# Modeling and Optimization of Airbag Helmets for Preventing Head Injuries in Bicycling

## Abstract

Bicycling is the leading cause of sports-related traumatic brain injury. Most of the current bike helmets are made of expanded polystyrene (EPS) foam and ultimately designed to prevent blunt trauma, e.g., skull fracture. However, these helmets have limited effectiveness in preventing brain injuries. With the availability of high-rate micro-electrical-mechanical systems sensors and high energy density batteries, a new class of helmets, i.e., expandable helmets, can sense an impending collision and expand to protect the head. By allowing softer liner medium and larger helmet sizes, this novel approach in helmet design provides the opportunity to achieve much lower acceleration levels during collision and may reduce the risk of brain injury. In this study, we first develop theoretical frameworks to investigate impact dynamics of current EPS helmets and airbag helmets—as a form of expandable helmet design. We compared our theoretical models with anthropomorphic test dummy drop test experiments. Peak accelerations obtained from these experiments with airbag helmets achieve up to an 8-fold reduction in the risk of concussion compared to standard EPS helmets. Furthermore, we construct an optimization framework for airbag helmets to minimize concussion and severe head injury risks at different impact velocities, while avoiding excessive deformation and bottoming-out. An optimized airbag helmet with 0.12 m thickness at 72 ± 8 kPa reduces the head injury criterion (HIC) value to 190 ± 25 at 6.2 m/s head impact velocity compared to a HIC of 1300 with a standard EPS helmet. Based on a correlation with previously reported HIC values in the literature, this airbag helmet design substantially reduces the risks of severe head injury up to 9 m/s.

### Keywords

Traumatic brain injury Concussion Head trauma Bicycle helmets Airbag helmets## Introduction

Traumatic brain injury (TBI) is a major cause of death and disability in the United States, contributing to about 30% of all injury deaths.14 Although contact sports elicit most of the media attention, bicycling is the leading cause of sports-related TBI. According to the American Association of Neurological Surgeons, bicycling was responsible for about 86,000 of the 447,000 sports-related brain injuries treated in emergency rooms in 2009.20 Bicycling was also the leading cause of sports-related brain injuries in children under 14, causing 40,272 injuries in total.45 Furthermore, many bicycle crashes are unreported and therefore not included in official statistics. In fact, some studies estimate that only less than 10% of bicycle crashes are officially reported.9,24

The classical approach in designing a bicycle helmet has not been sufficiently effective.8 Most currently used bike helmets are made of expanded polystyrene (EPS) foam with a thin plastic shell. Studies have shown that although wearing the EPS helmet decreases the risk of severe head injury by approximately 75%, the reduction in mild traumatic brain injury (mTBI) rates is statistically insignificant.1,43 The main variables involved in designing a bicycle helmet are the size and stiffness of the helmet, which directly influence the helmet’s energy absorption efficiency. Numerous studies show that low helmet usage rates especially in children is mostly related with self-image and comfort problems.16,23 Due to these aesthetic as well as practical concerns, helmet size has been limited to a few centimeters. These limitations have in turn governed the choice of material that can be used as a helmet liner. EPS has become the obvious choice given its light weight and impact absorption capacities.

The effect of size and stiffness in military helmet liners has been extensively studied. Moss *et al.* showed significantly increased protection with modest increases in military pad thickness.34 These findings have also been confirmed for bicycle helmets, where thicker pads were shown to perform better under impact conditions.33,35 Also for the same thickness and impact area, helmets with air-filled chambers fared better than foam pads.28,35

Unlike the amount of force the head experiences during an impact, the size of a helmet is not a physical limit but rather a technological limit, which can be eliminated by using an expandable airbag material by making use of the extra rattlespace (i.e., maximum allowable space for the relative motion between the head and helmet in the direction of the impact5). Also, the deformation limit shown in Fig. 1 is usually lower than the actual size of the helmet. This, however, would not be the case with a collapsible gas-filled helmet: A gas-filled helmet would be able to use its full stroke length, which provides more time to absorb the impact energy before the material condenses and exceeds the force limit. Even though expandable helmets can decrease the practical limitations regarding the helmet deformation limit, for years, the effect of increasing the size of the helmet and using a softer material has not been carefully studied because of the practical and technological obstacles. With the advent of inexpensive, high-rate MEMS sensors and high energy-density batteries, a reasonably sized “expandable helmet” can sense an impending collision and expand to potentially eliminate brain injuries in many scenarios. Air would be the ideal medium to utilize for such an expandable helmet design since it is fast-deployable and its mechanical paramaters can be tuned by merely adjusting the pressure value.

Recently, an airbag bicycle helmet called Hövding was invented in Sweden. It is in the form of a sash that inflates just before a head impact. One of the main concerns regarding Hövding and airbag helmets in general is the risk of bottoming out at low pressures and/or at severe impacts. Therefore, it is extremely important to scientifically evaluate this novel approach and airbag helmets in general. In a series of impact tests conducted by the Swedish company Folksam, Hövding helmet (with unreported pressure values) performed almost three times better than all the other conventional helmets in terms of peak accelerations at oblique impact tests (48 vs. 175 g at 5.42 m/s impact speed).17 They also noted an average 60% decrease in rotational accelerations compared with conventional helmets.

In this study, we aim to determine the optimal pressure and size of an airbag helmet against linear accelerations. Therefore, we present a simple reduced order model for impact dynamics of airbag and EPS helmets. EPS helmets serve as a control group to test the efficacy of airbag helmets. We then experimentally evaluate the performances of EPS and airbag helmets by using drop tests. We conclude by proposing a theoretical framework for the optimization of a soft and expandable helmet. We compare the optimal behavior with that of an ideal polymeric foam and previously published theoretical performance limit for a free-falling object.5

## Materials and Methods

The overall approach we followed in our study is as follows: In order to compare the effectiveness of EPS foam helmets and airbag helmets, we first modeled the impact dynamics of both helmets by assuming simplified geometries in the form of hemispherical shells (Fig. 2). In order to validate our simple theoretical models, we carried out anthropomorphic test dummy (ATD) drop test experiments. Then, we compared the theoretical predictions for acceleration traces with drop test results. Finally, we proposed a theoretical framework for the design of a soft expandable helmet model. The design algorithm makes use of the developed impact dynamics model for airbag and EPS helmets to minimize peak acceleration at a given helmet size.

**Analytical Models of Airbag and EPS Helmets**

*et al.*13 and was also considered in Do

*et al.*11 for impact attenuation of NASA’s Orion Crew Exploration Vehicle. We then constrained the deformation of the hemisphere helmet up to the skull-helmet interface, i.e., the helmet was effectively modeled with a shell geometry where the inner semi-circle represents the skull. The hemispheric impact geometry resulted in a contact area model which completely flattened at the deformation limit. We made use of the ideal gas law and derived the relationships for instantaneous pressure and contact area as a function of deformation of the airbag in the impact direction (Fig. 2a, also see Appendix).

Impact dynamics of the EPS helmet were modeled by assuming the same hemispherical shell geometry. For EPS material properties, we made use of the loading and unloading force-displacement curves of uniaxial compression of EPS20 foam (Fig. 2a).39 Although the force-displacement curves we use for EPS is under slow strain rates, it has been previously shown that there is not a substantial change in the stress–strain curves of EPS for several orders of magnitude of loading speeds.42,47 Also, based on relations for bouncing of an elastic body on a rigid surface, we calculated the coefficient of restitution for the EPS helmet to be 0.30 (see Appendix).

### ATD Drop Tests

We instrumented a custom-made 50th percentile headform4 (X2 Biosystems, Seattle,WA) with a tri-axial 500 g accelerometer (3273A1, Dytran Instruments, Inc., Chatsworth, CA, USA) at the CG of the headform, which was considered as ground truths. The sampling rate of the accelerometer was 10 kHz and we used CFC1000 filtering. The headform was dropped on an aluminum plate with a drop scaffold consisting of a net-rope mechanism. Before the drops, the heads were positioned in the net for the correct impact orientation, the rope was pulled to elevate the headform and then released. We used Bell Solar (Bell, CA) and Hövding (Hövding, Sweden, see Appendix A.4) as representatives of EPS and airbag helmets, respectively. Hövding was pre-inflated and had a thickness value of 12 cm. We tested these helmets at drop heights of 0.6, 0.9, 1.2, 1.5 and 1.8 m and pressure levels of 35, 42.5 and 50 kPa (for the airbag helmet). We did not test 35kPa airbag helmet at 1.8 m due to concerns of bottoming-out and damaging the dummy headform. We considered parietal and vertex orientations for the tests since these are two common head impact locations in bicycle accidents.2 Impact orientations for the ATD experiments are depicted in Fig. 3a. Each drop scenario was repeated 3 times for each orientation and EPS helmets were replaced after each trial to prevent repeatability errors due to material failure (i.e., fracture). Pressure of the airbag helmet was also measured before/after the tests to make sure there was no leaking, which would affect the performance. Contact forces between the helmet and the ground were measured for the dummy head free-fall experiments by using BodiTrack smart fabric sensor with 120 Hz sampling rate (Boditrak, Canada) (Fig. 4a). The pressure mat data was used to do a qualitative comparison between the contact areas predicted by the theoretical models and the experiment.

### Injury Risk Evaluation

In evaluating the head injury risks for experimental and theoretical results, we calculated the corresponding head injury criterion (HIC), which is the most widely used injury criterion.15 Previous studies have shown that a HIC of 1000 corresponds to 50% risk of skull fracture,22 a HIC of 700 is estimated to represent a 5% risk of a severe injury,31 and a HIC of 250 to represent a 50% risk of concussion in athletes.41 We should note that recent studies suggest the risk curve studied by Pellman *et al.*41 actually overestimates the low-end risks where a HIC value of 250 represented approximately a 1% risk of concussion.18

We also evaluated the peak linear accelerations obtained from ATD drop tests, which were defined as the peak value of the translational acceleration magnitude over time. Previously published data show that concussions have been observed for peak linear accelerations between 50 and 180 g.18,21,48

### Optimum Expandable Helmet Design

In order to construct a theoretical framework and optimize the airbag helmet design for a given impact scenario, we first studied the effect of size for an airbag helmet for a head impact at 6 m/s (1.8 m drop height). We then made use of the simple airbag model at the optimized size to minimize peak acceleration at impact velocities between 2-9 m/s by varying the pressure of the airbag between 20–100 kPa. We carried out numerical simulations over these system parameters and calculated the corresponding HIC to assess the severity of the moderate brain injury risks. During the simulations, we cross-checked the size of the helmet against the maximum deformation during the impact to detect bottoming-out, which occurs when the deformation exceeds the size of the helmet. We considered pressure values corresponding to bottoming-out cases as “failure” and omitted them from the optimization procedure.

## Results

### ATD Experiments

The results of ATD experiments were summarized in Figs. 3b and 3c in terms of the peak acceleration values and associated HIC values for vertex and parietal drop orientations (also see, Appendix A.3). The overall trend for impact orientations suggested that vertex drops result in higher acceleration values than parietal drops, both for airbag and EPS helmets. The airbag helmet at 35, 42.5 and 50 kPa pressure values performed similarly at 0.6 through 1.2 m drops, yielding around 20–40 g peak linear accelerations respectively (Fig. 3b). Values reported for the EPS helmet are consistent with those reported previously in the literature,6 where peak acceleration and HIC values for similar ATD experiments at 1.8 m drop were found to be 181 g and 1250 respectively (Figs. 3b and 3c). At the 1.5 m drop, the airbag helmet with 35 kPa pressure bottomed out at both parietal and vertex drops, approximately resulting in acceleration values around 70 g. In order not to damage the setup, we stopped testing the airbag helmet at 35 kPa for higher than 1.5 m for the ATD drops, which was the onset of bottoming-out. At the 1.8 m drop, the airbag helmet with 42.5 kPa pressure bottomed out at both orientations, resulting in higher values for the vertex orientation. Interestingly, the airbag helmet at 50 kPa resulted in at least a 5-fold reduction in peak acceleration values compared with Bell Solar at every drop height, the maximum reduction (6-fold reduction) being achieved at 0.6 m.

### Analytical Modeling of Airbag and EPS Helmets

The main motivation beyond constructing analytical models was to develop a framework for expandable helmet design optimization. Figure 2b depicts the acceleration profile of the theoretical EPS helmet model from a 0.6 m drop height. We note that the impact duration predicted for an EPS helmet at 0.6 m drop is 4 times shorter (around 10 ms) when compared with that of the airbag helmet, which was around 40 ms (Fig. 2b).

We compared our theoretical models’ predictions with ATD experiments at vertex orientation. The theoretical model for the airbag is able to predict peak linear acceleration values within a 10–30% error band (Fig. 4c) when data associated with bottoming-out conditions are not included. In this model, the errors were larger for lower pressure values, which is to be expected since the deformation is more nonlinear in these cases. The theoretical model for EPS helmet was also able to predict linear acceleration trends quite accurately, with relative errors between 10–20% for ATD drop tests (Fig. 4c). Note that our airbag model overpredicts the peak acceleration values in each pressure and drop height value. This is due to the fact that the model assumes maximum contact between the ground and the helmet, thus maximizing the contact area. In reality, the effective contact areas might be smaller, which would decrease the peak acceleration values. Another reason of overestimation is because we ignored the dynamical interaction between the head and the helmet by assuming rigid coupling.

Another parameter we compared between our theoretical model and the ATD experiments is the peak duration of the linear acceleration. The peak durations are captured within 0–15% range, where the airbag helmet impact durations are underestimated compared to the ATD experimental results (Fig. 4d). Note that this is consistent with the overestimation of peak accelerations, since it means our airbag helmet model is effectively stiffer than Hövding.

### Optimum Expandable Helmet Design

#### Size Optimization

In Figure 5b, we took a closer look at the effect of the helmet thickness in helmet performance, which was partially depicted for polymeric foams in Fig. 5a. The three curves in this graph represent the optimum HIC values of (1) optimum polymeric foam helmets from Fig. 5a, (2) airbag helmets with optimum pressure values (by using the simplified airbag impact model) and (3) theoretically minimal HIC values5 for varying thickness values between 2.5 and 18 cm, in the case of a 6 m/s head impact. The pressure of the optimum airbag helmet decreases as the thickness increases since the equivalent elastic stiffness needs to be smaller. Ideal airbag and foam curves have similar trends since both of the material models were made softer as the thickness increased (Figs. 5a and 5b). In Fig. 5b, we also superimposed the corresponding HIC values of 1.8 m ATD drop tests for Bell Solar and Hövding, which have corresponding average HIC values of 1080 and 220 respectively.

For the initial pressure optimization, we fixed our thickness to be 12 cm since after this thickness value, increasing the thickness has marginal improvements (Fig. 5b). We also wanted the thickness of the helmet to not go over the average width of a male human shoulder in order to prevent causing the head to contact the ground before the shoulder.30 However, this design parameter will show a gender and age variance, therefore needs to be calculated carefully.40

#### Initial Pressure Optimization

Since we experimentally demonstrated that one can achieve a substantial reduction in HIC values with an airbag helmet for impact velocities ranging from 3.4 to 6 m/s, in this section, we investigated whether we can optimize the airbag helmet parameters even further to achieve greater reductions in HIC. We utilized the simplified airbag impact dynamics proposed (Fig. 2) to simulate accident scenarios with varying head impact velocities between 2 and 9 m/s, which is a common head impact normal velocity range for bicycle accidents.2 Our proposed optimum expandable helmet strategy is based on minimizing HIC at a given impact velocity for a fixed helmet thickness of 12 cm.

## Discussion

The most common cycling accident scenario is a single fall, in which cyclists fall on their own.12,29 The average head impact velocity in a single fall2 varies between 4.8 and 6.2 m/s, which is close to the federal standard test speed of 6.2 m/s. In the context of these scenarios, our results highlight the limitations of the current 2.5 cm sized EPS foam helmets. We show that at a head impact velocity of 6.0 m/s, the current EPS foam helmet results in high HIC values, which signals both a high risk of concussion (>50%) and a high risk of severe injury (>50% skull fracture) (Figs. 3c and 5b). Even ideal foams and airbags below a thickness of 8 cm still result in substantial risk of concussion (50%), thus necessitating larger helmet designs (Fig. 5b). Expandable airbag helmets represent a practical method for increasing helmet thickness during an impact and our experimental results for Hövding (12 cm, 50 kPa) demonstrate that such designs can significantly curtail risk of concussions and severe injuries, reducing HIC scores 5-fold compared to standard EPS helmets (Fig. 5b). However, as the head impact velocity increases, these airbag helmets have a higher risk of bottoming-out. Therefore, a careful optimization of initial pressure for a given accident scenario is required.

Our study of helmet size also provides a possible future direction for the study of expandable helmets. Since the properties of an expandable helmet (pressure and thickness) can be altered in real time, the optimized airbag helmet design can be pushed even further towards the theoretically minimal acceleration curve (Fig. 5b). For instance, an active energy dissipation mechanism, such as a pressure relief system can be employed with an airbag impact protection system to minimize peak accelerations and/or head injury criteria (HIC) during the impact by using real-time sensory information. Furthermore, similar mechanisms could be used to dampen out the oscillating low-frequency bandwidths that are dangerous for the brain.27

Our study was solely designed to demonstrate a “proof-of-concept” for soft and expandable helmets. One main limitation here was the assumption of simple hemispheric geometry for airbag helmet impact dynamics. This was one of the main reasons behind the overestimation of the peak acceleration values by about 20% and the underestimation of the peak durations by about 10% on average.Effectively, our hemispherical airbag helmet model was stiffer than our experimental airbag helmet. Due to the simple geometry, our model did not have directional dependence for impact dynamics. In other words, as long as the same gravitational load is applied on the helmet by the head, the response of the airbag helmet in our model will be the same at a fixed impact velocity. Also, the model assumes that the airbag helmet completely flattens out at very large deformation levels, which is not very realistic. Since the deformation of an EPS helmet is much smaller than that of an airbag helmet, the contact model proposed is expected to perform better for EPS helmets. Finally, the model assumes falling on a flat ground normal to the ground plane and ignores any frictional effects between the helmet and the ground due to horizontal velocities.

Another limitation of the study was that we confined our performance criteria of helmets solely to linear accelerations. Rotational kinematics could play an important role in head injury mechanism during bicycle accidents25 and there have been efforts to design preventive equipment to reduce the effect of rotational kinematics.19,32 Therefore, an optimum expandable helmet should ideally help reduce rotational accelerations as well. Future efforts will therefore concentrate on the optimization of these helmets in different bicycle accident scenarios. We also plan to study the effect of expandable helmet impact dynamics on the mechanical response of brain tissue.

Another concern surrounding the expandable helmets is the risk of neck injuries. Expandable helmets need to be investigated for neck safety, as with any device that introduces new risks. Specifically, the coefficient of friction between an airbag helmet and the head might be higher when compared with an EPS/hard liner helmet, in which case the head‘s linear and rotational movability is constrained. This, in turn, might result in higher risks of neck injuries.3

Although this study is a first attempt to optimize the design of expandable helmets, there are a number of practical challenges that need to be addressed before these helmets can become widely accepted. For instance, these helmets can not be sold in US market currently since standards to test these types of helmets do not presently exist. Current evaluations of the effectiveness of bicycle helmets rely on simplified mechanical testing or the analysis of aggregated accident statistics along with other tests such as conditioning environments (temperature tests, water immersion), positional stability and dynamics strength of detention system. It is questionable whether expandable helmets would be able to pass some of these tests, e.g., positional stability during inflation and/or impact tests on sharp anvils.

Another important issue regarding the real-life implementation of expandable helmets remains to be the underlying triggering. MEMS sensors need to detect an accident scenario accurately both for false positives (since deploying the airbag in an unwarranted situation could be dangerous itself) and false negatives (since in such cases there is an accident in the absence of proper protection). The triggering will also be needed to be tested and appropriate standards will need to be determined. This will be a critical challenge for the expandable helmets before they are widely accepted and confidently worn among bicycle riders.

## Conclusions

Conventional helmet padding technology suffers from the practical limitation of a maximum wearable size. In this study, we optimized the thickness and the initial pressure values of an airbag helmet for varying head impact velocities and found that an airbag helmet with 0.12 m thickness at 72 ± 8 kPa reduces the HIC value to 190 ± 25 (at 6.2 m/s head impact velocity which is the federal standard) and skull fracture risks below 50% (at 9 m/s head impact velocity). The results show the potential of airbag helmets at reducing injury risk for cyclists and the inadequacies of the current helmet technology. However, before this technology becomes widely available, airbag helmets need more reliable impact triggering technologies and should be evaluated in more realistic bicycle accident simulations.

## Acknowledgments

The study was supported by the National Institutes of Health (NIH) National Institute of Biomedical Imaging and Bioengineering (NIBIB) 3R21EB01761101S1, Thrasher Research Fund, David and Lucile Packard Foundation 38454, Child Health Research Institute Transdisciplinary Initiatives Program, and NIH UL1 TR000093 for biostatistics consultation. Dr. Kurt is the recipient of the Thrasher Research Fund Early Career Award. A provisional patent application has been filed for a helmet design using the optimization strategy described in this paper and will be assigned to Stanford University.26 Royalties gained from any intellectual property granted for this work will be shared among the inventors, the department, and the school, according to Stanfords technology licensing policies.