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Many articles explain that the mechanism of a brain injury is via the relative motion of the brain and the skull due to acceleration, which may cause impacts to the brain with the inside of the skull. Aside from these impacts, to what extent does the shockwave of the initial impact (caused by the object outside of the person's body) damage the brain or contribute to the injury?

As an example, consider a head constrained in space so that it cannot move (placed against a wall). If a hard object impacts the head with a force not large enough to break the skull, can the brain be injured? To what degree? How can the shockwave, traveling through the fluid between the skull and the brain, damage cells? Note that the head does not accelerate and thus the brain does not impact the inside of the skull.

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  • Would you be a volunteer for such a study? Neither would anyone else. We don't have numbers like that, nor do we do such studies (on animals) without a decent reason. Yes, the brain can be injured without a skull fracture. To what degree depends on a lot of variables: how thick is the skull? How much CSF surrounds the brain? Where exactly was the blow (the skull isn't uniform in thickness)? What kind of object was used? How much force was applied? Most common head injuries are deceleration injuries: the skull stops but the brain keeps moving forward. Oct 7, 2023 at 18:50
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    Hi Carlos, this site requires that you have done some basic research and preferably provide references relevant to your question. For your question, if you Google "shock wave brain injury" you'll find a host of informative articles. For example neurosciencenews.com/shock-waves-tbi-neurology-3714/#:~:text=“We%20can%20see%20the%20formation,even%20post%2Dtraumatic%20stress%20disorder. Oct 7, 2023 at 18:53
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    I think what OP is trying to describe is coup contracoup injuries, but they're missing half the injury (the coup part). OP, try searching for that term and find out what it is. The initial blow (the coup) actually causes more injury than the brain bouncing off the opposite side of the skull (the contracoup) because... physics.
    – Carey Gregory
    Oct 7, 2023 at 19:57
  • There are a few different animal models for traumatic brain injury and some of them appear to be utilised for researching what you are asking about: nature.com/articles/nrn3407 but I‘m no expert on that at all
    – Narusan
    Oct 11, 2023 at 21:08

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Before we can focus on any discussion on the subject, per se, it would be invaluable to give a name to what you are trying to describe: concussion, or, more generally, blunt force trauma (to the head, as that is what your question is primarily concerned with, but doubt not, that any part of the body can suffer from this kind of traumatic mechanism).

OK, now let's go on to dispel just one more misunderstanding, before we carry on with the meat of the discussion:

Note that the head does not accelerate and thus the brain does not impact the inside of the skull.

This single (tremendously wrong) statement implies an important misunderstanding, not about Medicine, but about Physics. Let it be hereby told once, and be remembered forever after:

When a body is acted upon by a net force, the body's acceleration multiplied by its mass is equal to the net force.

You are correct, if you identified Newton's 2nd law of motion in these beautiful words. Now, I would be reluctant to distract the discussion with references on why Classical Mechanics are a fact of life, but it is really not an argument from authority. Any number of simultaneous forces acting upon a body, when their net sum is not zero, produce an acceleration, and it is thanks to this fact (among thousands of others) that we have made to space and, generally, into the Space Age (among many other achievements).

So, since your direct question is:

If a hard object impacts the head with a force not large enough to break the skull, can the brain be injured?

then you are, effectively, bringing forces into play. If you think the head does not accelerate because it is not visibly moving, you are simply wrong. There is a (perhaps not so apt) name for the kind of physical interaction you are presenting, namely a jerk. Typically, as you shall read, jerk is the rate of change of acceleration over time. This can be used along with an acceleration measure you probably have heard before, the gravitational force equivalent, or a g-force, in order to study short duration shocks and impacts.

To put it simply, during any blow to the head (and anything, really), mass accelerates and decelerates almost instantaneously. The shorter the duration, the larger the impact. I would also not want to distract from the discussion, by pointing to research that supports the fact that a blow actually leads to stresses that are imposed onto the material of the object undergoing the impact, and that this stress is distributed to the entirety of the object. You may have thought that car design, for example, is only a matter of appearance, but how a car behaves during a collision is much more important from a safety perspective, so entire scientific books are written on the subject of Vehicle Collision Dynamics.

Now, for some motivation, you are very right in feeling that impact dynamics, especially in the context of traumatic brain injury, is something pretty important in the field of medicine. Impacts to the head, such as what you have described, are, unfortunately, the bread and butter of Forensic Medicine.

In [1], coup and contrecoup are described as acceleration-deceleration injuries to the brain:

Blunt force trauma to the stationary head is generally associated with cortical-subcortical injuries located at the site of impact (i.e., coup contusions). We present 2 cases of cerebral contusion injury secondary to falling tree limbs hitting the head, illustrating an exception to this observation. In each case, the most prominent lesions were white matter hemorrhagic contusions similar to those associated with acceleration-deceleration types of injuries characterizing falls or motor vehicle accidents (i.e., contrecoup contusions). The proposed pathogenesis for these observed lesions is a forceful impact resulting in the acceleration of the head and brain of a magnitude comparable with that in a motor vehicle accident or a fall.

So, another thing you should have learnt, at this point, is the description of traumatic brain injury based on location with respect to the impact. Coup refers to the location of the brain under the site of impact. Contrecoup (techincally contralateral) refers to "the opposite side" of the site of injury. Why so? Well, the blow produces a very brisk acceleration to the brain, and the brain travels only slightly, inside the "water" (cerebrospinal fluid) it bathes in, before hitting the opposite side of the skull (obviously with its opposite side, of course, as it cannot "rotate") where it decelerates equally brutally, and then you have contrecoup contusions at the location opposite to that of the impact. Check the image below, which is from [2]:

Contrecoup injury

So, after laying a baseline frame of reference, let's address the main content of your question, regarding the forces that can be sustained before clinical manifestations of injury. Prior to discussing even remotely about the option of creating head models, let's talk about...

Sports

A good deal of head blows in various sports actually take place as a normal expectation from the contestants. Never in my life have I believed that I would make a mention of this event in a medical context, but take a look at this beautiful header from Pele (incidentally, one of the greatest saves in soccer history, by Gordon Banks). While Pele (as well as any professional soccer player) made multiple such headers during his lifetime, he didn't really ever need treatment for a neurosurgical emergency shortly after any of his professional career, specifically because of a header (head-to-head impacts are another story, of course). But is the force from such an impact quantifiable, or even relevant?

It most certainly is! First of all, this pilot project states:

The purposes of this project were (1) to determine the exposure to headers in elite men’s and women’s football, and to describe the effects of the headers on ocular markers, (2) to observe the occurrence of concussions in elite men’s and women’s football training and matches, and to describe the effects of concussion on ocular markers, and (3) to determine the reliability of players’ self-reporting the number of headers they make during a session.

From their study, they observed that (emphasis mine):

Female players made an average of 11 headers per player per session. Ninety percent of the headers were below 10G, and none were above 80G. Male players made an average of 3 headers per player per session, with 74% of the headers recording a G-force above 10G and 3% above 80G. There were no significant changes observed post-session in the ocular markers of the players, and no concussions were observed. Neither the women’s nor men’s football cohort were able to accurately self-report the number of headers they made in every session.

So, I can imagine that Cristiano Ronaldo has probably made at least one such 80-g header along the course of his professional life. But is 80-g enough to cause a concussion? How could we measure that?

Well, we would need two things: a) acceleration measurement sensors, and b) a concussion evaluation measure. It turns out we have both. The typical concussion evaluation measure these days, in sports, is the not-so-aptly-named-either SCAT3 (I. Am. Not. Kidding.).

Based on [3], it appears that SCAT (Sports Concussion Assessment Tool) is one of our best tools to identify concussions, and measurement of impact amplitude (power) does not readily correlate to concussion potential:

In the absence of definitive evidence confirming the diagnostic accuracy of sideline screening tests, consensus-derived multimodal assessment tools, such as the Sports Concussion Assessment Tool, are recommended. Sideline video review may improve recognition and removal from play of athletes who have sustained significant head impact events. Current evidence does not support the use of impact sensor systems for real-time concussion identification.

That is not a good answer, however, for curious researchers. From that point on, there are two ways to tackle questions regarding how something would behave in certain scenarios, when that "something" is, pretty much, outside of your grasp. So, since we cannot start breaking skulls in the context of a clinical trial, to see how the skull would respond to the impact, we have two options. Enter Biomechanics:

  1. Hit abstract, immaterial heads, described by dozens (but oftentimes hundreds or even thousands) of equations, and see how the process evolves (this is great, because we can actually study brain deformations for neurosurgical purposes using this scenario). Here, you can find a discussion of the multitude of ways (i.e. models) that have been developed in the literature to describe the actual behavior of an imaginary head, in an attempt to "simulate" a real head and its responses under stresses, such as high-speed impacts.

  2. Hit head counterparts, i.e. real anatomical head models created from actual materials that have been verified to exhibit a mechanical behavior as similar to the actual head composition as possible.

In [4], the authors used MADYMO, a model package that also includes a body model with each part replaced with an approximating ellipsoid shape, so that you get, in its totality, something like this (if you also consider the football itself):

MADYMO body with ball

The authors of 4 also considered the head as a "lumped mass" behaving as a single uniform unit, and modeled the force of the impact to the head by the ball using that. In either case, they found out that:

At 85 km/h (23.6 m/s), the goal kick appears to cause the highest speed football a player would voluntarily head in a match scenario.

Looking at their corresponding force-versus-ball-speed chart, at this ball speed, the blow imparts a force of around 2500 N, which, given the F=m*a formula, and a ball mass equal to 0.403 kg (again, from 4), we have in an acceleration equal to 2500/0.403 = 6.250 m/s^2, which, in g-force units (dividing by ~9.81) is equal to ~637.1-g. That looks a bit too much, right? But soccer players do it all the time, so I guess the human head can actually withstand some forces, let alone the values are typically smaller for most headers (excluding a strong goal kick) and the human head is not an actual lump, or a precise ellipsoid, for that matter. However, as a ballpark, those headers can be expected to apply a force on the order of a few hundreds of "gees" in the worst of cases.

In [5], people did actually go on and create a real head model of their own, to try to measure and determine how the impact affects the various anatomic locations of a brain:

Anatomical head model for weight-impact research

In their abstract, the authors of [5] state:

An anatomical head model was constructed using previously validated simulant materials: epoxy resin (skull), polyvinyl siloxane (scalp), agar/glycerol/water (brain) and modified intravenous fluid for the cerebrospinal fluid. An array of accelerometers (4 mm × 4 mm × 1.45 mm) was incorporated into the various layers of the head to measure forces in x- (anterior/posterior), y- (left/right) and z- (up/down) axis.

And what they found, is extremely interesting, and pretty much directly quantifies the distribution of the forces that you have been questioning about all along (again, taken from the abstract):

A weight (750 g) was dropped from a height of 0.5 m (n= 20). Impact forces (z-axis) of 1107.05 N were recorded on top of the skin, with decreasing values through the different layers (bottom of skin 78.48 N, top of skull 319.82 N, bottom of skull 87.30 N, top and centre of brain 47.09 N and base of brain 78.41 N. Forces in the x- and y-axes were similar to those of the z-axis. With the base of the brain still receiving 78.41 N, this highlights the potential danger of repetitive impact forces to the head.

The most important part of their results is the following table:

Force distribution table per head model layer

The actual weight is not what is as important here, neither is the actual force of the impact (which is, still, pretty damn large at the top of the head, at 1107.05 N, with an object of 0.75 kg, leading to about ~150-g at the top of the skin. What this table tells us is that the brain top and centre receive about 4.25% of the total force each, while the bottom receives more than that, at around 7.08% of the total impact force at the point of contact, measuring 78.41 N right there. Do you know what this force is equivalent to, at 1-g (i.e. just resting on a surface, under the acceleration of gravity)? An object of 7.841 kg. That is right,

Don't overgeneralise these results, of course. The force distribution along the various layers is also a function of the surface of impact on the head, smaller impact surface means that a much more focused region will be affected and bear the weight, while larger impact surface means a larger area of the head and brain will "share" the load. But just as a ballpark estimates, dropping a 0.75kg weight on your head from 0.5 m of height above it produces an impact that is like forcing an approximately 8 kg object to rest on your actual brain matter, for a moment.


1 Morrison AL, King TM, Korell MA, Smialek JE, Troncoso JC. Acceleration-deceleration injuries to the brain in blunt force trauma. Am J Forensic Med Pathol. 1998 Jun;19(2):109-12. doi: 10.1097/00000433-199806000-00002. PMID: 9662103.

2 Rauchman, S.H.; Albert, J.; Pinkhasov, A.; Reiss, A.B. Mild-to-Moderate Traumatic Brain Injury: A Review with Focus on the Visual System. Neurol. Int. 2022, 14, 453-470. DOI: 10.3390/neurolint14020038

3 Patricios J, Fuller GW, Ellenbogen R, et al. What are the critical elements of sideline screening that can be used to establish the diagnosis of concussion? A systematic review. British Journal of Sports Medicine 2017;51:888-894

4 Tierney, GJ, Power, J, Simms, C. Force experienced by the head during heading is influenced more by speed than the mechanical properties of the football. Scand J Med Sci Sports. 2021; 31: 124–131. DOI:10.1111/sms.13816

[5] Falland-Cheung L, Neil Waddell J, Li KC, Tong DC, Brunton PA. Anatomical head model to measure impact force transfer through the head layers and their displacement. Journal of Concussion. 2018;2. doi:10.1177/2059700218777829

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    There's a some physics misconceptions here, like the notion that all forces induce acceleration (they don't if the net force is zero), or that stationary objects actually accelerate and decelerate imperceptibly quickly. The descriptions of coup and contrecoup injuries don't make any sense under the premise of a stationary skull, a coup injury occurs when the skull moves backwards relative to the brain. If the skull is held stationary, a coup injury would require the brain spontaneously leaping forward toward the impacting object. Oct 11, 2023 at 20:26
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    @NuclearHoagie you are correct that not all forces induce acceleration, but there is a subtlety about objects accelerating and decelerating imperceptibly. If the material involved is elastic a collision can generate a sound wave/shock wave that is not visible to the casual observer. However, once the shockwave emerges into a different medium it can result in readily visible acceleration. A great visual example of this is a Newton's Cradle. Oct 11, 2023 at 21:28
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    Imagine the left hand ball in the video at the link to be the hard object, the stationary middle balls the skull, and the balls on the right to be the brain. Shock waves can result in terrible damage to the brain, even if the skull is apparently motionless. Bone is not as elastic as stainless steel, but it is somewhat elastic. Believe me, even if your head is completely immobilized, you don't want to be hit in the head with a hammer! Oct 11, 2023 at 21:29
  • @NuclearHoagie, I will amend the part where I state about forces inducing acceleration, you are correct about that. But, macroscopically, no collision is elastic, so the two fundamental premises actually fall apart: a) skulls do deform, and b) momentum during the collision (say, with a baseball bat) is not transferred instantaneously, so particles within the skull will necessarily accelerate, decelerate, dissipate some energy, spread energy along the object, and, of course, cause the impacting object (presumably a baseball bat) to bounce back, all in a finite amount of time. Oct 11, 2023 at 21:33
  • Technically, if a stationary skull is hit, some kinetic energy is transferred to the brain, thankfully with a lot of dissipation. The experiment in [5] proves that an object falling onto some stationary container (i.e. skull), inside which something other (brain) bathes within some fluid, this motion can actually transfer to the other object bathing inside the external container. Oct 11, 2023 at 21:46

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