than the temporary cavity of a passing projectile, given that the blast velocity of gunpowder is upward of 20,000 ft/s, manyfold greater than the velocity of even the highest-velocity small arms projectile (<4000 ft/s). In 1984, American television actor Jon-Erik Hexum killed himself on set when he fired a revolver loaded with blanks into his temple. Despite the absence of an actual projectile, the muzzle blast was contained by the skin and focused into his temple with sufficient force to cause a devastating brain injury that killed him instantly. The surgeon must take into account the circumstances of the wounding and the possibility that the tissue injury beneath the skin surface may be significantly greater than expected in the case of contact or near-contact shots.

Ballistic Myths Dispelled

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  Bullets do not ricochet within the body.¹⁷

  
  
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  Velocity is the main predictor of tissue destruction. Destructive force is a function of several factors pertaining to both the projectile and the target.^{7,11,12,13,17}

  
  
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  The largest portion of the temporary cavity is not closest to the surface, where the velocity is the greatest. The degree of cavitation depends on both the velocity of the projectile and its surface density along that portion of the trajectory (Fig. 1-3).^7,11,12

  
  
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  Bullets are not superheated when fired and thus not sterile on impact. Bullets can and do carry bacteria from the surface (clothes, skin) to the deeper tissues.^13,15

  
  
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  Bullets traveling at the speed of sound (>1.5 km/s) will not result in increased tissue disruption compared to parts of the trajectory, where the bullet travels subsonically.¹⁹

  
  
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  Bullets do not tumble in the air. Yaw actually decreases the farther it is from the barrel. A bullet’s yaw is negligible in flight and bullets will strike the target tip-first unless altered in their flight path by another force or object.^13,17

  
  
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  The amount of tissue destroyed does not usually significantly exceed the size of the bullet. The ability of tissue to absorb the energy of temporary cavitation will largely determine its ability to remain uninjured. As a result of both clinical and experimental studies, the recommendation is that surgeons limit debridement to what is grossly nonviable when indicated.^11,12,17

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.²⁰

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.²¹