Keegan Napier
email: kcnapier@students.latrobe.edu.au

Oliver Horst
email: horst@fortiss.org

Christian Prehofer
email: prehofer@fortiss.org

Comparably Evaluating Communication Performance within Mixed-Criticality Systems

HAL is

I. INTRODUCTION

To further reduce the space, weight and power consumption of embedded and real time systems, there is a trend towards integrating a number of components with differing criticality levels onto a single, common hardware platform. Inherently, tasks with a higher criticality level are accordingly more instrumental in the correct and safe operation of the system, and so there must be a higher degree of assurance that such tasks are not susceptible to failure. A system that has two or more distinct criticality levels is referred to as a mixed-criticality system (MCS) [START_REF] Vestal | Preemptive scheduling of multi-criticality systems with varying degrees of execution time assurance[END_REF].

As the complexity of mixed-criticality systems increase, there is a rising interest in moving from single core processor architectures to more capable multicore and manycore architectures. Making this migration, however, introduces the issue of sharing resources, such as the system bus, memory bus, memories and caches, between tasks of multiple different criticality levels. It is necessary that shared resource accesses are managed in such a way that tasks on one core are not capable of excessively delaying tasks on other cores that are trying to access the same resource [START_REF] Pellizzoni | Worst case delay analysis for memory interference in multicore systems[END_REF].

Within embedded systems, tasks will require the ability to communicate with memories and each other through the use of these shared resources. Therefore, communication must be managed so that it does not pose a significant risk of causing critical task failure. Should communication expose a critical task to an unexpected communication-related execution delay, it presents the risk that the task will not complete execution before its hard deadline. Similarly, should the communication within the system be capable of affecting the functional behaviour of the critical task in an undesirable way, this presents the risk that the critical task will malfunction. It is therefore essential that both temporal and functional properties of critical tasks are isolated from unexpected communication related faults and interference.

Providing isolation of critical task execution from communication within the mixed-criticality system, however, is a complicated problem with a number of factors, e.g. keeping critical communication predictable without detracting too much from performance, that must be considered when developing a suitable approach. Inherently, this has lead to a wide variety of approaches to mixed-criticality communication being developed, each of them aiming to take as many of these factors into account as possible [START_REF] Burns | Mixed criticality systems-a review[END_REF]. Through analysis of these approaches, it can be construed that there exist a range of properties that can be evaluated to demonstrate how well the communication protocol is limiting the impact of these factors.

As there currently exists, to the best of our knowledge, no standardised method of evaluating communication mechanisms within mixed-criticality systems, generally only properties that demonstrate specific results of the designed mechanism are evaluated, while others are overlooked. This has the added effect of allowing for these properties to be evaluated in ways that would produce results that are not directly comparable with another approach that is evaluating the same property.

In this paper, we focus upon improving the evaluation methods that researchers are utilising to evaluate their mixedcriticality communication mechanisms. We investigate how evaluations are currently being conducted, and use these investigations to suggest an empirical evaluation framework that would enable comparable evaluations to be made. Our contributions can be summarised as follows:

• We analyse a range of evaluations for current mixedcriticality communication mechanisms. We use this analysis to produce a set of general properties that indicate the performance of a communication mechanism within mixed-criticality systems. • We promote the need to evaluate each of these general properties in a more comparable manner, and propose the use of scenario-based evaluation to achieve this. • We propose a framework that would enable a researcher to develop evaluation scenarios for their system in a way that the same scenario may be executed upon a separate system.

The remainder of the paper will be organised as follows. Within Section II, we highlight properties that researchers commonly demonstrate to be of importance when evaluating communication within their system. We then suggest execution scenarios that would enable the measurement of these communication properties to be stressed in Section III, and propose an evaluation framework that simplifies the design and implementation of these scenarios in Section IV. Related work is detailed in Section V.

II. IMPORTANT COMMUNICATION PROPERTIES

Through the analysis of a diverse range of approaches to design and implement communication mechanisms within mixedcriticality systems, we identified a range of properties that are important to consider when evaluating such a mechanism. Within this section, we outline each of these properties with reference to research, and give an overview as to why they are important. For clarity, we have sorted each of these properties into the following categories: Predictability and Separation, Performance, and Scalability.

A. Predictability and Separation

It is a persistent trend throughout mixed-criticality systems that communication, especially critical communication, must behave in a predictable manner. Furthering this, the execution of tasks within the system should be separated from communication, i.e., communication within the system must not be capable of altering task execution in unexpected ways. To ensure an implemented communication mechanism offers suitable levels of predictability and separation, a number of properties should be present within the mechanism. These properties are discussed with reference to the field of research below:

1) Temporal Deadline adherence: First and foremost, critical transmission and resource access times must adhere to strict real time temporal deadlines, to avoid delaying the execution of critical tasks by an unexpected amount of time. Typically, these deadlines relate to the worst case scenario that would cause the greatest delays for communication, i.e., the worst case transmission time. It is therefore essential that as a basis for evaluating any communication mechanism, that it can be assured that critical temporal deadlines are consistently met.

2) Shared Resource Interference Management: When considering multi core architectures, communication delays fundamentally arise due to contention of accessing micro-architectural resources, e.g., system bus, shared memory. Should a task experience interference when communicating with any of these resources, the overall execution time of the task will increase. [START_REF] Kotaba | Multicore in real-time systems-temporal isolation challenges due to shared resources[END_REF], [START_REF] Bui | Temporal isolation on multiprocessing architectures[END_REF]. Calculating the worst case execution time of a critical task must take into account all of the time that the task may potentially spend waiting due to interference. Nowotsch et al. [START_REF] Nowotsch | Multi-core interference-sensitive wcet analysis leveraging runtime resource capacity enforcement[END_REF] emphasise this requirement through their explicit requirement of incorporating all potential communication interference into their calculation of the worst case execution times. For this reason, interference related communication delays must be predictable, to ensure that the worst case execution time does not have to be overestimated.

3) Predictable Critical Communication: In addition to ensuring that interference related communication delays should be predictable, critical tasks depend on being delayed due to communication for a predictable amount of time. Cilku et al. [START_REF] Cilku | A memory arbitration scheme for mixed-criticality multicore platforms[END_REF][8] suggest a dual-layer arbitration of the system bus, where highly critical tasks utilise a more predictable TDMA access scheme to access the shared system bus, while less critical tasks access the bus via a less predictable round-robin method. To stress and evaluate how predictably critical tasks are able to access the shared system bus, they have a single dummy task executing on each core of a dual-core processor. Each of these tasks make continuous accesses to shared memory, and they measure the standard deviation in the average and maximum execution times of the tasks as they alter how much interference their accesses cause with one another. Their evaluation shows the interest in determining how predictable communication related delays will remain while exposed to varying levels of interference.

4) Temporal Isolation: Delays that critical tasks face due to communication related should be temporally isolated from unexpected external interference. Researchers in the field have previously empirically demonstrated that their communication mechanism will consistently meet deadlines under unexpected circumstances by exposing their system to a variety of situations that stress the communication of the system in different unpredictable ways. Brandenburg [START_REF] Brandenburg | A synchronous IPC protocol for predictable access to shared resources in mixed-criticality systems[END_REF], for example, demonstrates that critical tasks utilising his shared resource access scheme will reliably gain access to shared resources before a calculated worst case access time, regardless of potential temporal disturbances caused by other tasks on the system. He does this by artificially causing other tasks to act in a faulty manner, and create a higher level of contention for shared resources. The faults that are introduced all aim to have an effect upon the access times of a particular critical task, including causing non-critical and critical tasks to make more frequent requests to access a shared resource, and executing a higher number of non-critical tasks upon each of the cores.

5) Functional Isolation: Communication should not be capable of causing an executing task to malfunction. As there are a range of ways that communication can influence Pellizzoni et al. [START_REF] Pellizzoni | Handling mixed-criticality in SoC-based real-time embedded systems[END_REF], for example, suggest that to functionally isolate task execution from communication, a set of formal properties that define the permissable communication behaviour of tasks during runtime must be specified, and all communication should be monitored during run time to ensure that no properties are violated. Through monitoring each of these properties during runtime, they are able to reject any faulty communication before it propogates through the system, and take any recovery actions if necessary.

Through analysis of each of these five key attributes related to providing predictability and separation within a communication mechanism, the important properties can be summarised to the following points:

• Critical communication must fundamentally meet all real time communication related temporal deadlines.

• Communication interference should be handled in a way that critical task execution is affected predictably. • Even under varying external disturbances, communication related delays must remain predictable. • Task execution behaviour should be functionally and temorally separated from the communication mechanism.

B. Performance

One of the main research challenges regarding designing a communication mechanism for use within mixed-criticality systems, is keeping performance overheads to a minimum, while still providing the aforementioned predictable properties. Areas of focus within this field aim to reduce the overhead that communication in the system puts upon task execution times, both critical and non-critical. A general overview of each of the properties that are considered in literature when determining the performance of a communication mechanism are outlined below:

1) Communication Medium Utilisation: One of the more predominant communication-related performance overhead is due to arbitrating the communication medium in a way that hinders task execution times. A variety of approaches have therefore been explored that aim to improve the overall utilisation of the communication medium to increase performance. Cilku et al. [START_REF] Cilku | A memory arbitration scheme for mixed-criticality multicore platforms[END_REF] [START_REF]A TDMA-based arbitration scheme for mixed-criticality multicore platforms[END_REF] demonstrate that their method of dual-layer arbitration offers better performance for non-critical communication by showing that when they execute a bubble sort algorithm upon each core of a quad-core processor, with two of the cores being treated as critical and the other two non-critical. They show that the average execution time of the bubble sort algorithm upon the non-critical cores utilising their method of bus arbitration is 3.1 times faster than if all cores were accessing the bus via a TDMA access scheme. Other approaches aim to offer non-critical tasks freedom to communicate, provided that the communication interference they cause for critical tasks can be bounded. Yun et al. [START_REF] Yun | Memory access control in multiprocessor for real-time systems with mixed criticality[END_REF] have implemented a memory access throttling algorithm that will limit non-critical tasks to a certain number of cache misses before their access to shared memory is throttled. They evaluate the performance that this throttling scheme offers non-critical tasks by playing back high definition video on two of the cores of a quad-core processor and determining how long each of the cores were throttled throughout execution.

2) Influence of critical communication upon non-critical communication: Non-critical tasks do not require strict assurance that they will meet their execution deadlines, and so non-critical communication does not require the same level of predictability that critical communication does. The objective of providing non-critical communication is to allow non-critical tasks to utilise a platform's communication media as efficiently as possible, while not causing critical communication to become unpredictable. This property was explored by Kim et al. [START_REF] Kim | A predictable and command-level priority-based DRAM controller for mixed-criticality systems[END_REF], who propose a direct memory access (DMA) scheme that offers tight bounding for critical task accesses, and better access times for non-critical tasks. To evaluate the performance benefits they give to non-critical tasks, they simulate system load by executing a number of standard embedded benchmarking programs that put differing levels of strain upon the memory. They assign programs from the Mälardalen WCET benchmark suite1 as critical tasks, and programs from the Mibench embedded benchmarking suite2 as non-critical tasks. For each execution run, they introduce an increasing number of critical tasks to the system, and measure how this affects the average memory access read times for the non-critical tasks. They then compare their results with average read times from a more predictable time division multiplexed (TDM) approach to show that their method offers lower average read times for non-critical tasks.

From analysis of these properties, it can be ascertained that when determining the performance of a communication mechanism, the important properties to be evaluated are:

• The communication medium should utilise the communication medium as effectively as possible, to reduce communication overheads.

• Non-critical communication should be implemented in such a way that it does not need to adhere to the same strict requirements of critical communication

C. Scalability

Due to the increase in complexity of mixed-criticality systems, one important property of a communication mechanism is how well it scales with a system that grows in complexity. An overview of properties that should be assessed with regards to scalability are detailed below.

1) Resource Arbitration Scaling: As an increasing number of tasks are added to the system, providing predictable shared resource interference can cause an increasing amount of execution overhead for tasks executing upon the system. Kelter et al. [START_REF] Kelter | Evaluation of resource arbitration methods for multi-core real-time systems[END_REF] highlight that for shared resource access arbitration within real time systems, the effect that the method of providing predictable interference has upon the real time execution deadline must be taken into consideration. They execute a variety of multi core embedded real-time benchmarking programs upon a single multi core ARM architecture and evaluate how each of a given set of resource arbitration methods perform as they are scaled to a higher number of cores. They demonstrate that shared resource access arbitration methods that offer higher average bus utilisation give a better average case execution performance as the number of cores within the system scale. However, they also show that these methods that offer the highest bus utilisation and lowest average case execution times often have a larger maximum overestimate on the calculated WCET of the executed tasks.

2) Multi/Many Core Scalability: As mixed-criticality systems are expanded to be executed upon multi/many core architectures, determining how well a communication mechanism scales when the number of processing cores that the system is executing upon increases is important. Sigrist et al. [START_REF] Sigrist | Mixedcriticality runtime mechanisms and evaluation on multicores[END_REF], for example, demonstrates how the overhead of differing mixedcriticality scheduling algorithms affects the range of task sets that they can assuredly schedule so that all tasks will meet their deadlines. As scaling to a larger number of cores enables more tasks to execute in parallel, this causes there to be more contention for shared communication resources. Therefore, when assessing the multi/many core scalability of a mixedcriticality communication algorithm, the focus is upon how this additional contention affects average case and worst case critical communication times.

There are two important aspects of a mixed-criticality communication mechanism that should be evaluated when determining how scalable it is:

• The employed shared resource arbitration method should utilize the communication medium well, even if the number of tasks executing upon the system grows. • The increase in average and worst case execution times of tasks upon the system as the number of tasks executing in parallel should be assessed.

III. EVALUATING IMPORTANT PROPERTIES

As it was outlined within Section II, there are a number of potential properties that can be evaluated when assessing the performance of the communication within a mixed-criticality system. There currently exists no standardised method of evaluating mixed-criticality communication performance, which has lead to a wide variation in how researchers are evaluating the performance of their systems. Due to the wide variation of attributes that are available to a researcher when evaluating the communication within their system, it is quite common that a researcher will:

• Evaluate only specific properties that their particular communication method excels in and disregard others, • And/or evaluate these properties in a way that differs to how other research has evaluated these attributes. Within this section, we discuss possible evaluation strategies for the properties presented in Section II. For each of these properties, we suggest potential scenarios that would strain the system in a way that each property can be accurately measured. We are focussing exclusively on an empiral measurement of the properties through a common evaluation framework, presented in Section IV. We favor this approach as it is easy applicable to new systems and thus suport our comparable evaluation goal. However, it should be noted that in certain cases an analytic approach might be favourable to exactly evaluate a property.

A. Predictability and Separation 1) Temporal Deadline Adherence:

As it is imperative that critical tasks do not miss execution deadlines, throughout the entire evaluation process, there should be no critical communication related deadlines missed. As demonstrated by Brandenburg [START_REF] Brandenburg | A synchronous IPC protocol for predictable access to shared resources in mixed-criticality systems[END_REF] and Bate et al. [START_REF] Bate | A bailout protocol for mixed criticality systems[END_REF], exposing a mixedcriticality system to a variety of different communication composure is one method of assessing whether all deadlines will be met in a range of circumstances. To alter the communication composure, the ratio of critical to non-critical tasks can be changed, and the frequency with which each of these tasks are attempting communication upon the system. It should be mentioned however, that should no critical deadlines be missed throughout any of the evaluation scenarios, this will not be enough to formally prove that critical communication related deadlines will not be missed under any circumstances. Analytic approaches could help here to provide formal proofs that critical deadlines will not be missed.

2) Shared Resource Interference Management:

To assess how predictably and efficiently communication interference will be handled, there are three properties of interest, especially if communication interference within the system rises:

• The worst experienced critical communication latency

• The average critical communication latency • The standard deviation of critical communication latencies

To reliably increase the amount of interference that critical tasks within the system are experiencing, we propose the following scenario: Separate tasks are executing upon differing cores of a platform, with each communicating a payload at specific time intervals (similar to [START_REF] Cilku | A memory arbitration scheme for mixed-criticality multicore platforms[END_REF]). Gradually, in successive runs of the scenario, the timing that the payloads are transmitted will overlap to produce an increasing amount of interference.

3) Temporal Isolation: Through observation of research, highlighting that critical communication cannot be temporally affected by external factors is not commonly done using empirical results alone. Brandenburg [START_REF] Brandenburg | A synchronous IPC protocol for predictable access to shared resources in mixed-criticality systems[END_REF], for example, demonstrates temporal isolation through a combination of mathematical proofs demonstrating that accesses from other tasks in the system can only affect critical tasks to a certain extent; and through runtime evaluation, by demonstrating that should other tasks upon the system start communicating in a faulty manner, critical tasks communication latencies will remain unaffected. Taking from this example, developing a scenario that demonstrates that critical communication is temporally isolated is a challenge. To measure this, tasks within the scenario, both critical and non-critical, would need to begin communicating in a faulty manner to demonstrate that critical tasks are continuing to meet their worst case execution deadlines. To guarantee that task execution is temporally isolated, a combination of an empirical and analytical approach should be employed.

4) Functional Isolation:

Similarly to temporal isolation, functional isolation is not easily guaranteed through runtime analysis alone as there are a wide range of ways in which functional isolation may be breached (tasks sending false messages, shared resources being left in an unsynchronised state etc.). Pellizzoni et al. [START_REF] Pellizzoni | Handling mixed-criticality in SoC-based real-time embedded systems[END_REF], for example, describes and models all acceptable communication behaviour within the system to ensure that task execution will not affect any tasks in the system in a detrimental manner. They do not, however, reinforce these claims with an empirical evaluation. Beside utilizing scenarios to determine whether critical communication within the system will be functionally isolated, we also think of questionnaire or analytic approaches that aim to determine whether the communication is suitably isolated.

1) Impact Upon Critical Communication: Measuring the impact that non-critical communication has upon critical communication can be achieved by introducing a higher ratio of non-critical to critical traffic and observing how this affects the average case communication related latency that critical tasks experience. A scenario that would offer suitable testing conditions for this consists of a set of critical tasks, and an increasing number of non-critical tasks. The communication latency that critical tasks experience can be measured after each addition of a non-critical task to determine whether non-critical traffic is having an adverse effect.

2) Communication Delay: Non-critical communication typically will experience delays within the system due to giving priority to critical communication. To determine the delays that are caused due to critical communication, the change in non-critical communication related latencies are measured as an increasing amount of critical traffic is introduced to the system. To measure this, similarly to what was described within [START_REF] Kim | A predictable and command-level priority-based DRAM controller for mixed-criticality systems[END_REF], a scenario that contains a set number of non-critical tasks and an increasing number of critical tasks can be utilised, and the effect that the increasing critical traffic has upon the non-critical communication delays can be observed.

C. Scalability 1) Scalability on Multi/Many Core Architectures: To evaluate how well a mixed-criticality algorithm scales to a higher number of cores, there are three key properties to assess as the system is expanded to cover a wider number of cores: The overestimation in the calculated worst case execution time for critical tasks when compared to the observed worst case execution time, the average execution time of critical tasks, and how effectively the communication medium is utilised throughout the evaluation period.

To provide a scenario that provides a common means of evaluating scalability, we adapt the evaluation approach utilised within [START_REF] Kelter | Evaluation of resource arbitration methods for multi-core real-time systems[END_REF], which was designed for assessing the scalability of single criticality real time resource arbitration schemes. The scenario will consist of a specific set of standard benchmarking tasks taken from common embedded benchmarking suites to provide the system with a realistic workload. Each of these tasks are divided into critical and non-critical tasks depending on whether the work within the benchmarking task is deemed to be of a critical nature.

To perform an evaluation of scalability using this scenario, the task set is first executed upon a single core, to determine their average case execution time without communication interference coming from tasks running in parallel. The scenario will then be performed further times, with the task set being divided across 2, 4 and 8 cores in subsequent runs to determine how the average case execution time of each critical task differs as more parallelism is introduced to the system.

IV. EVALUATION FRAMEWORK

In this section, we present a concept for an evaluation framework that will enable a researcher to design and reuse prebuilt evaluation scenarios for evaluating their specific communication mechanism. Each of the components that the framework is comprised of are described, focusing upon how each aims to enable reproduceable evaluation scenarios to be constructed. Figure 1 shows a block diagram overview of components that the framework is composed of, and a typical workflow that would enable a user to utilise a scenario to evaluate a communication property.

Scenarios will be created or added using the included scenario management software. This scenario management software will enable a user to construct scenarios from premade components, or import a scenario that another user has previously utilised in their evaluation. Each scenario that is created will consist of a set of stimuli tasks and stress tasks. Each of these tasks will have a different purpose throughout the evaluation process. Stimuli tasks will be specialised tasks, created by the user within the scenario management software, that will be utilised to stimulate the communication within the system in a particular way. For example, should the scenario require a task to flood the communication media with requests, a stimuli can be created that exhibits this behaviour during runtime. Tracepoints will automatically be inserted into the stimuli task upon creation, which will trace important communication information throughout execution, allowing for a specific result to be compiled by the measurement component. Stress tasks will be more standard tasks that can be inserted into the scenario to simulate a realistic system load. Each stress task will run a single program, for instance, a program taken from an embedded benchmarking suite. Multiple stress components can be integrated into a single scenario, allowing for distinctive and complex system loads to be created. The collection of tracepoint data will be transmitted to an external computing source, which runs the included measurement software. The measurement software is responsible for analysing tracepoints and presenting the analysed data to the user in a usable way.

We have currently implemented a prototypic version of the framework upon an Intel ® Core 2 Duo platform. We are looking, however, to extend this implementation to an 8 core ARMv8 architecture to enable us to demonstrate a wider range of scenarios with the framework, and evaluate the framework's performance. Currently, we are able to create and insert stress and stimuli components into a scenario to be executed, and then trace basic communication properties of this scenario. These tracepoints are processed and output as both a formatted CSV file, and PGF plot. The framework is abstracts from the communication mechanism so that only a few C functions are required to be updated by the user to port the framework to their specific communication mechanism.

V. RELATED WORK Although research into the field of providing communication for mixed-criticality systems has generated a range of different approaches, few have utilised or devised comparative evaluation methods. There are however previously utilised scenario-based methods of evaluation to commonly evaluate the properties of mixed-criticality scheduling schemes.

Harbin et al. [START_REF] Harbin | GMCB: An industrial benchmark for use in real-time mixed-criticality networks-onchip[END_REF] have designed a singular scenario based upon industry requirements to be used as a benchmark for stressing and evaluating the communication related performance of real-time mixed-criticality networks-on-chip. They thoroughly describe the benchmark that they have used, however, a single scenario does not give an evaluator the flexibility to demonstrate particular properties of their communication.

Bate et al. [START_REF] Bate | A bailout protocol for mixed criticality systems[END_REF] have utilised a scenario based evaluation method to comparably evaluate the performance of a variety of mixed-criticality scheduling schemes. They generate scenarios that simulate realistic workloads for the system and measure an array of important properties relating to the scheduling scheme. As their scenarios are generated, however, a truly comparable result could only be made should the evaluator have access to the exact scenario that they were utilising.

Sigrist et al. [START_REF] Sigrist | Mixedcriticality runtime mechanisms and evaluation on multicores[END_REF] similarly utilises a set of generated scenarios that cause the system to experience a workload with a normalised level of utilisation to evaluate a set of mixedcriticality scheduling schemes. Throughout the execution of each of these scenarios, they measure overheads produced by each scheduling scheme. For a separate researcher to evaluate their scheduling method comparably against their results, they would need to again, have access to the generated scenarios that they utilised within their evaluation.

VI. CONCLUSION

To summarise the contributions of this paper, we have identified a range of attributes that may be utilised to indicate the performance of communication within mixed-criticality systems, outlined how each of these attributes may be evaluated through the use of scenarios, and portrayed a more simplified method of evaluating using scenarios through the construction of an evaluation framework.

For future work, our aim is to make each of the scenarios more concise, and to implement the evaluation framework so that it may be used across a range of platforms.

Figure 1 .

 1 Figure 1. Block overview of Evaluation Framework

http://www.mrtc.mdh.se/projects/wcet/benchmarks.html

http://www.eecs.umich.edu/mibench/

ACKNOWLEDGMENT

The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement n°645119.


Céline Berni

Albert Herrero
email: albert.herrero@irstea.fr

B Camenen
email: benoit.camenen@irstea.fr

Celine Berni
email: celine.berni@irstea.fr

COMPUTATIONS OF TRAPPING COEFFICIENT FOR FINE SEDIMENT INFILTRATION

Keywords: sediment mixture, gravels, silts, infiltration

come

Computations of trapping coefficient for fine sediment infiltration

INTRODUCTION

Water management is currently recognized to be one of the most important issues in the world. Water is not only of primary use (drinking, irrigation and hydro-electricity) but also a source of potential risks (floods, pollutions, erosion). Specific issues are related to river management for rivers with poorly sorted sediments such as alpine ones. One of these issues is to understand how infiltration of fine sediment particles into a river bed occurs. This has an implication on the general sediment budget of the river. More importantly, infiltration may cause a clogging of the river bed (i.e. infiltration of very fine sediments within the coarser matrix forming the bed) that reduces the hydraulic conductivity between the flow and the hyporheic area or groundwater table [START_REF] Schälchli | The clogging of coarse gravel river beds by fine sediment[END_REF]. From an ecological point of view, benthos and fish habitat is deteriorated because the substratum is less oxygenated, therefore affecting the spawning process and egg survival [START_REF] Wood | Biological effects of fine sediment in the lotic environment[END_REF]. The vertical connectivity -i.e. water-mediated fluxes of material, energy, and organisms between the channel and the alluvial aquifer-is essential for the ecological functions of the river, and should be addressed since the EU Water Framework Directive obliges Member States to reach or maintain a "good" ecological status for water bodies no later than 2015 or 2027.

Infiltration dynamics has been widely studied over the last fifty years. Numerous laboratory experiments have been carried out to characterize the fine sediment content in a gravel substrate at equilibrium when recirculating fine sediments over a coarser bed (e.g. [START_REF] Einstein | Deposition of suspended particles in a gravel bed[END_REF][START_REF] Hamm | Fine particle deposition to porous beds[END_REF]. Previous studies have shown that fine sediment can either be localized at the top of the bed (bridging or sealing profiles) or with a homogeneous content throughout the vertical (unimpeded static percolation named hereafter USP) depending mainly on the grain size distribution of fine and coarse sediments [START_REF] Beschta | The intrusion of fine sediments into a stable gravel bed[END_REF][START_REF] Packman | Interplay of stream-subsurface exchange, clay particle deposition, and streambed evolution[END_REF][START_REF] Gibson | Vertical gradational variability of fines deposited in a gravel framework[END_REF][START_REF] Gibson | Bridging Process Threshold for Sediment Infiltrating into a Coarse Substrate[END_REF]. The two types of fine sediment content profiles are schematized in Figure 1.

2 It should be noted that flow variables and so bed shear stress also have an influence on the occurrence of either on type of profile or the other, as well as fine sediment concentration. These influences will not be discussed in this work.

An analysis of the shape of the sealing profile at equilibrium was undertaken by [START_REF] Wooster | Sediment supply and relative size distribution effects on fine sediment infiltration into immobile gravels[END_REF] and [START_REF] Cui | Theory of fine sediment infiltration into immobile gravel bed[END_REF], among others. They developed a filtration model based on a trapping coefficient. This trapping coefficient quantifies the proportion of fine sediment that is blocked in a layer of gravels when travelling vertically a unit distance. By assuming that this trapping coefficient is constant until the riverbed is clogged with infiltrated particles, an expression is derived for the steady-state fine fraction as a function of depth. Experimental data can be fitted with the resulted exponential profile and the trapping coefficient deduced empirically [START_REF] Wooster | Sediment supply and relative size distribution effects on fine sediment infiltration into immobile gravels[END_REF].

Trapping coefficient is often estimated using empirical analysis [START_REF] Wooster | Sediment supply and relative size distribution effects on fine sediment infiltration into immobile gravels[END_REF][START_REF] Leonardson | Exchange of fine sediments with gravel riverbeds[END_REF]. In this article, we explore the [START_REF] Lauck | A Simulation Model for the Infiltration of Sediment into Spawning Gravel[END_REF] stochastic model to compute the trapping coefficient that is based on a physical analysis and apply this model to experimental data by [START_REF] Gibson | Bridging Process Threshold for Sediment Infiltrating into a Coarse Substrate[END_REF].

TRAPPING COEFFICIENT COMPUTATION

Computation steps

Two different populations of sediments are considered. The first one forms the matrix of the bed and corresponds to the coarse fraction. The second one corresponds to the fine fraction that can infiltrate the bed. The computation of a trapping coefficient quantifying the proportion of fine sediment trapped in the bed using a stochastic model can be achieved as follows (see Lauck 1991):



First, assuming that we know the cumulative weight distribution of the two populations of sediment, the distribution in terms of occurrence of particles, i.e. the probability to find a particle of a specific size, is computed;  Then, the cumulative distribution of the pore size formed by the bed made of coarse particles is determined;  Finally, the trapping coefficient is computed as the convolution between the fine sediment distribution and the pore size distribution, which corresponds to the probability for a randomly chosen fine particle to be trapped in a pore formed by three coarse particles also randomly chosen. It can be interpreted as the percentage of fine particles that can be trapped in a layer of the coarse substrate.

It should be noticed that this percentage is in terms of the number of particles and can be also expressed in terms of weight. Each step of this process is detailed in the following section.

Grain size distribution : from weight distribution to probabilities of particles occurrence

A mixture of sediments is commonly described by a weight distribution defined at several diameters that correspond to the diameter of the sieves used to sort the mixture. At each sieve diameter (xi, i integer between 1 and n, the number of sieves), the percentile by weight distribution curve, G(xi), is formed by adding the weight that passed through the sieve and dividing by the total weight of the sample, w. From this distribution, the distribution in occurrence f(x), defined as the probability of particle occurrence with a diameter between x and x+dx, needs to be computed. The weight of particles of diameter between xi and xi+1 can be expressed as

𝑤 (𝐺(𝑥 𝑖+1 ) -𝐺(𝑥 𝑖 )) = ∫ 𝛼 𝑥 3 𝑁 𝑓(𝑥)d𝑥 𝑥 𝑖+1 𝑥 𝑖 [1]
where N is the total number of particles in the sample of total weight w, 𝛼 is a coefficient so that 𝛼𝑥 3 is the weight of one particle of diameter x, and N f(x) dx, the number of particles of diameter between x and x+dx. No information is available to 3 know how particles are distributed between xi and xi+1. We will assume that particles of each size are uniformly distributed within the interval with a probability f(xi), so that:

𝑤 (𝐺(𝑥 𝑖+1 ) -𝐺(𝑥 𝑖 )) = 𝑁 𝛼 𝑓(𝑥 𝑖 ) ∫ 𝑥 3 𝑑𝑥 𝑥 𝑖+1 𝑥 𝑖 [2]
and

𝑓(𝑥 𝑖 ) = 4 𝑤 𝑁 𝛼 𝐺(𝑥 𝑖+1 ) -𝐺(𝑥 𝑖 ) 𝑥 𝑖+1 4 -𝑥 𝑖 4 [3]
The total number of particles can be obtained integrating f(x) dx for all diameters

∑ 𝑓(𝑥 𝑖 ) (𝑥 𝑖+1 -𝑥 𝑖 ) 𝑛 𝑖=1 = 1 [4] ⇒ 𝑁 = ∑ 4 𝑤 𝑁 𝛼 𝐺(𝑥 𝑖+1 ) -𝐺(𝑥 𝑖 ) 𝑥 𝑖+1 4 -𝑥 𝑖 4 𝑛 𝑖=1
(𝑥 𝑖+1 -𝑥 𝑖 )

[5]

Moreover, we will assume that particles are spherical with a density 𝜌 𝑠 so that 𝛼 = 𝜋 6 𝜌 𝑠 .

As an illustration, both distributions (the cumulative weight distribution G and the probability to find a particle of a specified diameter f) are presented on Figure 2 for the sand 3 used by [START_REF] Gibson | Bridging Process Threshold for Sediment Infiltrating into a Coarse Substrate[END_REF]. The probability is directly related to the slope of the grain size distribution. It should be noted that as the proportion of particles within an interval [xi, xi+1] is given by 𝑓(𝑥)(𝑥 𝑖+1 -𝑥 𝑖 ), 𝑓(𝑥) can take values larger than one.

Pore throat size distribution

The probability distribution of occurrence of the coarse sediments can be computed as presented above. Using this distribution we can compute the pore throat size distribution. Firstly, three diameters in the coarse sediment distribution are picked, d1, d2 and d3 and the diameter dp of the pore throat constituted by three grains of these diameters is computed using Heron formulae [START_REF] Lauck | A Simulation Model for the Infiltration of Sediment into Spawning Gravel[END_REF]:

4 √(𝑑 1 + 𝑑 2 + 𝑑 3 ) 𝑑 1 𝑑 2 𝑑 3 = √(𝑑 1 + 𝑑 2 + 𝑑 𝑝 ) 𝑑 1 𝑑 2 𝑑 𝑝 +√(𝑑 1 + 𝑑 𝑝 + 𝑑 3 ) 𝑑 1 𝑑 𝑝 𝑑 3 +√(𝑑 𝑝 + 𝑑 2 + 𝑑 3 ) 𝑑 𝑝 𝑑 2 𝑑 3 [6]
The probability distribution of pore size dp is then computed based on the probability of size-occurrence of each of the three grains that contribute to the pore. A bias needs to be introduced to take into account that the probability for a grain to participate to a pore is not directly given by its probability of occurrence [START_REF] Lauck | A Simulation Model for the Infiltration of Sediment into Spawning Gravel[END_REF]. Indeed larger grains participate in more pores considering their surface but in a sediment layer, the number of finer grains is larger. The bias is introduced by multiplying the probability distribution 𝑓(𝑥 𝑖 )by xi m as it seems to be related to the size of the sediment. The value of m can be taken as 2 if we consider that the probability for a grain to participate to a pore is proportional to its surface or 3 if it is proportional to its volume. This value could be minored if we considered that within a layer of a specified thickness, the probability to find a grain is inversely proportional to its diameter. Considering these different options, it seems reasonable to consider that possible values for m range between 0 and 3. Thus, for each trio, the probability to obtain a pore of size dp is given by:

𝑝[𝑑 𝑝 ] = 𝑓(𝑑 1 )𝑑 1 𝑚 × 𝑓(𝑑 2 )𝑑 2 𝑚 × 𝑓(𝑑 3 )𝑑 3 𝑚 [7]
This probability is computed for each possible trio and the cumulative probability P[x] to get a pore which size is lower than a specified diameter x is computed by summation.

Trapping coefficient

The trapping coefficient β can be obtained as the convolution between the cumulative pore size distribution P and the fine sediment distribution f:

𝛽 = ∑ 𝑃[𝑥]𝑓(𝑥)𝑑𝑥 [8]
It gives the probability of a random fine particle to be smaller than a random pore For a large number of fine grains, this is the proportion of fine particles that are trapped in a bed layer. Now, larger fine particles are more likely to be trapped in a pore throat than smaller ones. Thus, to have an idea of the mass of sediment trapped within the bed, it could be more appropriate to use weighted-values of f. A trapping coefficient in terms of weight is then computed using the same process as exposed in section 2.2 as:

𝛽 𝑀 = ∫ 𝑃[𝑥]𝑓(𝑥)𝛼 𝑥 3 𝑑𝑥 = ∑ 𝑃[𝑥 𝑖 ]𝑓(𝑥 𝑖 )𝛼 𝑥 𝑖+1 4 -𝑥 𝑖 4 4 [9]
As the particles trapped are the largest ones, the trapping coefficient in terms of weight 𝛽 𝑀 is larger than the trapping coefficient in terms of the number of particles 𝛽.

RESULTS

In this section, trapping coefficients will be computed for the sediments used by [START_REF] Gibson | Bridging Process Threshold for Sediment Infiltrating into a Coarse Substrate[END_REF].

3.1 Overview [START_REF] Gibson | Bridging Process Threshold for Sediment Infiltrating into a Coarse Substrate[END_REF] carried out different experiments of fine sediment infiltration into a gravel bed. Eight types of gravels and ten types of fine sediments (silt and sands) were chosen. Fine sediments were recirculated over a gravel bed and the equilibrium profile of fine sediment content was measured. From these profiles, each combination of fine and coarse sediment was identified as a couple generating unimpeded static percolation, bridging or an intermediate state. We computed the trapping coefficient in terms of weight (βM) for each of these couples (Figure 3) with two values for the bias coefficient m, m=1 (left) and m=2 (right). In both cases, it seems that bridging occurs if βM > 10 -4 and unimpeded static percolation if βM < 10 -6 . These values may appear to be low. We will try to understand first what the effect of changing the bias coefficient is as it seems not significant here. Secondly, to better understand whether this trapping coefficient is appropriate and what bias to choose, we will investigate its sensitivity to the presence of low fine sediment content in the bed.

Bias in the pore throat size distribution

Results in the previous section have been computed considering two different values of the bias coefficient (m=1 and m=2) for the computation of the pore throat size distribution. As explained in section 2.3, these two values correspond to two different estimations of the probability for a grain to participate in a pore. Indeed, we can assume that the number of pores in which a grain participates is proportional to its surface x². On the other hand, there are less large grains than small grains in a layer of a given thickness and the proportion of sediment with a diameter d is inversely proportional to x. As a consequence, the probability for one grain of diameter x to participate to one pore is 𝑓(𝑥)𝑥 2 𝑥 ⁄ = 𝑓(𝑥)𝑥. However, one can argue that a grain participates to a number of pores proportional to its volume and not its surface or that the thickness should not be taken into account. It is then interesting to see the influence of this parameter in detail and understand why the difference is so small between the figures presented above.

The pore size distribution for the gravel G6 (d15 = 3 mm) computed for two values of m (m = 1 and m = 2) along with the distribution in occurrence for the sand 3 (d85 = 0.68 mm) of [START_REF] Gibson | Bridging Process Threshold for Sediment Infiltrating into a Coarse Substrate[END_REF] are presented in Figure 4. The trapping coefficient βM obtained was 0.26 for m = 1 and 0.23 for m = 2. The value of the bias coefficient for the pore size distribution parameter has an impact on the trapping coefficient. Nevertheless, considering the range of values of βM, the sensibility of βM to the coefficient m appears to be limited. Indeed, the pore size distribution remains almost identical considering the resolution of the initial cumulative weight distribution. But, our opinion, this is mainly due to the fact that the gravels considered are quite sorted. In the case of a gravel bed with fine sediments already trapped in the bed, we expect its influence on βM to be more pronounced. This hypothesis is tested in the following section.

Influence of fine sediment content in the bed

In this section, we try to better understand the process of bridging by quantifying how the trapping coefficient increases as fine sediments are added into the bed. With such computation, we can discuss the hypothesis of [START_REF] Cui | Theory of fine sediment infiltration into immobile gravel bed[END_REF] in their theory of fine sediment infiltration into immobile gravel bed. They propose the following model for β with respect to the fraction of fine sediments in the deposit relative to the total volume F:

𝛽 * 𝐶𝑢𝑖 = 𝛽 0 * exp (𝜙 𝐹/𝐹 𝑠 1 -𝐹/𝐹 𝑠 ) [10]
where β0* is the trapping coefficient for the clean gravel bed (F=0); Ф is a dimensionless coefficient that defines the shape of the β to F/Fs relationship (Ф>0); and Fs is the value of F when the bed matrix is saturated with fine sediments. This maximum sand fraction was computed according to empirical relationship developed by [START_REF] Ridgway | Particulate mixture bulk densities[END_REF]: The trapping coefficient is defined as the fraction of fine sediment-load trapped in the bed when traveling vertically a unit distance. To be compared to the above definition, it should be noticed that it needs to be multiplied by a characteristic length ∆𝑧 that represents the average distance between two pores. Following the work of [START_REF] Leonardson | Exchange of fine sediments with gravel riverbeds[END_REF], we will assume that this distance is the geometric mean of gravels diameters. For the range of fine sediment content studied, this geometrical diameter is approximately constant and 𝛽 * 𝐶𝑢𝑖 ∆𝑧 = ∆𝑧 𝛽 0 * exp (𝜙 𝐹/𝐹 𝑠 1 -𝐹/𝐹 𝑠 ) = 𝛽 0, this study exp (𝜙 𝐹/𝐹 𝑠 1 -𝐹/𝐹 𝑠 )

𝐹 𝑠 = 𝜃 𝑔𝑟 (1 -𝜃 𝑠 ) [
[12]

Thus, using β0 value we obtain with the model presented herein should lead to a dimensionless trapping coefficient.

On figure 3(a) we present the trapping coefficient values for the gravel G1 from the experiment by [START_REF] Gibson | Bridging Process Threshold for Sediment Infiltrating into a Coarse Substrate[END_REF] infiltrated with three sands, S2, S3 and S6 as well as G6 infiltrated with S3 for a bias coefficient m = 1. The same computation with m = 2 leads to the results presented in figure 3(b)l. As expected, in both cases, an increase of fine sediment content reduces the pore size. An increase in fine sediment content causes a decrease in the expected pore size and an increase of the trapping coefficient. However, results with m = 2 show a significantly different behavior.

Whereas for m = 1, a very small amount of fine sediment drastically changes the value of β from almost zero to one even for couples of sediments that provides USP profiles, for m = 2, the increase of β is less pronounced. It seems much more realistic as the building of sand piles on top of gravel grains can lead to a small amount of fine sediment without reducing the size of the pore throats. It underlines a major issue for this model: the mixture is considered as homogeneous, which is not the case when fine sediments deposited on coarser grains. It seems though that modifying the bias can partially overcome this difficulty and leads to variations of β with F in agreement with the model proposed by [START_REF] Cui | Theory of fine sediment infiltration into immobile gravel bed[END_REF].

Differences between couples can be analyzed for m = 2 (figure 3(b)). The transitional process type (red crosses) shows interesting features as it evolves in a similar way as USP case (filled squares) for small fine sediment contents but joins bridging curves for higher fine sediment content. The model presented herein may be used to better analyze and understand how and when this transitional process occurs. Cui 2008, eq [6] for Ф=50 and 200 respectively, β0 computed as presented herein for G1, S3 and Fs computed as [START_REF] Ridgway | Particulate mixture bulk densities[END_REF].

CONCLUSIONS

Following the work of [START_REF] Lauck | A Simulation Model for the Infiltration of Sediment into Spawning Gravel[END_REF], a stochastic model has been developed to compute the trapping coefficient in terms of weight. Computations have been carried out considering gravels and different types of sands corresponding to the [START_REF] Gibson | Bridging Process Threshold for Sediment Infiltrating into a Coarse Substrate[END_REF] experiments. Values of the trapping coefficient can be used to distinguish bridging and unimpeded static percolation cases. It also appears that even if the bias needed to compute the pore size distribution of gravels is not critical in the determination of the trapping coefficient for the sediment deposit void of fine sediment, it has a strong impact on the way it evolves with fine sediment content already trapped within the bed. Further studies are necessary to better take into account the building of sand piles on top of gravel grains that leads to inhomogeneous bed not well reproduced here.

Figure 1 .

 1 Figure 1. Schematic diagram to illustrate the two different infiltration profiles Sealing (or bridging) and USP.

Figure 2 .

 2 Figure 2. Cumulative weight distribution G and to find a particle of a specified diameter f for the sand 3 used by Gibson, et al. (2010).

Figure 3 .

 3 Figure 3. Experimental data of Gibson et al. (2010) plotted by the d85 of the sand and the d15 of the substrate with bridging (open circles, unimpeded static percolation (filled circles) and transitional processes (cross). The color of each symbols corresponds to log(βM), βM trapping coefficient in terms of mass computed with two different bias coefficients, on the left m=1, on the right m=2.

Figure 4 .

 4 Figure 4. Pore size distribution for two types of gravels (G6, plain; G1, dash-dotted) and grain size distributions (in occurrence) of two types of fine sediments (Sand 3, stars; Sand 6, cross). For each type of gravel, the two curves correspond to m = 0, 1, 2, 3, from left to right. Value of βM are summarize in the adjacent table.

  6

  7

Figure 5 .

 5 Figure 5. Trapping coefficient (in terms of weight) with regards to fine sediment content within the bed. (a) model presented in this article applied to gravel G1 (Gibson et al. 2010) infiltrated with sands S2 (green circles), S3 (red crosses) and S6 (purple squares) and gravel G6 sand S3 (blue diamonds) for different values of fine sediment content and m = 1. The value for F=0 is indicated with the horizontal dashdotted line.(b) Same results with m = 2. (c) Dashed and plain lines:Cui 2008, eq [6] for Ф=50 and 200 respectively, β0 computed as presented herein for G1, S3 and Fs computed as[START_REF] Ridgway | Particulate mixture bulk densities[END_REF].

ACKNOWLEDGMENTS

Irstea is acknowledged for the funding of Albert Herrero in post-doctoral position at Irstea Lyon-Villeurbanne.


Andrew S Mcintosh
email: as.mcintosh@bigpond.com

Declan A Patton

Bertrand Frechede

Paul-André Pierre

Edouard Ferry

Tobias Oberst

Bertrand Fréchède

Paul-André Pierré

The Biomechanics of Concussion in Unhelmeted Australian Football Players

Keywords: Neurological injury < NEUROLOGY, SPORTS biomechanics, head injury, modelling, sport 52 53

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peak resultant linear and angular acceleration from a database of no-injury and concussion head 115 impacts recorded using instrumented helmets. 16 21 24 Another database of head impacts recorded 116 using instrumented helmets, in addition to the anthropomtric test device (ATD) reconstructions 117 of Newman et al., [6][7][START_REF] Newman | Verification of biomechanical methods 441 employed in a comprehensive study of mild traumatic brain injury and the effectiveness of 442 American football helmets[END_REF] were used to asses the predictive capability of the CPC, which was found to 118 be a significantly better predictor in comparison to peak resultant angular acceleration.

119

In contrast to the cited studies on American football and ice hockey, helmets are not worn in 120 professional football codes in Australia; therefore, this research provides opportunities to 121 examine concussion in the unhelmeted athlete in vivo. A fundamental understanding of human 122 tolerance to head impacts is a prerequisite for the evaluation of concussion risk and the design of 123 methods, such as helmets, to mitigate those risks. [START_REF] Mcintosh | Sports helmets now and in the future[END_REF] The specific aims of the study were to (a) 124 investigate the dynamics, impact location and kinematics, of no-injury and concussive impacts to acceleration, the 13 suitable no-injury cases were reconstructed using methods reported by 149 Fréchède et al. 28 The reconstructions were simulated using the MAthematical DYnamic MOdels 150 (MADYMO) human facet model, which is widely used in the automotive industry as a seated 151 unaware occupant. The behavior of the model had previously been validated for blunt impacts at 152 various locations, but not for the head. The contact properties of the head were refined and 153 validated using data from cadaver impact experiments and finite element simulations. [START_REF] Mcintosh | Head and neck injury resulting from low 497 velocity direct impact[END_REF][START_REF] Neale | Comparative study between finite element 500 human and dummy head model responses under impact[END_REF][START_REF] Yoganandan | Biomechanics of skull fracture[END_REF] The 154 masses and inertias of body segments were scaled to the known anthropometry of the players, 155 using the GEnerator of BOdy Dimensions (GEBOD) scaling equations, [START_REF] Cheng | The development of the GEBOD program[END_REF] and lumped into the 156 models. Initially, the models were positioned in the same relative orientation as they were just 157 prior to impact in the game footage and a state of generic muscular activation was applied by 158 adding joint restraint torques. 28 The initial position, body segment velocities and joint restraint In the 30 games reviewed 122 no-injury head impact cases were observed and coded for impact 191 location, impacting object and potential for quantitative analysis. A comparison was made 192 between the head impact location and object striking the head for 122 non-injury cases and the 193 65 concussion head impact cases, which were previously reported by McIntosh et al. [START_REF] Mcintosh | The dynamics of concussive head impacts in 483 rugby and Australian rules football[END_REF] There was 194 a significant difference (P<0.001) in head impact location between concussion and no-injury 195 head impact cases. The proportion of impacts to the temporal region was significantly greater 196 (P=0.05) for concussion cases compared to no-injury cases, 60% to 23%, respectively. The 197 proportions of impacts for concussion cases were also compared to no-injury cases for other 198 impact sites: parietal, 6% to 25%; occipital, 17% to 19%; frontal, 11% to 21%; facial, 6% to 199 12%, respectively. There were no crown impacts for either no-injury or concussion cases. No 200 significant differences were observed between the objects striking the head for concussion and 201 no-injury cases.

202

Only 13 of the 122 no-injury head impact cases met the criteria for further quantitative analysis, 203 which required minimal parallax error in the impact video and presence of scaling methods, and 204 reconstruction. After deriving the closing speeds of the players from the video, the head impact 205 dynamics of 13 cases were then reconstructed using MADYMO. The no-injury results were 206 compared to 27 medically verified concussion cases that had previously been analysed using A significant difference (P=0.001), for mean peak linear acceleration between concussion, 103.4 210 g (s.d. 29.5 g), and no-injury, 59.0 g (s.d. 37.2 g), head impacts for the resultant (R) was 211 observed (Figure 2, Table 1). The mean peak inferior components of linear acceleration (-Z) also 212 had a significant difference (P<0.001) between concussion, 32.4 g (s.d. 24.6 g), and no-injury, 213 11.6 g (s.d. 8.9 g), cases. For peak angular accelerations in the coronal plane (X), a significant difference (P<0.001) was 217 found between the means of the concussion, 4823 rad•s -2 (s.d. 2096 rad•s -2 ), and no-injury, 1548 218 rad•s -2 (s.d. 1029 rad•s -2 ), cases (Figure 3). A significant difference (P<0.001) was also observed 219 between concussion, 5144 rad•s -2 (s.d. 2800 rad•s -2 ), and no-injury, 2523 rad•s -2 (s.d. 1753 rad•s - significant difference (P=0.001), for mean peak resultant angular acceleration, between 222 concussion, 7951 rad•s -2 (s.d. 3562 rad•s -2 ) and no-injury, 4300 rad•s -2 (s.d. 3657 rad•s -2 ), head 223 impacts was observed (Figure 2, Table 2).

224

< Figure 3> 225 <Table 2>

226

A significant difference (P<0.001) was observed for mean peak angular velocity of the head, for 227 the resultant (R) between concussion, 36.1 rad•s -1 (12.0 rad•s -1 ), and no-injury, 18.4 rad•s -1 (7.6 228 rad•s -1 ), cases (Figure 4). A difference with a similar level of significance (P<0.001) was found 229 between concussion, 23.1 rad•s -1 (11.3 rad•s -1 ), and no-injury, 8.8 rad•s -1 (5.5 rad•s -1 ), head velocity of the head in the transverse plane (Z) also had a significant difference (P=0.005) 232 between concussion, 21.8 rad•s -1 (12.4 rad•s -1 ), and no-injury, 12.2 rad•s -1 (7.6 rad•s -1 ), cases.

233

< Figure 4> 234 Logistic regression analyses of the kinematic parameters demonstrated that angular acceleration 235 of the head in the coronal plane had the strongest association with concussion (Table 3). This 236 parameter was both sensitive and specific, with the predicted percentage correct classifications 237 for no-injury and concussion cases being 92.3% and 92.6%, respectively. The 50% and 75% The results of the current study suggest that concussion is most strongly associated with impacts 243 to the temporal region of the head and angular kinematics of the head in the coronal plane. In 244 these cases, such impacts also resulted in linear acceleration of the head. A biomechanical 245 association exists between temporal impacts and coronal plane angular kinematics. Although it is 246 unlikely, there is a possibility that temporal impacts were more forceful than other impacts due to 247 the nature of the game and the phases of play in which players were injured. It is also possible 248 that the impacted player was unaware of the impending contact prior a temporal impacts, in 249 contrast to frontal impacts, which occur in a player's direct field of vision. However, there is 250 currently no evidence that neck strength is protective against concussion. 42 American football 251 studies using instrumented helmets have found that impacts to the front, top and back of the head were associated with injury; 19 21 however, in the current study, impacts to the temporal impacts 253 were found to be associated with concussion. The difference in results may be due to the 254 different structure of the two games or the use of helmets in American football.

255

The dataset of 40 reconstructed concussion and no-injury head impact cases analysed in this 256 paper is most comparable to the set of 58 cases by Newman et al.; [6][7][START_REF] Newman | Verification of biomechanical methods 441 employed in a comprehensive study of mild traumatic brain injury and the effectiveness of 442 American football helmets[END_REF] however, Newman et al. [6][7][START_REF] Newman | Verification of biomechanical methods 441 employed in a comprehensive study of mild traumatic brain injury and the effectiveness of 442 American football helmets[END_REF] 257 analysed helmeted impacts, used physical tests to reconstruct the impacts and used paired head-258 to-head impacts for the concussion and no-injury cases.

259

The mean maximum linear acceleration for the concussion cases in the current study, 103.4 g 260 (s.d. 29.5 g), was within the range of results, 73.6 g to 151 g (Table 1), reported by previous 261 studies, 6-8 12-14 16 18 20 21 24 with several reporting values close to 100 g. 6-8 14 16 18 24 Apart from the 262 players not wearing helmets, there were differences between studies in sample size, 263 biomechanical methods, selection criteria for no-injury cases and competition level. For the 264 current study, all players were adult male professional athletes like those studied by Newman et 265 al.; [6][7][START_REF] Newman | Verification of biomechanical methods 441 employed in a comprehensive study of mild traumatic brain injury and the effectiveness of 442 American football helmets[END_REF] however, the instrumented helmet studies assessed high school and collegiate players. In 266 the instrumented helmet studies, 13 14 16 18 20 21 24 all impacts that exceeded a pre-defined threshold 267 were recorded, while Newman et al. [6][7][START_REF] Newman | Verification of biomechanical methods 441 employed in a comprehensive study of mild traumatic brain injury and the effectiveness of 442 American football helmets[END_REF] used paired cases and the current study used a pre-268 determined selection criteria for no-injury cases. For no-injury cases, the mean maximum linear 269 acceleration in the current study, 59.0 g (s.d. 37.2 g), was higher than the range of results, 19.0 g 270 to 54.3 g (Table 1), reported by previous studies. 6-8 12-14 16 20 21 This difference is influenced 271 strongly by the no-injury case selection criteria, e.g. the acceleration threshold applied in the 272 instrumented helmets to record an impact will affect the mean acceleration of no-injury impacts; 273 whereas, in the current study, only clearly observable head impacts were analysed. Linear acceleration is currently used in the assessment of helmets and padded headgear. [START_REF] Mcintosh | Sports helmets now and in the future[END_REF] The 288 50% and 75% likelihood of concussion values for resultant linear head acceleration in this study 289 were 65.1 g and 88.5 g, respectively (Table 3). These levels are indicative of the extent to which 290 helmets are required to manage linear acceleration in an impact if they are to reduce the 291 likelihood of concussion. One reason why helmets or padded headgear may not prevent 292 concussion is because they are not able to meet this performance requirement. 43 Another reason 293 is that helmets are not specifically designed to manage angular acceleration or velocity.

294

The mean maximum resultant angular accelerations for the concussion and no-injury cases in the 295 current study were 7951 rad•s -2 (s.d 3562 rad•s -2 ) and 4300 rad•s -2 (s.d. 3657 rad•s -2 ), respectively 296 (Figure 2). The value for concussion cases, 7951 rad•s -2 , was slightly higher than the range reconstruction study by Newman et al. [6][7][START_REF] Newman | Verification of biomechanical methods 441 employed in a comprehensive study of mild traumatic brain injury and the effectiveness of 442 American football helmets[END_REF] and four instrumented helmet studies 16 21 23 24 reported 299 angular acceleration results. The value for no-injury cases, 4300 rad•s -2 , was substantially higher 300 than the values reported by the instrumented helmet studies of Broglio et al. 21 and Rowson et 301 al., 24 1627 rad•s -2 and 1230 rad•s -2 , respectively (Table 2), which again reflects the strong 302 influence of the no-injury case selection criteria. In addition to the mean peak resultant angular 303 acceleration of the head, significant differences (P<0.001) between concussion and no-injury 304 head impacts were observed for coronal and transverse components (Figure 3). The mean peak 305 coronal and transverse angular acceleration of the head, for the concussion cases, were 4823 306 rad•s -2 (s.d. 2096 rad•s -2 ) and 5144 rad•s -2 (s.d. 2800 rad•s -2 ), respectively. Duma et al. 13 recorded 307 a single concussion case during an instrumented helmet study and reported the peak coronal 308 angular acceleration of 5600 rad•s -2 ; however, the transverse component was not reported. 3). This parameter was both sensitive 316 and specific, with percentage correct classifications for no-injury and concussion cases of 92.3% 317 and 92.6%, respectively. The values for a 50% and 75% likelihood of concussion were 1747 318 rad•s -2 and 2296 rad•s -2 , respectively. Mean peak angular velocity, both the resultant and coronal 319 components, were also associated with concussion. This provides some support to the hypothesis particular region of the brain and, therefore, indicative of the probability of injury in that region; 322 however, brain tissue loading was not assessed in this study. This demonstrates that there are 323 impact direction sensitivities, e.g. angular head acceleration in the coronal plane, which may be 324 useful to consider in order to improve the predictive capabilities of instrumented helmets and in 325 systems to prevent brain injury. 19 It must be acknowledged that while associations exist between 326 component accelerations and concussion, all cases in the current study involved a direct head 327 impact and combinations of linear and angular head accelerations. The use of finite element and 328 other modeling methods will lead to a better understanding of the role of the component 329 accelerations on brain loading in concussion. In addition, methods that combine linear and 330 angular head kinematics in a single measure are important. Newman et al. 6 7 44 24 carried out linear regression analyses for the rotational 341 kinematic resultants. In the current study, a value of 6633 rad•s -2 for peak angular acceleration 342 was found to be associated with a 75% likelihood of concussion (Table 3), which compared well size was limited by resources, the laborious process of reconstruction and the quality of the 368 video. For future studies it would be advantageous to obtain all video feeds, not just the 369 broadcast video. Another limitation is that some signs of concussion are transient and may be 370 missed on video review and by team physicians. Although no no-injury case was recorded 371 contemporaneously as being concussed, the possibility remains that this was undiagnosed or 372 unreported. A valuable area of novel research would be to develop a reliable, valid and practical 373 method for instrumenting unhelmeted athletes. Such studies would be further enhanced by 374 collecting a broader range of clinical, neuro-psychological and radiological data for all head impact cases, both concussion and no-injury.

376

The results support the hypothesis proposed by Holbourn; 29 showing strong associations between 377 angular kinematics of the head, in the coronal plane, and concussion. These associations have 378 practical implications for concussion research and management. Firstly, kinematic parameters 379 can be measured in physical tests and in equipment tests to assess injury reduction potential. By 380 considering relevant injury mechanisms, human tolerance values, pass-fail criteria for a device 381 and impact severity, a test method can be developed that provides a performance target for 382 equipment manufacturers and policy makers. [START_REF] Mcintosh | Sports helmets now and in the future[END_REF] Secondly, the kinematic parameters can also be 383 measured within a helmet or head mounted package, which provides opportunities for on-field 384 monitoring and/or research, as evidenced already by the wide use of instrumented helmets. [13][14][15][16][17][18][19][20][21][22][23][24] 385 Finally, observation of where the player is struck in the head may assist sideline management of 386 concussion, where other technologies are absent. to evaluate the contact options for the head. Initially the models were positioned in the same relative orientation as they were just prior to impact in the game footage. The masses and inertias of each model's body segments were scaled to the known anthropometry of the players using the GEnerator of BOdy Dimensions (GEBOD) scaling equations 7 and lumped into the models segments. A state of generic muscular activation was applied to each model by adding joint restraint torques because it was difficult to determine the awareness of the player and correctly represent this in the simulation. Joint restraint torques, the initial position of the model and the initial velocity of each body segment, were slightly adjusted in order to correctly match the kinematic behaviour of the simulation to the video event. Where "s" and "θ" are linear and angular distance, respectively. Note: all kinematics are measured at the centre of gravity of the head.

Definitions

Head Injury Criterion

ܥܫܪ ൌ ሺݐ ଶ െ ݐ ଵ ሻ ቀ ଵ ௧ మ ି௧ భ  ܽሺݐሻ ௧ మ ௧ భ ݀ݐቁ ଶ.ହ
Where "t 1 " and "t 2 " are the initial and final times in seconds, respectively. Note: The maximum time duration of HIC 15 is limited to 15 ms. to evaluate the contact options for the head. Initially the models were positioned in the same relative orientation as they were just prior to impact in the game footage. The masses and inertias of each model's body segments were scaled to the known anthropometry of the players using the GEnerator of BOdy Dimensions (GEBOD) scaling equations 7 and lumped into the models segments. A state of generic muscular activation was applied to each model by adding joint restraint torques because it was difficult to determine the awareness of the player and correctly represent this in the simulation. Joint restraint torques, the initial position of the model and the initial velocity of each body segment, were slightly adjusted in order to correctly match the kinematic behaviour of the simulation to the video event.

Definitions

Linear acceleration

Angular velocity

Angular acceleration

Where "s" and "θ" are linear and angular distance, respectively. Note: all kinematics are measured at the centre of gravity of the head.

Head Injury Criterion

.

Where "t 1 " and "t 2 " are the initial and final times in seconds, respectively. Note: The maximum time duration of HIC 15 is limited to 15 ms.

  rad•s -2 and resultant angular velocity of 28.3 rad•s -1 . Rowson et al. 31 later 113 developed a new metric, the Combined Probability of Concussion (CPC), which combines the 114

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159

  torques were adjusted to correctly match the kinematic behavior of the simulation with the video 160 event. Through this process, two datasets were derived using the same methods: (a) 187 events 161 with a description of head impact location and impacting object (65 Australian rule football 162 concussion cases and 122 Australian rules football no-injury cases) and (b) 40 reconstructed 163 head impact cases (13 no-injury and 27 concussion). The 27 concussion cases included in this 164 paper had been selected from a larger database of 100 concussion cases, as per the methods 165 detailed in Fréchède et al., 27 which had previously been analysed quantitatively and qualitatively 166 by McIntosh et al. extracted and the angular acceleration curves were integrated in order 169 to obtain the angular velocity component and resultant profiles. The orthogonal components 170were defined in a head-based coordinate axis system with the origin at the centre-of-gravity: +X, 171 anterior; +Z, superior; +Y, latetral (left). Peak linear acceleration, angular acceleration and angular velocity were calculated for resultants and all unique directional components.173The influence of location of impact on concussion was first assessed using a Chi-Squared 174 analysis. Statistical t-tests were used to analyse the mean kinematic values of the concussion and 175 no-injury cases; the results were compared to previous concussion studies in American-football

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 41 peer review only -http://bmjopen.bmj.com/site/about/guidelines.

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 41 peer review only -http://bmjopen.bmj.com/site/about/guidelines.for concussion cases. In the current study, the inferior component of linear acceleration (-Z) had significant differences (P<0.001) between concussion and no-injury cases 277 (Figure1), with a mean peak acceleration of 32.4 g (s.d. 24.6 g) for concussion cases. This value 278 compared well to the mean peak acceleration of 35.4 g reported by McAllister et al. 23 for 10 279 concussion cases recorded using instrumented helmets. Rowson et al. 25 reported the mean values 280 of linear acceleration components for 1712 no-injury impacts recorded during collegiate 281 American football: anterior-posterior, 12.8 g; medial-lateral, 10.0 g; superior-inferior, 16.5 g. 282 The mean superior-inferior value reported by Rowson et al., 25 16.5 g, was similar to the no-283 injury mean value found in the current study, 16.2 g; however the anterior-posterior and medial-284 lateral values were higher in the current study: 32.8 g and 40.1 g respectively. Once again this 285 difference may be influenced strongly by the no-injury case selection criteria and the nature of 286 the two different football codes.

  287

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309

  Rowson et al.25 reported the mean values of angular acceleration components during 1712 310 collegiate American football head impacts where no-injury was recorded. Angular acceleration 311 components in all three directions were much lower than the values reported in the current study, 312 which again illustrates the strong influence of the no-injury case selection criteria and the 313 differing nature of the two football codes.314Based upon the logistic regression analyses, angular acceleration of the head in the coronal 315 plane had the strongest association with concussion (Table

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343 Page 17 of 41 For

 41 peer review only -http://bmjopen.bmj.com/site/about/guidelines.of 6945 rad•s -2 reported by Rowson et al.24 The maximum change angular velocity

387 Page 19 of 41 For

 41 peer review only -http://bmjopen.bmj.com/site/about/guidelines.Sport and its Prevention (ACRISP). ACRISP is one of the designated International Olympic408Committee centres for research into the prevention of injury and protection of athlete health.409The research reported in this paper was unfunded. All authors were at the time either employees 410 of the University of New South Wales (AMc, BF), research students (DP) or practicum students 411 at UNSW supervised by AMc (PAE, EF, TO). The assistance of Dr. Paul McCrory in providing 412 video is gratefully acknowledged. The original data are stored in the Faculty of Science at 413 UNSW. 414 Preliminary results related to this study were presented by McIntosh AS, Frechede B, McCrory 415 P, Ferry E, Oberst T & Pierre P. Biomechanics of concussion in sport -differences between 416 injury and non-injury cases, at the 2009 Australian Conference of Science and Medicine in Sport, 417 the Seventh National Physical Activity Conference and the Sixth National Sports Injury 418 Prevention Conference, Brisbane 14-17 October 2009. The short abstract from that conference 419 presentation is published in the Journal of Science and Medicine in Sport, 2009, 12 (6), soccer. J Trauma 2000;48(5):938-41. 451 13. Duma SM, Manoogian SJ, Bussone WR, et al. Analysis of real-time head accelerations in 452 collegiate football players. Clin J Sports Med 2005;15(1):3-8.

453 Page 22 of 41 ForPage 25 of 41 For

 4141 peer review only -http://bmjopen.bmj.com/site/about/guidelines.Brolinson PG, Manoogian SJ, McNeely D, et al. Analysis of linear head accelerations from Fréchède B, McIntosh AS. Use of MADYMO's human facet model to evaluate the risk of Benson BW, McIntosh AS, Maddocks D. What are the most effective risk reduction 516 strategies in sport concussion? From protective equipment to policy. Br J Sports Med 517 2013;47(5):321-26. 518 43. McIntosh AS, McCrory PR, Finch CF, et al. Does padded headgear prevent head injury in 519 rugby union football? Med Sci Sport Exerc 2009;41(2):306-13. 520 44. Newman JA. A generalized acceleration model for brain injury threshold (GAMBIT). 521 International Research Council on the Biomechanics of Impact Conference. Zurich, Switzerland: 522 IRCOBI, 1986:121-31. 523 45. Schmitt K-U, Niederer PF, Muser MH, et al. Head injuries. Trauma biomechanics: 524 Accidental injury in traffic and sports. 2 nd ed. New York, NY, USA: Springer, 2007:55-81. 525 peer review only -http://bmjopen.bmj.com/site/about/guidelines.

Figure 2 :Figure 3 :Figure 4 :Page 29 of 41 ForPage 30 of 41 ForPage 31 of 41 For

 234414141 Figure 2: Mean peak linear acceleration of the head, for all unique directional components (X, -

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 414141 peer review only -http://bmjopen.bmj.com/site/about/guidelines.Comparison of video and MADYMO reconstruction for a concussion case in Fréchède et al. (2009) 90x66mm (300 x 300 DPI) peer review only -http://bmjopen.bmj.com/site/about/guidelines.The head coordinate axis system used in the current study: X-Y, X-Z and Y-Z define the transverse, sagittal and coronal planes, respectively. Coronal plane head rotation occurs about the X-axis, sagittal plane head rotation occurs about the Y-axis and transverse plane rotation occurs about the Z-axis. 180x70mm (300 x 300 DPI) peer review only -http://bmjopen.bmj.com/site/about/guidelines.xhtml BMJ Open

  developed both 331 the Head Impact Power (HIP) and the Generalized Acceleration Model for Brain Injury

	332
	333	Threshold (GAMBIT) criteria; however, they were not examined in this paper as HIP was
	334	previously analysed by Fréchède et al., 28 while GAMBIT lacks validation and is seldom used as
	335	an index for head injury. 45
	336	No previous study has performed logistic regression analyses for individual kinematic
	337	components; however, Greenwald et al. 19 used principal component analysis to develop a new
	338	composite variable, weighted principal component score (wPCS), for use in predicting
	339	concussion. It was found that the wPCS head impact severity measure, which accounts for
	340	impact location, was more predictive than classical measures, such as the resultants of linear and
		angular acceleration. Rowson et al.

Tables 526 Table 1 :

 5261 Comparison of mean peak resultant linear head accelerations, for concussion and no-527 injury cases, reported in the literature.

					BMJ Open			Page 26 of 41
	528
		Mean peak resultant
		linear head acceleration	Number of cases
	Study		[g]			Sport	Level	Method
		No-injury	Concussion	No-injury	Concussion
	Naunheim et al. (2000)	29.2	-	132	0	American football	High school	Instrumented helmets
	Newman et al. (1999, 2000, 2005)	54.3	97.9	33	25	American football	Professional	ATD reconstructions
	Duma et al. (2005)	32.0	81	3311	1	American football	Collegiate	Instrumented helmets
	Brolinson et al. (2006)	20.1	103.3	11601	3	American football	Collegiate	Instrumented helmets
	Funk et al. (2006)	-	151	22701	3	American football	Collegiate	Instrumented helmets
	Guskiewicz et al. (2007)	-	102.8	0	13	American football	Collegiate	Instrumented helmets
	Schnebel et al. (2007)	-	105.9	0	3	American football	High school, collegiate	Instrumented helmets
	Broglio et al. (2009)	25.0	-	19224	0	American football	High school	Instrumented helmets
	Broglio et al. (2010)	25.1	-	54247	0	American football	High school	Instrumented helmets
	McAllister et al. (2012)	-	73.6	0	10	American football, ice hockey	High school, collegiate	Instrumented helmets
	Rowson et al. (2012)	-	103	300977	57	American football	Collegiate	Instrumented helmets
						Australian
	Current study	59.0	103.4	13	27	rules football, rugby	Professional	Rigid body simulations
						league
	529

For peer review only -http://bmjopen.bmj.com/site/about/guidelines.xhtml

Table 2 :

 2 Comparison of mean peak resultant angular head accelerations, for concussion and no-530 injury cases, reported in the literature.

	Page 27 of 41				BMJ Open
	531
		Mean peak resultant
		angular head	Number of cases
	Study	acceleration [rad•s -2 ]			Sport	Level	Method
		No-injury	Concussion	No-injury	Concussion
	Newman et al. (1999, 2000, 2005)	4159	6664	33	25	American football	Professional	ATD reconstructions
	Duma et al. (2005)	-	7912	3311	1	American football	Collegiate	Instrumented helmets
	Guskiewicz et al. (2007)	-	5312	0	13	American football	Collegiate	Instrumented helmets
	Broglio et al. (2010)	1627	-	54247	0	American football	High school	Instrumented helmets
	McAllister et al. (2012)	-	5025	0	10	American football, ice hockey	High school, collegiate	Instrumented helmets
	Rowson et al. (2012)	1230	5022	300977	57	American football	Collegiate	Instrumented helmets
						Australian
	Current study	4300	7951	13	27	football, rugby	Professional	Rigid body simulations
						league
	532

For peer review only -http://bmjopen.bmj.com/site/about/guidelines.xhtml

Table 3 :

 3 Summary of logistic regression analysis of kinematic injury predictors, significantly Flowchart of concussion and no-injury case selection.

					BMJ Open			Page 28 of 41
	533
	534	associated with concussion (P<0.001), ranked using the likelihood ratio test, pseudo-R 2 and
	535	percentage correct classification statistics.
		Variable	-2 log Likelihood Ratio Nagelkerke Pseudo-R 2 χ 2 P-value	Percentage Correct Classification	Concussion likelihood values 50% 75%
		Angular acceleration (coronal plane)	26.8	<0.001	0.68	92.5%	1747 rad•s -2	2296 rad•s -2
		Angular velocity (resultant)	21.9	<0.001	0.59	80.0%	22.2 rad•s -1	27.5 rad•s -1
		Angular velocity (coronal plane)	18.8	<0.001	0.52	85.0%	10.8 rad•s -1	15.9 rad•s -1
		Linear acceleration (resultant)	14.8	<0.001	0.43	82.5%	65.1 g	88.5 g
		Linear acceleration (inferior component)	14.1	<0.001	0.41	77.5%	12.3 g	20.7 g
		Angular acceleration (transverse plane)	12.3	<0.001	0.37	80.0%	1909 rad•s -2	3008 rad•s -2
		Angular acceleration (resultant)	10.2	<0.001	0.31	82.5%	3958 rad•s -2	6633 rad•s -2
	536

For peer review only -http://bmjopen.bmj.com/site/about/guidelines.xhtml

), head impacts for the peak transverse plane (Z) components of angular acceleration. A

Acknowledgements 406 Dr Andrew McIntosh is a lead researcher at the Australian Centre for Research into Injury in

This work was unfunded. All authors were at the time either employees 28 of the University of New South Wales (AMc, BF), research students (DP) or practicum students 29 at UNSW supervised by AMc (P-AP, EF, TO).

Each video was analysed to obtain descriptive data regarding the impact site and determine the closing velocities of the players, from which the change in velocity, momentum, impulse and energy of the head were estimated. McIntosh et al. 1 found the majority of impacts were to the tempero-parietal region and that concussion occurred with impact energy values between 50 J to 60 J.

In a subsequent study, Fréchède et al. 2 reconstructed 27 of the 100 concussion cases using rigid body methods. The impact selection criteria for reconstruction were that the video clearly described the event allowing for the determination of accurate boundary conditions and the assessment of the reliability of the simulation. The reconstructions were simulated using the MAthematical DYnamic MOdels (MADYMO) human facet model, which is widely used in the automotive industry as a seated unaware occupant. The model's behaviour had been previously validated for various blunt impact locations, 3 but not for the head. The contact properties of the model's head were refined using the results from a cadaveric head segment impact study. 4 The head of the model was further validated using experimental data from lateral and occipital head impacts on seated cadavers 5 and lateral impact drop tests on cadaveric head specimens. 4 The model's head behaviour was also compared to the results of finite element drop test simulations 6 Each video was analysed to obtain descriptive data regarding the impact site and determine the closing velocities of the players, from which the change in velocity, momentum, impulse and energy of the head were estimated. McIntosh et al. 1 found the majority of impacts were to the tempero-parietal region and that concussion occurred with impact energy values between 50 J to 60 J.

In a subsequent study, Fréchède et al. 2 reconstructed 27 of the 100 concussion cases using rigid body methods. The impact selection criteria for reconstruction were that the video clearly described the event allowing for the determination of accurate boundary conditions and the assessment of the reliability of the simulation. The reconstructions were simulated using the MAthematical DYnamic MOdels (MADYMO) human facet model, which is widely used in the automotive industry as a seated unaware occupant. The model's behaviour had been previously validated for various blunt impact locations, 3 but not for the head. The contact properties of the model's head were refined using the results from a cadaveric head segment impact study. 4 The head of the model was further validated using experimental data from lateral and occipital head impacts on seated cadavers 5 and lateral impact drop tests on cadaveric head specimens. 4 The model's head behaviour was also compared to the results of finite element drop test simulations 6 Page 37 of 41 For peer review only -http://bmjopen.bmj.com/site/about/guidelines.xhtml