Strategies of Parkour practitioners for executing soft precision landings

Keywords: Drop jump, traceurs, sports performance, eccentric contraction, energy dissipation

Parkour landing techniques differ from performances of other sports as they are practiced in urban spaces with uncontrolled surfaces and drop heights. Due to the relatively young age of the sport, few studies have tried to understand how practitioners --called traceurs --succeed at performing these dynamic performances. In this paper, we focus on the precision landing technique, which has a fundamental role in most of the Parkour motions. We analyzed the lower limbs motion of traceurs executing the precision landings from two different heights and compared their performance with untrained participants. We found that traceurs perform a soft landing extending its duration twice than untrained participants do (𝑝 < .001), increasing the range of motion (𝑝 < .001) and generating more mechanical energy ( 𝑝 < .01) to dissipate the impact. In the Parkour technique, the knee accounted for half of the energy dissipated. The peak joint torques (𝑝 < .001) and power (𝑝 < .0001) were reduced in the Parkour technique. The increase of the landing height did not modify the proportion of individual joint mechanical energy contribution for dissipation. Our results could be used to enhance Parkour performance, and to understand new ways in which sport practitioners can land in order to prevent injuries.

Introduction

Parkour is a lifestyle sport in which practitioners --called "traceurs" --have to overcome obstacles in the environment in the most efficient manner and where movements look risky, highly dynamic and complex [START_REF] Kidder | Parkour, The Affective Appropriation of Urban Space, and the Real/Virtual Dialectic[END_REF][START_REF] Gilchrist | Lifestyle sport, public policy and youth engagement: examining the emergence of parkour[END_REF][START_REF] Cazenave | Conduites À Risques et Variation de L'estime de Soi Chez Les Adolescents : L'exemple Du Parkour[END_REF]. One frequent and critical Parkour motion is landing which is commonly performed in urban spaces, onto a large variety of surfaces and from different drop heights. Parkour precision landing technique is used for short dropping heights and requires practitioners to land and stay with precision on their forefoot without heel contact with the ground, to flex their lower limb joints without any varus-valgus motion of the knees and to use their arms to counterbalance the movement and stabilize themselves (Figure 1). Figure 1. In a), an untrained landing trial. In b), a precision landing trial. The landings were performed from 60 cm height. The landing phase starts at initial contact with the ground (when the reaction force is more than 50 N) and ends at maximum knee flexion.

It has been reported that bad executions of Parkour landings are the principal cause of injury in this discipline, accounting for 61 % of the cases [START_REF] Wanke | Parkour--'art of Movement' and Its Injury Risk[END_REF].

In fact, high Ground Reaction Forces (GRF) may lead to bone injury at the lower limbs (See [START_REF] Gittoes | Biomechanical approaches to understanding the potentially injurious demands of gymnastic-style impact landings[END_REF] for a review). Nevertheless, biomechanical studies assessing the kinetics of Parkour [START_REF] Puddle | Ground reaction forces and loading rates associated with parkour and traditional drop landing techniques[END_REF][START_REF] Standing | A Comparison of the Habitual Landing Strategies from Differing Drop Heights of Parkour Practitioners ( Traceurs ) and Recreationally Trained Individuals[END_REF] landings have shown that traceurs are able to decrease the peak vertical GRF. According to the literature [START_REF] Devita | Effect of landing stiffness on joint kinetics and energetics in the lower extremity[END_REF] a knee flexion of more than 90 degrees from full extension corresponds to a soft landing, otherwise it is classified as a stiff landing. If GRF peaks are lowered and the landing is soft, then joint torques and joint power peaks might also be lowered by traceurs executing precision landings.

These dynamic characteristics are also important for injury prevention [START_REF] Devita | Effect of landing stiffness on joint kinetics and energetics in the lower extremity[END_REF][START_REF] Bisseling | Relationship between Landing Strategy and Patellar Tendinopathy in Volleyball[END_REF][START_REF] Bisseling | Are the Take-off and Landing Phase Dynamics of the Volleyball Spike Jump Related to Patellar Tendinopathy?[END_REF][START_REF] Rosen | Lower Extremity Kinematics During a Drop Jump in Individuals With Patellar Tendinopathy[END_REF] and might be of interest in other highly dynamic and complex sports such as gymnastics.

Moreover, Parkour requires rigorous training [START_REF] Grosprêtre | Performance characteristics of Parkour practitioners: Who are the traceurs?[END_REF]. It has been shown that Parkour training induces high development of muscular capacity like power or eccentric forces [START_REF] Marchetti | Differences in Muscular Performance between Practitioners and Non Practitioners of Parkour[END_REF]) and that traceurs can develop high eccentric joint torques in the knees when performing long jumps [START_REF] Grosprêtre | Performance characteristics of Parkour practitioners: Who are the traceurs?[END_REF]. Therefore, quantifying the contribution of joints in energy dissipation might provide clues about how the lower extremity muscles should be conditioned to execute precision landings.

In this research, we compare the Parkour precision landing with the landings performed in a natural style by untrained participants from two different heights. To the best of the authors knowledge, only kinetic studies of Parkour landings have been carried out and no study has quantified and compared the kinematics, dynamics and energetics of Parkour precision landings between traceurs and untrained participants. We hypothesized that traceurs should perform soft landings which induce an extended landing phase duration for energy dissipation and thus, lead to more mechanical energy dissipation. Furthermore, we expected that traceurs would use especially the knee to absorb the energy as it was observed by studies on soft landings [START_REF] Devita | Effect of landing stiffness on joint kinetics and energetics in the lower extremity[END_REF]. Moreover, we hypothesized that the Parkour technique would induce a reduction of lower extremity joint torque and power because of the soft landing that traceurs seem to perform and their ability to lower the vertical GRF. Lastly, we expected that increasing the landing height will induce an increment of the assessed variables in both groups except for the body configuration at initial contact with ground (joint angles of the hip, knee and ankle).

Material and Methods

Participants

Twelve healthy untrained male participants (age: 22.3 ± 3.3 y, height: 1.79 ± 0.08 m, mass: 71.2 ± 5.6 kg) and twelve healthy trained male traceurs (age: 22.2 ± 4.8 y, height: 1.73 ± 0.04 m, mass: 66.6 ± 5.1 kg) volunteered for this study. The traceurs' experience in Parkour practice was 5.4 ± 2.1 y. The subject exclusion criterion was based on history of lower extremity injuries or diseases that might affect landing biomechanics. The experiments were conducted in accordance with the standards of the Declaration of Helsinki (rev. 2013) and approved by a local ethics committee.

Procedures

All participants started with 5 min of warming up that was followed by 5 min of selfstretching. Two boxes of 30 cm height were used to achieve two landing heights from 30 cm and 60 cm (Figure 1). For each height, 2 blocks of 3 successful trials without randomization were executed as follows: one block of familiarization, followed by a second one of recordings including 30 seconds of rest in between. Untrained participants' trials were labeled as untrained trials while Parkour trials were labeled Parkour trials. All participants were instructed to land barefoot in a specified target and to avoid jumping up to not exceed the initial height. No instruction was provided regarding the use of the arms. The target was set with marker landmarks placed on the landing surface to limit the minimal and maximal horizontal landing distance at 50 ± 5 cm. In the Parkour trials, traceurs were instructed to land using the Parkour precision technique (Figure 1). In the untrained trials, participants were asked to land freely using the both feet together and to stabilize themselves on the force platform as they did not know how to perform precision landings. Kinematic data were collected using 12 infrared cameras sampling at 200 Hz (Vicon, Oxford Metrics, Oxford, UK) and recording 22 reflective markers placed on the subject's lowerlimbs. Two force plates (AMTI, Watertown, MA, USA) embedded into the floor were used to record GRF and moments at 2000 Hz for each limb. Markers were set based on Wu recommendations [START_REF] Wu | ISB Recommendation on Definitions of Joint Coordinate System of Various Joints for the Reporting of Human Joint motion-Part I: Ankle, Hip, and Spine[END_REF] as follows: the first and fifth metatarsal, calcaneus, lateral and internal malleolus, anterior tibial tuberosity, lateral and medial epicondyles of knee, greater trochanter, posterior superior iliac spine and anterior superior iliac spine. Kinematics and GRFs were filtered at the same cutoff frequency [START_REF] Kristianslund | Effect of low pass filtering on joint moments from inverse dynamics: implications for injury prevention[END_REF][START_REF] Mccaw | Filtering ground reaction force data affects the calculation and interpretation of joint kinetics and energetics during drop landings[END_REF] with a low-pass Butterworth digital filter of 4th order applied in a zero-phase. A cut-off frequency of 30 Hz was used after a residual analysis [START_REF] Winter | Biomechanics and Motor Control of Human Movement[END_REF]. Scaling parameters were computed according to Dumas (Dumas, Cheze, & Verriest, 2007). Inverse kinematics and inverse dynamics were performed using OpenSim [START_REF] Delp | OpenSim: open-source software to create and analyze dynamic simulations of movement[END_REF]. Results were analyzed with custom made algorithms in order to compute joint power and mechanical work, evaluate the data and perform the statistical analysis.

Data were analyzed during the landing phase. The landing phase was defined between the IC (0%) (defined as the time instant when vertical GRF was more than 50 N [START_REF] Standing | A Comparison of the Habitual Landing Strategies from Differing Drop Heights of Parkour Practitioners ( Traceurs ) and Recreationally Trained Individuals[END_REF]), and the maximum knee flexion (100%). In this study, we refer to this time interval as the "landing phase duration". Hip, knee and ankle relative joint angular configurations (Euler XYZ body-fixed rotation angles and body-segmental reference frames according to [START_REF] Delp | An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures[END_REF]) at initial contact with the ground "IC", Range Of Motion (RoM) of the joints, total time of the landing phase, joint torques, joint power and the eccentric mechanical joint work were also evaluated. Mechanical work calculation included the individual joint contribution to energy. GRF, joint torques, joint power and mechanical work were normalized by the subject's body mass. Joint power was computed as the scalar product of the joint torque vector and the joint angular velocity vector. Joint mechanical work was calculated as the eccentric work used for decelerating the lower extremity segments by integrating the negative joint power. The work contribution for energy dissipation was calculated by normalizing the calculated joint work by the total work (summation of the hip, knee and ankle eccentric work previously calculated) and multiplying by 100. Results were reported for the dominant leg as it has been reported to provide better conclusions for injury prevention [START_REF] Niu | Kinematics, kinetics, and electromyogram of ankle during drop landing: a comparison between dominant and non-dominant limb[END_REF].

Statistical Analysis

Data were extracted during the landing phase. The average of three trials in each recording block was calculated for each subject. Normality of the data was assessed using a Shapiro-Wilk test. A mixed model analysis of variance (Anova) with heights (30 cm and 60 cm) and joints (hip, knee, ankle) as the within factors (repeated measures effect), and with the groups (traceurs and untrained) as the between factor (group effect). The dependent variables were the time duration of the landing phase, the configuration at initial contact with the ground, the range of motion, the torque, the power and the mechanical work of the studied lower joints: hip, knee and ankle. The threshold level of significance was set to 𝑝 ≤ .05. Significant effects were evaluated with correlated and independent t-tests using the Bonferroni correction. Two correlated paired t-tests (p/2) were computed to assess the effect of dropping from a height of 30 and of 60 cm on the assessed variables (untrained 30 cm vs untrained 60 cm, precision 30 cm vs precision 60 cm).

Similarly two independent t-tests (p/2) were computed to compare the assessed variables of untrained trials with each of the parkour trials at the same height (untrained 30 cm vs precision 30 cm, untrained 60 cm vs precision 60 cm).

Results

Landing phase duration

The landing phase duration was significantly longer in the Parkour landing ( 𝑝 < 0.001).

In fact, for both heights the duration of the Parkour landings was around twice the duration of the untrained landings (Table 1).

Landing type and range of motion

Traceurs executed a soft landing. The knee joint was flexed up to 116 degrees (30 cm) and 129 degrees (60 cm) in the precision technique, while untrained participants landed stiffly (up to 65 degrees and 84 degrees respectively). The joint RoM was significantly different between populations and it was significantly different among joints. There was a significant interaction between joints and groups indicating that the RoM of joints changes differently in each group (Table 1). *landing from 30 cm significantly different from landing from 60 cm for the same trial (p ≤ .025). †free trial significantly different from precision trial for the same height (p ≤ .025).

Energy dissipation

The energy dissipation was significantly higher in Parkour landing and it was significantly different between joints. In the Parkour landings, the knee was always the most important contributor for energy dissipation compared to the hip (𝑝 < .001) and ankle (𝑝 < .001), around twice the contribution of both summed together. The hip and ankle shared equally the rest of the total energy dissipated by the lower-limbs. In the untrained landings, the mechanical energy for dissipation in the hip was significantly less than in the knee (𝑝 < .001) and the ankle (𝑝 < .001).

Only the mechanical energy at the hip (𝑝 < .001) and knee (𝑝 < .01) were significantly higher in Parkour landings compared to untrained landings. The hip worked also in concentric mode (Figure 2 and Table 2).

Body configuration at IC

The hip, knee and ankle joint angles overall effect was not significantly different between both groups. However there was a significant interaction between the joints and groups indicating that the joint angles at IC were affected by the group type. Moreover joints were significantly different among themselves (Table 3). *landing from 30 cm significantly different from landing from 60 cm for the same trial (p ≤ .025). †free trial significantly different from precision trial for the same height (p ≤ .025).

Ground reaction forces, Power and Torque

All GRF components were lower in parkour landings than in untrained landings (Table 3).

The joint torques and power peaks were significantly lower in Parkour landings than in untrained landings. The joint torques were significantly different among joints as well as the joint power.

The knee extensor (𝑝 < .001), the hip extensor (𝑝 < .05) and the ankle plantar-flexor (𝑝 < .01)

torques were significantly higher in untrained technique than in precision technique. The hip and knee power were higher in untrained landings although only the ankle power was significantly higher (𝑝 < .0001) (Figure 3 and Table 3). *landing from 30 cm significantly different from landing from 60 cm for the same trial (p ≤ .025). †free trial significantly different from precision trial for the same height (p ≤ .025).

Height effect

The landing phase duration was not significantly different between 30 cm and 60 cm. The joint range of motion increased significantly with height. Moreover, the height interacted significantly with the joints and thus the RoM of joints changed differently when the height increased. The energy dissipation increased significantly with height. In the Parkour landings, total energy dissipation increased significantly with height (𝑝 < 0.001), while individual joint energy contribution (in %) for dissipation was not significantly different. The hip was significantly more flexed in Parkour landings at IC than in untrained landings at 30 cm (𝑝 < .001). With the increase of the height, the joint angles of traceurs did not change significantly while untrained participants modified their joint angles significantly (𝑝 < .045). Ground reaction forces, joint torques and power were significantly higher at 60 cm than at 30 cm.

Discussion

In this research, kinematics, dynamics and energetics of Parkour precision during landing were presented for the first time. The Parkour precision technique appeared to lower the GRF, joint torques and power. This result provides interesting cues that can be of great interest for sports where landing dynamics are high. The configuration at IC, the landing phase duration and the joint mechanical energy dissipation appear to be invariants of the technique. Moreover, the knee appeared to be the principal mechanism for energy dissipation in Parkour landings. Thus, our results could be used to enhance Parkour training and performance. Moreover, results can be also used to understand new ways in which sport practitioners can land in order to prevent injuries like in gymnastic where the athletes tend to land with stiffer landings techniques [START_REF] Christoforidou | Landing from Different Heights: Biomechanical and Neuromuscular Strategies in Trained Gymnasts and Untrained Prepubescent Girls[END_REF].

Experiments show that in precision technique, when landing and stabilizing, traceurs extend the landing phase duration, flex more the lower extremity joints and increase the mechanical energy dissipated by the lower limbs. This strategy seems to help them landing smoothly and reducing the peaks of joint torques and joint power. The increase of jump height did not affect the strategy in terms of joint angles and joint contribution to energy dissipation.

The landing phase duration, the range of motion and the way traceurs dissipate the energy of the impact appear to be important parameters in the execution of the Parkour precision landings.

Interestingly, the precision technique induces more active energy dissipation than untrained landings which is less efficient in terms of energy transformation, which requires conditioning of extensor muscles. However, by increasing the landing phase duration, the mechanical joint energy and the RoM of the lower-limbs, traceurs are able to distribute torques along the landing phase duration in order to reduce the associated peak demands and to damp the impact forces.

In untrained technique, we observed that the ankle plantar-flexors and the knee extensors are the main mechanisms of energy dissipation through negative mechanical work, which is similar to previous results reported in the literature for stiff landing [START_REF] Devita | Effect of landing stiffness on joint kinetics and energetics in the lower extremity[END_REF][START_REF] Zhang | Contributions of lower extremity joints to energy dissipation during landings[END_REF]. Conversely, in Parkour trials the knee accounts for half of the mechanical work needed for energy dissipation while the hip and ankle share uniformly the rest of the energy dissipated within the lower-limbs. This result highlights the importance of the knee joint for energy dissipation in the Parkour technique, and a compromise for sharing equally the loads with the hip and ankle joints.

At IC, traceurs land with the hip and knee more flexed than untrained participants. It has been reported [START_REF] Cortes | Effects of Gender and Foot-Landing Techniques on Lower Extremity Kinematics during Drop-Jump Landings[END_REF] that when untrained participants land on their forefoot only, they

show significantly lower knee and hip flexion compared to landings that include heel contact.

Moreover, in the same study, it was suggested that the forefoot technique requires the participants to have a straighter position at initial ground contact to stabilize. However, for traceurs executing precision landing, stability was significantly higher compared to untrained participants (Maldonado, Bitard, Watier, & Soueres, 2015) suggesting that a straight pose does not necessarily increases stability. We suggest that, in the case of precision landings, the body configuration at IC allows traceurs to land with their center of mass closer to the center of the base of support.

Moreover, landing on their forefoot and with the body more flexed, allows traceurs to progressively flex their lower-joints in order to damp the impact and to control their balance using eccentric loading.

Considering inverse dynamics in the untrained trials, our results are consistent with those previously published [START_REF] Devita | Effect of landing stiffness on joint kinetics and energetics in the lower extremity[END_REF][START_REF] Mccaw | Filtering ground reaction force data affects the calculation and interpretation of joint kinetics and energetics during drop landings[END_REF][START_REF] Mcnitt-Gray | Kinetics of the lower extremities during drop landings from three heights[END_REF]. Our results

show that the hip also work in concentric mode at the beginning of the landing phase. It has been suggested [START_REF] Devita | Effect of landing stiffness on joint kinetics and energetics in the lower extremity[END_REF]) that the hip eccentric mode is used to dissipate the impact whereas the concentric mode is used to keep the upper body aligned over the legs. In the present study, upper trunk stability was achieved by both eccentric and concentric modes because flexors and extensors were used to maintain stability (landing from a horizontal distance of 50 cm). This phenomenon was principally observed in untrained landings. In the precision trials, the concentric mode is significantly less used than in untrained trials, presumably because the landing of traceurs is more stable due to a better postural control.

The knee extensor torque was significantly higher in the untrained trials than in the precision trials, maybe because extending the landing phase duration allows traceurs to redistribute torques along the time and thus decrease the peak joint torques and peak joint power demands.

Moreover, traceurs are able to reduce the GRF peak more significantly than untrained participants [START_REF] Puddle | Ground reaction forces and loading rates associated with parkour and traditional drop landing techniques[END_REF][START_REF] Standing | A Comparison of the Habitual Landing Strategies from Differing Drop Heights of Parkour Practitioners ( Traceurs ) and Recreationally Trained Individuals[END_REF] which might influence the joint torque level. In the present study, peak GRF of untrained and parkour landings were similar to those reported in the literature [START_REF] Puddle | Ground reaction forces and loading rates associated with parkour and traditional drop landing techniques[END_REF][START_REF] Standing | A Comparison of the Habitual Landing Strategies from Differing Drop Heights of Parkour Practitioners ( Traceurs ) and Recreationally Trained Individuals[END_REF][START_REF] Devita | Effect of landing stiffness on joint kinetics and energetics in the lower extremity[END_REF][START_REF] Zhang | Contributions of lower extremity joints to energy dissipation during landings[END_REF][START_REF] Mcnitt-Gray | Kinetics of the lower extremities during drop landings from three heights[END_REF] confirming that in Parkour landings the impact GRF is reduced. Moreover, we showed that parkour techniques permit to decrease anteroposterior and medial-lateral forces inducing less stresses at the joints. This may also help traceurs to land softly and control their balance without significantly deviating their center of mass.

Having no contact the heel with the ground in Parkour landings may increase the lever arm between GRF and ankle joint center but does not imply higher torques nor higher power than those generated at the ankle joint by untrained participants to counteract the induced rotational motion around the ankle. However, for important height, traceurs cannot continue rotating their lower extremity joints, higher torques might be necessary to counteract the motion. The ankle plantarflexor peak power is significantly higher in untrained trials probably because of the heel contact with the ground, which may have induced higher peak angular velocity of the ankle and also combined with the fact that the GRF were higher during untrained landings. Furthermore, it has been shown [START_REF] Grosprêtre | Performance characteristics of Parkour practitioners: Who are the traceurs?[END_REF]) that eccentric torque capability was greater in traceurs than in power athletes and gymnasts. In the present study, we observed that regardless of this capability, Parkour techniques induce less peak torques and peak power at the joints.

Mechanical work, torques and power increased with height, as reported in literature, essentially because the duration of the landing phase remains constant for both jumping heights, but the energy to dissipate is higher [START_REF] Yeow | Sagittal Knee Joint Kinematics and Energetics in Response to Different Landing Heights and Techniques[END_REF]. Similarly, precision and untrained techniques induced significantly more RoM of the hip, knee and ankle joints. The reason seems to be due to the initial landing velocity, which is higher at 60 cm and may have induced more flexion of the joints after ground contact. For untrained trials at 60 cm, RoM and initial joint angles reported in the literature [START_REF] Decker | Gender differences in lower extremity kinematics, kinetics and energy absorption during landing[END_REF] were similar to the results presented here. In Parkour trials, the joints configuration at IC and the proportion of individual joint mechanical energy contribution for dissipation did not change significantly. The invariance of these parameters seems to reflect their importance in the execution of Parkour precision landings.

It has been reported that a stiffer landing could manifest to patellar tendinopathy when peak joint velocities and torques increase [START_REF] Bisseling | Relationship between Landing Strategy and Patellar Tendinopathy in Volleyball[END_REF]. Therefore, Parkour coaches should closely monitor the landing strategy and the joint load frequency to reduce the patellar tendon loading and the risk of injury. Hip flexion at IC and no contact of the heel with the ground seem to help traceurs to execute soft landings [START_REF] Devita | Effect of landing stiffness on joint kinetics and energetics in the lower extremity[END_REF]) by increasing the lower-joints flexion. However, high impact pressure concentrated in metatarsal bones and high vertical reaction forces may cause metatarsal fractures [START_REF] Kavanaugh | The Jones fracture revisited[END_REF]. When possible Moreover, when the landing height is increased, ankle taping could be helpful to enhance peak plantar-flexion strength [START_REF] Hopper | Effect of ankle taping on angle and force matching and strength of the plantar flexors[END_REF]. In the Parkour community, an unwritten rule suggesting a maximum knee flexion of 90 degrees in landings is commonly used. However, in this study traceurs exceeded 90 degrees and this strategy appeared to be beneficial compared to landings performed with less than 90 degrees because it helps to smooth the mechanical parameters during landing impact. Furthermore, for optimizing the performance (considering the eccentric force-velocity relationship of the muscles) during the landing phase, extensor muscles should be warmed up and intense fatigue should be prevented. This may help traceurs to enhance and maintain their capacity of developing the required eccentric torques (De [START_REF] Ruiter | Similar Effects of Cooling and Fatigue on Eccentric and Concentric Force-Velocity Relationships in Human Muscle[END_REF]. Moreover, extensor muscles should be conditioned for executing Parkour landings taking into account that the knee accounted for half of the energy dissipated by the lower-limbs.

A limitation of this research is that traceurs were recorded inside a laboratory for limited heights and horizontal distances, which differs from natural Parkour practice. In fact, for safety reasons, jump height was limited because our protocol included untrained participants. However, higher drops with longer horizontal distances might induce higher antero-posterior forces and different biomechanics of the precision landing. Probably, the strategy will be adapted to maintain stability and dissipate the energy of the impact safely. Thus, an interesting direction for future work might be the study of such landings conditions and the performance of other Parkour landings such as the roll technique.

Figure 2 .

 2 Figure 2. Representative joint work profiles of the dominant leg for trials from 60 cm drop height. In blue a representative untrained trial and in red a representative precision trial.

Figure 3 .

 3 Figure 3. Representative joint torque and power landing profiles of the dominant leg for trials from 60 cm drop height. In blue a representative untrained trial and in red a representative precision trial.

(

  sometimes the surface imposes the landing technique), traceurs might use other Parkour landing techniques such as the roll landing technique (Puddle, & Maulder 2013) from higher heights in order to lower the GRF. Nevertheless, more studies comparing the precision with the roll technique from different heights are needed to assess up to which height the precision landing is safe.

Table 1 .

 1 Means (SD) of kinematic parameters assessed of the dominant leg. Notation. T, time; H, hip flexion; K, knee flexion; A, ankle plantar-flexion; S, total knee flexion from anatomical pose.

		Free	Precision
		30 cm	60 cm	30 cm	60 cm
	Landing phase duration (s)
	T	.15 (.03) †	.14 (.04) †	.33 (.08)	.33 (.09)
	Joint angle at initial contact with the ground (deg)
	H	2.9 (9.2) †	2.2 (11.4) †	25.6 (8.2)	23.5 (9.4)
	K 17.8 (3.3) * †	22.4 (3.6) †	32.1 (5.2)	33.7 (5.6)
	A	19.1 (10.7)	21.8 (10.2)	21.7 (10.8)	24.8 (9.1)
	Joint range of motion during the landing phase (deg)
	H 25.2 (9.4) * †	42.5 (18.9)	48.1 (8.6)*	59.0 (8.2)
	K 47.0 (5.8) * †	61.3 (9.4) †	84.1 (16) *	95.6 (13)
	A	43.1 (3.8) *	50.1 (5.0)	48.9 (8.9)*	54.4 (9.0)
	Knee range of motion (deg)
	S	64.8	83.7	116.2	129.3

Means (SD) of kinematic parameters assessed of the dominant leg. Notation. T, time; H, hip flexion; K, knee flexion; A, ankle plantar-flexion; S, total knee flexion from anatomical pose.

Table 2 .

 2 Means (SD) of energetic parameters assessed for the dominant leg. Notation. HE; hip eccentric, KE, knee eccentric; AE, ankle eccentric.

		Free	Precision
	30 cm	60 cm	30 cm	60 cm
	Mechanical work (J•Kg -1 )
	HE .23(.1) †	.32(.3) †	.53(.2) *	.83(.3)
	KE .72(.2) * †	1.12(.4) †	1.26(.5) *	1.99(.7)
	AE .85(.2) †	.88(.3)	.61(.1) *	.96(.3)
	Work contribution to energy dissipation per joint (%)
	HE 12.2(4.9) †	13.1(8.6)	22.9(7.4)	22.4(7.6)
	KE 40.4(9.3)	48.1(11.6)	51.3(9.0)	52.5(7.2)
	AE 47.4(9.1) * †	38.8(7.4) †	25.8(4.9)	25.1(4.2)

Means (SD) of energetic parameters assessed for the dominant leg. Notation. HE; hip eccentric, KE, knee eccentric; AE, ankle eccentric.

Table 3 .

 3 Means (SD) of dynamic parameters assessed for the dominant leg. Notation. HE; hip extension, KF, knee flexion; AP, ankle plantar-flexion.

		Untrained	Precision
		30 cm	60 cm	30 cm	60 cm
	Peak force (N•Kg -1 )
	ML	1.8 (.70) †	2.2 (1.0) †	0.9 (.4)	1.3 (.5)
	AP	3.2 (10) †	4.4 (1.4) † ‡ 2.1 (.5) *	2.7 (.5)
	V	17.8 (4.3) †	22.2 (4.7) † 10.3 (1.8) *	13.3 (1.6)
	N	19.6 (4.5) †	23.9 (5.3) † 10.8 (1.8) *	14.0 (2.1)
	Peak joint torque (N•m•Kg -1 )
	HE	2.18 (.4) †	2.45 (.7)	1.61 (.5)	1.82 (.4)
	KF	1.84 (.3) * †	2.41 (.5) †	1.50 (.2) *	1.90 (.3)
	APF	1.61 (.3) *	1.98 (.3)	1.31 (.2) *	1.67 (.3)
	Peak joint power (W•Kg -1 )
	HE	12.4 (5.0)	16.7 (10.2)	8.3 (3.3) *	12.4 (4.5)
	KF	15.4 (5.9) *	27.4 (11.6)	11.8 (3.2) *	19.5 (4.0)
	APF	24.6 (6.0) * †	36.8 (7.2) †	12.9 (5.6)	23.4 (7.0)

Means (SD) of kinetic and dynamic parameters assessed for the dominant leg. Notation. ML, medial lateral; AP, antero posterior; V, vertical; N, norm of the force. HE, hip extension; KF, knee flexion; APF, ankle plantar-flexion


Christophe Jacquet

Roger Erivan

Akash Sharma

Martine Pithioux

Jean-Noël Argenson

Matthieu Ollivier

Study of Three preservation methods (Freezing, Cryo-preservation

Keywords: Meniscus, Allograft, Conservation, Storage, Irradiation, Cryopreservation, Freezing, Mechanical Properties

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ABSTRACT.

Backgrounds: Three main menisci preservation methods have been used over the last decade: freezing, freezing with gamma-irradiation, and cryopreservation.

Hypothesis/Purpose: We hypothesized that all preservation methods will result in similar biomechanical properties as defined by traction and compression testing.

Methods: Twenty-four human lateral menisci were collected from patients operated on for total knee arthroplasty. The inclusion criteria were patients under 70 years of age, with primary unilateral (medial) femorotibial knee osteoarthritis. Cross sectionally each meniscus was divided into 2 specimens extending from the end of the central edge peripheral/capsular attachment to obtain 2 similar samples from the same meniscus. One sample was systematically cryopreserved constituting the control group (Cy;-140°c) and the other was used for either the simple frozen group (Fr;-80°c ) or the frozen + irradiated group (FrI;-80°c + 25kGy irradiation).

Evaluation was performed using compression and tensile tests (Instron 5566 Universal

Testing Machine) to analyze: 1) the Elasticity Modulus (Young's Modulus; YM) in compression, 2 )the YM in traction, 3)the Tensile Force at failure, 3)the Rupture Profile of the tensile stress-strain curve.

Results: A significant difference of the mean compression elasticity's modulus was observed between Cy group and the Fr group (respectively 28.86±0.77MPa vs 37.26±1.08MPa; mean difference 8.40±1,33MPa; p <0,001) and between the Cy group and the FrI group (respectively 28.86±0.77MPa vs 45.92±1.09MPa; mean difference 17.06±1.33MPa; p<0,001).

A significant difference of the mean tensile elasticity's modulus was observed between Cy group and the Fr group (respectively 11.66±0.97MPa vs 19.97±1.37MPa; mean difference 8.31±1.68MPa; p=0.008) and between the Cy group and the FrI group (respectively

What this study adds to existing knowledge:

Our study compared the three main preservations methods on identical samples using two different mechanical testings, aiming to approximate in-vivo loading.

Our results, first, confirmed that Freezing+Irradiation procedure should be used with caution, second, demonstrated that Freezing also have a detrimental effect on menisci mechanical properties, third, allowed us to conclude that Menisci Tissues preserved using Cryopreservation result in better mechanical outcomes.

INTRODUCTION.

The long-term damaging effects of total meniscectomy include: pain, potential instability and osteoarthritis [START_REF] Higuchi | Factors affecting longterm results after arthroscopic partial meniscectomy[END_REF][START_REF] Horský | Degenerative changes in the knee joint after meniscectomy[END_REF][START_REF] Krüger-Franke | Late results after arthroscopic partial medial meniscectomy[END_REF] . Menisci allografts have been advocated to treat these issues and potentially slow the onset of osteoarthritis. Mid-term results of this procedure demonstrate significant improvement in patient's pain scores [START_REF] Verdonk | Transplantation of viable meniscal allograft. Survivorship analysis and clinical outcome of one hundred cases[END_REF][START_REF] Verdonk | Meniscal allograft transplantation: long-term clinical results with radiological and magnetic resonance imaging correlations[END_REF] , as well as increasing survivorship without failure (85%) of meniscal allografts [START_REF] Hannon | Meniscal Allograft Transplantation A Comprehensive Historical and Current Review[END_REF][START_REF] Wirth | Long-term results of meniscal allograft transplantation[END_REF] . To play its biomechanical role, meniscus allograft tissue must resemble the qualities of native fibrocartilage [START_REF] Vangsness | Allograft transplantation in the knee: tissue regulation, procurement, processing, and sterilization[END_REF] . As such, graft preservation methods will play a vital role in the biological, mechanical and thus clinical success of menisci allograft techniques [START_REF] Fabbriciani | Meniscal allografts: cryopreservation vs deep-frozen technique. An experimental study in goats[END_REF] . Three main menisci preservation methods have been used over the last decade: freezing, freezing with gamma-irradiation, and cryopreservation [START_REF] Vangsness | Allograft transplantation in the knee: tissue regulation, procurement, processing, and sterilization[END_REF] .

In a recent comparative study Jacquet et al [START_REF] Jacquet | Effect of 3 Preservation Methods (Freezing, Cryopreservation, and Freezing + Irradiation) on Human Menisci Ultrastructure: An Ex Vivo Comparative Study With Fresh Tissue as a Gold Standard[END_REF] observed that Cryopreservation does not cause significant histological alterations as compared to fresh tissue. On the other hand, significant differences were only found comparing between freezing and freezing with irradiation processes to fresh tissue or cryopreserved samples. These ex-vivo microscopic findings need to be validated to estimate their clinical implication. This biomechanical study was designed to compare "preserved menisci allografts" mechanical properties defined by the elasticity's modulus during traction and compression testing, as there is nothing in the literature to confirm that preserving meniscal architecture preserves the biomechanical properties of the graft. We hypothesized that all preservation methods will result in similar biomechanical properties.

METHODS.

Following local board approval, twenty-four human lateral menisci were collected from patients operated on for total knee arthroplasty from September to October 2017. All patients gave written consent prior to their inclusion into the study. Inclusion criteria were: patients aged <70 years undergoing Total Knee Arthroplasty with isolated medial femoraltibial arthritis or femoral-patellar and medial femoral-tibial joint degeneration (but with an lateral femoral-tibial compartment graded Kellgrenn and Lawrence <2 [START_REF] Kohn | Classifications in Brief: Kellgren-Lawrence Classification of Osteoarthritis[END_REF] ) and no history of prior surgery, trauma, or developmental disease of the operated knee. An MRI was systematically performed 1 month pre-operatively to verify the absence of radiological meniscal lesion. If a grade 1 lesion was detected, the patients were not included in the study Patient's characteristics are summarized in Table 1. freezing process was used, progressively decreasing the temperature (starting at -4°C then decreasing at -2°C per minute to -40°C and then -5°C per minute to -80°C). 3) For the frozen + irradiated group, a simple congelation with a progressive decrease in temperature (starting at -4°C then decreasing at -2°C per minute to -40°C and then -5°C per minute to -80°C) was performed. The grafts were then transported in a dry ice-controlled container (stored at -80°C)

Patients

to be irradiated by gamma-rays by IONISOS factory ©. The doses received ranged between 22.7 and 27.8 kGy (2.2-2.7 Mrad). After this treatment, the samples were again stored at -80°C until analysis was undertaken. All samples were Stored at least 1 month prior to biomechanical testing

Biomechanical Testing

The compression and tensile tests were performed on an Instron 5566 Universal Testing Machine with a measurement error in displacement of 0.05% and the force transducer has a measurement error of 0.2% in tension and compression.

Compression test (Figure 3).

Each sample was subjected to 5 relaxation compression cycles with a maximum load of 50 N.

The speed of progression was 3mm / min.

The Stress-strain curve was then obtained using pre-test relaxed measurement of section and thickness. Elasticity Modulus (Young's Modulus) was calculated in the relaxation elastic phase of the 5th cycle [START_REF] Sweigart | Tensile and compressive properties of the medial rabbit meniscus[END_REF] .

Tensile test (Figure 4)

Each sample was attached to the ends of the tensile testing machine by jaws dedicated to handle soft tissue to prevent inadvertent movement (INSTRON 2716_015, force max 30kN with jaw face 0-0.25/25T/IN) [START_REF] Ollivier | Ropivacaine alters the mechanical properties of hamstring tendons: In vitro controlled mechanical testing of tendons from living donors[END_REF] . The positioning required 1/3 of the specimens' length in each jaw, the central 1/3 defining the initial length (L0) before traction. An increasing load (10 mm / min) was applied until the specimens' failed. A stress-strain curve was obtained for each specimen using the dimensions of the samples. Then, we calculated Young's modulus in the elastic phase of the testing curve. Moreover, tensile force at failure was noted.

Figure 3 compression test

Statistics

Prior to the initiation of the study a sample analysis estimated that 6 samples for each group will be necessary to be powered (80%) to distinguish ∆: 5±3 nm Young's modulus values.

Patients characteristics were expressed using the appropriate descriptive statistics for the type of variables. Descriptive statistics included mean with SD, or median with interquartile range, as appropriate, for continuous variables. The Student t tests were used to compare the distribution of continuous parameters between groups (or the Mann-Whitney test when the data were not normally distributed or when the homoscedasticity assumption was rejected).

All reported p values were 2-sided, with a significance threshold of \.05. Statistical analysis was performed using SPSS/JMP software (version 13; Microsoft software).

Results :

N: Newton

With the number available we did not find any significant difference regarding Force at failure between the different groups, the mean difference being 78.3N IC95% 16.02-131.33

between cryopreserved and frozen specimens (p=0.186) and 40.5 IC95% 28.95-107.25 and between cryopreserved and Frozen+Irradiated specimens (p=0.199) (Table 4)

The analysis of stress-strain curve between groups revealed a slow-slope curve with a nonabrupt rupture (ductile material) for cryopreserved samples (Figure 5A). A clear rupture of the stress-strain curve was observed for frozen and frozen + irradiated samples (more fragile material) (Figure 5B).

In addition, failure seemed to happen quicker for the frozen storage and frozen + irradiated specimens than in cryopreserved samples where the failure was more gradual, which is most probably due to the delamination of the fibers.

Strain

DISCUSSION

The key finding of this study is that Cryopreservation allows for more elastic and less fragile tissue than the simple freezing or freezing plus irradiation. We rejected our hypothesis that all preservation methods will result in similar biomechanical properties. We observed a significant change in the Young's modulus in both compression and traction testing when comparing Cryopreserved and Frozen specimens. These findings were more obvious when comparing differences between Cryopreserved and Frozen + irradiated specimens. All of our findings might be explained by an increased rigidity of the meniscal tissue related to the freezing and/or irradiation procedures.

The relatively large variability in tensile and compression stiffness amongst different preservation processes is multifactorial. In general, the tensile mechanical properties of biological materials depend on the relative contents of major extracellular matrix constituents, the organization of the matrix constituents and the interactions of these constituents meniscal.

Prior studies have reported that different preservation methods can alter meniscal ultrastructure [START_REF] Gelber | Freezing causes changes in the meniscus collagen net: a new ultrastructural meniscus disarray scale[END_REF][START_REF] Gelber | Cryopreservation does not alter the ultrastructure of the meniscus[END_REF] , which corroborates the differences we saw between cryopreservation, freezing and freezing + irradiation.

Whilst conducting this study we were also able to examine the meniscal Tensile Force at Failure and rupture profile of the tensile strain-curve. This is also defined as the ability of collagen tissue to absorb energy until it fractures. The Tensile Force at Failure of the Frozen and Frozen + irradiated samples were lower than for cryopreserved samples even if this difference was not statistically significant. This decrease in Tensile Force at failure could lead to more frequent lesions of Frozen and Frozen + irradiated grafts during transverse stresses occurring during flexion-extension movements. [START_REF] Lento | Meniscal injuries: A critical review[END_REF] .

Our analysis of the stress-strain curves demonstrates that the cryopreserved meniscal tissue has a very gradual rupture profile reflecting a "ductile material", where Frozen and Frozen + irradiated samples, present an acute rupture often found in "fragile material". This means that cryopreserved samples have the ability to deform without breaking at higher absorbed energy levels than frozen samples and frozen + irradiated samples during extreme traction [START_REF] Nawathe | Theoretical effects of fully ductile versus fully brittle behaviors of bone tissue on the strength of the human proximal femur and vertebral body[END_REF] .

No data was found in the literature with regards to estimating the elasticity's modulus of fresh meniscus (in compression or traction), or the force at failure.

Regarding tensile elasticity modulus, the available data is summarized in the table 5.

Mean tensile elasticity's modulus (MPa) Our values are slightly lower than elastic moduli presented in similar published literature.

Those differences can be explained by the fact that most of the studies [START_REF] Bursac | Influence of donor age on the biomechanical and biochemical properties of human meniscal allografts[END_REF][START_REF] Tissakht | Tensile stress-strain characteristics of the human meniscal material[END_REF] , utilized samples harvested from deceased donors without any information on the sampling sequences and the storage time. In our study, all samples were from living donors. In order to limit the deleterious effects of prolonged exposure to ambient temperature, the samples were immediately placed in a Cryo-kit at 8 ° C and the preservation process was carried out in less than 6 hours [START_REF] Fölsch | Effect of Storage Temperature on Allograft Bone[END_REF] . Using tissue from living donors instead of cadaveric tissue avoids bias related to death-induced hypoxia which could adversely affect the biomechanical tissue properties [START_REF] Makris | Developing functional musculoskeletal tissues through hypoxia and lysyl oxidase-induced collagen cross-linking[END_REF] .

In Ahmad et Al Study 1 , meniscus samples came from a patient with a tumor near the knee whom required a prosthetic replacement. No information was disclosed regarding possible radiotherapy treatment received, which would likely modify the biomechanical properties of the meniscus. In these three studies [START_REF] Ahmad | Cryopreservation versus fresh frozen meniscal allograft: A biomechanical comparative analysis[END_REF][START_REF] Bursac | Influence of donor age on the biomechanical and biochemical properties of human meniscal allografts[END_REF][START_REF] Tissakht | Tensile stress-strain characteristics of the human meniscal material[END_REF] no information was provided on the freezing process utilized, in particular the rate of descent of temperature, which has been described as a factor that may cause tissue damage [START_REF] Pegg | Mechanisms of freezing damage[END_REF] .

For compression testing, the only data identified from the literature comes from Chia et Al'.s study [START_REF] Chia | Compressive moduli of the human medial meniscus in the axial and radial directions at equilibrium and at a physiological strain rate[END_REF] which described a highly variable Young's Modulus (between 0,135 and 1,130 MPa) according to the preconditioning strain level (3%, 6%, 9% or 12% strain). In this study only ten cadaveric medial menisci were studied (in our study we only considered lateral menisci).

The authors did not indicate the time between death and freezing, the existence of degenerative or traumatic pathology, or the freezing process used. These differences may contribute and explain the greater variability of these published results in comparison to our conducted study.

One of the limitations of our study is the lack of fresh tissue group. However, it was impossible to obtain three different samples from the same meniscus because the amount of material was insufficient to perform the mechanical tests. More, testing fresh tissue suppose to be able to create and attach specimens into the loading device before tissue's ischemia. We did not found solutions in the actual literature to avoid this limitation. Most of the authors freezed their specimens before testing and do not estimate fresh tissue properties.

We recognize another limitation of our study, the mean age of our patients in which specimens were harvested were in comparison older than donors in others studies (average age 63.8 years in our study versus 53,5 in the register [START_REF] Cohen | Deceased Organ Donor Characteristics and Organ Utilization in Israel, 2004-2013[END_REF] ). Because of this, menisci evaluated during our analyses might have been altered by aging and degenerative processes. We tried to avoid limitation related to this methodological bias by excluding menisci with significant MIR's lesion and studying only non-arthritic joints (lateral compartment) from subjects suffering from only medial femoral-tibial degeneration. It's also described by Bursac et Al 2 that there are no significant correlations, between either the biochemical composition or the tensile mechanical properties and donor age of lateral or medial menisci. . Another difficulty encountered in this study was the creation of 2 samples from the same meniscus. Although there is no data in the literature that asserts that the superior and inferior parts of a meniscus have different biomechanical properties, we have randomly assigned each fragment (superior or inferior) in each group to limit this potential bias.

Finally, our study only approximates the physiological biomechanical environment of the meniscus. The compression tests simulate the loading of the meniscus during walking and thus its ability to absorb axial shocks during several loading cycles [START_REF] Fithian | Material properties and structure-function relationships in the menisci[END_REF][START_REF] Donahue | The sensitivity of tibiofemoral contact pressure to the size and shape of the lateral and medial menisci[END_REF] . But the compression forces are not distributed uniformly over the entire surface of the meniscus and essentially only concerns the middle segment [START_REF] Makinejad | Preliminary analysis of knee stress in Full Extension Landing[END_REF] . Our tensile tests simulate the transverse stresses applied to the horn-root junction of the meniscus during flexion-extension movements [START_REF] Yao | Magnetic resonance image analysis of meniscal translation and tibio-menisco-femoral contact in deep knee flexion[END_REF] . But in-vivo tensile strains are predominantly located at the root-horn junction, where the meniscus is adherent to the tibial plate [START_REF] Yao | Magnetic resonance image analysis of meniscal translation and tibio-menisco-femoral contact in deep knee flexion[END_REF] . We tried to reproduce this anatomical representation by placing the fixed point of the jaws at the ends of the menisci, near the insertion of the roots. During weightbearing and movement, the menisci are normally subjected to a combination of tension, compression, and shear forces. Shear forces could not be evaluated in this study because no device allowed to reproduce in vitro the impact of these forces. Thus, the ability of a meniscal allograft to withstand these forces after transplantation would appear to be a key element in the successful outcome of such a procedure.

Figure 1 :

 1 Figure 1 : Series' flow-chart Cy : cryopreservation Fr : Frozen

Figure 2

 2 Figure 2 Sample's preparation for the compression tests

Figure 4

 4 Figure 4 Tensile test

Figure

  Figure 5A Stress-strain curve of a cryopreserved sample

Table 1 Patient's characteristics

 1

		Age (yr)	Gender	Weight	Height	BMI
				(kg)	(cm)	(kg.m -2 )
	01	63	M	77		23.2
	02	65	M	82		23.7
	03	61	F	68		22.2
	04	64	F	56		22.4
	05	66	M	84		24.3
	06	67	M	79		24,1
	07	60	M	77		22.7
	08	59	F	63		24.3
	09	64	M	79		24.9
	10	62	F	57		22.5
	11	63	F	61		24,3
	12	61	F	63		22.7
	13	67	F	62		23.1
	14	63	F	56		22.2
	15	62	M	74		22.3
	16	69	M	77		24.0
	17	68	M	79		24.4
	18	62	M	77		24.6
	19	62	F	63		24.0
	20	64	F	59		21.2
	21	67	M	73		23.3
	22	68	F	64		23.8
	23	67	M	80		24.7
	24	61	F	68		23.8

BMI : body mass index

Table 3 - 4

 34

			Absolute value of	IC-95% (MPa)	P value
			Mean difference
			(MPa)
	Cryopreserved	Frozen	8.31	4.50-12.12 	p=0,008
	Cryopreserved	Frozen+ irradiated	33.59	29.78-37.39	p<0.001

)

A significant difference of the mean tensile elasticity's modulus was observed between Cy group and the Fr group (respectively 11.66 ± 0.97 MPa vs 19.97 ± 1.37 MPa; mean difference 8.31 ± 1.68 MPa with p = 0.008) A significant difference of the mean tensile elasticity's modulus was also noticed between the Cy group and the Fr group (respectively 11.66 ± 0.97 MPa f vs 45.25 ± 1.39 MPa; mean difference 33.59 ± 1.59 MPa with p<0,001) , Table

4

.

Table 3 Tensile Elasticity's modulus N: Newton

 3

			Absolute value of	IC-95% (N)	P value
			Mean difference (N)
	Cryopreserved	Frozen	78.33	16.02-131.33	p=0.186
	Cryopreserved	Frozen + irradiated	40.50	28.95-107.25	p=0.1993

Table 4 Force at Failure

 4

Table 5 summary of available data for the tensile elasticity modulus

 5

	Bursac et Al 2009 2	80.9 ± 24.6 20.3-129.1
	Frozen specimen from deceased donor
	Storage time: not disclosed
	Tissackh et Al 24 1995	72.85 ± 22.91 3.59-151.80
	Frozen specimen from deceased donor
	Storage time: not disclosed
	Ahmad et Al 2017 1	54.17 ± 19.54 NC
	Frozen specimen from living donor
	Storage time: 6 weeks

Compression test (Table 2)


Mathieu Emanuele Valea
email: valea@lirmm.fr

Da Silva
email: mdasilva@lirmm.fr

Giorgio Di Natale
email: dinatale@lirmm.fr

Marie-Lise Flottes
email: flottes@lirmm.fr

Sophie Dupuis
email: dupuis@lirmm.fr

Bruno Rouzeyre
email: rouzeyre@lirmm.fr

SECCS: SECure Context Saving for IoT Devices

Keywords: IoT, Security, Hardware Security, Context Saving

Energy consumption of IoT devices is a very important issue. For this reason, many techniques have been developed to allow IoT nodes to be aware of the amount of available energy. When energy is missing, the device halts and saves its state. One of those techniques is context saving, relying on the use of Non-Volatile Memories (NVM) to store and restore the state of the device. However, this information, as far as IoT devices deal with security, might be the target of attacks, including tampering and theft of confidential data. In this paper, we propose a SECure Context Saving (SECCS) approach that provides a context saving procedure and a hardware module easy to implement inside a System on Chip (SoC). This approach provides both confidentiality and integrity to all the CPU content saved into the target NVM.

I. INTRODUCTION

The Internet of Things (IoT) has known an extraordinary fast dissemination in the last years, leading to an alwaysincreasing number of devices connected to a network. Nonetheless, the access to the energy source can be difficult, according to the kind of infrastructure. Consequently, techniques have been developed, such as energy harvesting, which makes the device self-powered without needing any wired or battery-based power source. For this reason, these devices need to be designed in order to be robust against intermittent power supply. A common practice, called Context Saving, consists in saving the state of the device into a Non Volatile Memory (NVM) when the power supply cannot be guaranteed. The running process is resumed as soon as the energy is available by restoring the state from the NVM [START_REF] Hager | A scan-chain based state retention methodology for IoT processors operating on intermittent energy[END_REF].

More and more often, we witness the commercialization of IoT devices dealing with confidential and private data [START_REF] Mosenia | A Comprehensive Study of Security of Internet-of-Things[END_REF]. This establishes a need for security in many emerging IoT applications. We believe that this goes into contrast with the existing context saving techniques, which expose the content of the internal registers of the CPU to an external NVM without implementing security criteria. In fact, the interruption of the power supply can be maliciously triggered by an attacker in order to force the CPU to expose its content in convenient moments of the computation. In addition, NVMs can be observed and even tampered (possibly performing fault attacks) by any attacker that has physical access to the device, according to the implemented technology and the kind of NVM that is employed [START_REF] Sklavos | Hardware Security and Trust: Design and Deployment of Integrated Circuits in a Threatened Environment[END_REF].

We propose a SECure Context Saving (SECCS), based on a hardware module, which provides both confidentiality and integrity to all the CPU content that is saved into the target NVM. The module can be plugged into any SoC design and can be activated whenever the user wants the system to perform a secure context saving in the case of supply unavailability. Confidentiality is provided via encryption, while the integrity against memory tampering is provided via a Message Authentication Code (MAC) derived from the saved context.

II. SECURE CONTEXT SAVING

The SECCS module is interposed between the processor and the target NVM (Fig. 1). The processor monitors the supply voltage and, when needed, activates the context saving procedure. A Context Storing Phase (CSP) is activated when the supply power is going to run out and the context of the computation is moved out from the processor. The context data are encrypted using a stream cipher, and a MAC signature is also generated. The encrypted data and the signature are then stored into the target NVM and the system is turned off. The Context Loading Phase (CLP) is activated when the power supply is available again and the computation of the processor is restored by loading back the context of the processor. The context content is decrypted and the MAC signature is checked in order to verify the integrity of the recovered data. If the integrity check fails, that means that a tampering attempt has been performed on the NVM. The key generator (Fig. 2) produces two different secret keys during the CSP, one for the stream cipher and one for the MAC engine. The key generation process must be unpredictable in order to prevent the attacker from overcoming the encryption and integrity features. For this reason, a PUF-based architecture has been conceived. At first, a True Random Number Generator (TRNG) generates a random value. This value, stored into a dedicated NVM, is used as a challenge for the PUF to produce a response. The response obtained by the PUF is used as a secret key. During the CLP, the challenges, read from the NVM, are sent to the PUF in order to regenerate the same keys produced during the CSP. Even if the attacker reads the dedicated NVM of the key generator, he/she has only knowledge of the session challenges. Due to the unpredictability of the response given by the PUF, he/she is not able to rebuild the keys. The stream cipher performs encryption of context data coming from the processor during the CSP, and decryption of data coming from the target NVM during CLP. The stream cipher performs an XOR operation between the input data and the keystream generated by a Pseudo Random Generator (PRG). The PRG takes as input an initialization value, called seed, which is the secret key of the stream cipher. The key generator provides a different key each time a new encryption session starts. The context of the processor is encrypted and stored into the NVM. When the system is powered off, no secrets are revealed to an attacker trying to read out the content. During the CLP, context data are recovered from the target NVM after decryption and reintroduced inside the processor. The stream cipher is used with the same secret key used during the CSP.

The MAC engine is used to provide a signature of the context data. During the CSP, the signature is computed and stored into the target NVM together with the encrypted context data. During the CLP, the signature is read from the target NVM and compared with the signature computed from the decrypted context data. The MAC module verify if the two signatures are equal to ensure the integrity of the context data. The MAC module uses a secret key in order to compute the hash function of the data. With the same principle as the stream cipher key, the key generator generates a new key during the CSP and reuses the same during the CLP.

Table I reports the cost of an implementation that uses SHA-256 engine as MAC module, the Trivium stream cipher, a TRNG from the Synopsys DesignWare IP library and an Arbiter PUF.

III. CONCLUSION

This paper proposes a solution for IoT devices using a microprocessor and requiring security. We consider a system exploiting context saving in external non-volatile memories (NVM), activated when the available energy is not enough to continue the execution of the processes. We want to prevent attacks on the saved state of the device, including tampering and fault attacks. We proposed a SECure Context Saving (SECCS) providing a hardware module easy to implement inside a System on Chip (SoC). This solution ensures both confidentiality and integrity to all the CPU content saved into the target NVM due to the context saving procedure. The proposed solution can have a large impact on the area overhead of the system. However, the need for security cannot be ignored in many applications. For this reason, we believe that scarifying a part of the power budget can be necessary for higher security.

Fig. 1 .

 1 Fig. 1. Architecture of the SECCS module.

Fig. 2 .

 2 Fig. 2. Architecture of the key generator.

TABLE I .

 I AREA COST OF SECCS MODULE

	Submodule	Area (gate equivalent)
	TRNG	15000
	PUF	516
	MAC	10763
	Stream cipher	2016

ACKNOWLEDGMENT

This work has been partially funded by the French government under the framework of the PENTA HADES ("Hierarchy-Aware and secure embedded test infrastructure for Dependability and performance Enhancement of integrated Systems") European project.


Jessica Hanna

Sandy Rihana

David Helbert
email: david.helbert@univ-poitiers.fr

Rita Zrour

Philippe Carré

Carole Guillevin

A Wavelet-based Method for the Metabolite Detection and Quantification in Proton Magnetic Resonance Spectroscopy

Keywords: Magnetic resonance spectroscopy (MRS), signal processing, continuous wavelet transforms, quantification, peak detection

Purpose: In healthy tissue, metabolites are present in steady-state concentrations typical for that specific tissue. Metabolite concentrations may shift due to stress, functional disturbances, tumors or metabolic diseases. These changes are detectable with MRS, and provide valuable information for both diagnosis and therapeutic surveillance. Various methods have been developed to quantify the metabolite concentrations using methods ranging from the simple integration of spectral peak to complex algorithms.

Theory and Methods: The purpose of this work is to develop an analysis system for in vivo NMR spectroscopy for brain metabolites quantification based on continuous wavelet transforms without prior knowledge. Tests are done on both simulated and real in vivo MRS signals using spectroscopic data acquired in 16 healthy subjects (range 20-50) using 3T MR system.

Results: Results show that even with the presence of low SNRs and baseline, the proposed method is able to derive the parameters such as the frequencies, the amplitudes and the damping factors of metabolites directly from the raw data and without any beforehand preprocessing or prior knowledge.

Conclusion:

The CWT analysis has shown to be accurate, robust and in agreement with the time domain fitting method AMARES for the quantification of short echo time in vivo MRS data.

Introduction

Nowadays, Magnetic Resonance Spectroscopy is a non-invasive diagnostic test commonly used in medicine for measuring the biochemical changes in the brain, precisely in localizing tumors and consequently helping clinicians to detect tissue changes in stroke and epilepsy and to optimize the appropriate treatment. The first in vivo MRS was applied on Phosphorus, 31P, but now many other nuclei are detected by this modality such as Proton, 1H, Carbon, 13C, Fluorine, 19F, Sodium, 23Na and others, however 1H MRS predominates because of the high natural abundance of protons in human body, and also due to the high number of information contained in 1H MRS spectrum [START_REF] Laudadio | Subspace-based quantification of magnetic resonance spectroscopy data using biochemical prior knowledge[END_REF].

There are different metabolites, or products of metabolism, that can be measured to differentiate between tumor types: Amino Acids, Lipid, Lactate, Alanine, N-acetyl aspartate, Choline, Creatinine, Myoionisotol. mental. Unfortunately, in vivo studies of MRS has a number of drawbacks such as low Signal to Noise Ratio (SNR) due to the weak concentrations of the detected metabolites, poor homogeneity of the magnetic fields, macromolecular baseline and many other imperfections which make it very difficult to achieve accurate measurements [START_REF] Jiru | Introduction to post-processing techniques[END_REF].

The choice of an appropriate quantification method is crucial to estimate the intrinsic parameters of the signals and convert them into biochemical quantities. In fact the quantification methods can be divided into three main categories: time-domain methods, frequency-domain methods [START_REF] Poullet | Frequencyselective quantitation of short-echo time 1 h magnetic resonance spectra[END_REF][START_REF] Pravat | In vivo proton magnetic resonance spectroscopic signal processing for the absolute quantitation of brain metabolites[END_REF] and time-frequency domain methods [START_REF] Suvichakorna | Wavelet-based Techniques in MRS[END_REF]. In the time domain, the quantification methods can be classified into two main categories: iterative and non-iterative methods [START_REF] Poullet | Mrs signal quantitation: a review of time-and frequency-domain methods[END_REF]. The iterative approaches, such as the NLLS (Non-linear least square) methods, use the local or global optimization to reduce the difference between the model function and the MRS data. These methods allow the inclusion of prior knowledge such as the frequencies, the damping factors and the phases of certain metabolites. VARPRO (VARiable PROjection) is one of these time-domain methodologies [START_REF] Van Der Veen | Accurate quantification of in vivo31p nmr signals using the variable projection method and prior knowledge[END_REF] which in turn was improved by AMARES (Advanced Method for Accurate, Robust and Efficient Spectral) [START_REF] Vanhamme | Improved method for accurate and efficient quantification of mrs data with use of prior knowledge[END_REF][START_REF] Naressi | Java-based graphical user interface for the mrui quantitation package[END_REF]. This latter allows the inclusion of more prior knowledge, extracted either from phantoms or in vitro data, in order to enhance the efficiency and the overall accuracy.

AMARES performs fitting of Lorentzian, Gaussian or Voigt models to the signal [START_REF] Van Den Boogaart | Quantitative data analysis of in vivo mrs data sets[END_REF]. This method is supposed to give good results for a spectrum where the peaks are well separated. However if the spectrum is corrupted with noise and the nuisance peaks have large amplitude or are close to the metabolic peaks, this method will fail [START_REF] Knijn | Frequency-selective quantification in the time domain[END_REF]. Other iterative methods exists, they rely on a metabolic basis set [START_REF] Ratiney | Time-domain semi-parametric estimation based on a metabolite basis set[END_REF] for example the AQSES (Accurate Quantitation of Short Echo time domain Signals) [START_REF] Poullet | An automated quantitation of short echo time mrs spectra in an open source software environment: Aqses[END_REF] or QUEST (QUantum ESTimation). On the other hand, the non-iterative methods use either the linear prediction principle or the state space theory to derive the amplitudes of the metabolites present in the MRS spectrum [START_REF] Barkhuijsen | Application of linear prediction and singular value decomposition (lpsvd) to determine nmr frequencies and intensities from the fid[END_REF].

In the frequency domain, the quantification of metabolites can be also divided into two classes: the non-interactive methods which are based on the integration of areas under the peaks of interest; these tools allow good quantification when the peaks in the spectrum are well separated, however this is not the case in the in vivo studies. Therefore, in the frequency domain, the interactive methods which use the nonlinear least square fitting approach are more used [START_REF] Provencher | Automatic quantitation of localized in vivo1h spectra with lcmodel[END_REF]. Many frequency domain fitting algorithm exist, such as the LC-Model, which also allow the inclusion of prior knowledge [START_REF] Landini | Advanced image processing in magnetic resonance imaging[END_REF][START_REF] Aa De | Improved quantification of in vivo1h nmr spectra by optimization of signal acquisition and processing and by incorporation of prior knowledge into the spectral fitting[END_REF].

strong prior knowledge to provide good quantification of the metabolites and many of them are user dependent. Therefore the main goal of this work is to develop an automatic analysis system for in vivo MRS based on continuous wavelet transform allowing good quantification of the metabolites and operating directly on the raw data without any preprocessing beforehand or user interaction. This method is divided into two main parts: peak detection and quantification. To evaluate its performance both simulated and real MRS signals were used. Note that this tool is totally automatic and does not require any prior knowledge.

The paper is organized as follows. In the next section, the proposed automatic peak detection algorithm is introduced along with the mathematics behind the Continuous Wavelet transform used for MRS quantification and the result obtained for some simulated MRS signals used to evaluate the robustness of this method in different conditions. In the following section, the results for in vivo MRS signals are presented and discussed. These tests were conducted in order to validate the proposed algorithm. Finally the main conclusion and the perspectives were formulated.

Theory Time-Frequency Methods

Methods based on the time-frequency domain have been developed for analyzing MRS signals and present some advantages over the previous mentioned methods. These techniques are based either on the WT (Wavelet Transform) or on the STFT (short time Fourier transform); both will give a time-frequency representation of the FID signal [START_REF] Suvichakorn | Quantification method using the morlet wavelet for magnetic resonance spectroscopic signals with macromolecular contamination[END_REF]. A number of methods based on wavelet transform have been suggested for MRS quantification by different authors; Continuous wavelet transform (CWT) have been proposed by [START_REF] Antoine | Time-frequency and time-scale approach to magnetic resonance spectroscopy[END_REF][START_REF] Suvichakorna | Wavelet-based Techniques in MRS[END_REF] and discrete wavelet transform (DWT) such as the wavelet packet decomposition has been proposed by [START_REF] Luca | A wavelet packets decomposition algorithm for quantification of in vivo 1 h-mrs parameters[END_REF]. Nevertheless the DWT is not well adjusted to the underling physics of MRS, using it will lead to some difficulties. The principle of the discrete wavelet transform computation is indeed based on downsampling and upsampling operators in a filter bank. This operators do not allow to the transform to be translation-invariant [START_REF] Mark | The discrete wavelet transform: wedding the a trous and mallat algorithms[END_REF].

While the CWT is primarily a tool for analysis and feature determination, the DWT is the preferred technique for data compression and signal synthesis. Since the applications in NMR spectroscopy consist mainly in detecting particular features in the spectra, the CWT will be in general better adapted than the DWT [START_REF] Daubechies | Ten lectures on wavelets[END_REF][START_REF] Antoine | Twodimensional wavelets and their relatives[END_REF].

Wavelets Principles

A wavelet is a normalized function ψ ∈ L 2 (R) with a null mean. A family of time-frequency elements can be obtained by dilating with a factor a and by translating the wavelet with a factor τ :

ψ a,τ (t) = 1 √ a ψ t -τ a (1)
The wavelet coefficient W s (a, τ ) of s ∈ L 2 (R) at time a and scale τ is obtained by projecting the signal s onto the family {ψ a,τ (t)} of functions obtained by dilatation of a and by translation of τ of the mother wavelet ψ :

W s (a, τ ) = R s(t)ψ * a,τ (t)dt (2)
The wavelet transform denoted in the Eq. 1 is equivalent to a filter process. And the obtained coefficients indicate the correlation between the signal and the selected mother wavelet. Several families of mother wavelets exist and each type has its own time-frequency structure.

Simulated MRS Signals

To assess the performance of the suggested method in both ideal and contaminated environment where noise and baseline are present, we used simulated MRS signals with a Lorentzian lineshape denoted by Eq. 3.

s(t) = Ae -Dt e -i(ωt+φ) , (3)
where A is the amplitude, D the damping factor, φ and ω are the phase and the frequency of the signal respectively.

Methods

Theoretically, the spectrum of MRS is composed of pure Lorentzian profiles. Nevertheless, in real environment, the MRS spectrum might be corrupted by a wideband baseline signal generated by macromolecules and by the noise. Therefore the actual equation of the MRS signal containing one frequency component, in time domain, is represented by the following equation Eq. 4:

y(t) = s(t) + B(t) + (t), (4)
where y(t) is the experimental MRS signal in time domain, s(t) is the Lorentzian signal containing one frequency component, B(t) is the modeled baseline and (t) is the added Noise.

The baseline is characterized by a wide range of frequency in the MRS spectrum caused by the contribution of the macromolecules and thus it is supposed to decay faster than the pure signal. It can be modeled using 50 Lorentzian profiles with random amplitudes and large damping factor or using the cubic spline interpolation.

MRS signals quality could be affected by several sources of noise, such as the body noise, the noise originating from the electronics of the receiver and the thermal noise created by the coils.

The body noise, which is the result of electrolytes thermal variations inside the body, is considered as the main source of noise in MRS. This type of noise is usually characterized as being white, additive and Gaussian distributed [START_REF] Nishimura | Principles of magnetic resonance imaging[END_REF].

Real in vivo MRS Signals

In The MRS data considered in this project were acquired by a 3T whole-body system (Verio, Siemens, Erlangen, Germany) and were provided by the radiology department of CHU Poitiers (France). The MRS sequence was performed with a monovoxel short TE (TE: 35ms, TR: 1500ms) using a point-resolved single voxel spectroscopy (PRESS). A multiplanar reconstruction of 3D T1 volume was used to position the voxel in the region of interest. The sequence parameters were 156 signal averages, a number of samples of 1024, and a bandwidth of 1200 Hz. The voxel size was of 3.375 cm 3 . The common measures usually done in MRS studies, such as automatic shimming and eddy-currents compensation, were carried out for these acquisitions. Note that this data type is ideal for comparing and validating the proposed algorithm. Quantification for MRS data was attempted for N-acetylaspartate (NAA), Creatine (Cr), Choline (Cho) and Myo-inositol (Myo).In this study we examined the ratio of these metabolite to compare at the real value.

Automatic Peak Detection

The frequencies of the different metabolites could be considered as prior knowledge, however, in order to make the quantification method more suitable for real MRS signals analysis, where the frequency of each peak could slightly drift from the theoretical one, an automatic peak detection algorithm was proposed.

The aim of this method is to identify the location of each peak, using the continuous wavelet transform. For peak detection, the mother wavelet needs to have the main characteristics of a peak which consists of:

• Approximate symmetry,

• One main positive peak.

So for this analysis, we picked the Mexican hat wavelet (or Ricker wavelet) as mother wavelet [START_REF] Du | Improved peak detection in mass spectrum by incorporating continuous wavelet transform-based pattern matching[END_REF]. In fact the Mexican Hat is very suitable for edge detection, it is widely used to characterize the singularities of a signal and therefore it allows a geometric analysis. It is defined as the negative normalized second derivative of a Gaussian function.

The procedure of the peak detection is described as follow: First a continuous wavelet transform of the MRS spectrum is performed using the Mexican hat as mother wavelet and well-adapted scales to detect the peaks of interests then the scalogram is constructed and for every indices column the sum of the coefficients is calculated. The obtained values are used to build a 1D function. After that a standard peak detection is performed on this 1D function with one threshold: the peak height.

To choose the threshold, we used the noise level calculation method proposed by AUTOPSY [START_REF] Koradi | Automated peak picking and peak integration in macromolecular nmr spectra using autopsy[END_REF]; all the peaks with an amplitude below this level are ignored. The noise level calculation algorithm is described as follow: First, the 1D function is splitted into small windows and for each window a noise level value is computed. The length of each slice is usually 5 percent of the total length of the spectrum so that the standard deviation inside the window takes minimal value.

After that we distinguish between two noise levels: the base noise level θ b = min(θ i ), where θ i is the standard deviation of slice i, and the additional noise levels,

θ i = θ 2 i -θ 2 b .
The first exist in the entire spectrum and the latter can exist in each window. Next, the noise level is computed from the base noise level and the additional noise levels, and this value is considered the threshold which has only one frequency:

s(t) = Ae -Dt e -i(ωst+φ) . (6)
The 1D Fourier transform of the time signal is represented in Eq. 7 as

S(ω) = 2πAe iφ δ (ω -ω s + iD)) , ( 7
)
where D is the damping factor, φ the phase of the signal, ω s the frequency of the signal, A the amplitude of the signal and δ the Dirac delta function1 .

The Morlet wavelet denoted in Eq. 8 by g M (t):

g M (t) = 1 2 πσe -t 2 2σ 2 e iω 0 t , (8)
and

G M (ω) = e σ 2 2 (ω-ω 0 ) 2 (9)
where g M (t) is Morlet wavelet equation in time domain, G M (ω) is Morlet wavelet equation in frequency domain, ω 0 its frequency and σ its width. Morlet is considered among the wavelets which are well localized in the frequency space, it is build form a windowed Fourier atom and is very adapted to analyse the local energy distribution along the time or signal indice. The wavelet transform of a signal s(t) is given by the following equation Eq. 10:

S(τ, a) = 1 2π √ a R S(ω)G * M (aω)e -iωτ dω, ( 10
)
where a is the dilation parameter that represents the frequency of the signal, τ ∈ R is the translation parameter that specifies the time localization and G * M is the complex conjugate of G M (ω). Suvichakorn et al prove in [START_REF] Suvichakorna | Wavelet-based Techniques in MRS[END_REF] that the modulus of the WT at a r is defined by:

|S ar (τ )| = √ a r e σar D √ 2 2 |s(τ )| , (11)
where |s(τ )| = Ae -Dτ . Note that the scale here is computed according to the frequency of the metabolite.

ln

|S ar (τ )| = 1 2 ln a r + σa r D √ 2 2 + ln A -Dτ. (12)
Therefore the damping factor D is indicated by Eq. 13,

D = ∂ ∂τ ln |S ar (τ )| ( 13
)
The derivative is computed as the differences between adjacent elements of ln |S ar (τ )| along τ .

After computing the damping factor D we can now obtain the amplitude A of the signal denoted by the equation Eq. 14, [START_REF] Suvichakorna | Wavelet-based Techniques in MRS[END_REF]:

A = |s(t)| e Dt (14)

Illustration of the method robustness

To work closer to real acquisitions, experiments were done on a simulated signal containing 4 metabolites; Creatine (Cr) which is composed of two peaks at w=1332 rad/s and w=643 rad/s, Lipid (Lip09) at w=3037 rad/s, Glycerophosphocholine (GPc) at w=320 rad/s and Glycine (Gly) at w=2246 rad/s and to evaluate the robustness of this method in noisy environment and in the presence of macromolecular baseline both white Gaussian noise with SNR=10 dB, which almost matches the SNR measured in vivo and baseline model were added to the signal. Fig. 2 show the original spectrum before and after adding the noise and the baseline.

Fig. 3 shows the extracted amplitude versus the actual values. The results show that using a simple CWT method allows good estimation of the amplitudes of different metabolites contained in a single MRS spectrum.

Results

In this section, CWT analysis is applied to the acquired in vivo MRS signals, and the amplitudes of the four metabolites; NAA, Creatine, Choline and Myo-inositol, are derived using the following algorithm:

• The described peak detection algorithm is applied directly on the raw data.

• The analyzed signal contains more than 20 metabolites, therefore only the frequencies corresponding to the peaks of interest are automatically selected from the values obtained by the peak detection algorithm.

• MWT analysis is performed using Lorentzian lineshape.

• The parameters are derived and averaged in time in order to obtain smoother results. Then the amplitude of each metabolite is estimated.

• The metabolites ratios are calculated.

The bar charts in Fig. 4 show the metabolite ratios for the 16 patients obtained using the CWT approach and the mean value of these metabolite ratios along with their normal values in these three brain regions [START_REF] Shonk | Role of increased cerebral myo-inositol in the dementia of down syndrome[END_REF]. Statistics are provided for comparison in Tab. 2.

Discussions

The values of the metabolite ratios extracted using the CWT analysis from the 16 healthy volunteers are very homogeneous and very closed to the normal values. Here the CWT analysis shows its ability to extract the physical parameters directly from the raw in vivo MRS data without any preprocessing steps even when contaminated with noise and macromolecular baseline.

In the Tab. 2 we observe that standard deviations of computed metabolite ratios in the CCP and the Striatum are low. The t-tests shows that the distributions of patient values are similar at the distributions of the normal values except for Naa/CR in the CCP.

In addition this method is totally automatic and does not require any user interaction therefore it is well suitable for clinical applications and it has many advantages over the other MRS quantification methods such as the AMARES. In fact an AMARES analysis of the same data for the CCA region, presented in Tab. 3 and Fig. 5, shows less homogeneity compared with the CWT approach.

Note that strong prior knowledge is required by AMARES to obtain these ratios estimation along with numerous pre-processing steps. We also observe in Tab. 2 that the standard deviations of metabolite ratios in the CCA with our method is lower than those computed with AMARES presented in Tab. 3. Note that our method allows a good estimation for Naa/CR unlike AMARES which t-test rejects its estimation.

In addition, it is important to mention that these preprocessing steps used before the quantification might severely affect the analysis process, furthermore, removing the baseline beforehand and reducing the noise are unrecoverable, therefore if one of the peaks of interest in the MRS spectrum was removed by these preprocessing tools, it can never be recuperated in the later analysis, during the quantification.

In some cases, such as in the Striatum results for patient n o 5, the ratios diverge severely from the normal values and this is normal because in this spectrum the peaks are buried in noise. Note that, all the quantification method will give similar results in this case and the noise level here is considered unacceptable. So even though the analysis using this method could be performed automatically, this doesnt assure good results for severely distorted MRS acquisitions, hence the examination of results by a qualified spectroscopist or radiologist is necessary before interpreting the metabolic ratios.

Conclusions

In this work, an automatic MRS analysis system based on the Continuous Wavelet Transform was proposed. This method starts with a peak detection algorithm that identifies the location of each peak in the MRS spectrum. After that, the amplitudes of the metabolites of interest are estimated and the ratios are computed. Note that to select the right mother wavelet, the Mean Square Error we aim to compare this method to other existing methods such as Tarquin, AMARES, QUEST using data acquired from healthy patients and patients suffering from different pathologies and finally we aim to improve this method and make it suitable for Multivoxel studies. Moreover we propose introducing an adapted denoising method to increase the robustness of this method against the noise.

  order to validate the proposed algorithm, real in vivo signals are tested. 1H-MRS were performed on a sample of 16 healthy subjects (7 women, 9 men), their age was 32 years (range 20-50) for three different brain regions: Posterior Cerebral Cortex (CCP), Anterior Cerebral Cortex (CCA) and Striatum.

(

  MSE) was computed and based on the results, two different mother wavelets were considered, which gave the lowest values of the MSE: Mexican Hat for peak detection and Morlet for the quantification. According to the results, the CWT analysis has shown to be accurate, robust and in agreement with the time domain fitting method AMARES for the quantification of short echo time in vivo MRS data without any preprocessing beforehand or user interaction. As future work,

Figure 2 :

 2 Figure 2:

Figure 3 : 16

 316 Figure 3:

Figure 4 :

 4 Figure 4:

Figure 5 :

 5 Figure 5:

Table 1 :

 1 Comparison between the real values of the frequencies of the peaks and the detected ones.

		Detected Values 2 Real Values Error (in %)
	1	18.4462749	15	22.96
	2	239.801573	250	4.08
	3	313.586673	320	2.00
	4	387.371772	380	1.94
	5	510.346938	500	2.07
	6	657.917137	643	2.32
	7	953.057535	950	0.322
	8	1346.57807	1332	2.10
	9	2000.559998	2000	0.03
	10	3043.881305	3037	0.27
	11	4002.841648	4000	0.07

Table 2 :

 2 Metabolite ratios for the 16 healthy subjects in the CCP, Striatum and CCA, obtained using the CWT algorithm.

The Dirac delta function is defined by: δ(x) = +∞ if x = 0 else δ(x) = 0 and R δ(x)dx = 1.

for the peak detection:

where n is the number of slices.

Note that, this peak detection algorithm, based on the CWT, could be used directly on the raw MRS signals without any preprocessing steps and without removing the baseline. In fact, the baseline is assumed to be slow changing and monotonic around the peak area, therefore it will be directly suppressed while computing the CWT coefficients using a symmetric and zero-mean wavelet function, such as the Mexican Hat wavelet [START_REF] Du | Improved peak detection in mass spectrum by incorporating continuous wavelet transform-based pattern matching[END_REF]. To evaluate the robustness and the accuracy of this peak detection algorithm, a simulated signal of known frequency components was used.

The different steps of the proposed algorithm are summarized in the following Fig. 1 ) and baseline, along with its scalogram where the peaks are clearly observed.

By comparing the known frequencies of the 11 peaks and the identified one, as shown in Tab. 1, we can clearly see that the we were able to identified all the peak with an error range between 0.03 % and 23 %. Even with the high level of error (23 %), which occurs when the frequency of the peak is very low (at 15 rad/s), the algorithm seems to be applicable even when the MRS signals are buried in noise and contaminated with macromolecular baseline. Note that the statistics were done on 50 simulated MRS signals corrupted with random white Gaussian noise and baseline modeled using the cubic spline interpolation.

Quantification of a Lorentzian Signal

Identification of the Lorentzian signal by the Morlet wavelet Among the different types of wavelet transforms, using the continuous wavelet transform will allow the estimation of signals amplitudes directly from the modulus and the phase of the WT [START_REF] Suvichakorn | Quantification method using the morlet wavelet for magnetic resonance spectroscopic signals with macromolecular contamination[END_REF] and thus no linear model will be required as in the discrete wavelet transform [START_REF] Dancea | Automated protein nmr structure determination using wavelet de-noised noesy spectra[END_REF] . Next we will explain the mathematics behind the Morlet wavelet transform and how it is used to extract the different parameters of in vivo MRS signals [START_REF] Suvichakorna | Wavelet-based Techniques in MRS[END_REF].

Lets take a Lorentzian signal s(t), that models the time decay signal for one a specific metabolite