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The Physics of Concussions

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Judy Fan

on 29 May 2014

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Transcript of The Physics of Concussions

Force Required to Sustain a Concussion
What is a Concussion?
Because your Brain is suspended within your skull, when you are impacted by a
strong external force
, the cerebrospinal fluid protecting your brain is
not enough
to prevent it from impacting with your skull.

The technical explanation of a concussion is:
A pathophysiological (physical) injury impacting the human brain when it shifts and comes into direct contact with the hard surface of the skull. Resulting in the bruising, tearing and possible minor swelling of the neuro tissue.

Concussions are classified into
three different degrees
of severity.

The DYNAMICS of a Concussion
The dynamics of a concussions consists of the study of force thus,
Newtons 3 Laws of Motion.

The Brain
The brain is a soft organ, and is perfectly balanced inside the skull. It is
Cerebrospinal fluid
which provides the layer of
between the brain and the hard shell of the skull.
The Physics of Concussions
What Causes a Concussion?
A concussion is induced by a strong external biomechanical force, that results in the
sudden acceleration, or deceleration
of the brain within your skull.
Current studies show that angular and rotational movements are more culpable than linear ones.
I will be focusing more on linear impact injuries.
There are still many unanswered questions and mysteries when it comes to neurological injuries, concussions included.
Because there are many arguments regarding how much force is actually required to sustain a concussion, the values provided are only
Leading Causes
of Concussions In North America
Sports injuries
Motor Vehicle accidents
Newton's Second Law Of Motion
Newtons second law states that :

"When an
external non zero
acts on an object, the object

in the direction of the net force."
Types of Concussions
After a Concussion
Physics Concepts
of Concussions
> Kinematics
- Acceleration

> Dynamics
- Newtons Laws of Motion (Linear,
and angular relations)

> Momentum
To be able to understand the dynamics of a concussion, concepts from
must to be applied.
Like stated before, the
sudden acceleration and deceleration
of an individual causes the brain to jolt and impact the inside of the skull; the acceleration and deceleration need to be calculated using kinematics.
The sudden deceleration that immediately follows the acceleration causes the strong impact force.
The equation that illustrates this concept is:
But because the final velocity is often considered to be 0 m/s as the individual is assumed to be brought to a halt, the equation would then be:
a being the acceleration; Vi is the initial speed in a given direction, prior to the beginning of deceleration; d is the distance traveled in total; the value of g will be explained on the next slide.
Newtons First Law states that :

"An object at rest
stays at rest
and an object in motion
stays in motion
with the same speed and in the same direction
unless acted upon by an unbalanced force
The brain within your skull is an example of Newtons First Law.

It will
stay in inertia
until an external force acts on it, because it is SUSPENDED inside your skull, there is a
fraction of a second
when your
body is in movement
due to the external force from the sudden acceleration/deceleration movements but your
brain is still in inertia

When your
head is jerked
the Cerebrospinal fluid is pushed aside as your skull travels and comes into contact with your brain, acting as the
force causing the brain
itself to move which then extends to Newtons Second Law.
Newtons Second Law is able to explain what occurs after the skull initially comes into contact with the brain.
The force that the skull exerts on the brain is dependent on its
mass and initial acceleration that the skull (head) was traveling at.
mass of the brain
initial acceleration of contact
the force
on the brain
linear impacts
, when the skull strikes the brain, it causes the
brain to accelerate
in the direction of which the force was applied, this is called the
coup injury.
As the brain travels across your skull, it will come into contact with the
opposite side of the skull
, this is called the
counter coup injury
, as it is a result of the counter blow of the head, and it can be explained by Newtons Third Law of Motion.
Newtons Third Law of Motion
Newtons third law states that:

"For every action, there is an equal and opposite reaction"
As the brain accelerates towards, and eventually hits the opposite side of the skull, it bounces off the skulls inner surface.
This is explained by Newtons Third Law.
The force applied by the
brain onto the skull
is met with an equal but
reaction force of the
skull acting upon the brain
Because the skull has a greater mass, the
reaction force exerted on the brain
is much greater, causing the brain to ricochet off. The same concept is applied upon initial impact, where the skull first hits the brain. The mass of the brain is smaller than the skulls, thus causing the brain to accelerate in a given direction of the net force.

This is the same concept as a ball hitting a wall and bouncing back, because the mass of the wall is much greater than the mass of the ball, it does not move, but it does exert the equal amount of force onto the ball as the ball exerts onto the wall.
Action force
Reaction force
Initial Force
Reaction Force
Force Required to Sustain a Concussion
As stated before:
F = ma
Acceleration is still measured in the units of m/s^2 by a factor of g.
People of different masses, require different forces to sustain concussion. In the calculation, the acceleration is able to stay constant as it is the controlled variable, and the mass is the manipulated, thus producing varied forces according the the different masses.
If a 90 kg running back is running down the field at 4.568 m/s, then suddenly stops, his head is brought to a stop in a distance of 0.121 m. What force does his head exert?

a = a = -Vi^2 / 2dg
= -(4.568m/s)^2 / 2*0.121m*9.81m/2^2
= 8.7895738 g

F = ma
= 90kg*8.7895738g
= 7760.3147 N

The force may be different if the player were to be a different mass, but the acceleration is still the same as it was calculated with kinematics, because regardless the mass of the athlete, it is the acceleration that results in concussions.
Average Acceleration to Sustain a Concussion
It has been proven that an average high school football player takes hits up to 100-200G's
On average, the majority of concussions are sustained when approximately
95 - 110 G (linear)
[5582 rad/s (angular)]
are delivered to the human body upon impact.
1 in every 5 American High School football players sustain concussions throughout their 3-4 year time playing.
Treatment plans for post concussion individuals
vary on the severity
of the injury. Someone with a Grade III concussion may require therapy or special treatment, whereas someone with a Grade I concussion does not.
Though one condition after
(regardless of degree) is the need to
. The lack of movement and minimal strained use on the brain allows it to heal, rebuilding and decreasing the swelling within.
> Avoid television, computers or use of any
electronic device.

> Avoid operating any type of machinery


> Speaking softly, and slow movements

> No strenuous activity

To understand the dynamics of a concussion you must understand that the use of g in the kinematics formula allows the results to be in an
expression in terms of multiples of acceleration due to the gravitational force (g or G force)
. But in this case it is completely
independent of the concept of gravity
, it is only a constant used.

One g is equivalent to 9.81 m/s^2,
and two g's is
2*9.81m/2^2 = 19.62m/s^2.

Head thrown backward while
brain hits the front of the skull.
Head thrown forward while
brain hits the back of the skull.
Coup Injury
Counter coup injury
Pretend that the ball is the brain, and the wall is the skull.
MOMENTUM and Concussions
Angular / Rotational Injuries
When the terms acceleration and deceleration are used, it is in reference of the vectors. In linear impacts, it is a forward and back, or side to side relation. When changes in vectors occur, it complicates the sum of the forces acting upon the brain.

When the body is suddenly twisted or 'torqued', the head does not simply travel in a unidirectional fashion; it is
accelerating in a new vector, and decelerating in the original vector
, or in other words:
As a result of the multiple vectors acting simultaneously, the brain in this case does not experience the coup, and countercoup injures it does however result in the brain
scraping along side of the skull,
rather than just ricocheting off, resulting in much greater injuries like the tearing of the neuro tissue.
Crosby's infamous concussion from the 2011 Winter Classic is an excellent example of a
rotational/angular impact
resulting in a brain injury.
Momentum is often referred to
"mass in motion"
it is dependent on the mass of the object and the velocity it is traveling at.
This is not a topic studied in physics 20, thus I will no go into depth on it. However the brain inside the skull does experience momentum as it comes in contact with the skull. The
greater momentum
, results in the
greater force
at which it will ricochet off the skull.
Manipulated Variable
Controlled Variable
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