Rébecca Bonnaire
email: bonnaire@emse.fr

Marion Verhaeghe

Jérôme Molimard

Paul Calmels

Reynald Convert

Characterization of a pressure measuring system for the evaluation of medical devices

Keywords: Pressure measurement, pressure mapping system, medical device, mechanical characterization, metrology

The purpose of this study is to evaluate the possible use of four "FSA" thin and flexible resistive pressure mapping systems, designed by Vista Medical (Winnipeg, Manitoba, Canada), for the measurement of interface pressure exerted by lumbar belts onto the trunk. These sensors were originally designed for the measurement of low pressure applied by medical devices on the skin.

Two types of tests were performed: standard metrology tests such as linearity, hysteresis, repeatability, reproducibility and drift, and specific tests for this application such as curvature, surface condition and mapping system superposition.

The linear regression coefficient is between 0.86 and 0.98; hysteresis is between 6.29% and 9.41%.

Measurements are repeatable. The location, time and operator, measurement surface condition and mapping system superposition have a statistically significant influence on the results. A stable measure is verified over the period defined in the calibration procedure, but unacceptable drift is observed afterward.

The measurement stays suitable on a curved surface for an applied pressure above 50mmHg.

To conclude, the sensor has acceptable linearity, hysteresis and repeatability. Calibration must be adapted to avoid drift. Moreover, when comparing different measurements with this sensor the location, the time, the operator and the measurement surface condition should not change; the mapping system must not be superimposed.

Introduction

Low back pain is a major public health problem in developed countries. In France, prevalence of low back pain is higher than 50% [START_REF] Fassier | Prevalence, costs and societal issues of low back pain[END_REF]. Because of health care costs and sick leave [START_REF] Fassier | Prevalence, costs and societal issues of low back pain[END_REF][START_REF] Leclerc | Level of education and back pain in France: the role of demographic, lifestyle and physical work factors[END_REF], low back pain has adverse consequences on both the social and economic level. Many treatments have been proposed.

However, no guidelines are proposed to practitioners, particularly for chronicle evolution. Treatment propositions and success depend on the patient comportment, on the aetiology and/or mechanical causes of low back pain, on the evolution along the time and also on the physician's opinions. Lumbar belts are frequently proposed to treat low back pain. Several clinical trials have shown their clinical effectiveness [START_REF] Calmels | Etude de l'effet antalgique et fonctionnel du port d'une orthèse lombaire souple dans la lombalgie aiguë[END_REF][START_REF] Calmels | Effectiveness of a lumbar belt in subacute low back pain: an open, multicentric and randomized clinical study[END_REF]. Nevertheless, both the mechanical and the physiological effects of lumbar belts remain unclear.

It is assumed that the main mechanical effect of lumbar belts is the pressure applied on the trunk; therefore it has been decided to investigate experimentally this pressure. In the medical field, pressure measurement is already used to evaluate devices employed to prevent bedsores [START_REF] Vaisbuch | Effect of seated posture on interface pressure in children who are able-bodied and who have myelomeningocele[END_REF][START_REF] Fenety | In-chair movement: validity, reliability and implications for measuring sitting discomfort[END_REF][START_REF] Shelton | Conducting and interpreting interface pressure evaluations of clinical support surfaces[END_REF][START_REF] Tam | Pelvic movement and interface pressure distribution during manual wheelchair propulsion[END_REF][START_REF] Reenalda | Analysis of healthy sitting behavior: interface pressure distribution and subcutaneous tissue oxygenation[END_REF][START_REF] Rithalia | Assessment of alternating-pressure air mattresses using a time-based pressure threshold technique and continuous measurements of transcutaneous gases[END_REF][START_REF] Hamanami | Finding the optimal setting of inflated air pressure for a multicell air cushion for wheelchair patients with spinal cord injury[END_REF], to measure the interface pressure of compression stockings, compression bandages [START_REF] Partsch | Interface pressure and stiffness of ready made compression stockings: comparison of in vivo and in vitro measurements[END_REF][START_REF] Hafner | Instruction of compression therapy by means of interface pressure measurement[END_REF][START_REF] Damstra | Controlled, comparative study of relation between volume changes and interface pressure under short-stretch bandages in leg lymphedema patients[END_REF][START_REF] Damstra | Compression therapy in breast cancer-related lymphedema: A randomized, controlled comparative study of relation between volume and interface pressure changes[END_REF][START_REF] Dumbleton | Dynamic interface pressure distributions of two transtibial prosthetic socket concepts[END_REF][START_REF] Candy | Effect of different pressure magnitudes on hypertrophic scar in a Chinese population[END_REF][START_REF] Reich-Schupke | Resting pressure exerted by round knitted moderate-compression stockings on the lower leg in clinical practice--results of an experimental study[END_REF] and rigid orthosis [START_REF] Van Den Hout | Interface corrective force measurements in Boston brace treatment[END_REF][START_REF] Aubin | Évaluation tridimensionnelle et optimisation du traitement orthopédique de la scoliose idiopathique adolescente[END_REF].

Using pressure measurement to mechanically characterize lumbar belts can be considered as new approach.

Four types of interface pressure sensors exist: pneumatic (Example: PicoPress © , St Neots Cambridgeshire, United Kingdom), electro-pneumatic (Example: Salzmann © , St. Gallen, Switzerland), resistive (Example: Tekscan © , Boston MA, USA) or capacitive (Example: X-Sensor © , Calgary Alberta, Canada or Novel © , Munich Germany) sensors. Resistive or capacitive sensors may be assembled into a structure that enables the pressure to be measured at several points simultaneously; this structure is often called a pressure mapping system.

In this study, four identical FSA © pressure mapping systems were chosen and purchased (Vista Medical © , Winnipeg Manitoba, Canada). They are composed of resistive sensors, based on the piezoresistive properties of some materials. The resistivity of piezoresistive materials varies according to the forces exerted on this material. Resistivity is proportional to the electrical resistance which is converted into voltage. After calibration, measurement of voltage enables the interface pressure to be measured [START_REF] Fergenbaum | Development of a dynamic biomechanical model for load carriage: Phase 4, Part C2: Assessment of Pressure Measurement Systems on Flat Surfaces for the Dynamic Biomechanical Model of Human Load Carriage[END_REF].

These pressure mapping systems were chosen because they are thin and compliant, free from error of measurement on curved surfaces, sensitive in detecting a range of pressure as low as 0-100mmHg (0-13.3kPa), in accordance to in-vivo studies (free from temperature or moisture effects, dynamic range ≥10 Hz ) and give indications of pressure gradients in a context of spatial variations of support stiffness and shape [START_REF] Ferguson-Pell | Evaluation of a sensor for low interface pressure applications[END_REF][START_REF] Lai | Validation of the Pliance X System in measuring interface pressure generated by pressure garment[END_REF][START_REF] Chiang | An implantable capacitive pressure sensor for biomedical applications[END_REF]. Compared to the capacitive sensors, resistive sensors have a lower drift and are less expensive [START_REF] Polliack | Scientific validation of two commercial pressure sensor systems for prosthetic socket fit[END_REF][START_REF] Wheeler | MEMS-based bubble pressure sensor for prosthetic socket interface pressure measurement[END_REF].

Aim of this study is to evaluate these four identical pressure mapping systems, particularly in challenging applications such as lumbar belts. This evaluation is performed by two types of tests:

-classical tests of metrology such as linearity, hysteresis, repeatability, reproducibility and drift, -specific test for the application developed in this study, such as curvature, surface condition and mapping system superposition.

The goal of classical tests is to determine the proper functioning of sensors in their general use. The goal of specific tests is to characterize the pressure sensors in case of interface pressure measurement between the trunk and the lumbar belt. Actually, in this specific type of measurement, surfaces are soft and curved.

Moreover, the four pressure mapping systems may be partially superimposed during the measurement.

Methods

The FSA pressure mapping systems Four mapping systems are needed to measure the interface pressure all around the trunk. In this study, the mapping systems will be tested all together and no comparison between them will be done. Pressure mapping systems are composed of 12 by 32 piezoresistive sensors. Each sensor is a square with sides measuring 7.9mm, separated by 4.2mm. The active area is 382 by 142mm. The total size of the mapping system is 482 by 242mm. Sensor calibration is performed with the pressure range from 0 to 100mmHg.

During calibration, 50mmHg is measured for 60 seconds to compensate the drift effect. The FSA pressure mapping system is illustrated in Figure 1. The pressure mapping systems are denoted below A, B, C and D. [START_REF] Bipm | IUPAC, IUPAP, ISO, OIML. The international vocabulary of metrologybasic and general concepts and associated terms (VIM), 3rd edn[END_REF] Linearity test. For the linearity test, seven cylindrical steel weights were designed to apply pressure between 6 and 96mmHg on one sensor. Weights were randomly applied in sensors 1, 2 and 3 (see Figure 1). Thirty measurements were carried out for each sensor. The linear regression coefficient R² between applied and measured pressures, the dispersion and the standard deviation s p were calculated. The linear regression coefficient R² is defined by the following formula:

Classical tests of metrology

= ( , ) ( ) ( ) (1)
with P, the measured pressure value in mmHg and Pi, the applied pressure value in mmHg.

The dispersion is defined as the difference between the maximum and the minimum pressure measured for each applied pressure. The standard deviation s p of the measured pressure is defined by the following formula:

= ( ) ∑ ( -) (2)
with n, the size of the measured sample and P, the measured pressure value for each applied pressure in mmHg.

Hysteresis test. Two types of hysteresis tests were performed: an hysteresis test in only one sensor and an hysteresis test in all sensors at the same time of the mapping system.

For the first test, the same weights as for the linearity test, were increasingly and decreasingly applied on eight sensors. The position of these sensors is represented in Figure 1. For the second test, pressure mapping was placed on an air pocket and introduced between two wooden planks. Figure 2 illustrates this experimental device. The air pocket was inflated to apply increasing then decreasing pressure between 10 and 100mmHg to the mapping system.

Hysteresis is defined by the following formula:

(%) = !(" ) #(" ) $ * 100 (3)
with x i , the discrete values of applied pressure in mmHg, y m the measured pressure value during the increasing phase corresponding to a given x i in mmHg, and y d the measured pressure value during the decreasing phase corresponding to a given x i in mmHg. A specific design of experiments was used to evaluation reproducibility (Table 1). In this design of experiments, there are four independent factors: location, time, operators and weight applied to the mapping system. The interactions between each factor are considered. The selected design of experiments is factorial and follows this polynomial model:

Repeatability

= ∑ ( ) + ∑ ( + + ) ) + (4)
with P, the measured pressure (mmHg), β i or β ij , the polynomial coefficients and x i or x j , the input factor of the design of experiments.

Drift test. To determine if the pressure recorded changes over time, four weights corresponding to 26, 40, 52 and 80mmHg applied pressure were left on 1, 2, 3, 4, 5 and 6 sensors (see Figure 1) for a duration higher than that of the calibration to drift (30 minutes).

For each case, the range of stored drift, as defined by the minimum and maximum pressures measured during the testing, was determined. The relative pressure variation was expressed by the following formula:

∆ = | # . | . ( 5
)
with ∆ the relative pressure variation, / the measured pressure and the applied pressure.

Tests specific to the application

Curvature test. An experimental setup was developed to characterize the impact of measurement on curved surfaces. This experimental setup consists in a support on which it is possible to place cylinders of different radii. Radii used in this study were 60, 80, 100 and 125mm. Pressure mapping systems were placed on the cylinder. Pressure was applied on one single line of sensors using a 15mm band, at the end of which weights were hung on. This experimental setup is illustrated in Figure 3. Three lines were tested for one mapping system. As results were similar for these three lines, just one line was tested for the other three pressure mapping systems. Six or seven different pressures were applied per cylinder, per line and per pressure mapping system.

For each applied pressure, cylinder and pressure mapping system, normalized pressure was calculated according to the following formula:

= # . ( 6
)
with the normalized pressure, / the measured pressure and the applied pressure.

Surface condition test.

The possible application of this system is to measure the interface pressure applied by lumbar belts. Usually these belts are worn over garments (tee shirt, shirts, etc.). The surface condition of the measured zone is important. Two different surface conditions have been tested. Evaluation of the effect of the surface condition was done in two stages.

Firstly, a hysteresis test was performed with only one sensor and seven different medical fabrics placed between the table and the mapping system. For two of the tested fabrics, the pressure decrease was more than 50%. Therefore, these two fabrics were not considered for the statistical analysis. For the other five fabrics, two statistical analyses were performed. The first one was used to compare results with and without fabric between the pressure mapping system and the table . The second one was used to determine if results are different depending on fabrics inserted between the table and the pressure mapping system.

Secondly, the hysteresis test was conducted with only one sensor with weights surrounded by silicone and with froth positioned between the table and the mapping system. Statistical analysis was done to determine if there are statistical significant differences between results for this test and for the first test of hysteresis (test in one sensor). The linear regression coefficient was calculated thanks to equation 1.

Mapping system superposition test. To determine the impact of two superimposed pressure mapping systems on the results, the first hysteresis test (test in one sensor) was performed in three sensors stacking two mapping systems.

Statistical analysis was performed to determine if there are statistical significant differences between results for the pressure mapping system "from above" and the pressure mapping system "from the bottom". Absolute differences between measured pressures with or without superposition were calculated for each pressure mapping system.

Statistical analysis

Statistical analysis was used to determine differences between two or more than two distributions.

Depending on the number of data sets to compare, two types of statistical approach were used. A Jarque-Bera test was used to check whether or not data matched normal distribution.

To compare two sets of data, a Student t-test was used if they were distributed following a normal distribution, and a Wilcoxon signed ranks if not. The statistical analysis of two distributions was used for mapping system superposition and surface condition tests. Student t-test was also used for the linearity test to determine if the linear regression curve's slope is zero.

To compare more than two sets of data, an ANOVA was used if they were all distributed following a normal distribution, and a Kruskal-Wallis test if not. If needed, the post-hoc test of Tukey was used to find which of the data sets were different. The statistical analysis of more than two distributions was used for repeatability and surface condition tests.

All the statistical tests were performed with a risk α to be equal or smaller than 5%.

Results

Classical tests of metrology

Linearity. Linear regression coefficients and p-value of the Student's test on slope=0 are given in Table 2.

The results are illustrated for one sensor of one mapping system in Figure 4. The linear regression coefficient R 2 is between 0.86 and 0.98 depending on the sensor and the mapping system. The maximum dispersion and the maximum standard deviation to the measured pressure are 18.9 and 9.60mmHg respectively. Table 3 shows the results of maximum dispersion and maximum standard deviation for sensors with the best and the worst linearity.

Hysteresis. All results are given in Table 4. For the first test of hysteresis (test in only one sensor), hysteresis is between 0.228% and 27.9%. An example of results for the second hysteresis test (test in all sensors of a pressure mapping system) is given in Figure 5. For this test of hysteresis, the hysteresis is between 6.29% and 9.41%. All results are given in Table 5.

Repeatability. The Kruskal-Wallis test shows no difference (p-value = 0.88). Measurements are repeatable.

Reproducibility. Table 6 indicates the polynomial coefficient of the experimental design model and probability that the factor x i has at least a 95% chance of not significantly affecting the response to pressure of the sensors. x i can be time, space, operators, weight or interactions factors. The biggest polynomial coefficient corresponds to the weight influence and the smaller corresponds to the time influence. Location, weight, time coupling with operators and time coupling with location have statistical influence to the measured pressure.

Drift. No significant drift was observable during the first 60 seconds, i.e. the calibration time for drift.

After that period, three types of drift are obtained: measured pressure increases during the first few minutes and becomes stable, measured pressure decreases during the first few minutes and becomes stable and measured pressure is stable over time. Figure 6 represents these three typical results. For all sensors, measured pressure becomes stable and reaches its nominal value after 800 seconds.

Tests specific to the application Curvature. Figure 7 shows results for the mapping pressure system A. The results depend on the applied pressure. When the applied pressure is less than 50mmHg, the measured pressure is lower than the applied pressure. Nevertheless, when the applied pressure is more than 50mmHg, the difference between the applied pressure and the measured pressure is minor.

Surface condition. The probabilities of there being at least a 95% chance that results with and without fabric between the pressure mapping system and the table are different for the five tested fabrics are given in Table 7. All fabrics have a statistically significant influence on the results.

The Kruskal-Wallis test is significant (p-value < 0.001). The five fabrics are statistically significantly different. Only measured pressure for fabrics 1 and 2, 3 and 4, and 3 and 5 do not have a statistically significant difference.

For the second surface condition test, the linear regression coefficient R 2 is between 0.95 and 0.99, depending on the sensor and the mapping system. Hysteresis is between 4.2% and 15%. For the third surface condition test, the linear regression coefficient R 2 is between 0.92 and 0.98. Detailed results for the second and third tests are presented in Table 8.

Mapping system superposition. Mapping system superposition results consist of two distributions: measured pressure for the mapping systems "from above" and for the mapping systems "from the bottom".

Results for the test of Wilcoxon signed rank, to compare results for the mapping systems "from above" and "from the bottom", are given in Table 9. Table 10 indicates absolute differences between measured pressures with or without superposition for each pressure mapping system.

Discussion

In this study, four identical pressure mapping systems were evaluated in term of linearity, hysteresis, reproducibility and drift. Some other evaluations demonstrated the efficacy of the pressure mapping systems in the specific application of lumbar belts characterization. According to the results, pressure mapping systems are suitable for this application.

We found that linearity is acceptable according to the linear regression coefficient R² which is always greater than 0.85. Pressure measured with sensors is always underestimated. The maximum deviation is 15.4mmHg. The hysteresis of the pressure mapping system depends on sensors. On the whole, hysteresis is low between 6.29% and 9.41%. Measurements are repeatable. The reproducibility test shows the influence of experimental location, time and operator; the most influencing parameter is the location.

According to the drift test, the value remains stable if the measuring time remains lower than the drift calibration time, but dramatically changes afterward.

Thanks to our tests specific to the application, it is possible to conclude that curvature test results depend on the applied pressure. For applied pressure higher than 50mmHg, measurement is the same as on a flat surface. Nevertheless, for applied pressure less than 50mmHg, the measured pressure is lower than the applied pressure. This can be explained by the experimental device. It is supposed that the band sticks on the cylinder when the applied pressure is too low and the pressure estimation from Laplace's law is not valid any more. Thus, no conclusions to the impact of curvature for low measured pressure can be drawn from these results.

We also proved that the surface measurement has a significant influence on the measured pressure.

However, there is no change in hysteresis and linearity when pressure is measured between two soft surfaces. In this case, hysteresis is between 4.2% and 15% and the linear regression coefficient is between 0.92 and 0.98. Last, the superposition of two pressure mapping systems can have a significant influence on the measurement.

Comparison of the FSA pressure mapping system to the other resistive pressure mapping systems

Metrological results of other sensors have been collected from the literature: Flexiforce © [START_REF] Ferguson-Pell | Evaluation of a sensor for low interface pressure applications[END_REF], F-Socket © [START_REF] Polliack | Scientific validation of two commercial pressure sensor systems for prosthetic socket fit[END_REF] and F-Scan © [START_REF] Fergenbaum | Development of a dynamic biomechanical model for load carriage: Phase 4, Part C2: Assessment of Pressure Measurement Systems on Flat Surfaces for the Dynamic Biomechanical Model of Human Load Carriage[END_REF] sensors from Tekscan © , Rincoe's sensor [START_REF] Polliack | Scientific validation of two commercial pressure sensor systems for prosthetic socket fit[END_REF] and Lück sensor [START_REF] Völker | Auflagedruckmessung in der Dekubitusbehandlung[END_REF]. Measurement error and hysteresis are summarized in Table 11. For accuracy, FSA sensor is identical (Flexiforce © , F-Socket © ) or even better (Rincoe, Lück, F-Scan © ) than other pressure mapping systems. For hysteresis, performances of other resistive sensors are identical (Flexiforce © ) or lower (F-Socket © , Rincoe) than the FSA © sensor. Measurement is repeatable for all resistive sensors [START_REF] Ferguson-Pell | Evaluation of a sensor for low interface pressure applications[END_REF][START_REF] Lai | Validation of the Pliance X System in measuring interface pressure generated by pressure garment[END_REF]. Other resistive sensors drift as well: Flexiforce sensors' measurements increase or decrease with time [22] [26]; Rincoe SFS and F-Socket © from Tekscan © sensors' measurements increase with time [21] [25]. The increase or decrease of the measurement varies from 7.4% to 11.9% in twenty minutes [START_REF] Polliack | Scientific validation of two commercial pressure sensor systems for prosthetic socket fit[END_REF]. According to the literature, the curvature of the measurement surface has an influence, for other resistive sensors than FSA © sensor on the measurement regardless of the pressure range. The sensitivity of the Tekscan © 's Flexiforce © sensor is modified with radius of curvature [START_REF] Ferguson-Pell | Evaluation of a sensor for low interface pressure applications[END_REF]. For Rincoe SFS and F-Socket © sensors from Tekscan © , accuracy decreases, drift error increases and hysteresis can increase or decrease with radius of curvature [START_REF] Polliack | Scientific validation of two commercial pressure sensor systems for prosthetic socket fit[END_REF]. No data was found to compare the FSA © sensor with other resistive sensors in term of reproducibility, surface condition and superposition of two pressure mapping system.

Comparison of the FSA pressure mapping system to the capacitive pressure mapping system It is also possible, according to data from the literature, to compare the FSA © sensors with other types of pressure mapping systems for measuring interface pressure: the X-Sensor © capacitive pressure mapping system [START_REF] Fergenbaum | Development of a dynamic biomechanical model for load carriage: Phase 4, Part C2: Assessment of Pressure Measurement Systems on Flat Surfaces for the Dynamic Biomechanical Model of Human Load Carriage[END_REF][START_REF] Hochmann | Evaluierung der Messmethoden zur Bewertung des Therapeutischen nutzens von Antidekubitus-Systemen[END_REF][START_REF] Völker | Auflagedruckmessung in der Dekubitusbehandlung[END_REF] and Novel © distributed sensors [START_REF] Lai | Validation of the Pliance X System in measuring interface pressure generated by pressure garment[END_REF]. For linearity, the X-Sensor © is linear [START_REF] Hochmann | Evaluierung der Messmethoden zur Bewertung des Therapeutischen nutzens von Antidekubitus-Systemen[END_REF] and measures 75.1% of the applied pressure [START_REF] Fergenbaum | Development of a dynamic biomechanical model for load carriage: Phase 4, Part C2: Assessment of Pressure Measurement Systems on Flat Surfaces for the Dynamic Biomechanical Model of Human Load Carriage[END_REF]. The capacitive sensor may demonstrate a worse performance than FSA © . The maximum measurement error for X-Sensor © is 65% of applied pressure or 27mmHg [START_REF] Völker | Auflagedruckmessung in der Dekubitusbehandlung[END_REF]. Novel © 's sensor demonstrates a superior performance: its linear coefficient is 0.997 and the measurement error is less than 1mmHg [START_REF] Lai | Validation of the Pliance X System in measuring interface pressure generated by pressure garment[END_REF]. But capacitive sensors have a greater hysteresis than resistive sensors. For example, the X-Sensor © hysteresis is 14% [START_REF] Hochmann | Evaluierung der Messmethoden zur Bewertung des Therapeutischen nutzens von Antidekubitus-Systemen[END_REF]. Measurement with capacitive sensors is repeatable [START_REF] Lai | Validation of the Pliance X System in measuring interface pressure generated by pressure garment[END_REF][START_REF] Chiang | An implantable capacitive pressure sensor for biomedical applications[END_REF]. According to the drift test, measured pressure with capacitive sensors increases with time [21] [26]. Concerning the surface condition, capacitive sensors, X-Sensor © and Novel © , allow better or worse measurement on soft surfaces depending on the thickness of these surfaces [START_REF] Hochmann | Evaluierung der Messmethoden zur Bewertung des Therapeutischen nutzens von Antidekubitus-Systemen[END_REF]. No data was found to compare the FSA © sensor with capacitive sensors in terms of reproducibility, curvature and superposition of two pressure mapping systems.

Considerations on the use of FSA © pressure mapping system for the clinical study of lumbar belt

Based on these results, it is necessary to take into account some points to develop the experimental protocol. First, to be accurate, measurement must be done in the same place and preferably by the same operator and in short time frame. It's easy to perform measurement in the same place, but it's more difficult, in a clinical field, to respect the two other points, because measurements is often done by more than one experimenter and it's difficult to find enough subjects in a short time frame. However, these two parameters have influence on the results with coupled parameters. Secondly, drift result shows the importance in the choice of the drift calibration period, drift being uncontrolled if the measuring time is higher. Actually, during calibration, the central value of the calibration interval is measured for a flexible period. Pressure mapping system was calibrated in this study with a flexible period of 60 seconds, but the period can be increased to more than 800 seconds to avoid drift. This solution permits to perform dynamic measurements. Third, improving the curvature test is necessary before beginning the clinical study to ensure that the measurement of low pressure will be accurate on curved surfaces. Fourthly, surface condition having an influence on the results, pressure measurements will be done between lumbar belts and a tee-shirt of the same composition for all experiments and all subjects. Whatever the surface condition, pressure measurement remains accurate in term of linearity and hysteresis. Finally, the pressure mapping systems will be used to never overlap while covering the whole trunk. To overcome the difficulty of this condition, measures will be taken side by side. All these conditions allow a suitable measurement of pressure and to compare pressure applied by lumbar belt in term of lumbar belt's types and patient's morphology.

To conclude, the FSA © sensor performance can be considered as better than other resistive sensors and demonstrates an identical performance to the capacitive sensor X-Sensor © with lower hysteresis.

Nevertheless, the capacitive sensor Novel demonstrates a better performance than the FSA © sensor, but has a higher drift effect. FSA © sensors can be a good choice for the future clinical study developed to measure the static pressure applied by the lumbar belt on the trunk, because this study will be done in the same place, in a short time frame, with the same operator, with no overlapped mapping system and between same types of surface. Indeed, the procedure described earlier with FSA © pressure mapping system still lacks of robustness for a routine clinical practice to evaluate pressure applied by lumbar belts prescribed to the low back pain patients.

Conclusion

In this study, four FSA © pressure mapping systems were characterized in term of linearity, hysteresis, repeatability, reproducibility, drift, curvature, surface condition and mapping system superposition. It was found that these pressure mapping systems are suitable for our application: pressure measurement between two soft surfaces, lumbar belt and the human trunk. Linearity, accuracy and hysteresis are adequate. Measurement is repeatable and suitable on a flat surface. The curvature of the surface measurement has no significant impact on the measured pressure.

However, it is necessary to take into account some recommendations before performing measurements with this FSA © sensor. To compare the results of different experiments, measurement must be performed in the same place, over a short timeframe, with the same operator. Calibration must be adapted to prevent sensor drift. The measurements shall concern the same type of surface. Moreover, it is important to avoid overlap of pressure mapping systems.

Further study is needed to evaluate the performance of the sensor on a curved surface when applied pressure is lower than 50mmHg and also how the sensor behaves when temperature and humidity change. 9. Results of mapping system superposition: 95% probability of a significant difference between the mapping system "from above" and "from the bottom" Table 10. Results of mapping system superposition: absolute differences between measured pressures with or without superposition for each pressure mapping system drift for 40mmHg applied pressure for mapping system C in the sensor 1, c. drift for 26mmHg applied pressure for mapping system D in the sensor 3

+1: 79mmHg -1 -1 -1 -1 +1 -1 -1 -1 -1 +1 -1 -1 +1 +1 -1 -1 -1 -1 +1 -1 +1 -1 +1 -1 -1 +1 +1 -1 +1 +1 +1 -1 -1 -1 -1 +1 10 +1 -1 -1 +1 11 -1 +1 -1 +1 12 +1 +1 -1 +1 13 -1 -1 +1 +1 14 +1 -1 +1 +1 15 -1 +1 +1 +1 16 +1 +1 +1 +1
453 454 9. Results of mapping system superposition: p_value of the statistical test to determine the statistically significant differences between mapping system "from above" and "from the bottom" Sensors 1 2 3

Between mapping system A: "from above" and mapping system B:

"from the bottom" 0.010 0.43 0.038

Between mapping system C: "from above" and mapping system D:

"from the bottom" 0.0041 0.015 0.0058 Table 10. Results of mapping system superposition: absolute differences between measured pressures with or without superposition for each pressure mapping system in mmHg

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 :Figure 6 .

 123456 Figure 1. FSA Pressure mapping system Figure 2. Experimental device for the second hysteresis test Figure 3. Experimental device for curvature test Figure 4. Results of linearity: measured pressure depending on applied pressure for the sensor 1 of the pressure mapping system A Figure 5: Results of the second hysteresis test (test in all sensors of a pressure mapping system): mean measured pressure depending on applied pressure for mapping system A Figure 6. Results of drift: a. drift for 26mmHg applied pressure for mapping system A in the sensor 1, b.

Figure 7 .

 7 Figure 7. Results of curvature: normalized measured pressure depending on applied pressure and radius of cylinders Rc for mapping system A

Figure 1 .Figure 2 .Figure 3 . 494 Figure 4 .Figure 5 :Figure 6 . 3 Figure 7 .

 12349445637 Figure 1. FSA Pressure mapping system

  test. The repeatability of experiments was assessed by performing the first hysteresis test three times. Repetitions were compared by statistical analysis as explained in paragraph 2.4.

	Reproducibility test. The reproducibility of time, location and operators was tested. The first hysteresis
	test was performed in two different rooms, by two different operators and at two different times separated
	by two months.

Table captions Table 1 .

 captions1 Design of experiments to test the reproducibility of time, place and operators

Table 2 .

 2 Results of linearity: linear regression coefficient

Table 3 .

 3 Results of linearity: dispersion and standard deviation for sensor 1 and mapping system C

Table 4 :

 4 Results of hysteresis: test in only one sensor per mapping system

Table 5 .

 5 Results of hysteresis: test in all sensors per mapping system

Table 6 .

 6 Results of the design of experiments for reproducibility. t: time, o: operators, l: location, w: weight

Table 7 .

 7 Results of surface condition: 95% probability of a significant difference between measured pressure with and without fabric between the pressure mapping system and the table are different for the five tested fabrics

Table 8 .

 8 Results of surface condition: linear regression coefficient for the second and third surface condition tests

Table

Table 3 .

 3 Results of linearity: Dispersion and standard deviation for sensors with the best and the worst

	linearity.
	Sensors	Applied pressure (mmHg)	Dispersion (mmHg)	Standard deviation
		6.4	0	0
		13	1.74	0.641
	With the best linearity:	26	3.32	2.35
	sensor 1, mapping	39	2.97	1.54
	system C	53	3.99	1.97
		79	9.05	3.22
		96	15.6	6.30
		6.4	0	0
		13	0.103	0.0201
	With the worst linearity:	26	0.120	0.0320
	sensor 3, mapping	39	1.01	0.376
	system C	53	1.74	0.775
		79	4.35	1.97
		96	5.52	3.08

Table 4 :

 4 Results of hysteresis: test in only one sensor per mapping system

	Mapping system				A								B
	Sensor	1	2	3	4	5	6	7	8	1	2	3	4	5	6	7	8
	Hysteresis	15.2 16.9 7.63 4.58 11.9 7.84 16.1 10.1 3.51 6.38 11.7 0.228 18.3 15.7 27.9 9.20
	Eh (%)
	Mapping				C								D
	system
	Sensor	1	2	3	4	5	6	7	8	1	2	3	4	5	6	7	8
	Hysteresis	3.99 4.53 7.13 2.80 5.26 3.15 9.93 2.70 6.52 3.15 3.66 3.63 2.27 3.99 10.5 7.20
	Eh (%)

Table 5 .

 5 Results of hysteresis: test in all sensors per mapping system

	Mapping system	A	B	C	D
	Hysteresis Eh (%)	9.41	7.87	7.58	6.29

Table 6 .

 6 Results of the design of experiments for reproducibility. t: time, o: operators, l: location, w:

	weight
	Polynomial coefficient	Value	Probability
	β 0	67.76	0
	β t	0.28	0.70
	β o	1.47	0.054
	β l	2.08	0.0080
	β w	19.19	0
	β to	1.94	0.0013
	β tl	-3.84	0
	β tw	-0.17	0.82
	β ol	0.66	0.38
	β ow	1.24	0.10
	β tw	-0.73	0.33

Table 7 .

 7 Results of surface condition: p_value of the statistical test to determine the statistically significant differences between measured pressure with and without fabric between the pressure mapping system and the table.

	Fabric	1	2	3	4	5
		2.97e -21	3.36e -18	3.77e -47	2.48e -31	8.17e -57

Table 8 .

 8 Results of surface condition: linear regression coefficient for the second and third surface

	condition tests
	Sensors	1	2	5	7
	Second surface condition test	0.97	0.95	0.97	0.99
	Third surface condition test	0.92	0.93	0.98	0.95

Acknowledgements

The authors would like to thank Mr. Poirier for his assistance with this work.

Funding:

This research received no specific grant from any funding agency in the public, commercial, or not-forprofit sectors.

Conflict of interest

There is no conflict of interest in this study.


Manuel Davy

Benoit Leprettre

Christian Doncarli

Nadine Martin

Tracking of spectral lines in an ARCAP time-frequency representation

come


Kalthoum Ben M'barek

Diana Molino

Sandrine Quignard

Marie-Aude Plamont

Yong Chen

Philippe Chavrier

Jacques Fattaccioli
email: jacques.fattaccioli@ens.fr

Phagocytosis of immunoglobulin-coated emulsion droplets

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

Phagocytosis is a process that consists in the ability of a cell to internalize objects larger than 0.5 microns. Whereas unicellular organisms use phagocytosis to capture and eat preys, in multicellular organisms it represents a fundamental part of innate immunity, organ homeostasis and tissue remodeling. Innate immunity relies on a specialized subset of cells, the professional phagocytes, which patrol the organism, identify, ingest and eliminate pathogens. Among them, macrophages are versatile cells residing in tissues that are able to scavenge worn-out cells and participate to the activation of the adaptive immune response [START_REF] Guilliams | Dendritic cells, monocytes and macrophages: a unified nomenclature based on ontogeny[END_REF].

Phagocytosis by macrophages is triggered by the binding of the target to specific receptors, present at the surface of the phagocyte. Several receptors have been identified so far, each involving different signaling pathways and ingestion mechanisms [START_REF] Rosales | Molecular mechanisms of phagocytosis[END_REF]. In the case of Fcγ receptors-mediated phagocytosis [START_REF] Flannagan | The cell biology of phagocytosis[END_REF], antigens present at the surface of the target are bound by specific soluble immunoglobulins (IgGs). Fc regions of those IgGs are actively recognized [START_REF] Flannagan | Dynamic macrophage "probing" is required for the efficient capture of phagocytic targets[END_REF] by the Fcγ receptors (FcγR) from the phagocyte surface, which form clusters and trigger the internalization. Engulfment then occurs by an actin-driven membrane extension and closure [START_REF] Swanson | Shaping cups into phagosomes and macropinosomes[END_REF] of a phagocytic cup around the foreign body to create a specific degradative compartment: the phagosome [START_REF] Swanson | The extraordinary phagosome[END_REF].

Most of our current quantitative knowledge on phagocytosis is based on the use of various model particles such as heat-or chemically inactivated bacteria or yeast [START_REF] Underhill | Macrophage recognition of zymosan particles[END_REF] and polymer microparticles [START_REF] Tabata | Phagocytosis of polymer microspheres by macrophages[END_REF]. The versatility and reproducibility of the latter has allowed monitoring the influence of parameters such as size and surface chemistry [START_REF] Tabata | Phagocytosis of polymer microspheres by macrophages[END_REF][START_REF] Pacheco | Effects of microparticle size and Fc density on macrophage phagocytosis[END_REF][START_REF] Champion | Role of particle size in phagocytosis of polymeric microspheres[END_REF][START_REF] Park | Effect of shape and size of polymer particles on cellular internalization[END_REF][START_REF] Kawaguchi | Phagocytosis of latex particles by leucocytes. I. Dependence of phagocytosis on the size and surface potential of particles[END_REF][START_REF] Koval | Size of IgG-opsonized particles determines macrophage response during internalization[END_REF], shape [START_REF] Champion | Role of target geometry in phagocytosis[END_REF][START_REF] Clarke | Curvature recognition and force generation in phagocytosis[END_REF] and mechanical properties [START_REF] Beningo | Fc-receptor-mediated phagocytosis is regulated by mechanical properties of the target[END_REF] of the target on the mechanism of phagocytosis. It was observed that the uptake of polymer particles is the most efficient for 2-3 microns-large targets, increases with the density of IgGs attached to the surface [START_REF] Tabata | Phagocytosis of polymer microspheres by macrophages[END_REF][START_REF] Pacheco | Effects of microparticle size and Fc density on macrophage phagocytosis[END_REF][START_REF] Champion | Role of particle size in phagocytosis of polymeric microspheres[END_REF][START_REF] Park | Effect of shape and size of polymer particles on cellular internalization[END_REF][START_REF] Kawaguchi | Phagocytosis of latex particles by leucocytes. I. Dependence of phagocytosis on the size and surface potential of particles[END_REF][START_REF] Champion | Role of target geometry in phagocytosis[END_REF][START_REF] Sharma | Polymer particle shape independently influences binding and internalization by macrophages[END_REF][START_REF] Zhang | Coordination of Fc receptor signaling regulates cellular commitment to phagocytosis[END_REF] and depends on the local curvature of the target in contact with the cell [START_REF] Champion | Role of target geometry in phagocytosis[END_REF][START_REF] Clarke | Curvature recognition and force generation in phagocytosis[END_REF]. Antigens present on the surface of endogenous targets, such as erythrocytes [START_REF] Gallo | The influence of IgG density and macrophage Fc (gamma) receptor cross-linking on phagocytosis and IL-10 production[END_REF], cancerous and apoptotic cells [START_REF] Kershaw | Immunology. Making macrophages eat cancer[END_REF][START_REF] Brown | Eaten alive! Cell death by primary phagocytosis: "phagoptosis[END_REF] exhibit a lateral mobility [START_REF] Cherry | Rotational and lateral diffusion of membrane proteins[END_REF][START_REF] Edidin | Lateral diffusion of wild-type and mutant Ld antigens in L cells[END_REF] that can't be mimicked by adhesive proteins adsorbed on the solid surface of common polymeric targets [START_REF] Perica | Linking Form to Function: Biophysical Aspects of Artificial Antigen Presenting Cell Design[END_REF]. However, in the immunological context, phenomena as for example the formation of the immune synapse [START_REF] Iber | Formation of the B cell synapse: retention or recruitment?[END_REF][START_REF] Lee | The synapse assembly model[END_REF], or the fabrication of artificial antigen presenting cells [START_REF] Turtle | Artificial antigen-presenting cells for use in adoptive immunotherapy[END_REF], require the ability of antigens or receptors to be laterally mobile at the interface of the target. There is hence a need of novel particulate materials allowing the free diffusion of the adhesive molecules bound to their surface.

Oil-in-water emulsions have been already used since half a century as colloidal drug carriers for various therapeutic applications [START_REF] Tamilvanan | Oil-in-water lipid emulsions: implications for parenteral and ocular delivering systems[END_REF]. Versatile in terms of volume and surface composition, they can be fabricated with a narrow size distribution ranging from a few tenth of nanometers to several hundreds of microns [START_REF] Leal-Calderon | Emulsion Science: Basic Principles[END_REF]. Emulsions have also been used in a biophysical context as deformable objects to measure forces existing in living embryonic tissues [START_REF] Campàs | Quantifying cell-generated mechanical forces within living embryonic tissues[END_REF] and those generated by growing actin networks in-vitro [START_REF] Trichet | VASP governs actin dynamics by modulating filament anchoring[END_REF]. Carefully functionalized with biologically-relevant adhesive molecules, they are able to interact with cells in a specific manner [START_REF] Bourouina | Biomimetic droplets for artificial engagement of living cell surface receptors: the specific case of the T-cell[END_REF] and can be used as model particles for cell adhesion modeling [START_REF] Fattaccioli | Specific wetting probed with biomimetic emulsion droplets[END_REF][START_REF] Pontani | Biomimetic emulsions reveal the effect of mechanical forces on cell-cell adhesion[END_REF][START_REF] Bourouina | Formation of specific receptor-ligand bonds between liquid interfaces[END_REF]. In addition to giving access to a controlled range of biomolecules densities at the surface, emulsion droplets have a liquid interface allowing proteins bound to it to be laterally mobile [START_REF] Pontani | Biomimetic emulsions reveal the effect of mechanical forces on cell-cell adhesion[END_REF][START_REF] Bourouina | Formation of specific receptor-ligand bonds between liquid interfaces[END_REF][START_REF] Fattaccioli | Size and fluorescence measurements of individual droplets by flow cytometry[END_REF], as in our case the IgGs. However, to our knowledge there is no report of any observations at the scale of a single droplet interacting with a phagocyte, nor obvious elements about the possible influence of the nature of the interface (liquid vs. solid) on the uptake, despite its biophysical [START_REF] Brochard-Wyart | Adhesion induced by mobile binders: dynamics[END_REF] and biological relevance [START_REF] Flannagan | Dynamic macrophage "probing" is required for the efficient capture of phagocytic targets[END_REF][START_REF] Cherry | Rotational and lateral diffusion of membrane proteins[END_REF][START_REF] Edidin | Lateral diffusion of wild-type and mutant Ld antigens in L cells[END_REF].

We thus propose to use IgG-functionalized oil-in-water emulsion droplets for phagocytosis studies as probes able to mimick the lateral mobility of antigens present on the surface of cellular targets. Herein we decribe a fabrication route of monodisperse, IgG-coated emulsion droplets made from soybean oil and biotinylated phospholipids. We show that IgGs-coated liquid emulsion droplets are efficiently and specifically internalized through FcγR-mediated phagocytosis in-vitro. During the recognition by macrophages, we show that IgGs are driven in the contact zone and colocalize with an increase of the local concentration of FcγRs, while polymerized F-actin is visible during the extension and closure of the phagocytic cup. By comparing the phagocytosis efficiency of droplets and polystyrene particles in similar conditions of IgG coating, we suggest that the lateral mobility of the IgGs at the interface of a target enhances its ability to be internalized.

Materials and methods

Biotinylation and opsonization of the emulsion droplets

The lipid-containing oil was obtained by dilution of DSPE-PEG(2000)-Biotin phospholipids (Avanti Lipids, Alabama, USA) in soybean oil at concentrations ranging from 0.015 to 0.15 mg.mL -1 (30 min sonication followed by evaporation of the chloroform from the oil). This oil, cooled to room temperature, was dispersed and emulsified by hand in an aqueous continuous phase containing 15 %w/w of Poloxamer 188 block polymer surfactant (CRODA, East Yorkshire, UK) and 1 %w/w sodium alginate (Sigma-Aldrich, St. Louis, MO, USA) at a final oil fraction equal to 75%. The rough emulsion was sheared in a Couette cell apparatus at a controlled shear rate of 5000 s -1 following the method developed by Mason et al. [START_REF] Mason | Emulsification in Viscoelastic Media[END_REF] to narrow the droplet size distribution to 7 ± 2 µm. For storage and handling purposes the emulsion were diluted to an oil fraction of 60 %w/w with 1 %w/w of poloxamer 188 in the continuous phase and stored at 12°C in a Peltier-cooled cabinet for several weeks. Size distribution of the emulsion droplets was measured by microscopy and image analysis.

Coupling of IgGs to biotins present on the surface of the droplets was obtained after a 30 min incubation of the droplets in 0.003 -0.3 mg.mL -1 (2.10 -8 -2.10 -6 mol.L -1 with a molecular weight of 150 kDa) fluorescent antibiotin IgGs solutions (Alexa Fluor 488-conjugated IgG fraction monoclonal mouse anti-biotin (Jackson Immunoresearch, West Grove, PA, USA) at room temperature in phosphate buffer (PB, pH=7.2, 20 mM, 0.2 %w/w Tween 20). The droplets were rinsed twice in the same buffer and finally suspended in (DMEM, Life Technologies, Carlsbad, CA, USA) containing high glucose, no glutamine and no phenol red directly prior to use in cell assays.

Opsonization of the polystyrene beads by direct adsorption of IgGs

Polystyrene beads (6 µm diameter, Polysciences, Warrington, PA, USA) were functionalized by direct adsorption of rabbit anti-goat IgGs FITC conjugate (Sigma-Aldrich) at concentrations ranging from 0.4 to 1 mg.mL -1 for one hour at room temperature.

Opsonization of the polystyrene beads using biotinylated BSA and anti-biotin

IgGs

Polystyrene beads (6 µm diameter, Polysciences, Warrington, PA, USA) were incubated with biotin-conjugated BSA (Sigma-Aldrich, St. Louis, MO, USA) at a concentration of 5 mg.mL - 1 for 1 hour in a PBS buffer. Beads were then washed and incubated for 30 min at 37°C in a fluorescent antibiotin IgG solution (Alexa Fluor 488-conjugated mouse anti-biotin, Jackson Immunoresearch, West Grove, PA, USA) at concentration of 2.10 -1 mg.mL -1 in PBS.

Characterization of opsonization degree of the particles

Liquid and solid particles were characterized with a BD Accuri C6 cytometer (BD Biosciences, New Jersey, USA) according to a method we developed in the past [START_REF] Fattaccioli | Size and fluorescence measurements of individual droplets by flow cytometry[END_REF] for quasi-monodisperse emulsions. In brief, the fluorescence intensity of the particles is proportional to the amount of fluorescent proteins on their surface and can be converted in a total number of fluorophores per particle using a commercial quantification kit (Quantum™ Alexa Fluor® 488 MESF beads and Quantum™ FITC-5 MESF Premix, Bangs Laboratories, Fishers, IN, USA). The number of IgGs per droplet is then estimated by dividing the number of fluorophores per droplet by the average number of dyes per IgG, which ranges from 5-8 for Alexa 488 and 3-4 for FITC according to the manufacturer. Using a value of 5 Alexa 488 dyes per IgG (or 3 FITC), the number of IgGs ranges from 10 3 to 10 5 per droplet.

Cell culture

Lifeact-mCherry RAW 264.7 murine macrophages [START_REF] Riedl | Lifeact: a versatile marker to visualize F-actin[END_REF] were obtained from Pierre Jurdic (IGFL, ENS Lyon) and used as model macrophages. The cells were cultured at 37°C under a 5% CO 2 atmosphere in Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% heat inactivated fetal bovine serum (Life Technologies), 1.0 g.L -1 D-glucose, 1.1 g.L -1 sodium pyruvate (Life Technologies) and 1% penicillin-streptomycin (Life Technologies).

The expression of the Lifeact-mCherry was maintained through the intermittent addition of 4 µg.mL -1 puromycine (Life Technologies) to the culture medium. Confluent monolayers of cells were resuspended after trypsinization and plated in 6 wells cell culture plates lined with glass coverslips (20x20mm, VWR, Radnor, PA, USA) 24 hours prior to phagocytosis studies.

Experiments were performed with cell densities close to 10 6 cells per glass coverslip that correspond to ca. 60% confluence.

Experimental setup of the phagocytosis assay.

The custom-built chamber consisted of two glass coverslips assembled with 100 µm thick double-sided tape (3M) to form a 20 x 20 mm experimental chamber. The coverslips with the adherent cells were first washed with DMEM without FBS to eliminate dead cells. Lipid droplets or polystyrene beads suspended at an initial concentration of two drops per cell in DMEM without FBS were injected in the observation chambers and incubated at 37°C under 5% CO 2 for up to 120 min in the presence of the macrophages. For each time point, the solution in the chambers was replaced by a fixation solution for 20 min (4 %w/w paraformaldehyde in DPBS-1X, Sigma-Aldrich). Once fixed, the cells were washed again with DPBS-1X, and a mixture of Atto 555-phalloidin and DAPI (Sigma-Aldrich, St. Louis, USA) was added to each chamber for 30 min to respectively make polymerized actin filaments and cell nuclei fluorescent for further observation. The chambers were rinsed 3 times with DPBS-1X and observed under the microscope. Unless stated, all the experiments were run in triplicate.

Microscopy

Brightfield and fluorescent images of cells with attached and internalized droplets were acquired on a Zeiss Axio Observer Z1 microscope (Oberkochen, Germany) equipped with a Clara E CCD camera (Andor Scientific, Belfast, UK) and controlled by the µManager software [START_REF] Edelstein | Computer control of microscopes using µManager[END_REF]. Confocal microscopy observations were performed on a Zeiss LSM 710 microscope. Observations were performed in DMEM without FBS at 37°C for live-cell imaging.

Quantification of phagocytosis

Phagocytosis efficiency was characterized by manually measuring, over ca. 20 fields of observation, the percentage of cells having internalized from 0 to a maximum of 5 droplets on a subpopulation of around 200 randomly chosen macrophages per condition. The percentage of internalizing cells (%IC) after a given incubation time and the phagocytic index (PI) were calculated. PI is defined as the weighted arithmetic mean of the total number of internalized particles per cell. The data related to the phagocytic index are reported in the Supporting Materials. The evolution of %IC as a function of the IgG density on the droplets is fitted by a Hill equation [START_REF] Weiss | The Hill equation revisited: uses and misuses[END_REF] :

%IC = %IC !"#

RESULTS

Design of opsonized lipid droplets

A series of IgG-coated lipid droplets, with an average diameter of 7 ± 2 µm, were produced (Figure S1A) to study their internalization by macrophages in-vitro. Soybean oil was chosen for the lipidic core of the droplets as it gives stable and biocompatible emulsions that are commonly used both in pharmaceutical formulations and for biophysical studies [START_REF] Bourouina | Biomimetic droplets for artificial engagement of living cell surface receptors: the specific case of the T-cell[END_REF][START_REF] Fattaccioli | Specific wetting probed with biomimetic emulsion droplets[END_REF][START_REF] Chenevier | Interaction of cationic colloids at the surface of J774 cells: a kinetic analysis[END_REF][START_REF] Bottier | Active transport of oil droplets along oriented microtubules by kinesin molecular motors[END_REF]. Quasi-monodispersity was achieved by using the method developed by Mason et al. [START_REF] Mason | Emulsification in Viscoelastic Media[END_REF]. To induce FcγR-mediated phagocytosis, the surface of the droplets exposes the Fc domain of IgGs. To ensure functional opsonisation of the droplets, fluorescent mouse antibiotin IgGs were conjugated to biotins present at the surface of the droplets. This functionalization was obtained by first incorporating in the soybean oil phospholipids with a poly(ethylene)glycol spacer linked to a biotin (Figure 1A). The amphiphilic nature of the modified lipids makes them gather at the interface of the droplets (Figure 1B), allowing biotins to be further conjugated. The IgGs were chosen fluorescent to allow their visualization and the quantification of the opsonization on the surface of the droplets (Figure 1C) by flow cytometry (see Supplementary Information). Presence of biotinylated lipids at the interface is a necessary condition to have an attachment of IgGs on the surface of the droplets as direct adsorption of the IgGs alone is not efficient (Figure S1B). In our conditions, the number of IgGs per droplet varies from 10 3 to 5.10

Phagocytosis of the lipid droplets

RAW 264.7 murine macrophages were incubated with lipid droplets in custom-built observations chambers made from two glass coverslips and double-sided tape spacers (Figure 2A). Droplets are injected in the chambers at initial concentrations of 2 droplets per cell and then, chambers are turned upside-down during incubation to let the buoyancy force make the droplets encounter the cells. Incubation time was varied from 5 min to 2 hours.

Brightfield microscopy reveals that macrophages successfully engulf the droplets (Figure 2B) and that during the internalization by phagocytosis, the cell creates an actin-rich phagocytic cup by extending its membrane around the droplet (Figure 2C). To quantify the phagocytosis process, we measure the distributions of internalizing cells as a function of the number of internalized droplets at different exposure times. After 45 minutes, the system reaches a saturation where 50% of cells are able to internalize (Figure 3A) between 1 and 5 droplets (Figure 3B), with a majority of macrophages engulfing from 1 to 3 droplets. This plateau correspond to about 50% of the droplets initially added being internalized. Figure 3A shows that the phagocytosis assay has a characteristic time of ca. 15 min.

Once the phagocytic process starts, an IgG-coated droplet is fully internalized in approximately 5 minutes (Figure 3C), which is in accordance with what has been measured so far in the literature with polymer particles in the same size range [START_REF] Champion | Role of target geometry in phagocytosis[END_REF].

Specificity and IgG concentration-dependent phagocytosis

To assess the specificity of the droplets uptake towards the presence of IgGs on their surface we have compared the phagocytic efficiency of droplets with different amounts of IgGs: bare droplets made from pure soybean oil, biotinylated droplets made from soybean oil in which the biotinylated lipids have been dissolved, and opsonized droplets with anti-biotin IgGs on their surface. While bare and biotinylated droplets are almost inert towards phagocytosis, IgGs-coated droplets are efficiently internalized by the macrophages (Figure 4A and Figure S2C). The excellent level of control of opsonization density on the lipid droplets, in addition to the specificity of their phagocytosis, is used to measure the dose-response relationship of the phagocytosis by macrophages with the number of IgGs on the surface of droplets.

Nature of the interface and IgGs clustering in the zone of contact

To qualitatively evaluate the influence of the nature of the material on the ability of a target to be internalized, we have compared the phagocytosis of IgGs-coated droplets to IgGscoated solid polystyrene beads in the same size range (6 microns). As polystyrene beads are denser than water, the beads were allowed to settle down by gravity on the coverslips plated with cells, as shown on the Figure S5. Two opsonin densities within the plateau region of the dose-internalization curve (Figure 4B) were investigated. Figure 5A shows that polystyrene particles coated with a low density of IgGs are poorly internalized, whereas at higher opsonization densities, their uptake efficiency is comparable to the opsonized droplets value within the plateau region. As expected, the spatial distribution of the IgGs on the surface of the polystyrene beads remains homogeneous, no matter the IgG density. Conversely, droplets show a constant uptake efficiency over the range of IgG densities (Figure 5B) that have been considered. Figure 5B also shows that at a low IgG density, the spatial distribution of the IgGs is heterogeneous and exhibits a strong clustering of the opsonins in the zone of contact with the cells. At higher opsonization densities, however, no clustering is observed with hardly any effect on the phagocytosis efficiency as compared to the low IgG condition.

Immunolocalization experiments show that when an IgG-coated droplet (3.10 4 IgGs per particle) adhere to the macrophage, the IgG clusters colocalize with an increase of the local concentration of FcγRs (Figure 5C). At this stage, no nascent phagocytic cup is visible and the actin cortex is not yet modified. These clusters form within a few minutes of contact between a droplet and a macrophage and exhibit a highly dynamic behavior during the recognition phase (Figure 5D).

DISCUSSION

A wide range of liquid emulsified systems have been industrially developped these last decades with commercial applications in drug and oxygen delivery, in topical formulations or as dietary substitutes [START_REF] Tamilvanan | Oil-in-water lipid emulsions: implications for parenteral and ocular delivering systems[END_REF][START_REF] Leal-Calderon | The design of emulsions and their fate in the body following enteral and parenteral routes[END_REF]. Most of the characterization studies in which such materials are involved rely on macroscopic measurements made at the level of an organ or the whole organism with the aim to improve the stability and monitor the fate and the effect of emulsions on the body [START_REF] Leal-Calderon | The design of emulsions and their fate in the body following enteral and parenteral routes[END_REF]. In the context of in-vitro phagocytosis studies, emulsions coated by generic biomolecules (LPS, albumin, etc…) have enabled to monitor the effect of physico-chemical parameters such as temperature, surface composition or the presence of various drugs and chemical species in the medium [START_REF] Davis | The influence of emulsifying agents on the phagocytosis of lipid emulsions by macrophages[END_REF][START_REF] Forsgren | Quantitative phagocytosis by human polymorphonuclear leucocytes. Use of radiolabelled emulsions to measure the rate of phagocytosis[END_REF][START_REF] Iwamoto | Polysaccharide-coated oil droplets in oil-in-water emulsions as targetable carriers for lipophilic drugs[END_REF][START_REF] Matsui | Phagocytosis by macrophages. III. Effects of heat-labile opsonin and poly(L-lysine)[END_REF][START_REF] Stossel | Quantitative studies of phagocytosis by polymorphonuclear leukocytes: use of emulsions to measure the initial rate of phagocytosis[END_REF] on the phagocytic process. Although experimental procedures and sizes of objects used here are different, the timescales of the uptake reported on the Figure 3 are in accordance with former kinetics measurements reported in the literature related to the uptake of opsonized droplets [START_REF] Forsgren | Quantitative phagocytosis by human polymorphonuclear leucocytes. Use of radiolabelled emulsions to measure the rate of phagocytosis[END_REF][START_REF] Matsui | Phagocytosis by macrophages. III. Effects of heat-labile opsonin and poly(L-lysine)[END_REF] and polystyrene beads [START_REF] Koval | Size of IgG-opsonized particles determines macrophage response during internalization[END_REF][START_REF] Champion | Role of target geometry in phagocytosis[END_REF].

Specificity of the uptake towards the presence of opsonins is a crucial requirement when dealing with the conception of new materials relevant for phagocytosis studies and targeting. Figure 4A shows that whereas IgG-caoted droplets are efficiently internalized, bare and biotinylated droplets, from which IgGs are absent from their surface, are not uptaken by macrophages. This absence of internalization of non-opsonized droplets agrees with results reported in the past [START_REF] Davis | The influence of emulsifying agents on the phagocytosis of lipid emulsions by macrophages[END_REF] for non-opsonized emulsions fabricated with similar ingredients and in the absence of FBS in the medium in which the phagocytic assays were performed. As particles bearing a strong positive or negative surface charge are known to be readily internalized in a non-specific manner [START_REF] Tabata | Phagocytosis of polymer microspheres by macrophages[END_REF], we measured the ζ-potential of the different lipid droplets (Figure S4) to assess its variation upon opsonization. ζ-potential of the droplets is slightly negative, close to -20 mV, and does not depend on the functionalization of the droplet surface. Hence this parameter cannot account for the observed differences in terms of efficiencies between bare, biotinylated and IgG-coated droplets. Thus the strong phagocytosis efficiency of IgGs-coated droplets is a consequence of the sole presence of the IgGs on their surface.

The specific internalization of IgG-coated droplets allows measuring the phagocytic efficiency of emulsion droplets over a two orders of magnitude dynamics of IgG densities.

Uptake of the droplets increases with the amount of IgGs on the surface and reaches a maximum for IgG densities above ca. 2.10 4 IgGs per droplet (Figure 4B and Figure S3A).

This value corresponds to roughly 1% of a full monolayer of IgGs if we consider an occupation area of 120 nm 2 per IgG at the saturation of the interface [START_REF] Werner | The shape of immunoglobulin G molecules in solution[END_REF].

Recently, Gallo et al. [START_REF] Gallo | The influence of IgG density and macrophage Fc (gamma) receptor cross-linking on phagocytosis and IL-10 production[END_REF] studied the influence of IgG density at the surface of red blood cells (sRBC) on their phagocytosis by primary macrophages. RBCs were opsonized by IgGs in density ranges that are similar to those measured in our experiments. The analysis of the potency values of IgGs-coated droplets and opsonized sRBC shows that the uptake of droplets is one order of magnitude more sensitive to the IgG density than for sRBCs. Indeed, as few as 3.10 3 IgGs are sufficient to reach 50% of the saturation value for opsonized droplets, whereas this value is close from 3.10 4 IgGs in the case of RBCs. If we hypothesize that the two kinds of macrophages have comparable behaviors, we may conclude that IgG-coated droplets could constitute a valuable alternative material to model targets such as red blood cells for in-vitro studies.

Within the range of opsonins densities where the droplet uptake is maximal, our experiments reveal noticeable differences in terms of phagocytic efficiencies between liquid emulsion droplets and solid polystyrene particles. Whereas the phagocytic efficiency is the same for low and high opsonization densities, Figure 5A shows that polystyrene beads need to have their surface almost fully saturated with IgGs to be at the maximum of internalization.

This last observation is in accordance with previous studies performed with opsonized particles similar in size to the ones used in our experiments [START_REF] Flannagan | Dynamic macrophage "probing" is required for the efficient capture of phagocytic targets[END_REF][START_REF] Pacheco | Effects of microparticle size and Fc density on macrophage phagocytosis[END_REF][START_REF] Zhang | Coordination of Fc receptor signaling regulates cellular commitment to phagocytosis[END_REF].

For low IgG densities, the different internalization efficiency between the beads and the droplets could be a consequence of a difference in terms of mechanical properties of the targets. Indeed, in the case of polyacrylamide beads fabricated with various reticulation degrees, it has been shown that rigid particles are more efficiently uptaken than deformable ones [START_REF] Beningo | Fc-receptor-mediated phagocytosis is regulated by mechanical properties of the target[END_REF]. Our experiments are not following this tendency, since rigid polystyrene beads are less efficiently uptaken than deformable liquid droplets. This parameter is hence unable to explain the discrepancy between the internalization efficiency of opsonized beads and droplets.

Beads and droplets differ in terms of mechanical properties, but also in terms of the According to Zhang et al. for the case of polystyrene beads as large as the emulsion droplets of our study, the density of IgGs present on the surface of the particles controls the efficiency of the internalization, but has no influence on the kinetics of the cup closure [START_REF] Zhang | Coordination of Fc receptor signaling regulates cellular commitment to phagocytosis[END_REF].

We understand these results as characteristic from an all-or-none ingestion mechanism similar to the phagocytic trigger model [START_REF] Swanson | Phagocytosis by zippers and triggers[END_REF], and activated above a certain density of IgG-FcγR complexes in region of contact between the bead and the cell. According to this scheme, IgG-coated droplets have a competitive advantage over solid beads since sole passive diffusion on the liquid interface can help gather all the IgGs present on the droplet, increase the local concentration of opsonins in the zone of contact, increase the expression of receptors, cluster IgG-FcγR complexes and finally cross the threshold that activates the uptake, as sketched on the Figure 5E.

CONCLUSION

In conclusion, we have designed and characterized new synthetic targets for phagocytosis studies, IgGs-coated emulsion droplets, that are efficiently and specifically uptaken by macrophages. From the material point of view, droplets need one order of magnitude less opsonins on their surface as compared to polystyrene beads to reach the maximal internalization efficiency, which can be a valuable advantage if we think in term of particle design for e.g. pharmaceutical applications. Microscopic analyses have shown that the adhesion of droplets to macrophages is accompagnied by the formation of IgG clusters in the region of contact, which increase the local effective concentration of opsonins and finally triggers phagocytosis. To rationalize the characterization of the engineered droplets, we consider looking in a near future at the macrophage response cascade occurring following the internalization and the phagosome maturation, by assaying first cytokine secretion, respiratory burst and reactive oxygen species production, and second the fate of the droplets on a long-term timescale.

FIGURES AND CAPTIONS

Figure 4B and

 4B Figure S3Dalso shows that the proportion of macrophages internalizing more than one

  nature of their interface, with strong implications on the functionalization protocols: whereas IgGs present at the interface of the droplets are specifically bound to biotinylated phospholipids dissolved in the oil, those bound the the beads are directly adsorbed on the polystyrene surface. The functionality of an antibody deposited on a surface by adsorption can decrease either by a wrong orientation of the Fc region towards the FcγRs of the cells, or by its partial denaturation on the surface[START_REF] Nakanishi | On the adsorption of proteins on solid surfaces, a common but very complicated phenomenon[END_REF][START_REF] Rao | Oriented immobilization of proteins[END_REF]. The discrepancy between the beads and the droplets uptake at low IgG density could hence be a consequence of the coating strategy used for the beads on the functionality of the IgGs bound to them. In comparison to the measurement of the phagocytic efficiency of the IgG-adsorbed beads, we measured the internalization efficiency of polystyrene beads coated with an alternate functionalization route that avoids the contact of the IgGs with the solid surface. In this latter case, anti-biotin mouse IgGs are specifically bound to a primary and saturated layer of biotinylated BSA adsorbed on the beads, hence diminishing the possibility of the IgGs to be denaturated and possibly improving their orientation. The comparaison of the phagocytic efficiency of beads prepared following this protocol and beads opsonized by direct adsorption show that the functionalization strategy of the particles has no effect on the internalization efficiency (Figure5Aand FigureS6). The hypothesis of a bias in the measurements related to the chemical nature of the surfaces and its potential effect on the IgG functionality can be ruled out.Microscopic observations show drastic visual differences about the behavior of theIgGs present on the surface of the beads or the droplets during the adhesion step. The IgG distribution remains homogeneous around the polystyrene beads no matter the IgG density, as a consequence of the solid nature of the surface that forbids the lateral diffusion of the opsonins. Conversely, IgGs present on the surface of the droplets cluster in the zone of contact with the cell for low IgG densities whereas no clustering is visible for high IgG densities (Figure5A). Clustering of proteins bound to the interface of emulsion droplets has been reported in various experiments involving the adhesion of droplets to functional substrates[START_REF] Bourouina | Biomimetic droplets for artificial engagement of living cell surface receptors: the specific case of the T-cell[END_REF][START_REF] Fattaccioli | Specific wetting probed with biomimetic emulsion droplets[END_REF][START_REF] Pontani | Biomimetic emulsions reveal the effect of mechanical forces on cell-cell adhesion[END_REF]. It has been shown that when attached on a liquid interface through mobile linkers as phospholipids, adhesion molecules could migrate from the outer region of the droplets to the region of contact and form dense clusters. The clustering can be driven by non-specific interactions solely, which create an energetically more favorable environment within the zone of contact, without the need of the formation of ligand-receptor complexes, nor cytoskeleton remodeling[START_REF] Fattaccioli | Specific wetting probed with biomimetic emulsion droplets[END_REF]. A rough estimate of the IgGs density in the cluster shown on Figure5Bindicates that the opsonins are almost close-packed in the region of contact with the cell. Indeed, a random close-packed region containing all the 3.10 4 IgGs initially present on the droplet would occupy an area of 5 µm 2 for a molecular area of ca. 120 nm 2 per IgG[START_REF] Werner | The shape of immunoglobulin G molecules in solution[END_REF], thus constituting a lower limit of the cluster size that is consistent with the cluster dimensions. Immunolocalization experiments on the Figure5Cshow that IgGs colocalize with an increase of the local concentration of FcγRs on the cell surface. For the high IgG density condition, the surface of the droplets is almost saturated with opsonins, which makes the local variations in IgG surface densities barely observable by and explains why no cluster is visible in this case.

Figure 1 :

 1 Figure 1: (A) Schematic view of the immunoglobulin-functionalized phospholipids. (B)

Figure 2 :

 2 Figure 2: (A) Schematic view of the experiment. (B) Representative brightfield microscopy

Figure 3 :

 3 Figure 3: (A) Time evolution of the percentage of internalizing cells after incubation with IgG-coated lipid droplets (3.10 4 IgGs per droplet). (B) Evolution (after 5 and 45 min

Figure 4 :

 4 Figure 4: (A) Dependence of the percentage of internalizing cells upon surface functionalization of the droplets: fbare droplets, biotinylated droplets (0.03 mg.mL -1 DSPE-PEG-Biotin) and IgG-coated droplets (2.10 4 IgGs per droplet) after 45 min of incubation with

Figure 5 :

 5 Figure 5: Internalization of polystyrene solid beads (A) vs. liquid droplets (B) for two

  %IC Max , IgG 50 , n) are the adjustable parameters. %IC Max corresponds to the efficacy, i.e. the saturation value of the curve, IgG 50 to the potency, i.e. the number of IgGs per droplet necessary to reach 50% of the saturation value and n to the Hill slope. Distribution of data was assessed by d'Agostino & Pearson omnibus normality test. All data followed a non Gaussian distribution. Unless stated, statistical significance was evaluated by Wilcoxon signed rank test or ANOVA and Dunn's multiple-comparison test using Prism

	1 + software. P < 0.01 was considered significant: *** indicates p < 0.001 and ** indicates p < IgG 50 (IgG per droplet)
	0.01.
	Diode laser 405 nm was used to excite DAPI, argon laser 488 nm for Alexa Fluor® 488,
	helium laser 543 nm for Atto 555 and 633 nm for Alexa Fluor® 647. Emission was detected
	between 430 and 540 nm for DAPI, 485-540 nm for Alexa Fluor 488, 550-580 nm for Atto
	555, and 640-790 for Alexa Fluor® 647. Acquisition was made in channel-separated mode
	with a line averaging of 8.

!

where (

2.9. Immunolocalization

After a 15 min incubation with the droplets, cells were fixed and further incubated for 30 min with NH 4 Cl 50 mM and 30 min with 1% BSA (Sigma-Aldrich), at room temperature. For immunodetection of FcγRs, primary antibody anti CD16/CD32 was incubated overnight at 4°C at a concentration of 1 µg.mL -1 (Rat anti-mouse CD16/CD32 mAb 2.4G2, BD Pharmingen™ Biosciences, New Jersey, USA). After washing, samples were incubated for 1 hour at room temperature with secondary antibody at a concentration of 5 µg.mL -1 (Goat anti-rat Alexa Fluor® 647, Life Technologies, Carlsbad, CA, USA), DAPI and Atto 555phalloidin (Sigma-Aldrich). After extensive washing, coverslips were mounted in Fluoroshield (Sigma-Aldrich) and imaged on a Zeiss LSM 710 confocal microscope.

2.10. Statistical analysis

  5 , which corresponds to densities ranging from a very dilute to an almost close-packed monolayer (ca. 10 2 nm 2 per IgG[START_REF] Werner | The shape of immunoglobulin G molecules in solution[END_REF]) of opsonins at the interface. Most of the experiments are done with droplets coated with a intermediate amount of 3.10 4 IgGs per droplet that corresponds to a physiological density of ca. 2.10 2 IgGs per µm 2[START_REF] Gandour | Macrophage cell cycling: influence on Fc receptors and antibody-dependent phagocytosis[END_REF].

ACKNOWLEDGMENTS

We thank P. Jurdic and K. Pernelle (IGFL, Lyon) for having provided the Lifeact-mCherry RAW 264.7 macrophages cell lines; J. Bibette (ESPCI) for lending us the Couette emulsifier, J. Baudry and R. Gilles (ESPCI) for helping us with the emulsion formulation; A.M. Lenon (Institut Curie) for helping us with the immunolocalization experiments; C. Amatore, M. Guille and F. Lemaître for lending their cell culture facilities. We finally thank Jean-Bernard Baudin (ENS) for his continuous support. This work has received support from the Fondation Pierre-Gilles de Gennes (Foreign PhD Program 2011), the Région Ile de France (C'Nano PME), the CNRS (Prise de Risque Physique-Chimie-Biologie 2010), and the "Institut Pierre-Gilles de Gennes" (Laboratoire d'Excellence and Equipemend d'Excellence, "Investissements d'avenir" Program ANR-10-IDEX-0001-02 PSL and ANR-10-LABX-31)