MSc M Attias

PhD ; A Bonnefoy-Mazure

MD ; G De Coulon

PhD ; L Cheze

PhD ; S Armand

Influence of different degrees of bilateral emulated contractures at the triceps surae on gait kinematics: The difference between gastrocnemius and soleus

Keywords: contracture, gait, exoskeleton, simulation, gastrocnemius, soleus

Introduction: Ankle plantarflexion contracture results from a permanent shortening of the muscle-tendon complex. It often leads to gait alterations. The objective of this study was to compare the kinematic adaptations of different degrees of contractures and between isolated bilateral gastrocnemius and soleus emulated contractures using an exoskeleton.

Methods: Eight combinations of contractures were emulated bilaterally on 10 asymptomatic participants using an exoskeleton that was able to emulate different degrees of contracture of gastrocnemius (biarticular muscle) and soleus (monoarticular muscle), corresponding at 0°, 10°, 20°, and 30° ankle plantarflexion contracture (knee-flexed and knee-extended). Range of motion was limited by ropes attached for soleus on heel and below the knee and for gastrocnemius on heel and above the knee. A gait analysis session was performed to evaluate the effect of these different emulated contractures on the Gait Profile Score, walking speed and gait kinematics.

Results: Gastrocnemius and soleus contractures influence gait kinematics, with an increase of the Gait Profile Score. Significant differences were found in the kinematics of the ankles, knees and hips. Contractures of soleus cause a more important decrease in the range of motion at the ankle than the same degree of gastrocnemius contractures. Gastrocnemius contractures cause greater knee flexion (during the stance phase) and hip flexion (during all the gait cycle) than the same level of soleus contractures.

Conclusion:

These results can support the interpretation of the Clinical Gait Analysis data by providing a better understanding of the effect of isolate contracture of soleus and gastrocnemius on gait kinematics.

Introduction

Contracture is defined as the inability of a joint to move through its full range of motion and an excessive resistance during passive mobilization of this joint. The expression "soft tissue contracture" is often used to define contracture because the structures involved are mainly muscles, tendons, aponeurosis, and, but also ligaments and capsules, for which the extensibility may have been limited and the stiffness increased [START_REF] Gracies | Pathophysiology of spastic paresis. I: Paresis and soft tissue changes[END_REF]. Contracture is involved in many neurological conditions (e.g., cerebral palsy, multiple sclerosis, spinal cord injury, stroke) and can impair walking [START_REF] Ballaz | Ankle range of motion is key to gait efficiency in adolescents with cerebral palsy[END_REF][START_REF] Hoang | Prevalence of joint contractures and muscle weakness in people with multiple sclerosis[END_REF][START_REF] Fergusson | The epidemiology of major joint contractures: a systematic review of the literature[END_REF]. Among contractures, ankle plantarflexion contracture (APC) is one of the most common causes of gait deviations in many conditions (cerebral palsy [START_REF] Tylkowski | Outcomes of Gastrocnemius-soleus Complex Lengthening for Isolated Equinus Contracture in Children With Cerebral Palsy[END_REF], neuropathy [START_REF] Kwon | Comparison of muscle activity during walking in subjects with and without diabetic neuropathy[END_REF] and muscular dystrophy [START_REF] Armand | A comparison of gait in spinal muscular atrophy, type II and Duchenne muscular dystrophy[END_REF]) and can lead to other complications (e.g., metatarsalgia, neuropathic ulceration, plantar fasciitis and Charcot midfoot breakdown) [START_REF] Abdulmassih | Triceps surae contracture: Implications for foot and ankle surgery[END_REF]. Gait with APC is characterized by an absence of a first rocker (which enables a heel-toe pattern at initial contact [START_REF] Perry | Gait Analysis: Normal and Pathological Function[END_REF]) and a limitation of dorsiflexion during swing [START_REF] Houx | Simulation of unilateral equinus using an adjustable orthosis in children: design, feasibility and biomechanical effects[END_REF], causing an inadequate foot clearance [START_REF] Leung | The impact of simulated ankle plantarflexion contracture on the knee joint during stance phase of gait: A within-subject study[END_REF]. APC is caused by a contracture of the triceps surae that is composed of two muscles: gastrocnemius (a biarticular muscle which passes through on the ankle and knee joints) and soleus (a monoarticular muscle which passes through only on the ankle joint) [START_REF] Wren | Gastrocnemius and soleus lengths in cerebral palsy equinus gait-differences between children with and without static contracture and effects of gastrocnemius recession[END_REF][START_REF] Matjacic | Biomechanical characterization and clinical implications of artificially induced toe-walking: Differences between pure soleus, pure gastrocnemius and combination of soleus and gastrocnemius contractures[END_REF].

To rectify gait deviations, it is necessary to understand gait deviations; and to distinguish between primary deviations (directly resulting from the pathology) and secondary deviations (compensatory mechanisms) [START_REF] Schmid | Secondary gait deviations in patients with and without neurological involvement: a systematic review[END_REF]. Clinicians need to understand the influence of contracture of individual muscle to evaluate its biomechanical impact in terms of primary deviations and secondary deviations (compensations). Different approaches have been used to elucidate the effect of APC on gait and are described in a systematic review [START_REF] Attias | Effects of contracture on gait kinematics: A systematic review[END_REF]. These approaches include a comparison of APC in patients and matched healthy subjects (pathological contracture versus healthy controls) [START_REF] Gaudreault | Evaluation of plantar flexion contracture contribution during the gait of children with Duchenne muscular dystrophy[END_REF][START_REF] Svehlik | Genu recurvatum in cerebral palsy -Part A: Influence of dynamic and fixed equinus deformity on the timing of knee recurvatum in children with cerebral palsy[END_REF], comparison of patient's gait before and after treating APC (pre-and post-kinematics after surgical muscle lengthening) [START_REF] Chimera | The effect of isolated gastrocnemius contracture and gastrocnemius recession on lower extremity kinematics and kinetics during stance[END_REF][START_REF] Kadhim | Crouch gait changes after planovalgus foot deformity correction in ambulatory children with cerebral palsy[END_REF], and emulation of contracture(s) with an exoskeleton or an orthosis (simulated contracture versus healthy controls) [START_REF] Houx | Simulation of unilateral equinus using an adjustable orthosis in children: design, feasibility and biomechanical effects[END_REF][START_REF] Matjacic | Biomechanical characterization and clinical implications of artificially induced toe-walking: Differences between pure soleus, pure gastrocnemius and combination of soleus and gastrocnemius contractures[END_REF][START_REF] Attias | Faisabilité et ep odu ti ilité d'u exos uelette apa le de épli ue des o t a tu es us ulai es à la a he: application sur les gastrocnémiens et soléaires[END_REF][START_REF] Romkes | An electromyographic analysis of obligatory (hemiplegic cerebral palsy) and voluntary (normal) unilateral toe-walking[END_REF][START_REF] Attias | Feasibility and reliability of using an exoskeleton to emulate muscle contractures during walking[END_REF].

The systematic review by Attias et al. [START_REF] Attias | Effects of contracture on gait kinematics: A systematic review[END_REF] showed that it is difficult to isolate a contracture because it is always associated with other impairments, such as spasticity or muscle weakness [START_REF] Leung | The impact of simulated ankle plantarflexion contracture on the knee joint during stance phase of gait: A within-subject study[END_REF][START_REF] Herzenberg | Isolated recession of the gastrocnemius muscle: the Baumann procedure[END_REF]. A mixed of several impairments makes it difficult to establish a clear relationship between the impairments and the gait deviations. The isolation of a specific impairment (contracture) would permit to better establish this relationship. Two previous studies have compared the effects of gastrocnemius and soleus contractures on gait [START_REF] Matjacic | Biomechanical characterization and clinical implications of artificially induced toe-walking: Differences between pure soleus, pure gastrocnemius and combination of soleus and gastrocnemius contractures[END_REF][START_REF] Olensek | Muscle contracture emulating system for studying artificially induced pathological gait in intact individuals[END_REF] by emulating these contractures unilaterally with an exoskeleton. They found that on the ipsilateral side, soleus contracture mainly influenced the ankle angle increasing ankle plantarflexion during gait, whereas gastrocnemius contractures influenced the ankle and knee angles (increase of ankle plantarflexion but less than soleus associated with increase knee flexion during gait).

However, no studies have investigated the effect of gastrocnemius and soleus contractures bilaterally whereas equinus is commonly a bilateral gait impairment [START_REF] Armand | Identification and classification of toewalkers based on ankle kinematics, using a data-mining method[END_REF]. In cerebral palsy patient, equinus is the 4 th gait impairment for diplegic patient [START_REF] Wren | Prevalence of specific gait abnormalities in children with cerebral palsy: influence of cerebral palsy subtype, age, and previous surgery[END_REF].

Hence, with the support of an exoskeleton to emulate contractures, the aim of this study was 1) to compare the kinematic adaptations of varying degrees of emulated contracture for the isolated bilateral gastrocnemius (biarticular muscle) and soleus (monoarticular muscle)

2) to compare the kinematic adaptations between isolated bilateral gastrocnemius (biarticular muscle) and soleus (monoarticular muscle) at the same degree of emulated contracture.

Method

Participants:

Ten healthy participants (6 females, 4 males) aged 27.9 years ± 3.2, with a height of 1.71 m ± 0.09 and weight of 64.0 kg ± 10.3 and no known neurologic or orthopedic problems, participated in this study. Ethical approval and the participant's informed consent were obtained prior to data collection.

Gait evaluation

The participants were equipped with 34 reflective markers aligned to anatomical and technical landmarks on the head, trunk and pelvis and bilaterally on the arms, thighs, shanks and feet according to the full-body Plug-in-Gait model [START_REF] Davis | A gait data collection and reduction technique[END_REF]. All participants were requested to walk along a 10-meter walkway at a spontaneous, self-selected speed and were equipped with the MIkE exoskeleton (Figure 1a), which the characteristics and reliability were reported in a previous study [START_REF] Attias | Feasibility and reliability of using an exoskeleton to emulate muscle contractures during walking[END_REF]. The main components of the exoskeleton are listed below in order to allow the understanding of this article. The exoskeleton was built to bilaterally embrace the pelvis, thighs, and shanks with plastic cuffs, with modified shoes that include attachment points. Contractures were induced by ropes attached to rings (see Figure 1b). The characteristics of the ropes were chosen to avoid a sudden stop and to mimic a progressive increase of stiffness at the limit of the ROM as reported for muscle contractures. Because muscle insertion points are usually deep and multiple, only the main muscle lines of action were used to define the ropes attached to the rings [START_REF] Attias | Feasibility and reliability of using an exoskeleton to emulate muscle contractures during walking[END_REF]. In addition, the exoskeleton was built to induce unilateral and bilateral contractures in relation to the following main muscles or muscle groups affected by contractures in the lower body and identified in the literature: hamstring, iliopsoas, hip adductor, rectus femoris, gastrocnemius, soleus, tibialis posterior and peroneus [START_REF] Attias | Feasibility and reliability of using an exoskeleton to emulate muscle contractures during walking[END_REF]. A cut was made in the plastic cuffs to enable reflective markers to be placed directly on the skin as required for Clinical Gait Analysis (CGA). CGA is a clinical examination enabling to get quantitative information on the patient's gait including generally video, spatio-temporal, kinematic, kinetic and EMG data [START_REF] Carcreff | Analyse quantifiée de la marche[END_REF]. This exoskeleton was used in the current study to emulate gastrocnemius and soleus contractures bilaterally. Each participant also walked without the exoskeleton for a control condition (CC). Kinematic recordings were performed with a twelve-camera motion analysis system (Oqus 7+, Qualisys, Göteborg, Sweden). A minimum of five gait cycles was averaged to produce a single angular displacement of the pelvis segments, hip, knee, and ankle joints.

To emulate contractures, we selected four degrees of contracture, 0°, 10°, 20°, and 30° of plantarflexion on both muscles (soleus and gastrocnemius), based on the study by Drefus et al. [START_REF] Drefus | Simulated Ankle Equinus Affects Knee Kinematics During Gait[END_REF] that simulated ankle equinus but with an ankle foot orthosis not allowing the differentiation of soleus and gastrocnemius. The 0° level is considered to be a mild contracture and the 30° level is considered to be a severe contracture according to our experience. To set the contractures, the examiner adjusted the rope length of the exoskeleton in the position used for standard physical examination [START_REF] Viehweger | Testing range of motion in cerebral palsy[END_REF] and controlled it with a goniometer (Figure 1b). For soleus (monoarticular muscle), the knee was flexed at 90° (with the aim to set the contracture following the clinical examination procedure [START_REF] Viehweger | Testing range of motion in cerebral palsy[END_REF]), and the plantarflexion of the ankle was adjusted according to the desired degree of contracture. The adjustment of the soleus contracture with the exoskeleton did not affect the knee because the attachment points for soleus emulation were on heel and below the knee respecting muscle insertions (Figure 1b). For gastrocnemius (biarticular muscles), the knee was extended at 0° and the same procedure was used. The knee was considered for the adjustment of the gastrocnemius contracture because the attachment points for gastrocnemius emulation were on heel and above the knee respecting muscle insertions (Figure 1b).

Data analysis and statistics

As non parametric tests are used, median and 1st and 3rd quartile are reported: median (1st quartile; 3rd quartile) First, to evaluate whether there were significant differences in the different degrees of contracture for each muscle (gastrocnemius and soleus from 0° to 30° plantarflexion), a Kruskal-Wallis test and post hoc with Bonferroni correction were performed on the Gait Profile Score (GPS) [START_REF] Baker | The gait profile score and movement analysis profile[END_REF] and walking speed (right and left sides together). CC and different degrees of emulated contracture (0°, 10°, 20° and 30° plantarflexion contractures) were compared with Wilcoxon tests considering Bonferroni correction.

Second, to evaluate the kinematic differences between gastrocnemius and soleus contractures, a Wilcoxon test with Bonferroni correction was performed between the same degrees of contracture in walking speed, GPS and fourteen kinematic parameters per side in the sagittal plane: range of motion (ROM) and mean position for pelvis angle; ROM and minimum flexion for hip angle; flexion at initial contact (IC), minimum in stance and ROM during the gait cycle for knee angles; dorsiflexion at initial contact (IC), maximum in stance and ROM during the gait cycle for ankle angles; and mean foot progression angle. MATLAB R2012b (MathWorks, Natick, Massachusetts, USA), the open-source Biomechanical ToolKit package for MATLAB [START_REF] Barre | Biomechanical ToolKit: Open-source framework to visualize and process biomechanical data[END_REF] and SPSS Version 23 (IBM, Armonk, NY, USA) were used for data analysis, statistics and figure creation.

Results

The comparisons between CC and different degrees of emulated contracture are shown in Table 1 for walking speed, GPS and kinematic parameters. Figure 2 depicts differences between each degree of contracture and CC for respectively gastrocnemius and soleus concerning the walking speed and GPS.

Comparison with CC:

Concerning the walking speed and GPS (Table 1 and Figure 2), significant differences were found for each muscle (gastrocnemius and soleus from contractures 0° to 30°). For gastrocnemius, the walking speed was decreased for contracture 30° compared to CC. The GPS was increased for contractures 20° and 30° compared to CC. For soleus, the walking speed was not different between the different degrees of contracture and CC. The GPS was increased for contracture 30° compared to CC.

Concerning the foot angle progression, more internal rotation was observed for contracture 30° for soleus muscle compared to CC (mean foot angle progression for CC:-5.5° (-11.2;-3.2) vs. for soleus 30°: 6.0 (-1.2; 9.9), p < 0.01).

Concerning the ankle joint, reduced dorsiflexion were observed for the dorsiflexion at initial contact for contractures 10°, 20° and 30° of gastrocnemius and soleus. In addition, reduced dorsiflexion were observed for maximum of dorsiflexion during the stance phase for contractures 10°, 20° and 30° of soleus and for contractures 20° and 30° of the gastrocnemius.

Concerning the knee joint, a decrease of ROM was observed for contracture 30° for soleus (CC: 67.2 (65.1; 69.4) vs. soleus 30°: 37.7 (33.9; 50), p < 0.01). For the gastrocnemius, an increase of flexion was observed for the flexion-extension at initial contact and a decrease of ROM for contractures 10°, 20° and 30°. In addition, reduced knee extension was observed in minimum of flexion during stance for contracture 0°, 10°, 20°, 30° for gastrocnemius compared to CC.

Concerning the hip joint, no significant differences were observed for soleus muscle.

However, a decrease of ROM were found for contractures of 0°, 20° and 30° and reduced hip extension was observed in minimum flexion during the stance phase for contractures 0°, 10°, 20° and 30° of the gastrocnemius. Concerning the pelvis, an increase anteversion was found for the mean position for a contracture 30° of gastrocnemius (CC: 9.3° (5.9; 12.9) vs. gastrocnemius 30°: 16.8° (12.4; 21), p<0.01).

Comparison between soleus and gastrocnemius contractures:

There were significant different effects of soleus and gastrocnemius were observed in the ankle, knee and hip kinematics (Table 1 and Figure 3). At the ankle, only the ROM plantarflexion was different for contractures 20° and 30° with less ROM for soleus compared to gastrocnemius. At the knee, minimum flexion in stance and knee flexion at initial contact were increased for gastrocnemius contractures at 0°, 10°, 20° and 30° compared to soleus contractures at the same degrees; ROM of knee flexion was decreased for gastrocnemius contractures at 0°, 10°, and 20° compared to soleus contractures. At the hip, the mean position was increased and minimum of flexion was decreased for gastrocnemius contractures at 0°, 10°, 20°, and 30° compared to soleus contracture. No differences were found for the pelvis angles and the foot progression angle between soleus and gastrocnemius contractures at the same degree.

Discussion

This study aims to describe kinematic differences between different degrees of contracture and CC as well as between isolated bilateral gastrocnemius and soleus contractures.

Compared to CC, we observed that soleus contractures have no impact on walking speed and a low impact on gait quality (GPS) in contrary to gastrocnemius contractures for which walking speed is reduced for contractures 30° and GPS increased for contractures 20 and 30°.

In addition, gastrocnemius and soleus contractures impact gait kinematics differently. Indeed, it appears from our results that soleus contractures cause a more pronounced limitation of dorsiflexion and decrease of ankle ROM than gastrocnemius contractures. On the other hand, gastrocnemius contractures cause a more important knee flexion (during stance phase) and hip flexion than soleus contractures.

Our results are in agreement with anatomy. Soleus is a monoarticular muscle and can mainly act on the ankle joint, whereas gastrocnemius is a biarticular muscle and can act simultaneously on the ankle and knee joints [START_REF] Wren | Gastrocnemius and soleus lengths in cerebral palsy equinus gait-differences between children with and without static contracture and effects of gastrocnemius recession[END_REF]. Therefore, contractures of gastrocnemius or soleus limit the maximum ankle dorsiflexion during the gait, as reported by other authors [START_REF] Houx | Simulation of unilateral equinus using an adjustable orthosis in children: design, feasibility and biomechanical effects[END_REF][START_REF] Leung | The impact of simulated ankle plantarflexion contracture on the knee joint during stance phase of gait: A within-subject study[END_REF][START_REF] Olensek | Muscle contracture emulating system for studying artificially induced pathological gait in intact individuals[END_REF][START_REF] Ota | Acute influence of restricted ankle dorsiflexion angle on knee joint mechanics during gait[END_REF]; contractures of gastrocnemius also cause a flexed knee in the stance phase of the gait despite the fact that the hamstrings is not short and there are no other impairments. Our results, obtained with bilateral contractures, are similar to unilaterally induced soleus contracture studies (with an emulation system applied only on the ankle level without direct link with knee) concerning maximum dorsiflexion in stance: Goodman et al. [START_REF] Goodman | Secondary gait compensations in individuals without neuromuscular involvement following a unilateral imposed equinus constraint[END_REF] (mean APC at -24°: -7° (±7.8), Houx et al. [START_REF] Houx | Simulation of unilateral equinus using an adjustable orthosis in children: design, feasibility and biomechanical effects[END_REF] (APC at -20°: -6.08° (±3.82), our study (30° of soleus (-3.9° (-7.6-2.5)). These results point out the differences between the degrees of contracture setting up in static with the emulation device and the maximal dorsiflexion during gait. In literature and our study, we can expect to have more agreement between these two measurements for soleus contractures. These differences, observed also in patients, can be attributed to several factors: 1) the reliability to measure dorsiflexion with a goniometer is moderate with a minimal detectable change ranged from 6° to 8° [START_REF] Krause | Measurement of ankle dorsiflexion: a comparison of active and passive techniques in multiple positions[END_REF], 2) the force applied by the evaluator at the ankle is inferior to the force applied during walking [START_REF] Maas | Decrease in ankle-foot dorsiflexion range of motion is related to increased knee flexion during gait in children with spastic cerebral palsy[END_REF]; 3) patients/participants are not fully relaxed during clinical examination [START_REF] Van Trijffel | Inter-rater reliability for measurement of passive physiological movements in lower extremity joints is generally low: a systematic review[END_REF]; 4) the measurement of ankle kinematics considering one foot segment overestimates ankle dorsiflexion [START_REF] Pothrat | One-and multi-segment foot models lead to opposite results on ankle joint kinematics during gait: Implications for clinical assessment[END_REF]. Moreover, these differences could explain a part of the poor relationships between clinical examinations and CGA results [START_REF] Aktas | Evaluation of rotational gait abnormality in the patients cerebral palsy[END_REF][START_REF] Bonnefoy-Mazure | Are clinical parameters sufficient to model gait patterns in patients with cerebral palsy using a multilinear approach?[END_REF][START_REF] Desloovere | Do dynamic and static clinical measurements correlate with gait analysis parameters in children with cerebral palsy? Gait Posture[END_REF].

Concerning the effect of induced soleus contracture on the knee, literature results (based on induced contractures) are contradictory. Leung et al. [START_REF] Leung | The impact of simulated ankle plantarflexion contracture on the knee joint during stance phase of gait: A within-subject study[END_REF] found a knee recurvatum during stance whereas Goodman et al. [START_REF] Goodman | Secondary gait compensations in individuals without neuromuscular involvement following a unilateral imposed equinus constraint[END_REF] found a permanent knee flexion. Houx et al. [START_REF] Houx | Threshold of equinus which alters biomechanical gait parameters in children[END_REF] and Matjacic et al. [START_REF] Matjacic | Biomechanical characterization and clinical implications of artificially induced toe-walking: Differences between pure soleus, pure gastrocnemius and combination of soleus and gastrocnemius contractures[END_REF] found a small increase of knee flexion at IC but no effect at knee for maximal flexion in stance. Our results (based on bilateral induced contractures) are in agreement with those of Houx et al. [START_REF] Houx | Threshold of equinus which alters biomechanical gait parameters in children[END_REF] and Matjacic et al. [START_REF] Matjacic | Biomechanical characterization and clinical implications of artificially induced toe-walking: Differences between pure soleus, pure gastrocnemius and combination of soleus and gastrocnemius contractures[END_REF]. Moreover, Svehlik et al. [START_REF] Svehlik | Genu recurvatum in cerebral palsy -Part A: Influence of dynamic and fixed equinus deformity on the timing of knee recurvatum in children with cerebral palsy[END_REF] reported in cerebral palsy children that equinus position of the foot can lead to knee hyperextension. However, they did not specify whether soleus or gastrocnemius contracture were considered. Galli et al. [START_REF] Galli | Gait analysis before and after gastrocnemius fascia lengthening in children with cerebral palsy[END_REF] analyzed ankle and knee kinematics after gastrocnemius fascia lengthening; they reported increased ankle dorsiflexion and less knee flexion at initial contact. Our study also shows that gastrocnemius influences the ankle and knee angles (increase knee flexion with increase degree of gastrocnemius contracture), whereas soleus mainly influences the ankle angle. Nevertheless, the finding of our study does not rule out that soleus contracture can alter the knee biomechanics, in particular by the effect of plantarflexorknee extension couple [START_REF] Sangeux | Sagittal gait patterns in cerebral palsy: the plantarflexor-knee extension couple index[END_REF].

Hence, we suspect that knee hyperextension during gait observed by Svehlik et al. [START_REF] Svehlik | Genu recurvatum in cerebral palsy -Part A: Influence of dynamic and fixed equinus deformity on the timing of knee recurvatum in children with cerebral palsy[END_REF], Galli et al. [START_REF] Galli | Gait analysis before and after gastrocnemius fascia lengthening in children with cerebral palsy[END_REF] on cerebral palsy patients and by Leung et al. [START_REF] Leung | The impact of simulated ankle plantarflexion contracture on the knee joint during stance phase of gait: A within-subject study[END_REF] on healthy participants with induced contractures could be due to soleus contracture associated with the plantarflexionknee extension moment [START_REF] Sangeux | Sagittal gait patterns in cerebral palsy: the plantarflexor-knee extension couple index[END_REF]. However, Leung et al. [START_REF] Leung | The impact of simulated ankle plantarflexion contracture on the knee joint during stance phase of gait: A within-subject study[END_REF] specified that a minority of their subjects walked with knee flexion. In our study most participants walked with a knee flexion pattern during gastrocnemius contractures and with quasi-normal knee flexion/extension or knee extension during soleus contracture (only one participant in the contractures 0°, 10°, 20° and 30° had a knee recurvatum pattern with emulated contractures on the soleus). The differences between studies concerning knee kinematics could be explained by different possible ways for the participants to walk with the same contracture. Future studies with a large sample size permitting to use classification methods are needed to better investigate adaptations chose by the participants and by the patients. It is possible that different gait adaptations are related to different optimization such as minimise energy expenditure or balance [START_REF] Selinger | Humans Can Continuously Optimize Energetic Cost during Walking[END_REF].

Our study was the first study to investigate the influence of emulated bilateral contractures on the gastrocnemius and the soleus. As already mentioned, our results showed the same influence that unilateral emulated contractures on the ipsilateral side [START_REF] Houx | Simulation of unilateral equinus using an adjustable orthosis in children: design, feasibility and biomechanical effects[END_REF][START_REF] Leung | The impact of simulated ankle plantarflexion contracture on the knee joint during stance phase of gait: A within-subject study[END_REF][START_REF] Matjacic | Biomechanical characterization and clinical implications of artificially induced toe-walking: Differences between pure soleus, pure gastrocnemius and combination of soleus and gastrocnemius contractures[END_REF][START_REF] Drefus | Simulated Ankle Equinus Affects Knee Kinematics During Gait[END_REF][START_REF] Goodman | Secondary gait compensations in individuals without neuromuscular involvement following a unilateral imposed equinus constraint[END_REF][START_REF] Houx | Threshold of equinus which alters biomechanical gait parameters in children[END_REF].

Limitations

The first limitation concerns the small number of participants [START_REF] Houx | Simulation of unilateral equinus using an adjustable orthosis in children: design, feasibility and biomechanical effects[END_REF] in this study, which does not permit the use of parametric tests and reduces the power of inference tests. For example, we observed some tendencies between the different degrees of gastrocnemius and soleus contractures concerning the pelvis motions (the pelvis tends to be more tilted with increasing degrees of contracture) as well as in foot progression (the foot tends to be more in-toeing with increasing degrees of contracture). The second limitation concerns the short adaptation time to contracture emulations. Indeed, adaptation time can play an important role in the gait strategies of the participants. The third limitation is that no combinations of gastrocnemius and soleus contractures were evaluated. A future study could investigate the relative contribution of these muscle contractures to gait deviations through different combinations of contractures of these two muscles.

Conclusion

Soleus contractures act mainly on ankle kinematics with no effect on the knee kinematics, whereas gastrocnemius contractures act on ankle and knee kinematics due to its biarticular role. A flexed-knee gait can be caused by a gastrocnemius contracture without other impairments. These findings can help for clinical interpretation and therefore support future treatment decisions.

Table 1: Walking speed, Gait Profile Score (GPS) and kinematic parameters (median, 1 st and 3 rd quartile) at different degrees of emulated contracture (control condition (CC), 0°, 10°, 20° and 30° plantarflexion contractures) for the gastrocnemius and soleus muscles with the significant difference (p-value) between the two muscles and compared to CC.

Figure 2 :

 2 Figure 1a: The exoskeleton, " MIkE" Muscle contracture Induced by an Exoskeleton (Attias et al. 2016)

Acknowledgments

This study was funded by the Swiss National Science Foundation (SNF) project 325230_146801.

This study was funded by the Swiss National Science Foundation (SNF) project 325230_146801.

Conflicts of interest

There are no conflicts of interest associated with this research.

Gastrocnemius Soleus

Figure 3: Mean (and standard deviation) kinematics for the pelvis, hip, knee, and ankle in the sagittal plane and foot progression at different degrees of emulated contracture for the gastrocnemius and soleus muscles.


Marie Dietemann
email: marie.dietemann@mines-albi.fr

Fabien Baillon

Fabienne Espitalier

Philippe Accart

Rachel Calvet

Mike Greenhill Hooper

Dietemann Marie

Baillon Fabien

Espitalier Fabienne

Accart Philippe

Greenhill-Hooper Mike

Amorphous magnesium silicate synthesized by precipitation

Keywords: silicate de magnésium, talc, précipitation, taille, agglomération magnesium silicate, talc, precipitation, size, agglomeration

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

Introduction

The plastic and rubber industries are very interested in natural talc because it can be used as a high performance filler in polymers. According to [START_REF] Ciesielczyk | Evaluation of synthetic magnesium silicate as a new polymer filler[END_REF], it improves their properties by delivering excellent mechanical reinforcement and barrier effects. In order to get a good dispersion in a polymer matrix, particles should be, in an ideal case, nano-sized (Martin et al., 2006). But with conventional milling processes, it's difficult and expensive to obtain particles smaller than one micrometer. The aim of this work is to develop a process that would be an alternative to milling. This process is a synthesis of nano-sized magnesium silicate particles. These amorphous particles can be used as directly as filler particles or converted in a separate second step into crystalline lamellar nano-sized particles with a talc-like structure.

Experimental 2.1 Materials

The product is synthesized by a precipitation, according to the following equation (Martin et al., 2006)

Procedures and methods

Synthesis of magnesium silicate

The synthesis is made in a 1L tank with a top stirrer and four baffles. All experiments are conducted at room temperature and at a stirring speed of 500 rpm. Three addition modes are tested (Fig. 1). The first mode, called slow addition, involves drop by drop addition of magnesium chloride solution to sodium metasilicate solution already introduced in the tank. The second mode, called fast addition, involves fast addition of one reactant to the other which is already in the tank. Fast addition is not depicted in Figure 1 because materials are the same as slow addition. The only difference is that magnesium chloride solution is added instantaneously. In the third mode, both solutions are added in parallel to the tank by a Y-shaped mixing system (H≈6 cm, D≈4 cm). Solutions are fed to the mixing system using peristaltic pumps. Rates and speed of flow are 125.25 g.min -1 and 0.30 m.s -1 for sodium metasilicate solution and 81.30 g.min -1 and 0.19 m.s -1 for magnesium chloride solution. Mixing occurs inside the system at the exit of pipes which come from pumps. An ultrasound probe can be added to the mixing system in order to destroy flocs formed during the contact of reactants. The tank is before filled with 100 mL of demineralised water.

The influence of reactants' addition mode, addition order and reactants' concentrations on product properties is studied. At the end of the synthesis, the suspension is filtered with a Büchner-membrane system and the cake is washed four times with water in order to eliminate salt formed during the synthesis. Then the product is dried at 100°C during 12 hours. As the dried product is very agglomerated, it's then milled.

Properties of synthetic magnesium silicate

During the synthesis, conductivity, temperature and pH of the suspension are measured. The suspension and the synthesized powder are submitted for physical chemistry analysis. Particle size distribution of samples of the suspension is determined using Malvern Mastersizer 2000 with the dynamic light scattering technique. This enables particle size distribution to be followed during the synthesis. Samples of dried products are examined by scanning electron microscopy (SEM-FEG, Philips XL 30) in order to define surface morphology and agglomeration state of particles.

BET specific surface area is estimated using nitrogen adsorption/desorption isotherms and a Micrometrics ASAP 2010 K2 apparatus. Meso-porous volume is calculated by using the Barret, Joyner and Halenda method (B.J.H. method) on the desorption field of the adsorption/desorption isotherm. Micro-porous volume is calculated by using the Horvath-Kawazoe method (H. -K. method) with split pore geometry on the adsorption field of the adsorption/desorption isotherm. Density of dried products is measured using a Micrometrics AccuPyc 1330 helium pycnometer.

Results and discussion

The Table 1 summarizes solid properties (d 50 , density, specific surface area and pore volumes) as a function of operating conditions. The product densities seem to be independent of studied operating conditions: 2.1853±0.0365 g.cm -3 . All synthesized solids are amorphous, whatever studied process parameters. Diffractograms (Fig. 2) don't present any real peack, only a large initiation of a peak at 46.5°2θ . It's difficult to exploit it because of its low density. 3.1 Agglomeration state of the powder Synthetic magnesium silicate is made up of agglomerates (Fig. 3): the powder is very agglomerated. Amorphous magnesium silicate may be made up of secondary agglomerates (Fig. 3A) made up of primary spherical agglomerates made up of primary particles (Fig. 3B-C-D). The dynamic light scattering measures primary and secondary agglomerates sizes. Measured d 50 isn't the size of primary particles. SEM analysis would show that primary particles size is about 100 nm but this measure is very approximate. This structure is not influenced a lot by process parameters: whatever reactants' addition mode and order and reactants' concentrations, the product is made up of these two kinds of agglomerates. Therefore, primary particles might be smaller with mixing system and ultrasound (Fig. 3D). With the mixing system, the product seems to be more compact. Figure 4 shows that both products have micro-pores: gas is absorbed at very low relative pressures. The mean diameter of micro-pore is about 0.5 nm. Both products present only an inter primary agglomerates meso-porosity. Meso-pores might be inside secondary agglomerates, between primary agglomerates whereas micro-pores might be inside primary agglomerates, between primary particles. The meso-pore diameter is 3.5 nm for sample 2 and 24.16 nm for sample 6. The structure of secondary agglomerates is deformed under capillary condensation of nitrogen. The hysteresis observed for the sample 6 is probably due to this inter-granular porosity. Secondary agglomerates of sample 6 present a more rigid structure than those of sample 2.

Figure 4: Adsorption/desorption isotherms of products 2 and 6 (Table 1).

Figure 5 shows that ultrasound, applied during the size measurement, influences particle size distribution of the product. The sizes distributions are shifted towards fine particle sizes after ultrasound use. Ultrasound causes disaggregation of the solid. Over two minutes of ultrasound use, agglomerate size distribution doesn't change any more. Every sample, presented in this paper, is subjected to ultrasound in the granulometer during two minutes. Whatever process parameters, particle size distribution doesn't seem to be influenced by the time. In all experiments, a weak shift of size distributions towards large particle sizes is observed (Fig. 6). It would be due to agglomeration of solid particles in the synthesis vessel. Figure 6 (on the right): Sampling time influence on particle size distribution (addition mode: parallel addition with mixing system, C MgCl2 , 6H2O =0.81 mol/L). Samples are taken of every 2 minutes and, after the end of reactant'addition, every 15 minutes

Influence of reactants' addition mode

The smallest particles seem to be synthesized by addition with the mixing system (Fig. 7). The three particle size distributions have the same width (700 nm-80 µm) but with the addition with mixing system, particle size distribution is composed of smaller particles under 7 µm. With the fast addition, the particle size distribution shows less agglomerates under 10 µm but more agglomerates between 10 and 100 µm. These differences may be due to the micromixing effect. 3.3 Influence of ultrasound used during the synthesis At low reactants' concentrations, particles made by parallel addition with mixing system are smaller when ultrasound are used during the synthesis (Fig. 8). Particle size distributions are very different. With ultrasound during the pre-mixing, particles are smaller than 20 µm as against 100 µm without ultrasound.

Influence of reactants' concentrations

At high reactants' concentrations, the particle size distribution obtained with the mixing system and ultrasound is almost the same as distribution got with no mixing system (Fig. 9, on the left). Smaller agglomerates are synthesized with low reactants' concentrations. The same tendency is observed with the fast addition (Fig. 9, on the right). With the highest concentrations, the supersaturation is higher, so the number of synthesized particles increases, agglomeration phenomena is more important and agglomerates are bigger. Therefore by increasing concentrations and so supersaturation, primary particles may be smaller. This result has been observed by [START_REF] Zauner | Mixing effects on product particle characteristics from semi-batch crystal precipitation[END_REF] and confirmed by Baldyga and Jones (2007). So with the highest concentrations, synthesized particles may be more agglomerated but smaller. 3.5 Influence of reactants' addition order Reactants' addition order has a weak influence on particle size distribution: a weak shift of size distribution towards large particles sizes is visible with addition of reactant 2 to reactant 1.

3.6 Disaggregation of the powder Synthetic magnesium silicate disperses better in water than in the other solvents (Fig. 10). In water, at the end of the dispersion test, agglomerates size is almost the same than agglomerates size in suspension at the end of the synthesis (Table 1). So the synthesized product disperses well in water, that is to say in a polar solvent. On the contrary, its disaggregation is poor in non-polar solvents and virtually impossible in dodecane: an aggregation is observed instead of dispersion. Secondary agglomerates might be fragile because of meso-pores that would exist inside them, that would explain easy disaggregation of powder in polar solvents. Adsorption analysis are in progress in order to confirm this hypothesis.

Conclusions

The formation of magnesium silicate is instantaneous. The synthesis length depends on the addition mode (from few minutes with the mixing system to one hour and half with the slow addition). The amorphous solid obtained is made up of two kinds of agglomerates (primary and secondary). The size distributions are very dependent on mixing conditions and reactants' concentrations. The parallel addition with mixing system would enable to synthesize the product made up of smaller particles and agglomerates. Moreover, low concentrations and ultrasound used during the synthesis would enable to synthesize smaller particles too. The measured smallest size is about 4 µm but it should be agglomerates size. Primary particles size is difficult to estimate but it would be about 100 nm. A study perspective is to make product disaggregation in the polymer easy and to "release" small primary particles in order to reach the objective size. Moreover by decreasing reactants' concentrations, synthetic product is less compact. The dried product disperses best in polar solvents. The product appears to be hydrophilic.

Figure 1 :

 1 Figure 1: Experimental schemes of slow addition (on the left) and of parallel addition by a mixing system (on the right).

Figure 2 :

 2 Figure 2: Diffractogram of a product (addition mode: parallel with mixing system, C MgCl2 , 6H2O =0.81 mol/L) get by X-Ray diffraction at 0.154 nm (Cu) (measurement step=0.0334 °2theta; duration measurement=50 secondes).

Figure 3 :

 3 Figure 3: SEM analysis of products synthesized by slow addition (A and B), fast addition (C) and with mixing system and ultrasound (D).

Figure 5 (

 5 Figure 5 (on the left): Ultrasound influence on particle size distribution (addition mode: slow addition, C MgCl2,6H2O =1.50 mol/L).

Figure 7 :

 7 Figure 7: Particle size distributions as a function of the addition modes (C MgCl2, 6H2O =1.50 mol/L, samples taken of after 90 minutes).

Figure 8 :

 8 Figure 8: Particle size distributions as a function of ultrasound used during the synthesis (addition mode: parallel with mixing system, C MgCl2, 6H2O =0.81 mol/L, samples taken of after 90 minutes).

Figure 9 :

 9 Figure 9: Particle size distributions as a function of reactants' concentrations (On the left: addition mode: parallel with mixing system and ultrasound, C MgCl2 , 6H2O =0.81 mol/L and 1.50 mol/L, samples taken of after 210 minutes; on the right: addition mode: fast addition, C MgCl2 , 6H2O =0.78 mol/L and 1.50 mol/L, samples taken of after 210 minutes).

Figure 10 :

 10 Figure 10: Disaggregation tests of a magnesium silicate (addition mode: slow addition, C MgCl2, 6H2O =1.50 mol/L) in different solvents (water, sunflower oil, squalane, dodecane).

  : 4 Na 2 OSiO 2 , 5 H 2 O + 3 MgCl 2 , 6 H 2 O + 2 HCl → Si 4 Mg 3 O 11 n(H 2 O) + 8 NaCl + H 2 OIn this study, 4.6<n<4.85. Aqueous solutions of magnesium chloride, called reactant 2, and of sodium metasilicate, called reactant 1, are used (supplier Prolabo). Different concentrations are tested for both solutions, but molar ratio Mg/Si is always 0.75, corresponding to that of natural talc. Hydrochloric acid 1M is added in aqueous solution of magnesium chloride in order to maintain stoichiometry of reaction (supplier Prolabo). The used water is demineralised.

  Disaggregation tests are made to study product behaviour dispersed in different solvents and to simulate its behaviour in a polymer matrix. This test, made in the granulometer, is described in the US patent (US 6,610,261 B1) deposited by the Compagnie Générale des Etablissements Michelin in 2003. A dried synthetic magnesium silicate is dispersed in a solvent. Four solvents are tested: water, sunflower oil, squalane and dodecane. During this test, the evolution of the median diameter is measured as a function of time. At the beginning of the test, three consecutive measurements are made without ultrasound to determine the initial diameter. Then the ultrasound generation is set at a power of 100%. (around 3 mW) The median diameter is measured every 10 seconds during 8 minutes.

Table 1 :

 1 Physical properties of synthetic magnesium silicates.

										Specific	B.J.H.	H. -K.
		Addition	Addition [MgCl 2 ,6H 2 O] [Na 2 SiO 3 ,5H 2 0] d 50	Density	surface meso-pore micro-pore
	Trial	mode	order	(mol.L	-1 )	(mol.L	-1 )	(µm) (g.cm -3	area (m 2 .g -1 )	volume (cm 3 .g -1 )	volume (cm 3 .g -1 )
	1	slow	2 to 1	1.50	1.43	20.9 2.2085
	2	fast	2 to 1	1.50	1.43	26.1 2.2182	349±1	0.40	0.14
	3	fast	1 to 2	1.50	1.43	22.3 2.2041
		mixing
	4	system	parallel	1.50	1.43	19.2 2.2027
		+ultrasound
		mixing
	5 system (no	parallel	0.81	0.72	11.2 2.1312
		ultrasound)
		mixing
	6	system	parallel	0.81	0.72	4.3	2.1472	460±1	0.50	0.19
		+ultrasound

Acknowledgements

The authors acknowledge the Agence Nationale de la Recherche for the financial support of ANR-09-MAPR-0017 project. The authors also thank Ms S. Del Confetto, Ms C. Rolland and Ms S. Patry for specific surface area measurements, microscopy analysis and X-Ray diffraction analysis.