Jockeys hurt as Bay Story takes deadly tumble: Von Mises stress levels and axonal strain injury

Bay Story crashes through the railing, throwing jockey Mark Zahra as Bling Bling and jockey Greg Childs fall -Photo: Getty Images The Sydney Morning Herald November 6, 2007 by Craig Young

British trainer, Brian Ellison, a former jumps jockey watched in horror as one-time Melbourne Cup aspirant Bay Story crashed when leading in the Lavazza Long Black causing  rival Bling Bling to also carom over the top rail.

Bay Story, who lead into the straight, had just been passed by the eventual winner, Red Lord, when he suddenly shifted ground, with his hind leg collapsing underneath him.

Bay Story had to be put down and jockey Mark Zahra was taken to hospital with a broken leg.

Bling Bling’s rider Greg Childs returned to the enclosure nursing a sore head.

Bling Bling cut his head on the railing but Childs said the injury was not serious. “

Greg Childs having been launched onto the verdant grass carpet was no easy spill especially for his complaints of a sore head. But what about Childs head protection within the mayhem of this accident, what might he have reviewed in his mind?  Afterwards playing back the movie memory loop in his mind’s eye,  his ride dissolved beneath him with that big green coming at him, he remembers screaming at the top of his lungs during the impact moment. Then the terrible sadness of seeing both the other rider Mark Zahra badly hurt with big Bay Story crumpled nearby on the grass. That night this horror movie kept playing over and over in Childs’s mind. It was like being lost deep in a canyon at night until sunrise that still sends shuddering shivers down his spine, making his skin feel clammy all over again.

M.A. Forero Rueda, L. Cui & M.D. Gilchrist (2011): Finite element modelling of equestrian helmet impacts exposes the need to address rotational kinematics in future helmet designs, Computer methods in Biomechanics and Biomedical Engineering, 14:12, 1021-1031.

” The use of helmets by equestrian jockeys is widespread, and it is a mandatory equipment for a jockey in  professional competitive racing. Using a helmet considerably reduces the risk of sustaining serious head injury (Harrison et al. 1996; Turner et al. 2002). Equestrian jockeys, especially jump racing jockeys, fall very frequently and have a high risk of suffering head injury. Data from Britain, France and Ireland (Forero Rueda et al. 2010) show that of all the injuries in both jump and flat racing populations of amateur and professional jockeys, 15% are concussive head injuries, more than half of which involve loss of consciousness.”

“Research into equestrian helmets considerably lags behind the technologies which are commonly used for other types of helmets. Nevertheless, due to the high incidence and risk of head injury to jockeys, horse riding helmets merit dedicated research. Research techniques such as finite element modelling (FEM), which have been employed on other types of helmets, could be applied to analyze existing equestrian helmet standards and helmets in order to identify improvements to the next generation of head protective measures for horse riders.”

University College Dublin Brain Trauma Model (UCDBTM)

Surprisingly, most studies involve comparing ways by using various foam densities to reduce linear acceleration within the liners of helmets like the one that Greg Childs was wearing during his fateful crash, as a performance characteristic of a particular liners kinetic energy absorption by measuring force displacement within each different foam density. But acceleration is the single force criteria to asses head injury risk especially for bicycle helmet evaluations. The real world of sidewalk-head  impacts like we have every day here in Montreal especially awkward oblique or even head over heels bike crashes are simply not finite element modeled. They should be, because those kinds of crash impacts are the normal.

The  kind of forces to cause tissue loading within the brain that bracket the modelling approach of using finite element analysis toward the probability of sustaining axonal injury are usually measured in kilo Pascals. The head is not a simple linear body that receives loads during impacts. The finite element analysis looks at brain tissue loads now known to be associated with sources of brain injury within the actual makeup of brain tissue stress or strain behaviors. In the parlance of these researchers, current brain finite element analysis modeling within the brain architecture can output biofidelic orders of magnitude for capturing these type of brain loads associated with concussion forces.

” Depending on the particular modelling approach, it was found that peak Von Mises stresses of 9.1–44.5 kPa gave a 50% probability of axonal injury and 7–8.6 kPa for a 50% chance of contusion. Anderson et al. (1999) suggested levels of 8–16 kPa for diffuse axonal injury (DAI) based on an experimental and finite element (FE) study with sheep heads. An FEM of cerebral contusions in the rat was developed and compared to experimental injury maps demonstrating blood–brain barrier breakdown (Shreiber et al. 1997). The values for Von Mises stress were in the range of 6.1 to 10.8 kPa, but no statistical significance was found relating these quantities to injury. In a more recent FE study by Kleiven (2007), the region of the corpus callosum showed the highest correlation with injury, with a 50% probability of concussion to be related to a Von Mises stress of 8.4 kPa. These levels are within the values observed by Shreiber et al. (1997).”

“Von Mises Stress is actually a misnomer. It refers to a theory called the “Von Mises – Hencky criterion for ductile failure”.

In an elastic body that is subject to a system of loads in 3 dimensions, a complex 3 dimensional system of stresses is developed (as you might imagine). That is, at any point within the body there are stresses acting in different directions, and the direction and magnitude of stresses changes from point to point. The Von Mises criterion is a formula for calculating whether the stress combination at a given point will cause failure.

There are three “Principal Stresses” that can be calculated at any point, acting in the x, y, and z directions. (The x,y, and z directions are the “principal axes” for the point and their orientation changes from point to point, but that is a technical issue.)

Von Mises found that, even though none of the principal stresses exceeds the yield stress of the material, it is possible for yielding to result from the combination of stresses. The Von Mises criteria is a formula for combining these 3 stresses into an equivalent stress, which is then compared to the yield stress of the material. (The yield stress is a known property of the material, and is usually considered to be the failure stress.)

The equivalent stress is often called the “Von Mises Stress” as a shorthand description. It is not really a stress, but a number that is used as an index. If the “Von Mises Stress” exceeds the yield stress, then the material is considered to be at the failure condition.

The formula is actually pretty simple, if you want to know it:
(S1-S2)^2 + (S2-S3)^2 + (S3-S1)^2 = 2Se^2
Where S1, S2 and S3 are the principal stresses and Se is the equivalent stress, or “Von Mises Stress”. Finding the principal stresses at any point in the body is the tricky part.”

“Margulies and Thibault (1992) proposed human injury tolerance curves for diffuse axonal injury (DAI) and milder forms of axonal injury such as cerebral concussion. They suggested critical strain for moderate to severe DAI ranges from 5 to 10%. Galbraith et al. (1993) carried out experiments to determine the levels of elongation required to damage the squid giant axon. They showed that a stretch ratio of 1.12 resulted in reversible injury, that axons subjected to elongation above 20% never fully recovered, and that structural failure resulted when axons were stretched by more than 25%.”

“Bain and Meaney (2000) carried out stretching experiments on the right optic nerve of an adult male guinea pig. The liberal threshold, intended to minimize the detection of false positives, was a strain of 0.34, and a conservative strain, intended to minimize the detection of false negatives, was 0.14. The optimal threshold strain criterion that balanced the specificity and sensitivity measures was 0.21.”

So if you were to assign a magic criteria number for concussions that would be the evaluation value of 0.021 strain. (Since this strain is an index there are no units) One of the referenced authors Kleiven S reported this level of maximum strain within the corpus callosum that a 50% probability of concussion is found for a level of 0.21 and for 0.26 in grey matter. The corpus callosum (Latin: tough body), also known as the colossal commisure is a wide, flat bundle of neural fibers beneath the cortex  in the eutherian brain  at the longitudinal fissure. It connects the left and right cerebral hemispheres and facilitates inter hemispheric communication. It is the largest white matter  structure in the brain, consisting of 200–250 million contra-lateral  axonal  projections.

Grey’s Anatomy study, impact simulations using an FEM of the

Their study employed detailed impact simulations of human brain, using finite element analysis creating, ” the University College Dublin Brain Trauma Model (UCDBTM) (Horgan and Gilchrist 2003, 2004), in conjunction with various equestrian helmet models, which were performed and compared with impact simulations done with a standard headform. This was done to determine whether and how a rigid headform could reflect brain tissue loads. As seen before, there are relationships between brain tissue loads (Von Mises stress and longitudinal strain) and brain injuries. The output parameters of the UCDBTM are compared to the rigid headform outputs to determine how a rigid headform could be used to reflect actual brain tissue loads within the human brain.”

“The UCDBTM (Horgan and Gilchrist 2003, 2004, (Figure 1)) was developed in University College Dublin to simulate real-life impact scenarios and relate injury types and severity to various engineering values that have been found to correlate with different types of head injury. The model was compared with cadaver tests, showing good agreement with the results (Horgan and Gilchrist 2004).
The resulting 3D FEM of the skull–brain complex consists of scalp, three-layered skull (cortical and trabecular bone), dura, cerebrospinal fluid (CSF), pia, falx, tentorium, cerebral hemispheres, cerebellum and brain stem. The material properties used in the model were defined by Horgan and Gilchrist (2003, 2004). The interaction between the skull and the brain in the UCDBTM has been approximated in the present simulations by modelling the CSF as an incompressible solid of low stiffness and modelling the interface between the CSF and the skull as a penalty contact surface pair with no separation with a friction coefficient of 0.2. The brain tissue parameters analyzed in this study using the UCDBTM were Von Mises stress and maximum principal strain, which have been verified to cause brain injury. ”

The helmet geometry resembles  a typical jockey helmet but not a particular brand. The size was also a typical size used by equestrian jockeys involving a liner density within the typical range of 64 kg/m3. Here is the authors descriptions of the shell and liner parameters., “The outer helmet shell is modeled as a linear elastic material, and the rubber ring at the lower edge of the helmet is modeled as a rubber elastomer with Poisson’s ratio approaching 0.5 (almost incompressible). When it is not otherwise mentioned, the shell stiffness used in most of this study was 7.25 GPa, typical of most equestrian racing helmets in the marketplace. The foam block between the shell and foam liner is modeled as hyper-elastic elastomeric compressible foam with material constants specified by experimental test data using the ABAQUS hyperfoam model (ABAQUS 2009). The foam block in the actual helmet is made of low density elastomeric PE foam of 21 kg/m3 density. The purpose of the foam block is to bond the shell and liner together and also to leave a small gap between the shell and liner to allow the shell deform and absorb some energy before the foam liner crushes in an impact. The shell–liner contact interface was defined as a general contact interaction, all with self (available in ABAQUS/Explicit), with a penalty friction formulation (coefficient of 0.2) injury.”

The actual angulation of the simulated impact positions were: 45 degree on the side, 45 degree front down on the forehead and directly onto the crown of the head/helmet impacts. I’m not going to get into the actual load parameters which I could easily do since I have a mathematics background which will probably cause most people to gloss over these details anyways. The authors do look at different combinations of foam thicknesses and densities toward reducing the strain forces getting into the various helmeted head configurations. Their main concern centers on impact position and how this changes the loads actually getting into the heads. But what is most important are their concerns how angular acceleration is also demonstrating a good correlation with maximum and average Von Mises stress and strain which was not the observation with their linear acceleration tests. The reason they reported this concern was that loads into the helmets from a linear acceleration perspective did not translate into reduced brain tissue loads, since it’s sensitivity was different for each impact position. Their conclusion is that it is very difficult to predict brain injury based on linear acceleration alone within their finite element analysis. Such an expert assessment will have dramatic influence on future helmet design that should be designed to meet angular acceleration criteria for certification purposes to reduce stress and strain in the brain during a concussive impact.

I’ll leave the final emphasis to these good authors. “These studies show how it could be possible to use what is currently known regarding the mechanics of head injury to develop helmet tests capable of gauging actual impact injury. Nevertheless, there is still considerable work to be done to determine the criterion that is capable of predicting brain injury accurately. This requires extensive forensic, experimental and simulation work to establish accurate thresholds for head impacts, and to reach an agreement on the testing methods to design and certify protective headgear. More accurate constitutive models and material property data would also serve to make model predictions of value for specific impact cases. Nevertheless, it is still possible to use the UCDBTM to establish comparative trends between impact scenarios, to determine how a change in external loads affects changes in brain stress and strain. From the trends given by the UCDBTM in this study, it can be seen that future head protection mechanisms could be designed in order to minimize angular acceleration in order to reduce stress and strain in the brain.

All of this suggest that angular acceleration is more important for the purposes of
predicting brain injury than linear acceleration, which, in turn, suggests that angular acceleration needs to be considered when designing protective headgear.”

Mathematical definition

The angular acceleration can be defined as either:

{\alpha} = \frac{d{\omega}}{dt} = \frac{d^2{\theta}}{dt^2} , or
{\alpha} = \frac{a_T}{r} ,

where {\omega} is the angular velocity, a_T is the linear tangential acceleration , and r(usually defined as the radius of the circular path of which a point moving along) is the distance from the origin of the coordinate system that defines \theta and \omega to the point of interest.

Equations of motion

For two-dimensional rotational motion, Newton’s Second Law can be adapted to describe the relation between torque and angular acceleration:

{\tau} = I\ {\alpha} ,

where {\tau} is the total torque exerted on the body, and I is the mass moment of inertia of the body.

Constant acceleration

For all constant values of the torque, {\tau}, of an object, the angular acceleration will also be constant. For this special case of constant angular acceleration, the above equation will produce a definitive, constant value for the angular acceleration:

{\alpha} = \frac{\tau}{I}.

Non-constant acceleration

For any non-constant torque, the angular acceleration of an object will change with time. The equation becomes a differential equation instead of a constant value. This differential equation    is known as the equation of motion of the system and can completely describe the motion of the object. It is also the best way to calculate the angular velocity.

Let’s see now by modeling stress and strain within the brain after concussion sounds a lot like that brain tensio natat term I coined for Snelson’s floating tension net that I have been blogging about for the last year, on


About cerebrovortex

Montreal Grandmother, Agnes Kent was saved by Raul Wallenberg from certain death, when he provided papers for her and her Mom to escape away from the Nazis. Today when asked what that escape meant, she replied,"Remind people, that while statesmen and whole countries remained silent and did nothing, a single individual chose to act, with ramifications that proved enormous. Similar choices confront us today. Write that simple truth she said, it can never be repeated often enough because the world keeps forgetting it."
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