Shi Shang

Catherine Masson

David Teeling

Max Py

Quentin Ferrand

Pierre-Jean Arnoux

Ciaran Simms
email: csimms@tcd.ie

Kinematics and dynamics of pedestrian head ground contact: a cadaver study

Keywords: Pedestrians, vehicle contact, ground contact, cadaver test analysis

Pedestrians struck by vehicles are generally injured by the primary vehicle contact but also the secondary ground contact. However, experimental evidence for ground contact injuries is limited.

Here we report on six staged cadaver tests at 20-30km/h with passenger cars/vans in which we recorded the whole process from first pedestrian contact until after the end of the ground contact is complete using high-speed video and accelerometers mounted in the cadavers. Results show distinct phases for pedestrian flight and ground contact in addition to the already established vehicle contact phases. No skull fractures were observed in any of the tests. However, for the speed range tested, the linear and angular head injury risk (evaluated using HIC/3ms & BrIC respectively) is generally higher from the ground contact compared to the vehicle contact.

Although not yet clearly understood, angular head injury risk during ground contact is higher for the 20km/h tests compared to the 30km/h tests. A good comparison was observed with respect to previously predicted ground contact mechanisms and head impact speeds from multibody modelling. These results emphasize the importance of ground related injuries to pedestrians when struck by vehicles at speeds of 20-30km/h and provide a unique dataset for computational model validation of pedestrian ground contact.

Introduction

The World Health Organization reports nearly 300,000 pedestrian fatalities annually (WHO, 2013), with many more injured. Injuries occur during the primary vehicle contact and, following separation from the vehicle, significant additional injuries often occur during ground contact. In early collision reconstruction work, Ashton and Mackay [START_REF] Ashton | Benefits from changes in vehicle exterior design-field accident and experimental work in Europe[END_REF] showed that for vehicle impact speeds below about 25km/h, ground contact injuries exceed those of vehicle contact, but at higher speeds injuries from vehicle contacts predominate.

Pedestrian injuries in contacts with vehicles are generally well understood, with vehicle speed/shape/stiffness and pedestrian age/height/stance all influencing injury outcome [START_REF] Kalra | Pedestrian safety: an overview of physical test surrogates, numerical models and availability of cadaveric data for model validation[END_REF]Li et al., 2017a;Li et al., 2017b;[START_REF] Niebuhr | Pedestrian injury risk and the effect of age[END_REF][START_REF] Rosen | Literature review of pedestrian fatality risk as a function of car impact speed[END_REF]Shang et al., 2018b;[START_REF] Simms | Sports utility vehicles and older pedestrians[END_REF][START_REF] Simms | Pedestrian and Cyclist Impact[END_REF]. However, pedestrian ground contact involves a wide range of contact orientations and a complex combination of slide, roll and bounce to rest. The resultant injury mechanisms are not well understood as significant challenges persist in predicting the kinematics of this long timeframe event and in attributing injuries observed to either vehicle or ground contact [START_REF] Simms | Pedestrian and Cyclist Impact[END_REF]. However, recent analysis of the German collision database GIDAS showed that the head, thorax and spine dominate AIS4-5 ground contact injuries, and ground contact injury severity increases with pedestrian age and vehicle speed (Shang et al., 2018b). For collisions below 40 km/h, about two thirds of pedestrian injury costs were attributed to ground contact, emphasising the importance of ground contact injuries for low impact speeds (Shang et al., 2018b). Badeo-Romero and Lenard assessed UK collisions and also found a significant role for ground contact [START_REF] Badea-Romero | Source of head injury for pedestrians and pedal cyclists: Striking vehicle or road?[END_REF].

Of particular interest is the manner in which pedestrian ground contact injuries are influenced by vehicle speed and design in the speed range 20-40 km/h, since this could lead to vehicle-based methods to reduce the severity of ground contact injuries in cases where pedestrian injuries from vehicle contact are mostly survivable. Computational modelling studies have posited various relationships between vehicle shape and ground contact injuries [START_REF] Crocetta | The influence of vehicle front-end design on pedestrian ground impact[END_REF][START_REF] Gupta | Effect of vehicle front end profile on pedestrian kinematics and biomechanical responses using a validated numerical model[END_REF][START_REF] Gupta | Effect of vehicle front end profiles leading to pedestrian secondary head impact to ground[END_REF][START_REF] Kendall | The causes of head injury in vehicle-pedestrian impacts: comparing the relative danger of vehicle and road surface[END_REF][START_REF] Tamura | A study on the potential risk of traumatic brain injury due to ground impact in a vehicle-pedestrian collision using full-scale finite element models[END_REF][START_REF] Tamura | Effects of ground impact on traumatic brain injury in a fender vault pedestrian crash[END_REF][START_REF] Xu | Are electric self-balancing scooters safe in vehicle crash accidents?[END_REF]. In particular, Crocetta et al. [START_REF] Crocetta | The influence of vehicle front-end design on pedestrian ground impact[END_REF] reported on six identifiable ground contact "mechanisms" distinguished by the amount of whole body rotation of the pedestrian prior to ground contact, with average head impact speed varying between the different mechanisms. Some support for identifying an influence of vehicle design on pedestrian ground contact was found by Shang et al (Shang et al., 2018b) who used collision data to show that the normalised bonnet leading-edge height (bonnet height/hip height) is a risk factor for adult pedestrian AIS2+ groundrelated head injuries. Further, [START_REF] Han | Analysis of pedestrian kinematics and ground impact in traffic accidents using video records[END_REF] found from video analysis of real-world collisions that vehicle front shape and impact speed both influence ground contact kinematics. However, no pedestrian models are validated for ground contact and establishing initial conditions and injury outcomes in real world video cases is challenging.

Cadaver tests provide model validation data and have the potential to greatly strengthen our understanding of pedestrian ground contact. However, previous tests have mainly focused on vehicle contact, with limited reference to ground contact [START_REF] Kerrigan | Pedestrian kinematic response to mid-sized vehicle impact[END_REF][START_REF] Masson | Pedestrian-vehicle accident: Analysis of 4 full scale tests with PMHS[END_REF][START_REF] Paas | Head boundary conditions in pedestrian crashes with passenger cars: six-degrees-of-freedom post-mortem human subject responses[END_REF][START_REF] Subit | Pedestrianvehicle interaction: kinematics and injury analysis of four full scale tests[END_REF] or else crash test dummies were used [START_REF] Hamacher | Assessment of active and passive technical measures for pedestrian protection at the vehicle front[END_REF][START_REF] Taneda | Experiment on passenger car and pedestrian dummy collision[END_REF]. In early work, [START_REF] Cavallero | Improvement of pedestrian safety: influence of shape of passenger car-front structures upon pedestrian kinematics and injuries: evaluation based on 50 cadaver tests[END_REF] concluded that head-ground contact location and speed could not be predicted from vehicle shape. However, tests were performed only at 32 km/h, vehicle shapes have changed substantially and no ground contact kinematics or injuries were reported. More recently, cadaver studies performed in the US and France have used a range of vehicle shapes and pedestrian sizes [START_REF] Kerrigan | Pedestrian kinematic response to mid-sized vehicle impact[END_REF][START_REF] Paas | Head boundary conditions in pedestrian crashes with passenger cars: six-degrees-of-freedom post-mortem human subject responses[END_REF][START_REF] Subit | Pedestrianvehicle interaction: kinematics and injury analysis of four full scale tests[END_REF], but ground contact kinematics/injuries were not evaluated. In fact, the sequence of pedestrian motion following head contact on vehicle has received little attention and is poorly described.

In summary, pedestrian ground contact kinematics remain poorly understood. Model predictions of ground contact mechanisms have been presented, but validation is lacking. Real-world collisions show the importance of ground contact, but the role of vehicle design in mediating pedestrian ground contact injury remains uncertain and existing cadaver data is limited. Accordingly, the aims of the current study are to:

1) perform staged vehicle impact tests using cadavers to study the kinematic chain of events in a pedestrian collision, starting with first vehicle contact and ending after the pedestrian strikes the ground. 2) assess pedestrian post-impact kinematics as well as head ground contact, including linear and rotational components of head injury risk. 3) assess potential interactive effects of vehicle speed and normalised bonnet leading edge height on pedestrian head injury risk during ground contact.

2.Methods

Cadaver Test Setup

As part of the Faculty of Medicine of Marseille, the Laboratory of Applied Biomechanics is enabled to perform full body human testing from body donations. Six cadaver tests were conducted to study pedestrian ground contact at Aix-Marseille Université: Faculté de Médecine-secteur Nord Marseille, see Table 1. Winckler's preparation (Winckler, 1974) or zinc chloride [START_REF] Goodarzi | Zinc Chloride, A new material for embalming and preservation of the anatomical specimens[END_REF] was used for tissue preservation. For each subject, up to 54 anthropometric measures were performed, and the external anthropometries are listed in Appendix A. The study was approved by the Ethical Committee of Aix-Marseille University. Three vehicle types (Appendix B) were tested to achieve different normalized bonnet leading edge heights (NBLEH), and each vehicle type was tested twice under similar conditions (different cadavers but approximately the same initial stance). Damaged vehicle components were replaced as necessary. The expected ground contact "mechanism" (Appendix C) based on the simulation study by Crocetta et al [START_REF] Crocetta | The influence of vehicle front-end design on pedestrian ground impact[END_REF] for each case is also shown. Five 1000 fps cameras captured the whole pedestrian trajectory (Appendix D). Impact speeds of 20 or 30km/h were applied. The cadavers were held by a magnetic locking system which automatically released just before vehicle contact, see Figure 1a. Fiducial markers recorded landmark positions on the head, extremities, pelvis and chest. The approximate initial lower extremity joint angles are shown in Appendix E. Full braking (μ ≈ 0.8) was applied after first pedestrian contact. Six triaxial accelerometers (10 kHz sample rate, -3dB AA hardware filter) were inserted in the cadavers (see Figure 1b): one was inserted in the chest, two were screwed on the left and right thigh bones, two were inserted in the ilium (left and right side) and one was inserted in the mouth to represent an approximate head CG. The mouth accelerometer was pressed against the palate and expanding foam was used to fill the mouth cavity. The accelerometer position was maintained during setting and curing. When dry, the surplus was removed and the head was equipped with a hood. Only the head accelerometer data is presented in this paper.

Video Data Analysis

Head trajectories in the X (vehicle forward direction) and Z (vertically upward) directions were estimated by manually tracking the location of the forehead marker (Figure 1c) every 10ms (or every 1ms during head contacts). Linear velocities were obtained using a central difference scheme. Rotational kinematics for the head during both vehicle and ground contacts were estimated using Model Based Image Matching (MBIM), introduced by [START_REF] Bahr | Understanding injury mechanisms: a key component of preventing injuries in sport[END_REF] and recently applied to head impacts [START_REF] Tierney | An assessment of a novel approach for determining the player kinematics in elite rugby union players[END_REF][START_REF] Tierney | Assessment of model-based image-matching for future reconstruction of unhelmeted sport head impact kinematics[END_REF]. MBIM uses multiple camera views to build an environment based on known background dimensions. The user manually fitted a skull model (from the Poser platform) to the envelope of the head from videos at each time frame (1ms), see Figure 1(d). The rotation matrix for the head was then extracted at each time step, and a central difference scheme was used to compute body local angular velocity components. Each case was reconstructed by two independent researchers. Tierney et al [START_REF] Tierney | Assessment of model-based image-matching for future reconstruction of unhelmeted sport head impact kinematics[END_REF] previously reported that MBIM is repeatable for both single and multiple researchers.

Head injury assessments

The Head Injury Criterion (HIC) is commonly used to assess skull fracture risk [START_REF] Hutchinson | The head injury criterion (HIC) functional[END_REF][START_REF] Versace | A review of the severity index[END_REF]:

                 2 1 2.5 t m 2 1 t 2 1 max 1 HIC = a (t)dt (t -t ) t -t ,
where t1 and t2 are initial/final times (in seconds) to maximize HIC, and am is the resultant head CG acceleration (units of g), with time duration (t2 -t1) constrained to be less than 15 ms. However, since our accelerometers were fixed in the mouth instead of the head CG (Figure 1c) for practical reasons, strict computation of HIC was not possible with our available instrumentation. Instead, we define the "approximate Head Injury Criterion" (aHIC), calculated by applying the HIC computation to our head accelerometer data. To verify this approach, a virtual sensor was inserted in the same location in the 50 th percentile male MADYMO pedestrian model to check the difference between HIC and aHIC in a simulation similar to those in (Shang et al., 2018a). Results showed an approximate 10% difference, suggesting this approach is reasonable. The reported threshold for HIC is 700 for an approximate 30% chance of skull fracture [START_REF] Schmitt | Trauma Biomechanics[END_REF]. The 3ms acceleration criterion for the head was also calculated, used in regulations (ECE, 2008(ECE, , 2010) ) to assess energy dissipation in a vehicle, and it requires that accelerations of duration greater than 3ms do not exceed 80g [START_REF] Got | Results of experimental head impacts on cadavers: the various data obtained and their relations to some measured physical parameters[END_REF].

To assess the risk of rotationally induced brain injuries, the Brain Injury Criterion (BrIC) [START_REF] Takhounts | Development of brain injury criteria[END_REF] during vehicle and ground contact was assessed using the MBIM results. The BrIC is associated with traumatic brain injuries (TBI), which has been used to assess the brain injuries of vulnerable road users [START_REF] Gabler | Assessment of kinematic brain injury metrics for predicting strain responses in diverse automotive impact conditions[END_REF][START_REF] Gabler | Development of a metric for predicting brain strain responses using head kinematics[END_REF][START_REF] Kimpara | Mild traumatic brain injury predictors based on angular accelerations during impacts[END_REF][START_REF] Mueller | Comparison of HIC and BrIC head injury risk in IIHS frontal crash tests to real-world head injuries[END_REF] and athletes [START_REF] Aomura | Brain injury risk estimation of collegiate football player based on game video of concussion suspected accident[END_REF]. [START_REF] Gabler | Development of a metric for predicting brain strain responses using head kinematics[END_REF]) also proposed another criterion, UBrIC, to assess rotationally induced brain injury. However, evaluation of UBrIC requires a measure of angular acceleration which could not be reliably predicted with the available equipment. The BrIC score is found from the peak body local head angular velocities:

                    2 2 2 y x z xC yC zC ω ω ω BrIC = + + ω ω ω ,
where , and are the peak head angular velocity components and = 66.3 / , = 56.5 / , = 42.9 / are critical values proposed by Takhounts et al [START_REF] Takhounts | Development of brain injury criteria[END_REF]. The BrIC score was used to estimate the risk of an AIS3+ brain injury [START_REF] Takhounts | Development of brain injury criteria[END_REF]) in this study.

3.Results

Pedestrian kinematics during the whole process of vehicle impact

Figure 2 and Table 2 summarize overall kinematics, impact timings and intervals of the impact phases, with timings determined from the head accelerometer. Establishing the approximate contact time interval for both head-to-vehicle and head-to-ground contact in all tests was achieved by a combination of the filtered accelerometer and video data. For the onset of contact a sharp change in the accelerometer time curve could be readily identified in each case and verified by comparison with the video data. Establishing the effective end time for each contact was more challenging and no general criterion could be applied. Instead the end time was estimated by inspecting the acceleration time-history and comparing this to the video data.The time of first contact between the vehicle and pedestrian is t0. The pedestrian rotates onto the bonnet during phase 1. The time of first head impact on vehicle is t1. The pedestrian moves with the vehicle in phase 2. At t2, the pedestrian separates from the vehicle due to braking. The pedestrian has a flight period (phase 3) until t3, when first ground contact occurs (any body part). Then t4 is the time of first head ground contact (in some cases t4 = t3). There follows a period of slide/roll and bounce (phase 4) until the pedestrian becomes stationary at t5. Appendix F shows the pedestrian head trajectories in the X (horizontal) and Z (vertical) directions for all six tests. Head impact locations on the vehicle are shown in Appendix G. The vehicle contact phase has been previously well documented [START_REF] Kerrigan | Pedestrian kinematic response to mid-sized vehicle impact[END_REF][START_REF] Subit | Pedestrianvehicle interaction: kinematics and injury analysis of four full scale tests[END_REF]. Instead, our focus is on the subsequent ground contact. Following t1 (first head contact on the vehicle, which occurs in all tests except Test 03 where shoulder contact & low impact speed prevent direct head contact), there is continued interaction of the pedestrian with the bonnet/windscreen area for about 500ms until separation commences. Figure 3 shows velocity changes of the head during the impact process. To aid in understanding and motivated by the principle of conservation of momentum, straight line approximations of the head linear velocity have been added to Figure 3, showing that no significant impacts occur between head contact on the vehicle and separation from the vehicle. Following separation, the head acceleration is close to gravity. Contact with the ground is predominantly vertical, with small horizontal head velocity changes. Figure 4 shows the head resultant acceleration during the vehicle and ground contact phases. Unfortunately, the accelerometer recording for Test 06 was corrupted during ground contact. Furthermore, to address potential accelerometer vibration (mounted in the cadaver's mouths using expanding foam), we employed a low-pass filter prior to injury assessments. Based on previous studies [START_REF] Kang | Comparison of Hybrid III rigid body dummy models[END_REF]SAE, 1995) and in order to achieve a reasonable agreement between the predicted velocity changes during both vehicle and ground contact derived from differentiated video positions and integrated accelerometer curves (see Appendix H), we chose a CFC120 filter (3dB cut-off frequency = 200Hz), see Figure 4. With reference to Appendix H, a higher or lower cut-off threshold than 200Hz resulted in respectively over/ under-prediction of the velocity change compared to the video-based estimates. The significance of this approach is further addressed in the Discussion.

Head injury risk assessments

The aHIC scores for skull fracture risk based on the filtered acceleration curves for both vehicle and ground contacts are shown in Figure 5 3(c) compares the expected and actual ground impact "mechanisms" using the categories of [START_REF] Crocetta | The influence of vehicle front-end design on pedestrian ground impact[END_REF], while Table 3(d) compares the corresponding head impact speeds. The "agreement" in Table 3(c) is based on the proposed "mechanisms" obtained from a previous simulation study [START_REF] Crocetta | The influence of vehicle front-end design on pedestrian ground impact[END_REF]. For pedestrian collisions from a compact car at 20 kph, almost all predicted cases were "M2". For pedestrian collisions with a compact car or big car or SUV at 30 kph, the most frequently predicted mechanism was M1. If the mechanism observed from the cadaver test meets the most frequent mechanism from Crocetta et al, the "agreement" in Table 3(c) was categorised as "Yes". If the observed mechanism was one of the less frequently predicted ones, the agreement was "Partial". If the observed mechanism was not predicted, then the agreement was "No".

4.Discussion

Whole-body kinematics during the complete pedestrian impact process

We present the first detailed overview of the kinematic process of pedestrian ground contact using cadavers (see Table 2 andFigure 2). The very limited previous data on pedestrian ground contact from cadaver tests limits comparison to the published literature. Whole body kinematics can be classified into several critical events and phases: phase 1 (duration ~100-170ms) starts with first pedestrian-vehicle contact and ends with first head-vehicle contact; in phase 2 (duration ~550-625ms) the pedestrian moves together with the vehicle; phase 3 (duration ~185-280ms) is separation and first pedestrian ground contact; phase 4 (duration ~1-1.8s) is slide, roll and bounce to rest. First head ground contact occurs after about 1s and the process is complete after about 2.0-2.8s. Pedestrian ground contact occurs at the end of a highly non-linear chain of events, such that small changes in initial configuration result in significant changes in head ground impacts (compare Test 01 to Test 02) and this has been well flagged in the literature [START_REF] Simms | Pedestrian and Cyclist Impact[END_REF]. However, considering the ground contact "mechanisms" proposed by [START_REF] Crocetta | The influence of vehicle front-end design on pedestrian ground impact[END_REF] -see Appendix C, surprisingly good agreement was observed (Table 3c) and head velocity prior to ground contact was similar to the range presented for each mechanism except for Test 03 (Table 3d). These results show multibody modelling is generally successful at predicting whole body motion of pedestrians during ground contact. Nonetheless, given variations in head ground impact observed in similar cadaver tests (especially Test 01 vs Test 02), the capacity to predict injury risk in specific ground contact cases is low, as per modelling observations (Li et al., 2017b).

Head kinematics throughout the impact process

Head velocity changes (Figure 3) clearly identify the head/vehicle and head/ground contact processes. It is instructive to conceive of the head velocity changes in terms of net forces acting vertically and horizontally: the horizontal head velocity changes in phase 1 are due to neck forces induced during body rotation. Then there is the vehicle contact, after which the horizontal velocities during phases 2 and 3 are largely constant (almost zero net force) during separation from the vehicle through to first pedestrian ground contact, after which sliding and rolling to rest during phase 4 reduce the horizontal velocity to zero. The vertical head velocity changes in phase 1 are again due to neck forces induced by body rotation. Then there is the vehicle contact, after which the vertical velocity changes approximately follow gravity during separation from the vehicle through to first pedestrian ground contact, which again effectively reduces the vertical component of head velocity to zero.

Head ground contacts

The cadavers mostly struck the ground after around 1s (Test 05 was earlier but in this case there was an unusually low subject mass). The head impacts the ground more than once in each test, indicating significant restitution. However, estimates of head/ground contact stiffness using a spring-mass model with restitution were variable, between ca. 180-1750 kN/m, see Appendix J. Figure 3 shows that ground contact is predominantly vertical, with small horizontal velocity change during ground impact in all six tests. In contrast, the vertical velocity change during ground contact is chiefly responsible for the acceleration peaks in Figure 4. The peak accelerations, aHIC and 3ms scores from ground contact are generally higher than those from vehicle contact, see Figure 5. The high stiffness of the ground contact evidenced by the shorter contact interval compared to the vehicle contact (Figure 5c) is probably the main reason for this, since Appendix H shows the speed change in the vehicle contacts is mostly higher than in the ground contacts. This highlights the need to find solutions to pedestrian ground contact injury for pedestrian protection at impact speeds of 20 -30 km/h, where further improvements in vehicle front safety may be less beneficial than approaches to preventing pedestrian ground contact. These results are in line with our recent GIDAS analysis which found 72% of injury costs in pedestrian collisions below 30km/h are associated with ground related injuries (Shang et al., 2018b).

Head accelerometer filtering

According to the X-ray after each test, there were no skull fractures. This provides further justification for the 200 Hz filter, as the peaks in the unfiltered accelerations in Figure 4 would almost certainly imply some skull fractures. In addition, a retrospective assessment of the GIDAS data analyzed for the work published in (Shang et al., 2018b) shows the proportion of crashes involving skull fracture from ground contact is less than 4% in the speed range 25-34 km/h and less than 1% in the speed range 15-34 km/h, which also complies with the absence of skull fractures in our cadaver tests.

Head linear versus rotational loading during ground contact

A comparison of the relationship between aHIC/3ms linear head injury risk with the rotationally assessed AIS3+ risk computed from the BrIC score shows mixed results, see Figure 6. The aHIC score reduces with increased AIS3+ rotational head injury risk suggesting a compensatory pattern between head linear and angular injury risk which might depend on the geometry of head ground contact, but this pattern is not replicated for the 3ms score. It is thus unclear how to interpret these results and computational modelling may be needed to further elucidate this.

Unexpected Results

There were a number of unexpected findings that may lead to future insights: Figure 5(f) and Table 3b show a substantially higher risk of rotationally induced brain injury for the two 20 km/h tests than the four 30 km/h cases. The reason for this is the combination of a larger ω_z component with the smaller threshold for this axis in the BrIC equation. By checking the headground contact mechanisms from the videos, the motion of the pedestrian heads in tests 03 and 04 was more complex (bending and twisting). In contrast, for the other tests, the heads showed mainly bending rotation during contact with the ground. An underlying biomechanical explanation and whether this predicted increased risk at 20kph occurs in real world collisions remains unclear, but future computational modelling may help elucidate this.

We had expected to identify a relationship between NBLEH and head injury risk as this was observed in our recent analysis of GIDAS data (Shang et al., 2018b), but Table 3a shows no clear relationship between either linear or rotational head injury risk assessments in ground contact and the NBLEH in our cadaver tests. The absence of a trend may be due to the small sample size.

Limitations

A larger sample size would be needed to better understand the influence of vehicle design and pedestrian ground contact. However, the current experimental findings could be combined with computational modelling to better understand these effects. Additional high-speed cameras and markers on the head would have been beneficial for the MBIM process, as the region of interest to be covered during the whole process from first contact to rest is large.

The CFC 120 filter applied to the accelerations gave the closest speed change by comparison with the MBIM data than any other filter we investigated, and we therefore believe it is appropriate to apply this filter setting. However, we acknowledge this filter not only reduces the peak but can also slightly change the contact time defined, see Figure 4. In future, a study dedicated to establishing appropriate filters for pedestrian ground contact would be helpful.

The accuracy of the angular velocity time histories derived from the MBIM process cannot be measured as there is no gold standard, and this is a limitation. However, compared to [START_REF] Tierney | Assessment of model-based image-matching for future reconstruction of unhelmeted sport head impact kinematics[END_REF], we expect a higher accuracy as the frame rate is higher and there are four cameras instead of three and the image resolution is better. The intraclass correlation coefficients for the results of the two independent researchers applying MBIM are given in Table I.1. An assessment of rotationally induced brain injury which includes a measure of angular acceleration would be preferable, however, unfortunately we were not able to estimate angular acceleration in this study due to limitations in the available sensors. Furthermore, we recognise the limitations of BrIC which include a lack of validation data and its possible weakness for predicting more severe injuries.

A nine accelerometer array suitable for computing head CG accelerations would have permitted more precise 3ms, HIC calculations and would also facilitate UBrIC computation. A method for enforcing known initial limb angles would be beneficial, but also difficult to achieve in these cadaver tests. Furthermore, the cadavers' lack of muscle tone may result in different kinematics compared to live pedestrians, especially for the two 20 kph tests. In this paper only head kinematics are presented, but the GIDAS data (Shang et al., 2018b) shows lower limb and spinal injuries also occur during pedestrian ground contact and these should be a focus of future work.

6.Conclusions

This paper presents the first detailed analysis of pedestrian ground contact kinematics using staged cadaver tests addressing a range of vehicle shapes and pedestrian heights and impact speeds of 20 and 30 km/h. In addition to the well-established kinematics of pedestrians up to the time of head contact on the vehicle, we have observed around 500 ms of continued interaction of the pedestrian on the vehicle until separation commences, followed by a flight period of around 200 ms which terminates in ground contact. The linear accelerations in ground contact for vehicle impact speeds of 20 and 30 km/h are generally higher than the acceleration in the vehicle contact, though the contact intervals are shorter. No skull fractures were observed in any cases, but the 3ms scores are close to or above the injury threshold in several cases. The predicted risk of rotationally induced brain injury computed from model based image matching applied to ground contact is high for the 20 km/h tests, highlighting the risk of pedestrian injuries from ground contact even at very low speeds. We were unable to identify a clear relationship between vehicle shape/pedestrian height and ground contact head injury risk in these six tests. The data pertaining to these six pedestrian ground contact tests can be made available upon request for the purpose of human body model development.

  (a) Pre-impact scenario; (b) accelerometer positions and nominal orientations; (c) head accelerometer, CG and forehead marker positions;(d) Sample head MBIM matching using multiview camera images

Figure 2 :

 2 Figure 2: Sequences of vehicle-pedestrian impact for the six cadaver tests

Figure 3 :Figure 4 :

 34 Figure 3: Head velocity time-histories from central difference (blue and cyan) with straight line approximations between major impact phases (black).(Black dash: t1 start; Green dash: t1 end; Red dash: t2; Yellow dash: t3; Cyan dash: t4 start; Purple dash: t4 end)

  (a)Erreur ! Source du renvoi introuvable.. The corresponding 3ms peak accelerations are shown in Figure 5(b), with head contact intervals in Figure 5(c). The BrIC score (including the range drive from the two independent MBIM estimates) and probabilities of AIS3+ brain injury risks are shown in Figures 5(d) & 5(e) respectively. A comparison of the variability in computed BrIC and linear velocity change scores between the two MBIM operators is given in Appendix I. Tables 3(a)&(b) summarize the vehicle and ground injury assessments. Figure 5(f) shows average ground related rotational brain injury risk for 20km/h and 30km/h cases. Table

  Figure 5: Summary of head injuries for vehicle and ground contact

Figure 6 :

 6 Figure 6: Comparison of the relationship between aHIC/3ms linear head injury risk with the rotationally assessed AIS3+ risk for Test 01-05 (the accelerometer malfunctioned in the ground contact in Test 06)

  Figure F1: Cadaver head displacement in X and Z directions for the six tests

Table 1 :

 1 Summary of tests performed

	Test number	Vehicle speed (km/h)	Pedestrian/ vehicle size	NBLEH	Expected mechanism (M1-M6) (Crocetta et al., 2015) -see Appendix C
	Test 01	30.5	Peugeot 307 (sedan) + (Male, 88 y/o, 1.74m, 66kg)	0.7	M1 (most frequent) or M3 (less frequent)
					mechanism for adults struck by compact car at
	Test 02	30.4	Peugeot 307 (sedan) + (Male, 83 y/o, 1.72m, 69kg)	0.7	30 kph) -Figure 8 in (Crocetta et al., 2015)
	Test 03	20.4	Citroen C4 (compact)+ (Male, 94 y/o, 1.67m, 64kg)	0.9	M2 (most frequent mechanism for adults struck
					by any vehicle at 20 kph) -Figure 7 in
	Test 04	21.0	Citroen C4 (compact)+ (Male, 83 y/o, 1.67m, 55kg)	0.9	(Crocetta et al., 2015)
	Test 05	30.1	Renault Kangoo II (van)+ (Female, 94 y/o, 1.58m, 38kg)	1.2	M2 (most frequent) or M1 (less frequent)
					mechanism for adults struck by a Van at 30
	Test 06	30.4	Renault Kangoo II (van)+ (Male, 86 y/o, 1.62m, 69kg)	1.1	kph) -Figure 8 in (Crocetta et al., 2015)

Table 2 :

 2 Key vehicle and ground contact events (s)

			Phase		Phase		Phase			Phase
	Key time	t0	1 duration	t1	2 duration	t2	3 duration	t3	t4	4 duration	t5
	Description	1 st vehicle pedestrian contact		1 st head vehicle contact		pedestrian & vehicle separate		1 st ground contact (any)	1 st head ground contact		Pedestrian at rest
	Test 01 (30.5 kph)	0	0.145	0.145	0.625	0.770	0.203	0.973	0.995	1.270	2.265
	Test 02 (30.4 kph)	0	0.153	0.153	0.557	0.710	0.276	0.986	0.986	1.019	2.005
	Test 03 (20.4 kph)	0	-	none	-	0.834	0.195	1.029	1.180	1.303	2.483
	Test 04 (21 kph)	0	0.169	0.169	0.571	0.740	0.185	0.905	0.970	1.824	2.794
	Test 05 (30.1 kph)	0	0.098	0.098	0.549	0.647	0.213	0.86	0.860	1.374	2.234
	Test 06 (30.4 kph)	0	0.110	0.110	0.617	0.727	0.202	0.929	0.936	1.193	2.129

Table 3a :

 3a Summary of head/vehicle contact injury assessments

	Test number	Impact speed (km/h)	NBLEH	aHIC15	3ms (g)	AIS3+ (from BrIC)
	Test 01	30	0.7	152	41.5	10%
	Test 02	30	0.7	194	54.4	40%
	Test 03	20	0.9	---	---	--
	Test 04	21	0.9	203	55.5	2%
	Test 05	30	1.2	248	55.3	72%
	Test 06	30	1.1	579	84.1	35%

Table 3b :

 3b Summary of head/ground contact injury assessments

	Test number	Impact speed (km/h)	NBLEH	aHIC15	3ms (g)	AIS3+ (from BrIC)
	Test 01	30	0.7	559	47	20%
	Test 02	30	0.7	943	90	7%
	Test 03	20	0.9	309	69	50%
	Test 04	21	0.9	258	68	61%
	Test 05	30	1.2	608	44	8%
	Test 06	30	1.1	--	---	18%

Table 3c :

 3c Expected and observed pedestrian ground contact mechanisms[START_REF] Crocetta | The influence of vehicle front-end design on pedestrian ground impact[END_REF]

	Test number	Expected	Actual	Agreement
	Test 01	M1 (most frequent) or M3 (less frequent)	M1	Yes
	Test 02	M1 (most frequent) or M3 (less frequent)	M3	Partial
	Test 03	M2	M2	Yes
	Test 04	M2	M2	Yes
	Test 05	M2 (most frequent) or M1 (less frequent)	M1	Partial
	Test 06	M2 (most frequent) or M1 (less frequent)	M1	Partial

Table 3d :

 3d Expected and observed ground contact speeds[START_REF] Crocetta | The influence of vehicle front-end design on pedestrian ground impact[END_REF]

	Test number	Cadaver head velocity (m/s) at ground contact	Average ± std dev. head velocity (m/s) at ground contact from multibody predictions (Crocetta et al., 2015)
	Test 01	5.1	4.7± 0.8
	Test 02	2.6	2.9± 0.6
	Test 03	5.1	3.2± 1.4
	Test 04	3.9	3.2± 1.4
	Test 05	4.4	4.7± 0.8
	Test 06	5.5	4.7± 0.8

Table A .

 A 1-1 External anthropometry

	Table A.1-2 External anthropometry (continued)
	Anthropometry	Test 01	Test 02	Test 03	Test 04	Test 05	Test 06
	30 abdomen width	37	36	29	37	26	33
	8 pelvis width	35	35	26.5	26	26.5	28
	Anthropometry 9 bi-trochanter width	Test 01 39	Test 02 36	Test 03 39	Test 04 33	Test 05 27	Test 06 36
	1 total height 21 thoracic axillary thickness	174 27	172 22	167 23	167 12	157 9	163 12
	2 eyes / ground height 3 acromion / ground height 24 thoracic thickness under sternum	166 149 -	161 144 22	162 145 18	155 137 18	147 121 15	153 141.5 21
	4 elbow / ground height 33 abdomen thickness	116 18	110 17	109 17	106 14	97 25.5	110 21
	5 iliac spine / ground height 35 buttocks thickness	95 16	94 17	91 19	91 14	84 12	95 15
	6 trochanter / ground height 26a head / forehead depth	88 26	89 21	82 19	86 18	78 16	89.5 18
	7 hauteur interligne genoux/sol 26b head height	46 28	46 23.5	45 20	44.5 21.5	42 20	49 23
	43 ankle height 26c head width	6 17.5	8 18	7 16	10 14	5 12	8.5 15
	44 a arm high circumference 27 head circumference	27.5 55.5	31.5 58	31 56	25.3 56	18 52	28.5 56.5
	44 b arm low circumference 28 chin-occipital circumference	26 72	28 69	28 63	24 59	17.5 62	27 61
	48 a forearm high circumference 29 neck circumference	27 41.5	24 48	28.5 40.5	25 39	16.3 33.5	25.7 48
	48 b forearm low circumference 18 forearm + hand length	19 46	19 44	20 37	19 41.5	12.5 34	18 44.5
	49 hand length 19 arm length	20 33.5	18 32	19 32	18 32	13 26	20 30
	36 thigh high circumference 10 seat height	42 98	46 88	46.5 85	40.5 92	33.5 72	47.5 85
	37 thigh low circumference 11 eyes / seat height	35.5 90	38 77	39 80	36 83	27 62	39.5 75
	38 knee circumference 14 cervical / seat height	37.5 79	38 70	36.5 70	37.5 68	33 55	37 67
	39 calf circumference 12 acromion / seat height	30.5 73	31 60	29.5 63	30.5 65	20 48	29 63.5
	40 ankle circumference 13 elbow / seat height	26 40	25 16	26.5 27	26.5 33	22.5 26	25 37
	41 foot width 42 foot length 22 axillary thoracic circumference	10 27.5 93	10 27 104	10.5 26.5 93	10.5 22.5 89	7 20 79	85 23 98
	10 shoulder width 20 axillary thoracic width 25 thoracic circumference under sternum	43 36 85	48 35 93	39.5 31 87.5	40.5 39 75	28.5 27 77	36 34 101
	23 thorax width under sternum 31 abdominal circumference (navel)	35 83	34 88	31 78	31.5 75	24 78	31 91
	32 pelvis circumference	88	94	90	87	72	96
	16 knee / ground height	46	51	51	43	41	48
	17 buttocks / knee length	40.5	52	38	30	35	29
	34 pelvis / heel (stretched leg) length	88	93	93	82	78	97.5
	45 T1 -coccyx length	75	68	65	-	47	64
	46 sternum length	17	19	19	22	19	20
	47 xiphoid angle (a, b, c)	16 17 20	20 12 25	19 10 26	17 7 34	13 7 23	20 13 33
	479
	480
	481

Acknowledgement

The support of the China Scholarship Council (CSC) is highly appreciated.

Conflict of Interest

The authors have no conflict of interest related to the present work to disclose. Appendix J: Estimated head ground contact stiffness.

Table J1 shows the tests in which the ground contact mechanisms were suitable for estimating head ground contact stiffness. Consequently, Table J2 shows the reasons for the remaining tests.

, where e is the coefficient of restitution, which is defined as the rebound velocity divided by the velocity prior to contact. Values of pre/post impact velocity were taken from the MBIM results.


Léo Lamassoure

Justine Giunta

Giuseppe Rosi

Anne-Sophie Poudrel

Romain Bosc

Guillaume Haïat
email: guillaume.haiat@cnrs.fr

Using an Impact Hammer to Perform Biomechanical Measurements during Osteotomies: Study of an Animal Model

Keywords: Rhinoplasty, Osteotomy, Impact Hammer, Bone

Osteotomies are common surgical procedures used for instance in rhinoplasty and usually performed using an osteotome impacted by a mallet. Visual control being difficult, osteotomies are often based on the surgeon proprioception to determine the number and energy of each impact. The aim of this study is to determine whether a hammer instrumented with a piezoelectric force sensor can be used to i) follow the displacement of the osteotome and ii) determine when the tip of the osteotome arrives in frontal bone, which corresponds to the end of the osteotomy pathway.

Seven New Zealand White rabbit heads were collected, and two osteotomies were performed on their left and right nasal bones using the instrumented hammer to record the variation of the force as a function of time during each impact.

The second peak time τ was derived from each signal while the displacement of the osteotome tip D was determined using video motion tracking.

The results showed a significant correlation between τ and D (ρ² = 0,74), allowing to estimate the displacement of the osteotome through the measurement of τ. The values of τ measured in the frontal bone were significantly lower than in the nasal bone (p < 10 -10 ), which allows to determine the transition between the nasal and frontal boneswhen τ becomes lower than 0.78 its initial averaged value.

Although results should be validated clinically, this technology could be used by surgeons in the future as a decision support system to help assessing the osteotome environment.

I. INTRODUCTION

Osteotomes are used in various disciplines such as orthopedic, maxillofacial and plastic surgery. They are employed in combination with a hammer, or mallet, following the same principle as a chisel, and their function is essentially to cut bone and cartilage tissues. For instance, in maxillo-facial surgery, they are used to cut the maxilla bone or split and expend the bone ridge to improve bone density and primary stability of dental implants [START_REF] Summers | A new concept in maxillary implant surgery: the osteotome technique[END_REF][START_REF] Ferrigno | Dental implants placement in conjunction with osteotome sinus floor elevation: A 12-year life-table analysis from a prospective study on 588 Iti® implants[END_REF]. In orthopedic surgery, osteotomies are performed to cut bone tissue and to shave off osteoperiosteal grafts as well as to remove the cartilage and subchondral bone [START_REF] Swiontkowski | Operating room equipment and techniques[END_REF]. Osteotomes are also important tools in plastic surgery [START_REF] Stucker | Rhinology and facial plastic surgery[END_REF] and in particular for nose surgery where it is used to correct nasal deviation, narrow the bony nasal vault, or reduce the dorsal hump [START_REF] Siemionow | Nasal reconstruction and aesthetic rhinoplasty[END_REF][START_REF] Daniel | Mastering rhinoplasty: a comprehensive atlas of surgical techniques with integrated video clips[END_REF]. Despite their frequent clinical use, osteotomies are still associated with a certain number of risks. An important issue lies in that the surgeon usually does not have any visual feedback on the state of the targeted tissue during the osteotomy. Various technologies allowing image-guided surgery (e.g. using PET, SPECT, DTI, fMRI, or electrophysiology) have been developed and are now used in the operating room [START_REF] Nijmeh | Image-guided navigation in oral and maxillofacial surgery[END_REF][START_REF] Schulz | Intraoperative image guidance in neurosurgery: development, current indications, and future trends[END_REF]. However, they are usually not adapted to osteotomies because of their complexity or radiating features. Moreover, the aforementioned techniques imply an important increase of the duration of the surgical procedure. Therefore, most surgeons still rely so far on their proprioception and experience to perform osteotomies.

Biomechanical approaches represent interesting modalities because they can be used to retrieve information about the properties of the tissue surrounding the osteotome tip, which could be used by the surgeon as a decision support system during the procedure. For example, in rhinoplasty, nasal bone tissues are thicker where they connect to frontal bones and thinner in their inferior part where they articulate with the maxilla and the upper lateral cartilage [START_REF] Dobratz | Osteotomies[END_REF]. An estimation of bone thickness during the osteotomy could therefore allow the surgeon to locate more precisely the tip of the osteotome. Such estimation is important during rhinoplasty since errors on the osteotome pathway could result in permanent deformities [START_REF] Dobratz | Osteotomies[END_REF][START_REF] Shiffman | Advanced aesthetic rhinoplasty: art, science, and new clinical techniques[END_REF]. Moreover, an estimation on the progress of the osteotome position would also be of interest, as well as any information about the mechanical properties of the tissue in contact with the osteotome, which could be used to help the surgeon adjust the impact energy and to detect the apparition and propagation of cracks.

Incomplete fractures are sometimes preferable in older patients to avoid uncontrolled cracks, which can cause a collapse of the nasal vault, leading to an inverted V deformity [START_REF] Siemionow | Nasal reconstruction and aesthetic rhinoplasty[END_REF][START_REF] Dobratz | Osteotomies[END_REF][START_REF] Duron | Ostéotomies en rhinoplastie[END_REF]. All these phenomena may be particularly difficult to detect, especially for young surgeons [START_REF] Yeolekar | The learning curve in surgical practice and its applicability to rhinoplasty[END_REF], and additional information on the properties of the osteotomy site could provide an interesting insight and potentially reduce the failure risks of these procedures.

Over the last few years, our group has developed a technology based on impact analyses aiming at measuring implants stability. It consists in a hammer instrumented with a piezoelectric force sensor, which measures the variation of the force as a function of time during each impact. The results showed that this approach can be used to assess the primary stability of acetabular cup implants and the insertion endpoint of femoral stems. Various indicators derived from the signal [START_REF] Mathieu | Variation of the impact duration during the in vitro insertion of acetabular cup implants[END_REF][START_REF] Michel | Monitoring the press-fit insertion of an acetabular cup by impact measurements: Influence of bone abrasion[END_REF][START_REF] Michel | In vitro evaluation of the acetabular cup primary stability by impact analysis[END_REF] were tested in vitro, and then ex vivo [START_REF] Nguyen | Influence of anisotropic bone properties on the biomechanical behavior of the acetabular cup implant: a multiscale finite element study[END_REF][START_REF] Raffa | Dependence of the primary stability of cementless acetabular cup implants on the biomechanical environment[END_REF][START_REF] Michel | Finite element model of the impaction of a press-fitted acetabular cup[END_REF]. Static [START_REF] Nguyen | Influence of anisotropic bone properties on the biomechanical behavior of the acetabular cup implant: a multiscale finite element study[END_REF][START_REF] Raffa | Dependence of the primary stability of cementless acetabular cup implants on the biomechanical environment[END_REF] and dynamic [START_REF] Michel | Finite element model of the impaction of a press-fitted acetabular cup[END_REF] finite element models were developed to better understand the mechanical phenomena occurring during implant insertion. Eventually, preclinical studies were carried out on anatomical subjects to validate the device under more realistic conditions [START_REF] Ogreden | Histopathological comparison of bone healing effects of endonasal and percutaneous lateral osteotomy methods in rabbit rhinoplasty model[END_REF][START_REF] Michel | Ex vivo astimation of cementless acetabular cup stability using an impact hammer[END_REF].

Based on the results obtained in the context of hip implants, the same approach consisting in using an instrumented hammer was considered in a preliminary in vitro study aiming at investigating the possible applications of this technique to osteotomies [START_REF] Hubert | Using an impact hammer to estimate elastic modulus and thickness of a sample during an osteotomy[END_REF]. The objective was to determine whether information about the properties of a sample impacted by the osteotome could be retrieved using an instrumented hammer. One hundred samples made of different composite materials and with various thicknesses were considered and a model-based inversion technique was developed based on the analysis of two indicators derived from the analysis of the variation of the force as a function of time. This study, which also included an analytical model, showed that it was possible to i) classify the samples depending on their material types, ii) determine the materials stiffness and iii) estimate the samples thicknesses, which opened the path for the application of this approach to preclinical testing using an animal model.

The aim of the present study is to determine whether an instrumented hammer can be employed in an animal model in order to i) determine the displacement of the osteotome during an impact and ii) estimate when the tip of the osteotome enters frontal bone tissue. To do so, our approach is to use the rabbit heads, which is a validated animal model for rhinoplasty [START_REF] Badran | Anatomy and surgical approaches to the rabbit nasal septum[END_REF].

II. MATERIALS AND METHODS

A. Sample Preparation

The New Zealand White rabbit was chosen for the animal model since it is commonly used to model osteotomies [START_REF] Stein | Acute and chronic effects of bone ablation with a pulsed holmium laser[END_REF][START_REF] Ogreden | Histopathological comparison of bone healing effects of endonasal and percutaneous lateral osteotomy methods in rabbit rhinoplasty model[END_REF] and because it presents similarities with the human anatomy [START_REF] Badran | Anatomy and surgical approaches to the rabbit nasal septum[END_REF]. Seven rabbit heads were obtained from the National veterinary school of Alfort (Maisons-Alfort, France). They were collected in the 24 hours following the animal's euthanasia and were then frozen for storage. They were taken out of the freezer one day before the experiment and were thawed at room temperature to allow them to be completely unfrozen by the time the experiment was performed. The study has been approved by the ethical committee of the Alfort National Veterinary School (ENVA).

The sample preparation followed several steps. First, the surrounding soft tissues were carefully scrapped away to reveal parts of the supraoccipital and squamosal bones in order to be able to hold the sample properly. Second, the posterior part of the head was embedded in a fast hardening resin (Smoothcast 300, Smooth-On, Easton, PA, USA) in order to be able to hold the sample in a vise, following the procedure followed in [START_REF] Michel | Ex vivo astimation of cementless acetabular cup stability using an impact hammer[END_REF]. Third, the snout was excised, and an incision was performed along the nose's axis. The skin flaps were pulled aside in order to reveal the nasal bone, the anterior part of the frontal bone, and the upper part of the premaxilla, as shown in Fig. 1.

B. Instrumented Hammer

A 260 g surgical mallet (32-6906-26, Zepf, Tuttlingen, Germany) was used in this study to impact an osteotome (32-6002-10, Zepf, Tuttlingen, Germany) with a 10 mm long cutting edge. The hammer and the osteotome are the same as the ones used in clinics. For each impact, the osteotome was held manually, similarly to what is done in the clinic. A dynamic piezoelectric force sensor (208C04, PCB Piezotronics, Depew, NY, USA) with a measurement range up to 4.45 kN in compression was screwed in the center of the impacting face of the hammer to measure the force applied to the osteotome. A data acquisition module (NI 9234, National Instruments, Austin, TX, USA) with a sampling frequency of 51.2 kHz and a resolution of 24 bits was used to record the time variation of the force exerted on the osteotome. The data were transferred to a computer and recorded with a LabVIEW interface (National Instruments, Austin, TX, USA) for a duration of 2 ms. A schematic description of the experimental setup is presented in Fig. 2.

C. Experimental Procedure

For each rabbit, an osteotomy was performed on each nasal bone (right and left), resulting in a total of 14 osteotomy pathways. Both osteotomy pathways are indicated in Fig. 1. The experiments were realized by an experienced maxillofacial surgeon. The position of the osteotome tip was filmed using a camera (L-920M3, Spedal, Taiwan) during the entire experiment.

The osteotomies were set to begin at the anterior end of the nasal bone and consisted in consecutive hammer impacts of the instrumented hammer on the osteotome having its blade in contact with bone tissue. The variation of the force as function of time was recorded by the force sensor for each impact and the maximum value of the force was noted F. The following protocol was followed by the surgeon.

A series of approximately 10 impacts was realized with a relatively low energy, the value of F for each impact being comprised between 100 and 400 N. The corresponding impacts were denoted as "weak" in what follows. Then, a series of around 10 impacts was realized with a relatively high energy, the value of F for each impact being comprised between 800 and 2000 N. The corresponding impacts were denoted as "strong" in what follows. Then, the aforementioned procedure was repeated so that series of "weak" impacts were followed by series of "strong" impacts and conversely. The series of strong impacts were used to fracture bone tissue and induce a displacement of the osteotome. Crack propagation may occur, leading to a movement of the osteotome in bone tissue during the series of strong impacts. The aim of the series of strong impact was to determine whether the instrumented hammer could be used to determine the displacement of the osteotome due to crack initiation. In turn, the aim of realizing a series of weak impacts was to determine whether such approach, which has the advantage of being noninvasive since it is not likely to modify the position of the osteotome, could be used to determine whether the osteotome was located in nasal or frontal bone. The choice of the range of variation chosen for F for the two series of impact will be discussed in section 4. Note that the surgeon had only access to the value of F during the experiments to help them stay within the selected range, but not to the value of τ and D, that was obtained by post-processing.

The alternation of the strong and weak impact series was pursued until the tip of the osteotome appeared to have reached the frontal bone, which was determined empirically by the surgeon using his proprioception. In particular, similarly as what is done in the clinic, the surgeon relied on his sight (an open procedure is used and bone tissue is fully visible) and his hearing, since the arrival of the osteotome on the frontal bone is associated with a subtle change of the noise produced during the impact.. In order to study the transition between nasal and frontal bone, a dozen additional impacts were performed to obtain measurements in frontal bone before ending the trial, so that the last series of impact corresponded to weak impacts.

D. Data Processing

Data processing was done following the same method as the one used for the previous study [START_REF] Hubert | Using an impact hammer to estimate elastic modulus and thickness of a sample during an osteotomy[END_REF]. The time dependence of the force applied to the osteotome during a given impact was measured with the force sensor described above, leading to a signal denoted s(t). Two examples of typical signals are shown in Fig. 3. A dedicated signal processing technique was applied to s(t) using information derived from the different peaks obtained in the signal. For the first (p=1) and second (p=2) peaks of s(t), the maximum peak amplitude ap, the time of its center tp, and the root mean square width wp were determined by fitting a Gaussian function with a time windows centered on the interval corresponding to s(t) > ap/5. The second peak time τ was defined based on the difference between the times of the second and first peaks of s(t). Figure 3 shows the resulting value of τ for two typical signals. The average and standard deviation of all values of τ was determined for each osteotome pathway when the osteotome tip was in nasal (respectively frontal) bone and were noted 𝜏 𝑛 𝑚 and 𝜏 𝑛 𝑆𝐷 (respectively 𝜏 𝑓 𝑚 and 𝜏 𝑓 𝑆𝐷 ). For each osteotomy pathway, Mτ was defined as the averaged value of 𝜏 𝑛 𝑚 obtained for the first two series of weak impacts for the corresponding osteotomy pathway.

Based on the video of the sample and of the osteotome, a parameter D was defined as the absolute displacement of the tip of the osteotome corresponding to a given strong impact. To do so, a tracker software (Tracker, National Science Foundation, Alexandria, USA) was used to compare the images corresponding to the position of the osteotome relatively to the sample obtained before and after the impact (Figure 4). Two analyses were carried out. First, the relationship between τ and D obtained for strong impacts only was analyzed using a linear regression analysis. Second, the variation of τ was analyzed according to the type of bone where the osteotome tip was located (nasal or frontal bone).

III. RESULTS

Figure 5 shows an example of the values of F and of τ obtained for a given osteotomy pathway. Figure 5A illustrates the alternating series of weak and strong impacts. The weak impacts correspond to lower and more stable values of τ.

The values of τ for the strong impacts are usually higher but show a sudden decrease at the arrival in the frontal bone, as illustrated in Fig. 5B for impacts #97-100. Over the full database, the average values of 𝜏 𝑛 𝑆𝐷 (nasal bone) and of 𝜏 𝑓 𝑆𝐷 (frontal bone) were equal to 0,2 ms and 0,3 ms, respectively, which corresponds to the reproducibility of the measurement of τ for weak impacts.

The values of τ and D are compared for all strong impacts where D was not equal to zero in Fig. 6. The values of τ and D are found to be significantly correlated, with a Spearman correlation coefficient ϱ² = 0,74 (p < 10 -10 ).

The measurements realized during the weak impacts allowed to study the evolution of the values of τ along the osteotome pathway. Figure 7 shows the distribution of the values of τ for each osteotomy pathways when the osteotome is located in nasal and frontal bone. The values of 𝜏 𝑛 𝑚 , 𝜏 𝑛 𝑆𝐷 , 𝜏 𝑓 𝑚 and 𝜏 𝑓 𝑆𝐷 are indicated in Fig. 7. An ANOVA analysis

shows that the values of τ were significantly lower in frontal bone compared to the nasal bone for all osteotomy pathway (p<10 -10 ). A comparison of these values can be seen on Fig. 7. For all osteotomy pathways, the osteotome tip was found to enter frontal bone when 𝜏 𝑛 𝑚 < 0,78𝑀 𝜏 , which therefore corresponds to a critical value below which the osteotome is located in frontal bone. The impacts performed after the arrival in frontal bone are indicated. For both A and B, the data is represented in dark grey for the weak impacts, and light grey for the strong impacts.

IV. DISCUSSION

The originality of the present ex vivo study is to show that the instrumented hammer could be used to i) detect the moment when the osteotome tip arrives in frontal bone and ii) estimate the displacement of the osteotome in bone tissue due to impacts. These results are in agreement with the preliminary study realized with composite materials, which has shown that the indicator τ was sensitive to the rigidity of the material in contact with the tip of the osteotome [START_REF] Hubert | Using an impact hammer to estimate elastic modulus and thickness of a sample during an osteotomy[END_REF].

The physical interpretation of the mechanical phenomena occurring during each impact of the hammer on the osteotome has been discussed in detail in [START_REF] Hubert | Using an impact hammer to estimate elastic modulus and thickness of a sample during an osteotomy[END_REF], in particular thanks to the development of an analytical model. Note that finite element numerical simulations were also realized for an instrumented hammer used to assess acetabular implant stability [START_REF] Michel | Finite element model of the impaction of a press-fitted acetabular cup[END_REF]. Briefly, the force applied by the hammer to the osteotome during the first contact induces an acceleration of the osteotome, which then bounces back and forth between bone tissue and the head of the hammer (which has a significantly higher mass than the osteotome). Such phenomenon leads to the different peaks of the force shown in Fig. 3 because several iterations of contact and rupture of contact occur during a single impact between the hammer and the osteotome. Therefore, the time between the first and second peak (denoted τ herein) is related to the rigidity of the material around the osteotome tip. In particular, the frontal bones of rabbit (as well as of humans) are denser and thicker than the nasal bones [START_REF] Norton | Bone classification: an objective scale of bone density using the computerized tomography scan[END_REF][START_REF] Frank | Age and gender differences of the frontal bone: a computed tomographic (CT)-based study[END_REF], which explains the higher values of τ obtained in nasal bone compared to frontal bone (see Fig. 7). The aforementioned phenomenological explanation may also explain qualitatively the correlation obtained between D and τ (see. Fig. 6) because the displacement of the osteotome D is related to a crack initiation due to a strong enough impact. First, crack initiation leads to a decrease of the rigidity of bone tissue located in front of the osteotome, which leads to an increase of τ, as shown in [START_REF] Hubert | Using an impact hammer to estimate elastic modulus and thickness of a sample during an osteotomy[END_REF]. Second, after crack propagation in bone tissue, the osteotome shall move forward into the crack and then bounce back on the crack tip. The presence of the crack will therefore lead to a delay before the osteotome comes back to the hammer because of the time necessary to reach the crack tip. Therefore, when D increases, the delay before the osteotome comes back to the hammer also increases, which leads to an increase of τ.

Note that this phenomenological interpretation may also explain the results shown in Fig. 5 and in particular i) the higher values of τ obtained for weak impacts (when no crack may propagate) compared to strong impacts and ii) the better reproducibility value of τ obtained for weak impacts (when no crack may propagate) compared to strong impacts.

The two aforementioned phenomena concur in the positive correlation of D and τ shown in Fig. 6.

The range of variation of the force obtained for weak impacts (100-400 N) was chosen to be as low as possible while being high enough to trigger the recording of an acceptable signal. The range of variation of the force obtained for strong impacts (800-2000N) was set to be similar to the one used in clinics during real rhinoplasty procedures, following the recommendation of the maxillofacial surgeons. The size of both force ranges comes from the difficulty for the operator to impact the osteotome with a precise force.

Although we could have expected that D could increase as a function of the peak force (since the osteotome would be more likely to progress when the impact energy is higher), no correlation between the peak force and D was found (data not shown). An explanation for this absence of correlation between D and the peak force is that D does not only depend on the impact energy but also on the biomechanical properties of the tissue in contact with the tip of the osteotome, which seems to be the main determinant for the apparition of fractures that allow the osteotome to move forward. For each impact, the biomechanical phenomenon at work could be explained as follows. Below a certain threshold, the impact force is too low to generate a fracture, leading to a displacement of D = 0. Above that threshold, a fracture is created and its size is likely to depend more importantly on the properties of the tissue than the impact force. Note that τ is likely to depend both on bone mechanical properties and on bone thickness.

This study presented several limitations. First, a rabbit model has been employed, although other animal models, such as minipigs, rats, and goats, have been considered for maxillofacial surgery [START_REF] Wiggenhauser | In vivo evaluation of a regenerative approach to nasal dorsum augmentation with a polycaprolactone-based implant[END_REF][START_REF] Atespare | Utility of cartilage grafts wrapped with amniotic membrane in dorsal nasal augmentation[END_REF] and osteotomies [START_REF] Yazar | Comparison of piezosurgery, percutaneous osteotomy, and endonasal continuous osteotomy techniques with a caprine skull model[END_REF][START_REF] Dini | Training rhinoseptoplasty, sinusectomy, and turbinectomy in an animal model[END_REF]. However, the rabbit remains the most widely animal model used for rhinoplasty [START_REF] Badran | Anatomy and surgical approaches to the rabbit nasal septum[END_REF]. Note that due to ethical reasons, it was not possible to perform the experiments in anatomical subject without validating the approach in an animal model.

Although fresh-frozen samples would have been the preferred solution (30) since freezing may impact bone mechanical properties [START_REF] Cartner | Can we trust ex vivo mechanical testing of fresh-frozen cadaveric specimens? The effect of postfreezing delays[END_REF], all samples underwent the same freezing/thawing protocol. Note that a previous study [START_REF] Bosc | Influence of soft tissue in the assessment of the primary stability of acetabular cup implants using impact analyses[END_REF] using an instrumented hammer to retrieve the acetabular cup implant stability showed that the results did not depend on the amount of soft tissues located under the embedded bone sample.

Second, the 2-D view obtained with the video (see Fig. 4) induces sources of error in the determination of D. In order to minimize this error, the camera was always positioned with its axis normal to the surface of interest (i.e., the nasal bones). For each osteotome pathway, the error due to perspective related issues was checked using scales of know dimensions as references and was always lower than 3%.

Third, the same osteotome was used for all experiments. Surgeons actually have access to a variety of osteotomes with different geometry, which is likely to affect the results of the surgical procedure [START_REF] Kuran | Comparison of four different types of osteotomes for lateral osteotomy: a cadaver study[END_REF]. The choice of the osteotome is also likely to modify the signal obtained with the instrumented hammer and further studies are required in order to assess the effect of the osteotome on the results. Moreover, the load sensor is uniaxial and only the force perpendicular to the axis of the osteotome was measured. The surgeon was instructed to impact the osteotome in the direction of its axis and an angle between the osteotome axis and the impact direction may cause discrepancy of the measurement.

The influence of such an angle should be investigated in future works.

V. CONCLUSION

The long-term objectives of this research are to (1) detect a change of the tissue material properties during an osteotomy, (2) determine the stiffness of the bone tissue around the osteotome tip, and (3) estimate the thickness of the materials being osteotomized. These three pieces of information may be used to assist surgeons during osteotomy procedures via a decision support system.

The results obtained with this ex vivo animal model suggest that the instrumented hammer could be used as a decision support system to assist surgeons during osteotomy procedures. In particular, we focused on i) the detection of the transition between nasal and frontal bone and ii) the correlation between the indicator τ obtained using the instrumented hammer and the displacement of the osteotome during the corresponding impact.

Future studies should consider anatomical subjects similarly as what was done in [START_REF] Michel | Assessing the acetabular cup implant primary stability by impact analyses: A cadaveric study[END_REF][START_REF] Dubory | A cadaveric validation of a method based on impact analysis to monitor the femoral stem insertion[END_REF] in the context of hip implants, in order to confirm the results obtained for i) the between τ and D and ii) the possibility to detect the arrival of the osteotome tip on frontal bone. The advantage of cadaveric experiments is that it will be possible to measure D and to work with an open surgery. The tool should then be calibrated using cadaveric experiments and machine learning technique can also be considered, similarly as what was done in [START_REF] Hubert | Using an impact hammer to estimate elastic modulus and thickness of a sample during an osteotomy[END_REF]. Once the tool is actually calibrated in cadaveric experiments, clinical trials will be carried out and the results will then be compared to the surgeon proprioception and, if possible, to video motion tracking. Moreover, it will also be necessary to focus on the phenomena responsible for crack initiations.

Fig. 1 .

 1 Fig. 1. Image of the sample corresponding to the New Zealand White Rabbit head after preparation and just before the beginning of the experiment. The head was embedded into the resin and held in a vise. The nasal bones are completely uncovered, and the planned osteotomy pathways are represented by white dashed lines.

Fig. 2 .

 2 Fig. 2. Schematic description of the experimental setup.

Fig. 3 .

 3 Fig. 3. Example of two typical signals s(t) corresponding to the variation of the force as a function of time obtained during an impact (strong series) of the instrumented hammer on the osteotome. The corresponding values of the parameter τ are given. The different parameters of the signal are indicated for the signal in black: a1 and a2 are the amplitudes of the first and second peak, respectively; w1 and w2 are the root mean square width of the first and second peak, respectively; t1 and t2 are the time of the center of the first and second peak, respectively.

Fig. 4 .

 4 Fig. 4. Illustration of the measurement of displacement of the osteotome D. A: Configuration before a given "strong" impact. B: Configuration after the same impact. The position of the tip of the osteotome is indicated by a cross.

Fig. 5 .

 5 Fig. 5. Evolution of the maximum peak force F (A) and the parameter τ (B) for a given entire osteotomy pathway.

Fig. 6 .

 6 Fig. 6. Relationship between the parameter τ and the displacement D. The Spearman correlation coefficient ϱ² and the corresponding p-value are indicated. The dashed line corresponds to the linear regression analysis and has the following equation: 𝜏 = 0.4725 × 𝐷 + 1.0214.

Fig. 7 .

 7 Fig. 7. Average and standard deviation of all values of τ for each osteotomy pathway when the osteotome tip was in nasal (respectively frontal) bone, noted 𝝉 𝒏 𝒎 and 𝝉 𝒏 𝑺𝑫 (respectively 𝝉 𝒇 𝒎 and 𝝉 𝒇 𝑺𝑫 ). The error bars correspond to standard deviation values.

ACKNOWLEDGMENT

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 682001, project ERC Consolidator Grant 2015 BoneImplant).

The authors would like to acknowledge the support of the "Prématuration programme" of the CNRS through the Osteome project.