Understanding Head Injuries Through Biomechanics and Math (Technical)

Often, the first thing that a person newly exposed to a particular sport has to learn is the rules of the game.  Rules are important in any sporting event because they serve as guidelines or limitations to what a player may or may not do.  The rules to any sport are handcrafted by the inventors of the game, redesigned with time, and enforced by officials during game-time.  However, it’s not just the rules of the game, but also the rules (or “laws”) of physics – such as gravity, momentum, and friction – that govern all sporting events. Additionally, there are biophysical laws that also govern the players such as physiological energy production, cardiovascular cooling mechanisms, pain detection, etc. Both of these types of laws, external and internal to the player, must be written in a quantitative language to be conveyed meaningfully.  This language—universal in its nature—is mathematics.

Almost as universal as mathematics is the sport of soccer, known as “football” by international audiences. An estimated 33 billion viewers watched the 1998 FIFA World Cup – over the 64 matches (Kirkendall, Jordan & Garrett 2001).  While most people can’t disagree with the fact that soccer is governed by mathematics and physics, some fail to see the relevance of science in soccer.  One area where science and soccer intersect is sport-related injuries and biomechanics.

The number of sport-related injuries has been reported to be at least 300,000 per year in the US, and in a study of elite soccer players, 89% of the men were found to have some history of head injury, including concussions (Barnes et al. 1998). Within the past few decades, computational power and technology has grown exponentially, permitting advancements in areas that had been “asleep” for centuries.  Engineers and scientists are now able to solve mathematical equations that describe the behavior of biophysical phenomena.  Physicians and sport trainers are now teaming up with engineers to answer injury-related questions for which, up until now, there had only been empirical and observational data.  This new and exciting field is called biomechanics.

Within the sport of soccer alone, the revolutionary field of biomechanics can provide quantitative results that will not only help to better treat and prevent injuries, but also to numerically measure and compare competitions, improve athlete performance and ultimately provide individualized coaching.  For example, sport scientists discovered that merely increasing quadriceps strength will actually decrease jump height with use of the same coordination, but that jump height will increase if jumpers alter their coordination (Bobbert et al. 1996).  Further unanswered questions that have perplexed soccer coaches and physicians for centuries can now be addressed, such as: How much does heading a soccer ball affect the player (see Figure 1)? When are soccer players too young to head the ball? Besides brain tissue deformation, are there other tissue groups adversely affected during heading such as the neck or spine (Al-Kashmiri & Delaney 2006; Bartsch et al. 2012)? Can we compare repetitive long-term ball heading to punches to the head in boxing? How will training and injury treatment be adapted to individual players according to their particular body type?

In biomechanics, systems in motion – such as the impact of a ball on a player’s head – are described or “modeled” by mathematical differential equations.  The solutions to these differential equations show the direct relationship between the dependent and independent variable(s).  The dependent variable may, for example, be the spatial deformation of brain tissue in response to the forces exerted to it by heading the soccer ball.  In this example, the independent variable could be the acceleration or force of the ball to the head of the player at time of impact.  The solution to this equation would tell the coach or physician how much brain tissue is deformed as the force or acceleration of the ball increases.  The answer to these equations can then be coupled with conventional clinical knowledge to establish new safety regulations or adequate sport gear.

Figure 1 Visual of brain tissue deformation under lateral loading

While theoretically biomechanics seems to be the long waited-for solution to understanding sports science in a more quantifiable and accurate manner, it must still overcome many challenges.  The first challenge is the current separation between the two main fields involved in biomechanics: medicine and mechanics (engineering).  Another major challenge is found in attempting to measure and model the mechanical properties of biological tissue.  It is easy to measure mechanical properties of aluminum or steel parts because they are chemically homogeneous and relatively symmetric.  However, most tissues are extremely heterogeneous histologically, even in the microscopic scale, and they also have vague boundaries as they join different tissues.  Furthermore, tissue mechanical properties often are dependent on temperature, pH or external forces and they can change over time.  This makes in-vitro results differ from in-vivo ones and may challenge the model’s validity.  When mechanical properties cannot be kept constant, the differential equations become extremely time-consuming and costly to solve.  Even when mechanical conclusions are reached, certain aspects of pathophysiological processes, such as concussions, are still not fully understood (Kohler 2003).

Despite the obstacles, engineers and doctors have made great strides in biomechanical research.  Many methods have been developed to measure biological tissue properties and predict biomechanical behavior and outcomes.  One common apparatus for measuring strain and deformation of objects is the strain gage and accelerometer.  These gages attach to the subjects and are able to detect mechanical deformation as external forces are exerted (See Figure 1).  Image analysis is another preferred technique to measure the dynamics of systems.  Other widely known techniques include opto-reflective technology, dynamometrics, electromyography, EEG, CT, neurologic exams (Asken & Schwartz 1998) and the newly adapted anthropomorphic test device (Bartsch et al 2012).  Information from these techniques is necessary and often the first step before the mathematical equations come into play.

When deriving differential equations, engineers often “craft” the differential equations on a piece of paper.  The next step usually involves 2D or planar analyses, which augment the complexity of the system of equations but provides more in-depth results.  Head-neck dynamic responses, one of the original research studies in this area, were developed in the sagittal plane in the 1960’s (Mertz & Patrick 1967).  Engineers have only recently started to delve into 3D space.  However, in 3D space, scientists are able to analyze impulsive loading hitting a target in several degrees of freedom (Ivancevic 2009). After a mathematical model, whether 2D or 3D, is finished, it is compared to experimental data in order to be validated.

Using validated models, scientists have been able to establish correct techniques of heading, frequency of impacts, preventative methods and more (Asken & Schwartz 1998). Recent results have shown that lateral headshot impacts cause higher linear acceleration than front or oblique front impacts.  Also, low-energy impacts have been found to produce more uniform stress distribution than high-energy impacts (Bartsch et al 2012).  Others have found that individual impacts cause linear and angular accelerations lower than the levels associated with traumatic brain injury, but attribute damage to constant repetition (Bayly et al. 2002).  Other researchers have similarly found no acute cerebral damage from ball heading (Broglio et al. 2004) but for people who head the ball 1000 – 1500 times per year, lasting damage may develop (Punnoose 2012).  Lastly, even the materials of the soccer ball used during the FIFA World Cup have been reevaluated for better design (Dvorak, Junge & McCrory 2012).  However, even if headshots do not raise as much concern as was expected, biomechanics will still give answers to injury prevention for other types of impacts such as head-to-head and joint impacts (McCrory 2003). Though the direction of biomechanics is still hazy, one thing is certain: it provides important insight into the world of sports injuries and may impact the way athletes play the game.


By: Cristian Clavijo, University of Utah
Cristian Clavijo is a native of Peru, moved to the US in the 8th grade, and is now a Masters student in Mechanical Engineering at the University of Utah.  As an advocate for the Hispanic underserved population in Utah, Clavijo is involved in educating children and parents on how basic scientific and medical knowledge can help them progress and become collaborators of their communities.  He plans to pursue a PhD in Mechanical Engineering next year.


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Articles by Cristian Clavijo.

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