Cranial Protective Hydrogel And Hydrogel-Like Helmet Padding

Abstract

An example embodiment of a helmet employs a hydrophilic porous material as padding in the helmet in an arrangement designed to protect the brain against impacts that can occur in impact sports, such as football. The amount of reduction of the average magnitude of the acceleration of the head due to padding in the helmet as a result of an impact of the helmet with a surface is limited by the thickness of the helmet padding. There is evidence, however, that the peak acceleration rather than the average acceleration is a significant cause of brain injury. Therefore, the helmet may reduce brain injury that occurs as a result of an impact by using the disclosed padding material in the arrangement with the helmet to “tune” the acceleration of the skull so that it is never significantly higher than its average during the impact of the helmet with a surface.

Description

RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No. 62/613,099, filed on Jan. 3, 2018. The entire teachings of the above application are incorporated herein by reference.

BACKGROUND

It is estimated that there are as many as 3.8 million sports related concussions each year in the United States, with the largest number of such injuries resulting from football [1,2]. Recently a good deal of public attention has focused on the possibility that multiple concussions might have long-term effects [3-5], including neurocongnitive deficits [6-8]. The study of the possible causes of brain injuries that result from head impacts is an on-going active area of research [9]. The ideal way to protect the brain from injury during an impact is to reduce the acceleration of the head sufficiently to prevent severe traumatic brain injury. Assuming as a first approximation that during an impact of a helmeted head with a hard surface, the helmet stops moving instantaneously and the padding compresses by an amount x as it reduces the speed of the head to zero, the average acceleration of the head can be found from

V₀²+2a_avx=V²=0   (1)

where V₀ and V are the initial and final velocities of the brain, respectively, and a_av is the average acceleration. Then, it follows that

$\begin{array}{cc}{a}_{\mathrm{av}}=-\frac{V_0^2}{2x}& \left(2\right)\end{array}$

In this discussion, the term acceleration refers to negative acceleration or deceleration that reduces the initial velocity of the head, just before the impact, to zero. Then, for example, if the helmet padding thickness is 0.025 m (˜1 in), the mass of the head is 3 kg and V_o=5 m/s, the impact energy of the head is E=37.5 J and from Eq. (2) the minimum possible value of a_av=500 m/s. Obviously, the average deceleration may be reduced by increasing the thickness of the padding, but there are practical limits on how thick one can make the padding, i.e., the helmet must accommodate the head and the padding. Thus, there is a practical limit on the magnitude of the average deceleration that can be achieved with a helmet, regardless of what padding materials are used.

Rowson and Duma [10], however, demonstrated that there is a strong correlation between large peak acceleration of the head during an impact and the occurrence of concussions. They put forward a function which gives the probability of a concussion for a given peak acceleration during an impact, based on a logical regression analysis of injury rates on the field correlated with drop tests of helmets. Their function for the probability of a concussion as a function of peak acceleration is

$\begin{array}{cc}R\left(a_{\max }^{\prime }\right)=\frac{1}{1+e^{-\left(\alpha +\beta a_{\max }^{\prime }\right)}},& \left(3\right)\end{array}$

Where a′_max=a_max/g and g is the gravitational acceleration. Using statistics from NCAA college games, they obtain the following values for the parameters: α=−9.805 and β=0.0451. Using statistics for NFL games they have the values: α=−9.828 and β=0.0497. Using the value a_max=821 m/s², or 83.8 g as shown in the example worked out in the next section, R=0.0040 and 0.0035 for the NCAA and NFL parameters, respectively. For comparison, for foam used in typical football helmets for an impact energy of 30 J, which corresponds to V_o=4.47 m/s [11], a_max=408 g and R is almost equal to one, implying a high probability of head injury.

SUMMARY

Fowler et al. [12] proposed using shear thickening fluids (STF) as helmet padding. These are colloids whose viscosity increases rapidly as the rate of applied stress increases. For a 3.3 cm thick pad of STF, the a_max=119 g for a 30 J impact, which gives R=0.02. Thus, hydrogels and STF's provide better head protection than the foams currently used for helmet padding. The hydrogels, however, can do a better job, because they can reduce the maximum deceleration to lower values. One reason for this is that the hydrogels provide significant deceleration at the beginning of the impact, in contrast to the STF's for which the initial acceleration is zero. This makes it easier to achieve a nearly constant deceleration during the impact, which reduces a_max and the possibility of producing brain injuries that result from very large peak accelerations.

Example embodiments of the invention apply theory and materials design, specifically of a hydrogel padding, to achieve a padding for which the peak deceleration is never significantly larger than its average value. The padding currently used in football helmets used today is either a polyurethane or vinyl nitrate foam, which has the disadvantage that it results in a very large peak deceleration [12]. Details of the example embodiments are disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.

FIGS. 1-5 are schematic mechanical diagrams or plots that illustrate example embodiments disclosed herein.

DETAILED DESCRIPTION

A description of example embodiments follows.

The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.

Preliminary Work on the Problem

How a Gel Prevents the Peak Deceleration of the Head from Becoming too Large. Consider a porous padding material, which is initially swollen with water, when it has an impact with an object of mass m with a velocity V_o. (This is equivalent to a padded helmet, enclosing a head of mass, m, moving with an initial velocity V_o and making an impact with a massive object which brings the helmet to a sudden stop.) The padding could be a polymer hydrogel or three-dimensional fibrous hydrogel mat swollen with water. Let the initial and instantaneous thicknesses of the material be l and z, respectively. Assume that as the material is compressed, the pore size is reduced by an amount proportional to the extent of compression such that the permeability, k, changes as k=k_o(z/l), where k_o is a constant. The force that the surface of the porous material must exert on the object (i.e., the head) to decelerate it is given by

$\begin{array}{cc}F=m\frac{d^2z}{{\mathrm{dt}}^{2}}.& \left(4\right)\end{array}$

Consider a gel contained in a porous cylinder that allows the fluid to escape as the gel is compressed, but with a solid bottom and piston that blocks the pores on the top and bottom of the gel so that the fluid can only escape out the edges, see FIG. 1. (In practice the gel also needs to be enclosed in a loose watertight soft wrapper to catch fluid that is expelled during compression.) Since the rate of decrease of the volume of the gel is equal to the volume flow rate of fluid out the edges of the gel,

$\begin{array}{cc}{L}^2\frac{\mathrm{dz}}{\mathrm{dt}}=4\mathrm{zLv},& \left(5\right)\end{array}$

where v is the velocity of fluid flow out the edges (the cross-section of the gel is assumed to be a square of sides L). Using the fact that

v˜(k/η)(F/L³)(2/L)   (6)

where k is the permeability, η is the viscosity of water, F/L² is the fluid pressure and L/2 is the mean distance that the fluid must flow. There will also be a contribution to the force from the osmotic pressure which keeps the gel swollen with water, but at the liquid flow velocities that occur when a gel is compressed in impacts typical of those in football, this contribution is much smaller than that due to water friction described above. In any case, certainly at the beginning of an impact with this material, F is likely to be dominated by the force needed to expel the fluid absorbed by this material when it is compressed by the impact. Combining Eqs. (5) and (6), we obtain

$\begin{array}{cc}\frac{\mathrm{dz}}{\mathrm{dt}}--8\mathrm{kzF}/\left(\eta L^4\right)=-\frac{8k_0z^2m}{\mathrm{\eta }L^4}\frac{d^{2}z}{{\mathrm{dt}}^{2}},& \left(7\right)\end{array}$

which can be written as

$\begin{array}{cc}\frac{d^2z}{{\mathrm{dt}}^{2}}=-\frac{\mathrm{\eta }L^4}{8k_0z^2m}\frac{\mathrm{dz}}{\mathrm{dt}}=\frac{a_0{}^2}{V_0z^2}\frac{\mathrm{dz}}{\mathrm{dt}},& \left(8\right)\end{array}$

where V₀ is the velocity on impact (when z=l) and a₀ is the initial acceleration. Integrating Eq. (8), we obtain

$\begin{array}{cc}\frac{\mathrm{dz}}{\mathrm{dt}}=-V_0-\left(a_0/V_0\right)\left(1-\frac{}{z}\right).& \left(9\right)\end{array}$

From this equation, dz/dt=0 when

$\begin{array}{cc}\frac{z}{}=\frac{a_0/V_0^2}{1+a_0/V_0^2}.& \left(10\right)\end{array}$

The parameter that governs the compression of the padding material is (a_ol/V_o²), where V_o²/(2 l) is the average acceleration of the object striking the padding material if the pad thickness was compressed to zero. FIG. 2 plots the acceleration of the head as a function of the padding compression for a_ol/v_o²=1. The maximum value of d²z/dt² is approximately not much larger than a_o. Thus, we see that this model allows there to be a relatively small peak deceleration. The goal of the research is to understand how to design hydrogels that produce results similar to those shown in FIG. 2. That includes understanding the relationships between the hydrogel microstructure and the deformation caused by an impact with the gel. Also part of the objective is to learn how to design the hydrogel for repeated impacts without damaging the mechanical integrity of the material. For example, there are double-network hydrogels that are tough because they contain a sacrificial brittle network that fractures at high strains. Although those materials are among the toughest examples of hydrogels, because of the fracture of brittle network, they are not suitable for applications with repeating impacts.

Robert Weiss and Bryan Vogt, of the University of Akron, have been investigating for about 17 years the structure and properties of hydrophobically-modified, physical hydrogels prepared by copolymerization of alkyl-acrylamides (A-Am) with either 2-(N-ethylperfluoro-octane sulfonamido) ethyl acrylate (FOSA) or 2-(N-ethylperfluoro-octane sulfonamido) ethyl methacrylate (FOSM). Those materials exhibited unusually high modulus and fracture toughness for hydrogels that could be tailored by the copolymer composition, see. These hydrogels had fracture toughness values approaching 10⁴ J/m². The exceptional mechanical properties of the A-Am hydrogels is a consequence of the nanostructure of these materials, which include ˜6 nm diameter hydrophobic domains that act as physical crosslinks for an A-Am network. The hydrophobic interactions within the nanodomains can dissociate under stress and pull-out of a nanodomain, which provides energy dissipation. Once the stress relaxes or the external stress is released, the hydrophobic entity finds itself in an unfavorable aqueous environment and it rejoins a nanodomain. It is improbable that all the hydrophobic groups can pull out of the nanodomains simultaneously, so the crosslink structure is able to withstand high stresses, due to the high association energy that arises from the cooperative association of 30-160 FOSA groups within each nanodomain. Because of their ability to dissipate considerable deformation energy and the ability of the network to self-heal following deformation, these types of supramolecular copolymer hydrogels would appear to be excellent candidates for the application discussed here. We will refer to these materials as self-healing hydrogels. An example embodiment of the invention may employ synthesized supramolecular hydrogels in order to tailor their energy dissipation properties to achieve near constant deceleration of a gel padding when impacted.

Preliminary Impact Tests on Hydrogel Samples. We have measured the compression as a function of time for several tough hydrogel samples when a weight was dropped on the sample using a device consisting of a pipe to guide the weight and to hold and constrain the samples. This apparatus is shown in FIG. 3.

The position of the weight as a function of time was measured with a high speed camera, which allowed us to calculate the speed at impact and deceleration of the weight during the compression of the gel. Each hydrogel sample was swollen to equilibrium with water and then cut to fit the sample holder, i.e., the bottom section of the pipe. The observation of the position of the weight as a function of time after impact, when the weight was in contact with the sample, provided a means to determine the compression of the sample and the deceleration of the weight as it was slowed to a stop by the hydrogel sample.

On Oct. 25, 2017, a drop test was done on the two self-healing gel sample disks stacked together. Since the last test, the newer sample had softened and expanded a little. In this test the weight was dropped from 1.14 m, and hence the impact velocity was about 4 m/s, compared to 2.7 m/s in the last drop test. The results are shown in FIG. 4.

In this case, the sample compresses by 0.73 cm out of a total thickness of close to 4 cm or 18%. This speed is comparable to that for an impact in a football game. You can see that the sample produces to a good approximation constant deceleration. It looks more like constant deceleration than what we obtained in earlier drop tests on double-network samples, in the sense that the fit to the constant acceleration expression for the height as a function of time was very good, as can be seen by the absence of fluctuations seen in the figure. The sample includes two self-healing hydrogel disks, one of which became quite soft, as a result of sitting in water since the end of July impact test. The second one (the newer sample) had softened a little since the first impact test was done on it a week or so before. One issue is that the deceleration is over 1000 m/s², which is still larger than we would like it to be, if we want this to be superior to competing padding technologies. This high deceleration rate occurs because, even though these samples are quite soft, when the constrained sample is compressed, it does not compress enough to produce the lower deceleration rate that we desire. This could be because the permeability is not quite large enough, although it is still obviously much larger than what we would expect on the basis of water being forced through the spaces between the polymers, at least if we assume traditional non-slip boundary conditions, but there is reason to believe that at the nanometer scale non-slip boundary conditions are not valid. There are, however, methods that we can use to synthesize self-healing hydrogels with higher permeability.

Sample Helmet Design

A side view of an example embodiment of a helmet using hydrogels as padding material is shown in FIG. 5.

In the example embodiment, the rods that push the pistons in the cylinders, placed around the inside of the outer shell, are attached to ball bearings in sockets, which are in contact with the inner shell. This allows the inner shell, along with the head, to rotate relative to the outer shell as a result of angular acceleration of the helmeted head. There are cylinders around the outer edges of the inner shell, to prevent peak angular accelerations of the inner shell and the head. This is a variation of the MIPS helmet. The cylinders can have a rectangular cross-section. The ones on the edges of the inner shell can be much longer in the direction along the inner shell than in the direction normal to the inner shell, so as to get the required area of the piston needed to give the optimum deceleration profile of the head. This diagram is only a sketch of an embodiment of a helmet using hydrogels as padding. The relative dimensions of the different components are not meant to be relative dimensions for an actual helmet. For example, dimensions for the example embodiment may be that the hydrogels inside the cylinders are about 1½ inches thick, and the rods need only be long enough to clear the top of the cylinder when the gel is maximally compressed. It remains to be verified experimentally, but it may be possible to do away with the cylinders and simply coat the inside of the helmet with a single 1½ inch thick hydrogel, because the head only impacts one region of the gel, and the neighboring regions can provide the required constraint on that region.

REFERENCES

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While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.

Claims

1. A helmet as illustrated in the accompanying figures and described herein.