PhD Nathalie Loos
email: nathalie.loos@u-picardie.fr

György Thuróczy

Rania Ghosn

Valérie Brenet-Dufour

Sophie Liabeuf

Brahim Selmaoui

Jean-Pierre Libert

Véronique Bach

Momar Diouf

René De Seze

Is the effect of mobile phone radiofrequency waves on human skin perfusion non-thermal?

Keywords: thermostatic laser Doppler flowmetry, skin microcirculation, radiofrequency exposure, skin micro blood flow, skin temperature skin micro blood flow Tsk: skin temperature

OBJECTIVE: to establish whether skin micro blood flow can be modified by exposure to the radiofrequency waves emitted by a mobile phone when the latter is held against the jaw and ear.

METHODS:

Variations in skin micro blood flow and skin temperature in adult volunteers were simultaneously recorded with a thermostatic laser Doppler system during a 20-minute "radiofrequency" exposure session and a 20-minute "sham" session. The skin microvessels' vasodilatory reserve was assessed with a heat challenge at the end of the protocol.

RESULTS:

During the radiofrequency exposure session, skin micro blood flow increased (vs. baseline) more than during the sham exposure session. The sessions did not differ significant in terms of the skin

INTRODUCTION

With the increasing use of mobile phones, the question of whether the associated radiofrequency fields have harmful effects on various target organs has become very important. The most frequent complaints relate to (i) a heating feeling when the face is directly in contact with the mobile phone and (ii) headache. Symptoms related to skin vascularization and heating include a burning sensation in the eyes or over the face, skin rashes and sunburn-like redness [START_REF] Röösli | Radiofrequency electromagnetic field exposure and non-specific symptoms of ill health: a systematic review[END_REF] . It has been shown that the heat released by a mobile phone's electronic components increases the local

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This article is protected by copyright. All rights reserved. skin temperature (Tsk) [START_REF] Anderson | Measurements of skin surface temperature during mobile phone use[END_REF][START_REF] Straume | Skin temperature increase caused by mobile phone: a methodological infrared camera study[END_REF]. However, there is much debate as to whether there is a causal relationship between exposure to mobile phone electromagnetic fields and the occurrence of symptoms unrelated to heating. No correlation between the occurrence of these symptoms and exposure to electromagnetic fields has been demonstrated in double-blind studies [START_REF]Electromagnetic fields and public health: Electromagnetic Hypersensitivity[END_REF]. Some researchers have reported changes in cerebral blood flow during and/or after mobile phone exposure [START_REF] Huber | Electromagnetic fields, such as those from mobile phones, alter regional cerebral blood flow and sleep and waking EEG[END_REF][START_REF] Huber | Exposure to pulse modulated radio frequency electromagnetic fields affects regional cerebral blood flow[END_REF][START_REF] Haarala | Effects of a 902 MHz mobile phone on cerebral blood flow in humans: A PET study[END_REF][START_REF] Aalto | Mobile phone affects cerebral blood flow in humans[END_REF][START_REF] Volkow | Effects of cell phone radiofrequency signal exposure on brain glucose metabolism[END_REF]. Vasodilatory processes in intracranial and extracranial blood vessels may be related to the self-reported symptoms (such as headache and tinnitus) that occur during exposure to electromagnetic fields [START_REF] Moskowitz | Neurotransmitters and the fifth cranial nerve: is there a relation to the headache phase of migraine?[END_REF][START_REF] Vass | Direct evidence of trigeminal innervation of the cochlear blood vessels[END_REF][START_REF] Abdel-Rassoul | Neurobehavioral effects among inhabitants around mobile phone base stations[END_REF][START_REF] Hutter | Subjective symptoms, sleeping problems, and cognitive performance in subjects living near mobile phone base stations[END_REF][14][START_REF] Chia | Prevalence of Headache among Handheld Cellular Telephone Users in Singapore: A Community Study[END_REF]. Only one study has shown that facial skin micro blood flow (SkBF) could be modified by mobile phone exposure when the phone was in contact with the skin [START_REF] Monfrecola | Non-ionizing electromagnetic radiations, emitted by a cellular phone, modify cutaneous blood flow[END_REF]. However, the latter study did not feature a control situation (e.g. a sham exposure session) and did not monitor Tsk (which is known to influence SkBF). Hence, it is difficult to say whether the observed increases in SkBF were solely due to the heat produced by the mobile phone. Lastly, the ambient temperature (which can also influence the skin's blood flow reactivity) was not controlled [START_REF] Monfrecola | Non-ionizing electromagnetic radiations, emitted by a cellular phone, modify cutaneous blood flow[END_REF].

Objectives:

We sought to establish whether the elevation of SkBF induced by mobile phone contact could be solely explained by the heating produced by the device when either emitting radiofrequency waves (in an exposure session) or not (in a sham session). To this end, control exposures were performed (i.e. a sham session versus radiofrequency exposure) and the room's ambient temperature was closely controlled. The same sets of parameters were measured on the other side of the face (i.e. to compare the exposed side with the non-exposed side), in order to determine whether a putative effect affected the exposed side only or (through a systemic reaction) both sides of the face. To check these hypotheses, SkBF and Tsk were recorded at the same sites during sham exposure (i.e. heating only) and radiofrequency exposure (i.e. heating + radiofrequency exposure) on the exposed and non-exposed sides of the face.

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Moreover, the potential effect of mobile phone use on skin microvessel reactivity has never previously been studied. Here, we studied this parameter by applying a heat challenge under the various exposure conditions.

MATERIALS AND METHODS

Inclusion/exclusion criteria and characteristics of the study population

Twenty Caucasian, healthy, young adult volunteers were included in this two-session study. The protocol was approved by the local independent ethics committee (Comité de Protection des Personnes Nord-Ouest II, Amiens, France). The trials were performed in a licensed facility (Clinical Research Centre, South Hospital, Amiens University Hospital, Amiens, France). The characteristics of the study population were as follows: 12 women, 8 men; mean ± standard deviation (SD) age: 25 ± 3.9 yr; body weight: 68.3 ± 11.4 kg; height: 173 ± 9.5 cm, systolic/diastolic blood pressure: 121/75 ± 12/9 mmHg; resting heart rate: 69 ± 9 bpm, pulse oxygen saturation: 98.2 ± 0.6 % (using an SpO 2 /blood pressure/heart rate monitor from CIC MED, Amiens, France). The subjects were told not to take vasoactive or anti-inflammatory drugs for the 10 days preceding the study. Subjects known to have a personal medical history of hypertension, diabetes, hypercholesterolemia or any cardiovascular, sensory or neurological disease were excluded from the study. Tea, coffee and alcohol were forbidden on the day before the experiments. The subjects did not exercise or consume food for at least 1h prior to each experiment. The use of facial cosmetics was prohibited, although male subjects had to have shaved on the day of the experiment. The test sessions were performed at the same time of the day, in order to minimize ultradian variations in cutaneous vascular parameters. Subjects wore light clothes and were studied in a semi-recumbent, supine position.

The subject was not covered with a blanket. The room temperature was kept constant at 24.0 ± 0.6 °C (relative humidity: 45-50%; air velocity: ≤0.10 m.s -1 , i.e. natural convection conditions). The bed was located in the centre of a naturally lit room (i.e. far from the windows, in order to reduce air currents and

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This article is protected by copyright. All rights reserved. radiative heat exchanges). Potentially conductive jewellery (ear-rings, etc.) was prohibited, to avoid disturbance of the laser Doppler signals.

Laser Doppler measurements of SkBF and Tsk

Laser Doppler system. A thermostatic laser Doppler system (Flowmeter Periflux System 5010, Perimed, France) was used to continuously record SkBF and Tsk. This method has a high time resolution and has been specifically designed for studying SkBF at a wavelength of 780 nm. The system measures local skin microcirculatory blood perfusion provided by the arterioles and arteriovenous anastomoses. Relative SkBF was expressed in perfusion units (PUs), which corresponds to the number of blood cells in the measured volume multiplied by the latter's mean velocity.

Calibration. The equipment was calibrated before each session. The arbitrary PU was directly related to a physical motility standard, which is based on the signal produced by Brownian motion in a 0.5% suspension of 0.48 µm diameter polystyrene microspheres at 20°C (normal value: 250 ± 5 PU).

Measurements. To investigate changes over time in SkBF and Tsk at the same anatomical site, two small, angled, thermostatic laser Doppler probes (PROBE 457, Perimed, France) were stuck to the cheek (1 cm in front of the ear lobe) on the ipsilateral side (i.e. the side exposed to mobile phone) and the contralateral (non-exposed) sides of the face. Particular care was taken to firmly attach the probes to the skin with special laser-translucent, double-sided adhesive strips (PF 105-3, Perimed) that avoided local vasoconstriction. Each probe contained two optical fibres; one carried the laser beam to the tissue, whereas the other captured the beam back-scattered from the tissue and carried it to the photodetectors for conversion into an electronic signal. Flow measurements were coupled with temperature recordings in the

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This article is protected by copyright. All rights reserved. same skin area; the thermostatic probe was integrated into the miniature, spherical laser Doppler probe (with a black, insulating, protective envelope; diameter: 10 mm; thickness: 8 mm; fibre separation: 0.25 mm). These thermostatic laser Doppler probes were also used to measure blood perfusion during a local heat challenge performed at the end of the protocol and in which the thermostatic system warmed the whole tissue area under the probe (i.e. 1 cm in diameter).

Radiofrequency exposure and dosimetry

The exposure and sham session were performed in random order. The "radiofrequency" or "sham" mobile phone was positioned against the left ear (using a helmet-like holder), as during normal vocal mode use.

The holder freed the subject from the need to hold the mobile phone over the laser Doppler probe without changing the position or pressure. Hence, the mobile phone touched (but did not greatly press against) the thermostatic laser Doppler probe. The subjects were exposed to a commercially available, dual-band GSM mobile phone (PHOENIX, model: Nokia 6650). The phone was connected to a personal computer to standardize and set the required frequency and radiofrequency power using service software (Nokia Corp., Finland). The participants received GSM-modulated exposure at the mobile phone's full power (peak: 2 W; average: 250 mW, pulse modulated with a 1/8 duty cycle) at 900 MHz for 20 minutes.

During the exposure, the phone was placed so that its long axis was aligned with an imaginary line from the opening of the ear canal to the corner of the mouth. Actual or sham radiofrequency exposure was performed by respectively connecting a 50-Ohm resistive load or an open-circuit dummy load to the mobile phone's remote antenna connector. The resistive load and the open-circuit dummy load had the same shape and structure, in order to maintain the study's double-blind nature.

The specific absorption rate (W/kg) was measured with a twin Specific Anthropomorphic Mannequin phantom (Antennessa, Rennes, France) filled with standard brain tissue-equivalent liquid (Satimo, Brest,

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France). A small electric field probe (O6-EP64, Satimo, Brest, France) connected to a microvoltmeter (Keithley Instruments Inc., Cleveland, OH, USA) was used to measure the electric field strength within the liquid. Calibration was based on immersing an open-ended coaxial cable connected to a vector network analyser (Wiltron 360B, Anritsu-Wiltron Company, Morgan Hill, CA, USA). The phone was held against the phantom in the ''touch position'' with a non-metallic holder, according to the European Committee for Electrotechnical Standardization (CENELEC) standard EN 50361 [START_REF]CENELEC EN 50361, Basic Standard for the measurement of Specific Absorption Rate related to human exposure to electromagnetic fields from mobile phones (300 MHz-3 GHz)[END_REF]. The probe was moved by a servo-driven XYZ positioning system fitted with a robotic 3D stepper motor (Charlyrobot SA, France). The maximum specific absorption rate was 0.49 W/kg, when averaged over 10 g of tissue.

To confirm the effectiveness of the load, the sham mobile phone's specific absorption rate and surface electric field were measured. Indeed, the specific absorption rate for the sham mobile phone was below the system's limit of detection (0.001 W/kg) at all positions on the phantom. No radiofrequency fields were detected at the sham mobile phone's surface.

Protocols

A rest period of at least 30 minutes was imposed (so that the Tsk could stabilize) before SkBF measurements. The subject was instructed not to speak or smile, so as not to disturb the laser Doppler signal. All sources of noise and distraction (music, nearby conversations, etc.) were excluded. The subject was instructed to relax, avoid intense mental activity and remain in a state of quiet wakefulness with his/her eyes open. Two crossover exposure sessions were performed under double-blind conditions, with "radiofrequency" and "sham" exposure in random order and by using the corresponding phones. Each exposure was preceded by a 5-minute control baseline period. The phone was carefully removed (without touching the laser Doppler probe) after 20 minutes of exposure, in order to mimic actual mobile phone use. Mean values of SkBF were analyzed for 1-minute blocks of continuous recordings at the following time points in each session: (i) 5 minutes before the start of exposure (as a baseline control, before placing

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the phone against the ear), (ii) after 1, 5, 10, 15 and 20 minutes of actual or sham exposure and (iii) 1, 5, 10, 15 and 20 minutes after the end of actual or sham exposure. A heat challenge was performed 25 minutes after the end of exposure by locally heating both sides of the face to 44°C for 1 minute, followed by a 30-minute period for the return to baseline. This hyperthermia challenge induces local hyperaemia, which reflects the skin microvessels' ability to dilate in response to heating [START_REF] Minson | Thermal provocation to evaluate microvascular reactivity in human skin[END_REF]. This early increase in perfusion was stable for some minutes (a typical example is shown in Figure 1). This early perfusion peak is related to local nervous sensory activity only and not to systemic endothelial activity (e.g. nitric oxide mechanisms), which appear later (at the called "plateau") during prolonged, heat-induced vasodilatation [START_REF] Charkoudian | Skin blood flow in adult human thermoregulation: how it works, when it does not, and why[END_REF][START_REF] Roustit | Non-invasive assessment of skin microvascular function in humans: an insight into methods[END_REF][START_REF] Boccalon | Doppler au laser: méthodes d'exploration de la microcirculation chez l'homme[END_REF][START_REF] Cracowski | Methodological issues in the assessment of skin microvascular endothelial function in humans[END_REF].

Data processing and statistics

Data processing. Data were sampled at 32 Hz, stored and then analyzed using Perisoft software (version 2.10, Perimed). Output data were exported and processed with Microsoft Excel® (version 2007) and then GraphPad Prism® software (version 5.02, GraphPad Software, San Diego, CA, USA). Analyses of variance (ANOVAs) and post-hoc analyses were performed with SAS® software (version 9.2, SAS Institute Inc., Cary, NC). Descriptive parameters for our population were presented as mean ± SD for quantitative variables. For the analysis of baseline values, a mixed ANOVA model with random intercept was used to study a possible relationship between exposure conditions (radiofrequency vs. sham exposure), the side of the face (the mobile phone side vs. the control side) and SkBF (an independent variable). The threshold for statistical significance was set to 0.05. A Wilcoxon signed rank test was used to perform pairwise comparisons of SkBF on the mobile phone side and on the control side of the face during the radiofrequency session. As two comparisons were performed, Bonferroni-Holm adjusted pvalues were computed to control for inflation of the type 1 error.

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The main SkBF parameters were then calculated: the area under the curve (AUC) and the maximum value (Max) recorded in the first 20 minutes of exposure provide accurate indexes of the time course of the blood flow. As there was no change in SkBF or skin temperature on the contralateral side of the face during either the radiofrequency or the sham exposure, these data for that side were not analyzed further.

The normality of the data distribution for SkBF and Tsk AUC and Max on the phone side was then checked with the D'Agostino-Pearson omnibus K2 test. The radiofrequency and sham sessions were then compared for the exposed side of the face using a Student's paired t-test. A Bonferroni-Holm correction was applied when multiple tests were performed on non-independent variables: for the two tests applied to the AUC and Max, the p-value was multiplied by a factor of 2. The same tests were used to compare Tsk data in the two exposure conditions.

Due to the well-known overall asymmetry of blood flow when comparing the left and right sides of the face [START_REF] Johnson | Laser-doppler measurement of skin blood flow: comparison with plethysmography[END_REF][24], heat challenge responses for the phone-exposed side and the contralateral side cannot be compared directly. Hence, the radiofrequency and sham exposure sessions were compared for each side of the face separately.

RESULTS

Baseline period:

Skin perfusion.

For a given side of the face, the radiofrequency and sham exposure sessions did not differ significantly in terms of the SkBF (radiofrequency SkBF = 25.5±14.2 PU; sham SkBF = 28.4±13.1 PU; p=0.15, paired-ttest in 20 subjects for the exposed side of the face; radiofrequency SkBF = 28.6±12.4 PU; sham SkBF = 32.6±13.6 PU; p=0.13, for the contralateral side).

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For the radiofrequency exposure session, the mean baseline SkBF on the exposed side of the face did not differ significantly from the value on the contralateral side: p=0.25. For the sham exposure session, the mean baseline SkBF was slightly lower on the exposed side than on the contralateral side: p=0.04. Skin temperature. For the radiofrequency exposure session, the mean baseline Tsk on the exposed side of the face was 33.0±0.6°C and differed significantly from that on the contralateral side of the face (33.3±0.7°C, p=0.02). This inter-side difference was not found for the sham exposure session (33.2±0.7°C vs. 33.3±0.8°C, p=0.39). The radiofrequency and sham exposure sessions did not differ significantly in terms of the mean baseline Tsk on the exposed side of the face (p=0.22) or on the contralateral (non-exposed) side (p=0.97).

Exposure period:

On the control side of the face, the sham and radiofrequency exposure sessions gave rise to similar response profiles for the mean SkBF and mean Tsk values (Figures 2A and2B). During radiofrequency exposure, the SkBF on the exposed side was much greater during radiofrequency exposure than during sham exposure (p=0.0496 for SkBF AUC (t=3.1; df=19) and p=0.0062 for SkBF Max (t=2.1; df=19), in pairwise comparisons). No significant radiofrequency vs. sham difference was observed for the skin temperature Tsk (p>0.05).

The heat challenge:

When heating the skin locally to 44°C on both sides of the face at the same time, the early peak value for SkBF (i.e. the raw data after 1 minute) on the exposed side of face was significantly greater after the radiofrequency exposure session than after the sham exposure session (p<0.0001) (Figure 3). As a

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positive control, no difference on the contralateral (non-exposed) side was found when comparing radiofrequency and sham exposure sessions (201 ± 66 PU vs. 186 ± 65 PU, respectively; p=0.28).

DISCUSSION

Anatomical and physiological links between peripheral and central (intracranial) vascularization allow

heat exchanges between blood vessels in the face and those of the brain. It is known that selective brain cooling can occur during hyperthermia (such as during intensive physical exercise, in a warm bath or in fever situations) [START_REF] Boulant | Neuronal basis of Hammel's model for set-point thermoregulation[END_REF][START_REF] Cabanac | Open loop increase in trunk temperature produced by face cooling in working humans[END_REF]. In an attempt to maintain a constant brain temperature, the rise in body temperature (up to 39°C) triggers an increase in blood flow from the brain to the face (notably through the emissary veins) [START_REF] Boulant | Neuronal basis of Hammel's model for set-point thermoregulation[END_REF][START_REF] Cabanac | Open loop increase in trunk temperature produced by face cooling in working humans[END_REF][START_REF] Hertzman | Regional rates of evaporation from skin at various environmental temperatures[END_REF][START_REF] Caputa | Significance of cranial circulation for the brain homeothermia in rabbits. II. The role of the cranial venous lakes in the defence against hyperthermia[END_REF][START_REF] Narebski | Human brain homeothermy during sleep and wakefulness: an experimental and comparative approach[END_REF]. In the present study, the absence of a blood flow increase on the contralateral side of the face means that the observed effect was local and was not related to hemodynamic changes in the body as a whole (which would have been evidenced on both sides of the face). Hence, it is unlikely that cutaneous heating induced by a mobile phone can trigger significant hemodynamic changes in cerebral vessels via the conductive heating of blood per se. An echo Doppler study performed under the same experimental conditions and with the same radiofrequency exposure did not show any significant change in flow from the brain arteries [START_REF] Ghosn | Effects of GSM 900 MHz on Middle Cerebral Artery Blood Flow Assessed by Transcranial Doppler Sonography[END_REF]. These observations show that the brain's haemodynamics were not perturbed by local skin heating.

During the baseline control period, the raw PU values were relatively low and constant for each subject. This indirectly reflects the skin vasomotor tone activity (mainly controlled by the vasoconstrictor α 1adrenergic nervous system) at a comfortable, thermoneutral ambient temperature of 24°C for humans wearing light clothing at rest [START_REF] Hardy | Differences between men and women in their responses to heat and cold[END_REF][START_REF] Iso | Ergonomics of the Thermal Environment Analytical Determination and Interpretation of Thermal Comfort Using Calculation of the PMV and PPD Indices and Local Thermal Comfort Criteria Geneva[END_REF][START_REF] Natsume | Preferred ambient temperature for old and young men in summer and winter[END_REF][START_REF] Tanaka | Effects of Decreasing Air Temperature on Peripheral Thermal Reactions in Males and Females Masatoshi[END_REF]. Direct heating effects at ∼+2°C over baseline (i.e. increases in Tsk due to the mobile phone's electronic components) were observed in both sham and radiofrequency

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exposure sessions. This corresponds to the well-known "passive vasodilation" phenomenon (inducing an increase in SkBF) caused by a decrease in the baseline sympathetic vasoconstrictor tone [START_REF] Rasch | Vasomotor response of the human face: laser-Doppler measurements during mild hypo-and hyperthermia[END_REF][START_REF] Charkoudian | Mechanisms and modifiers of reflex induced cutaneous vasodilation and vasoconstriction in humans[END_REF].

By assessing Tsk with an infrared camera, Straume et al. also observed similar heating after 30 minutes of exposure to a mobile phone [START_REF] Straume | Skin temperature increase caused by mobile phone: a methodological infrared camera study[END_REF]. Using a laser Doppler technique, Monfrecola et al. [START_REF] Monfrecola | Non-ionizing electromagnetic radiations, emitted by a cellular phone, modify cutaneous blood flow[END_REF] concluded that SkBF was greater with a mobile phone turned on than with a mobile phone turned off. However, as there was no sham group, it is difficult to say whether this finding was related to the study design or to a specific effect of radiofrequency exposure. Skin temperature was not recorded at the same time as SkBF.

Moreover, the room temperature was not reported and it is known that ambient temperature can strongly modify peripheral skin vasomotricity. Hence, it was impossible to say whether or not the elevation of SkBF was solely due to the local heating produced on skin by the mobile phone. In the present study, we simultaneously measured SkBF and Tsk with the same spatiotemporal resolution. We found that skin vasodilation on the mobile phone side of the face was much greater during radiofrequency exposure than during sham exposure -even though the two sessions did not differ significantly in terms of Tsk (i.e. an increase of 2.7°C over the baseline after 20 min of radiofrequency exposure or sham exposure). Given that the Tsk curves for sham and radiofrequency exposure sessions were exactly the same (i.e. superimposable, with a mean temperature at 20 min=35.9°C in both sessions), the difference in SkBF curves between the radiofrequency exposure session (mean SkBF at 20 min=65 PU) and the sham session (mean SkBF at 20 min=40 PU) exposures can be attributed to a specific effect of radiofrequency waves on the skin's microcirculation. The SkBF curve of the radiofrequency exposure session reflects the sum of the radiofrequency effect and the heating effect due to the mobile phone's battery and electronic components.

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Our results show for the first time that the effect of radiofrequency exposure on skin vasomotricity reported by Monfrecola et al. [START_REF] Monfrecola | Non-ionizing electromagnetic radiations, emitted by a cellular phone, modify cutaneous blood flow[END_REF] (see the SkBF data for the radiofrequency-exposed side in the present study) potentiates the electronic components' thermal influence (see the SkBF data for on sham exposed side) and is non-thermal.

It is important to emphasize that the measurements of local cutaneous temperature were performed under normal conditions, i.e. the cutaneous temperature under the laser Doppler probe was not controlled thermostatically. This is possible because the ambient temperature was closely controlled and the subject was close to thermoneutrality (see Materials and Methods section). In this case, the overlap between the two curves of exposure session (see Figure 2B) is real.

As mentioned above, the SkBF corresponds to the product of the blood cell velocity and the concentration of moving blood cells. Since cannot vary of the studied here, a larger signal must be due to an increase in blood cell velocity, which at the capillary level can only result from an increase in arteriolar diameter, i.e. vasodilation. The latter can be caused by two main processes: inhibition of the sympathetic, noradrenergic vasoconstrictor system and activation of the non-noradrenergic, active vasodilatory system. Cutaneous vasodilation can be due to the release of sympathetic noradrenergic vasoconstrictor tone [START_REF] Rasch | Vasomotor response of the human face: laser-Doppler measurements during mild hypo-and hyperthermia[END_REF][START_REF] Charkoudian | Mechanisms and modifiers of reflex induced cutaneous vasodilation and vasoconstriction in humans[END_REF]. The main contributors to non-adrenergic vasodilation are endothelial factors such as nitric oxide, vasoactive intestinal peptide, neuropeptide Y, substance P and histamine [START_REF] Charkoudian | Mechanisms and modifiers of reflex induced cutaneous vasodilation and vasoconstriction in humans[END_REF][START_REF] Kellogg Dl | Neuronal nitric oxide synthase control mechanisms in the cutaneous vasculature of humans in vivo[END_REF][START_REF] Mccord | Prostanoids contribute to cutaneous active vasodilation in humans[END_REF][START_REF] Zhao | Electrical stimulation directly induces preangiogenic responses in vascular endothelial cells by signaling through VEGF receptors[END_REF]. These neuronal and endothelial factors can modify the basal arteriolar myogenic tone [START_REF] Osol | Prologue: vascular myogenic mechanisms[END_REF], which has been defined as "a maintained basal state of contraction which arises within a muscle, without involvement of external factors" [START_REF] Johansson | Myogenic tone and reactivity: definitions based on muscle physiology[END_REF]. Possible ways of determining the process that is predominantly involved in the effect observed here will be discussed below.

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The hyperaemic response

During application of a 1-minute post-exposure heat challenge, the hyperaemic response showed that radiofrequency exposed skin microvessels dilated more than sham-exposed microvessels did.

Given that the laser Doppler technique uses 2 measurement probes (one for each side of the face), the two sides' respective hyperaemic responses to the heat challenge cannot be compared because it is known that SkBF values differ from one anatomical site to another in a given person [START_REF] Johnson | Laser-doppler measurement of skin blood flow: comparison with plethysmography[END_REF][24]. Hence, the heat challenge on the contralateral (non-exposed) side was just used to check that the challenge was working well (i.e. as a positive control). The radiofrequency and sham exposure sessions were always compared for the same side of the face.

The radiofrequency-exposed vessels thus appeared to have a larger vasodilatory reserve at the onset of the hyperaemic response. Dilatory ability depends on the mechanical properties of the skin arterioles and arteriovenous anastomoses, which act as resistances. Hence, large changes in the vessels' diameter can trigger substantial changes in SkBF [START_REF] Lossius | Fluctuations in blood flow to acral skin in humans: connection with heart rate and blood pressure variability[END_REF]. The vasoconstrictor tone of the skin's microvessels (mainly the arterioles) is abolished during this "early" peak of the hyperaemic response (within the first minute of heating) [43]. It is important to bear in mind that a neuropeptide-Y-mediated nociceptive loop reflex is activated when the skin is heated above 42°C (as was the case here for the heat challenge) [44-45]. Our results suggest that this reflex could be exacerbated by radiofrequency exposure (relative to sham exposure), since the skin vessels' hyperaemic response was much stronger. The facial skin's nervous inputs are also connected to the trigeminal sensory nuclear complex, which receives somatosensory inputs and provides feedback modulation to higher brain centres [46][47][48]. It would be interesting to see whether or not these loop-reflex nervous mechanisms are involved by chemically inhibiting their activity.

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Conclusion

By measuring SkBF and controlling Tsk with the same spatiotemporal resolution in human subjects at thermoneutrality, we identified specific, athermal modifications of the skin blood flow during mobile phone radiofrequency exposure. The cumulative effect of radiofrequency exposure and heating by the mobile phone leads to strong increases in skin perfusion. The athermal effects of radiofrequency exposure on SkBF were seen both during and after acute exposure.

Perspectives

Further research is now required to understand the physiological mechanisms that underlie the observed changes in the activity of the neurogenic and non-neurogenic components controlling skin vasomotricity.

One such approach could involve a fast Fourier transform analysis of the laser Doppler perfusion signal over several minutes: low observed frequencies would suggest a myogenic mechanism (0.02-0.06 Hz) and high frequencies would suggest a neurogenic mechanism (0.06-0.2 Hz). Given that the vasodilatory mechanisms controlling skin vasomotion are more active during radiofrequency exposure than during sham exposure, it would be interesting to see whether or not the increase in SkBF (on the mobile phone side) is due to a change in the sympathetic activity controlling vasomotor tone [START_REF] Rasch | Vasomotor response of the human face: laser-Doppler measurements during mild hypo-and hyperthermia[END_REF][START_REF] Charkoudian | Mechanisms and modifiers of reflex induced cutaneous vasodilation and vasoconstriction in humans[END_REF]. The relative contribution of various vasodilators (mediated by neurogenic and non-neurogenic processes) could be investigated by using intradermal microdialysis [START_REF] Mccord | Prostanoids contribute to cutaneous active vasodilation in humans[END_REF] and the administration of specific inhibitors (such as L-nitroarginine methyl ester for nitric oxide) [START_REF] Kellogg Dl | Neuronal nitric oxide synthase control mechanisms in the cutaneous vasculature of humans in vivo[END_REF]. It would also be interesting to look at the possible longterm consequences of repeated increases in vasodilatation.

ACKNOWLEDGMENTS

We thank the staff at the Clinical Research Centre at Amiens University Hospital for their help in recruiting and selecting subjects and for performing the clinical examinations. We also thank Joe Wiart for providing the experimental facility for radiofrequency dosimetry and Sami Savela and Jafar Keshvari for technical assistance with the mobile phone test software used in the study. We thank Jonathan Meynier (Clinical Research Centre, North Hospital, Amiens, Picardy, France) for his expertise in statistical analysis and David Fraser (Biotech Communication SARL, Damery, France) for advice on the manuscript's English.

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This article is protected by copyright. All rights reserved. 24. Benedicic M, Dolenc VV, Stefanovska A, Bosnjak R. Left-right asymmetry of the facial microvascular control. Clin Auton Res. 16(1):58-60, 2006.

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Legends for illustrations

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Legend: Data for one-minute periods are expressed as the mean ± SD in 20 young adult subjects at baseline (0) and after 1, 5, 10, 15 and 20 minutes of real or sham exposure and then 1, 5, 10, 15 and 20 minutes after the end of radiofrequency or sham exposure. Raw skin perfusion data are expressed in arbitrary perfusion units (PUs). The skin temperature is expressed in °C. The conditions are as follows:

SkBF on the side of the head with the real mobile phone (RF-S MP : black circles) and on the contralateral side (RF-S CTR : white circles), during and after a radiofrequency exposure session; SkBF on the side of the head with the sham mobile phone (Sham-S MP : black squares) and on the contralateral side (Sham-S CTR : white squares), during and after a sham exposure session.

Accepted Article

This article is protected by copyright. All rights reserved.


Guillaume Fayet
email: guillaume.fayet@ineris.fr

Patricia Rotureau

Carlo Adamo

On the development of QSPR models for regulatory frameworks: the heat of decomposition of nitroaromatics as a test case

Keywords: Quantitative Structure-Property Relationships, heat of decomposition, nitroaromatic compounds, constitutional and topological descriptors Highlights:

Many regulatory frameworks, e.g. related to the Transport of Dangerous Goods, the Registration, Evaluation, Authorisation and restriction of chemicals (REACH) or the Classification, Labelling and Packaging of substances and mixtures (CLP), require the characterization of the hazards of chemicals, which could be complex. In particular, the REACH regulation involves an extensive quantity of works, to gather toxicological, eco-toxicological and physico-chemical properties for a large number of compounds. So, the full characterization by experimental way is time-consuming and cost-expensive. Alternative methods are therefore encouraged to complement experimental tests. The Quantitative Structure-Property Relationships (QSPR) approach is one of the recommended methods, provided that they are developed within the rigorous guidelines proposed by the Organization for Economic Co-operation and Development (OECD). In this context, a series of nitroaromatic compounds has been analyzed to achieve new QSPR models for the prediction of their heat of decomposition respecting the requirements for application in regulatory frameworks.

Three multilinear models were obtained upon the set of descriptors considered for their development (constitutional, topological or both) that do not need any preliminary time expensive quantum chemical calculations. They were tested by internal and external validation tests. Good performances for the two ones including constitutional descriptors were obtained in particular in terms of predictive power in a well defined applicability domain (R² IN =0.81-0.87). They are easier to apply than our previous quantum chemical based model, since they do not need any preliminary calculations.

Introduction

To characterize the intrinsic hazard of chemical compounds, the Recommendations on the Transport of Dangerous Goods (UN, 2011) listed a series of tests. Among the involved physico-chemical properties, heats of decomposition are considered as a pre-selection criterion to identify substances that could present explosive properties. Measured by calorimetric analyses, the heat of decomposition evaluates the amount of energy released during the decomposition of chemicals. Among available methods, differential scanning calorimetry (DSC) [START_REF] Chervin | Method for estimating decomposition characteristics of energetic chemicals[END_REF][START_REF] Grewer | Thermal Hazards of Chemical Reactions[END_REF][START_REF] Jones | Evaluation of systems for use in DSC measurements on energetic materials[END_REF][START_REF] Yoshida | Safety of Reactive Chemicals[END_REF] providing heats of decomposition with uncertainties of measurement of about 5-10% [START_REF] Ando | Analysis of differential scanning calorimetric data for reactive chemicals[END_REF] is a typical example of an experimental screening test.

Such tests are also considered in the new European REACH (EC 1907(EC /2006) and CLP (EC 1272(EC /2008) ) regulations. This new regulatory framework implies the systematic characterization of a tremendous number of substances, since more than 143 000 were submitted in the pre-registration phase of REACH between June and December 2008 [START_REF] Echa | Pre-registered substances[END_REF]. Unfortunately, such volume of work is incompatible with the imposed calendar, i.e. until 2018 for existing substances (depending on quantities of chemicals produced or imported). So, the use of methods, alternative to experimental testing, such as quantitative structure property relationships (QSPR), was explicitly recommended to obtain information data (physico-chemical, toxicological and eco-toxicological) required by REACH.

Indeed, QSPR models represent powerful tools already successfully used for biological [START_REF] Winkler | The role of quantitative structure -activity relationships (QSAR) in biomolecular discovery[END_REF], toxicological [START_REF] Cronin | Q)SARs for Predicting Effects Relating to Reproductive Toxicity[END_REF][START_REF] Netzeva | Review of (Quantitative) Structure-Activity Relationships for Acute Aquatic Toxicity[END_REF], pharmaceutical (Grover, Singh, Bakshi, & Singh, 2000a, b) and physico-chemical applications [START_REF] Dearden | Silico Prediction of Physicochemical Properties: European Commission[END_REF][START_REF] Katritzky | Quantitative Correlation of Physical and Chemical Properties with Chemical Structure: Utility for Prediction[END_REF]. Five principles have even been proposed by the Organization for Economic Co-operation and Development (OECD) for their validation in the context of regulatory uses (OECD, 2007). At first, the endpoints of models have to be fully defined, i.e. including the description of experimental protocols. Secondly, algorithm must be transparent, so that the model equations (or structures) and all the related computational parameters must be clearly defined.

Then, domains of applicability must be defined so to determine on which systems accurate predictions are expected or not. Performances have to be evaluated on a series of validation tests, including the characterization of predictivity on an external set of compounds. Finally, the fifth principle recommends, when possible, a mechanistic interpretation of models to link their parameters to the subjacent mechanisms involved in the studied properties. These principles have already been taken into account for the development of various QSPR models in the last years for toxicological endpoints [START_REF] Benigni | Collection and Evaluation of (Q)SAR Models for Mutagenicity and Carcinogenicity: European Commission[END_REF][START_REF] Gramatica | Principles of QSAR models validation: internal and external[END_REF] as for physicochemical properties [START_REF] Fayet | Predicting the thermal stability of nitroaromatic Compounds using Chemoinformatic Tools[END_REF]Fayet, Rotureau, Joubert, & Adamo, 2011;[START_REF] Öberg | Extension of a prediction model to estimate vapor pressures of perfluorinated compounds (PFCs)[END_REF][START_REF] Papa | Development, Validation and Inspection of the Applicability Domain of QSPR Models for Physicochemical Properties of Polybrominated Diphenyl Ethers[END_REF]Prana, Fayet, Rotureau, & Adamo, in press). Moreover, the applicability of such models in an industrial context has been demonstrated [START_REF] Patlewicz | Non-testing approaches under REACH -help or hindrance? Perspectives from a practitioner within industry[END_REF].

Concerning the heat of decomposition of nitroaromatic compounds, only few QSPR studies have been carried out. First attempts used limited datasets that did not allow any external validation. Saraf proposed a correlation with the number of nitro groups [START_REF] Saraf | Prediction of reactive hazards based on molecular structure[END_REF] with a fitting error of 8% for a very limited number of compounds (19 nitrobenzene derivatives). In previous works, a series of preliminary multilinear models were derived from a data set of 22 molecules with high correlations (up to R²=0.98) by introducing quantum chemical descriptors (Fayet, Joubert, Rotureau, & Adamo, 2009a;Fayet, Rotureau, Joubert, & Adamo, 2009[START_REF] Tropsha | Best Practices for QSAR Model Development, Validation, and Exploitation[END_REF]. Unfortunately, the size of these datasets did not allow any external validation. In more recent works [START_REF] Fayet | Predicting the thermal stability of nitroaromatic Compounds using Chemoinformatic Tools[END_REF]Fayet, Rotureau, Joubert, & Adamo, 2011), we obtained very robust models, following the OECD principles, by analyzing a more extended data set of 77 nitrobenzene derivatives. An accurate model for the whole diversity of structures included into this dataset was obtained through a qualitative decision tree with high predictivity (82% of correct predictions obtained on a validation set of 22 molecules) [START_REF] Fayet | Predicting the thermal stability of nitroaromatic Compounds using Chemoinformatic Tools[END_REF]. Another reliable model (Fayet, Rotureau, Joubert, & Adamo, 2011), based on a quantitative multilinear regression with a predictivity in its applicability domain of R² IN =0.86, was issued from a data set restricted to the compounds presenting no substituent in ortho position to the nitro group considering the fact that the presence of such ortho substituent possibly involves particular decomposition mechanisms. However, these two models require a preliminary determination of quantum chemical properties which could be time-consuming and not necessarily straightforward.

Starting from these "proofs of principles" on the possibility to develop robust QSPR models respecting OECD principles, new multilinear models were developed based on the same data set, in particular for non-ortho substituted nitroaromatics, by considering only simple constitutional and topological descriptors. Based on these descriptors, models will be easier to apply by industrials in the context of REACH for example, since they do not need any prior quantum chemical calculations.

Materials and methods

Experimental data set

Heats of decomposition (-ΔH) of 42 nitroaromatic compounds have been used to derive high predictive models. Experimental data represent a critical point of the QSPR analysis, since they have to be obtained following a single protocol in order to satisfy the first principle of the OECD guidelines (OECD, 2007). Indeed, this ensures the compatibility between data and then it reduces uncertainties that could propagate in the model during the fitting procedure. For this reason, all experimental data were extracted from a single reference [START_REF] Ando | Analysis of differential scanning calorimetric data for reactive chemicals[END_REF]. The heats of decomposition were measured using a pressure differential scanning calorimetry (DSC) apparatus, on 1-2 mg samples in aluminum cells with pin-hole, with a heat rate of 10 K/min.

It has to be noticed that the studied compounds (presented in table 1) consisted in nitrobenzene derivatives substituted by a variety of groups (e.g. nitro, amino or halogens), with the particularity to present no substituent in ortho position to a nitro group. Indeed, ortho substituted compounds potentially undergo to specific decomposition mechanism involving the interaction of the nitro group with the adjacent substituent as evidenced on nitrotoluene derivatives (Fayet, Joubert, Rotureau, & Adamo, 2009b;Fayet, Rotureau, Joubert, & Adamo, 2011).

To evaluate the predictivity of the developed models, this data set was divided into two parts. A training set of 31 molecules was used for the development of the model and a validation set of 11 compounds was used to compute an external validation. The partition between sets defined in previous work (Fayet, Rotureau, Joubert, & Adamo, 2011) was kept as it ensured the same distribution in property values in both training and validation sets (as shown in Figure 1). Moreover, no bias in the diversity of chemical structures was observed in each set.

Molecular descriptors

The molecular structures of the selected nitroaromatic compounds were characterized by a series of 88 molecular descriptors that can be extracted from a simple 2D structure. Constitutional descriptors are the simplest descriptors that reflect the molecular composition. They count the number of specific atoms or bonds in molecules (e.g., number of O atoms and number of single bonds). Topological descriptors, like the Wiener index, are based on atomic connectivity tables and provide information about the size and shape of molecules. All these descriptors do not require quantum chemical computations and have been evaluated using the Codessa software (Codessa, 2002). More information is available in the books of [START_REF] Karelson | Quantum-Chemical Descriptors in QSAR/QSPR Studies[END_REF] and [START_REF] Todeschini | Handbook of Molecular Descriptors[END_REF]. In addition, external descriptors that do not need any expensive calculation times were added, like the occurrence and count of specific molecular groups identified in the molecules of the database (e.g. number of nitro groups).

QSPR modeling

In this paper, multilinear regressions were derived. Such models are based on the following formula:

∑ + = i i i X a a Y 0 (Eq. 1)
where Y is the calculated property, X i are the molecular descriptors and a i the regression constants.

To be accurate, models have to be constituted by an optimized set of descriptors. Indeed, a too large number of descriptors involve large errors in prediction due to the inclusion of parameters that are not really related to the property and to inter-correlated descriptors that represent redundant pieces of information. So, to achieve reliable QSPR models, a parameter selection, using the Best Multi Linear Regression technique, as implemented in Codessa software, was realized among the 88 calculated descriptors. This stepwise approach , already successfully used in previous works [START_REF] Fayet | QSPR Modeling of Thermal Stability of Nitroaromatic Compounds: DFT vs. AM1 Calculated Descriptors[END_REF], 2011), started with constructing two-parameter models based on non-intercorrelated descriptors (with R² between descriptors lower than 0.1) and then it built higher rank models by adding new non-intercorrelated descriptors (i.e. with R² lower than 0.6 with each of the previous ones). By this way, this method guarantees that two intercorrelated descriptors are not selected in the same model. Finally, the algorithm gave, at each rank (i.e. for each number of descriptors), the model presenting the higher correlation with the studied property.

The final model was chosen among these regressions as the one representing the best compromise between the correlation refinement and the number of descriptors. The pertinence of each descriptor in the model was also checked based on a student t-test at a 95% level of confidence (presented in Supporting Information, Tables S1-S3).

Internal and external validations

To investigate the performances of the developed models, a series of internal and external validation tests were performed [START_REF] Tropsha | Best Practices for QSAR Model Development, Validation, and Exploitation[END_REF][START_REF] Witten | Data Mining: Practical Machine Learning Tools and Techniques[END_REF]. The goodness of fit was evaluated for the molecules of the training set by the coefficient of determination (R²) and the relative mean absolute error (MAE TR (%)).

Leave-one-out (LOO) and leave-many-out (LMO) cross validations were computed, to estimate the robustness of the model, i.e. the dependence of the fitting of the model to any molecule(s) of the training set, via the Q² LOO , Q² 10CV and Q² 5CV coefficients (for LOO, 10-fold and 5-fold cross validations, respectively). These coefficients were expected to be stable upon partition size and close to R².

The models were also evaluated against chance correlation by Y-randomization [START_REF] Rücker | y-Randomization and Its Variants in QSPR/QSAR[END_REF]. Property values were randomized within the training set by 500 successive iterations. From each new randomized data set, a new model was computed again, with performances expected to be low. Finally, the average value and the standard deviation in R² coefficients for the randomized models (denoted R² YS and SD YS , respectively) were calculated, to check that the original model was strongly more performant than the randomized ones.

Then, the predictive powers of the models were estimated for the molecules of the validation set by the coefficient of determination (R² EXT ), the relative mean absolute error (MAE EXT (%)) and the Q² EXT coefficient proposed by OECD guidelines (OECD, 2007).

Applicability Domain

The applicability domain (AD) of each model, i.e. the domain in which predictions can be considered as accurate, was defined by the molecules of the training set. It was built, for each descriptor, by the range of values represented among the molecules of the training set. The AD ranges for each descriptor in each model are available in Supporting Information (Table S4).

So, for new predictions, future users will simply have to preliminary check if descriptor values are in the intervals defining the AD to know if the model is applicable for the molecules they want to consider.

To evaluate the real predictive capability of the models in the context of future predictions, the predictive performances of all models were finally re-evaluated taking into account ADs (noticed R² IN , MAE IN (%) and Q² IN , respectively).

Results

Model based on constitutional descriptors

A first model was developed based only on 50 constitutional descriptors. The BMLR procedure proposed equations including up to 16 descriptors and the best compromise between the correlation and the number of descriptors was obtained for a four-parameter model:

-ΔH = -594.5 + 2381.6 n db,rel + 306.5 n NO2 -791.4 n O,rel + 83.4 n conj (Eq. 2)

where n db,rel and n O,rel are the relative numbers of double bonds and oxygen atoms, respectively, and n NO2 and n conj are the numbers of nitro groups and conjugated bonds, respectively. It has to be noticed that nitro groups contain two conjugated bonds.

In this equation, all descriptors presented the same importance in the regression with close absolute values of t-test (from 2.2 to 5, in table S1). The presence of n NO2 should be particularly noticed. Indeed, already included in previous models addressing the prediction of the same property [START_REF] Fayet | Predicting the thermal stability of nitroaromatic Compounds using Chemoinformatic Tools[END_REF]Fayet, Rotureau, Joubert, & Adamo, 2011), this descriptor is pertinent from a chemical point of view since the energy released during decomposition is linked to the loss of nitro groups [START_REF] Brill | Kinetics and mechanisms of thermal decomposition of nitroaromatic explosives[END_REF].

From a statistical point of view, this model performed quite well with R²=0.84 (see table 2 andFigure 2). Internal validations were also satisfactory. LOO and LMO cross-validation coefficients (Q²) ranged between 0.78 and 0.80 and Y-randomization ensured against a chance correlation with an average correlation coefficient R² YS =0.13 and a low standard deviation (SD YS =0.08) over the 500 randomization iterations (as shown in Figure 3). Finally, the predictive power was remarkable with R² EXT =0.81 and Q² EXT =0.81, in particular in its AD since no molecule of the validation set was out of it (so, R² IN =0.81 and Q² IN =0.81).

Model based on topological descriptors

In a second step, 38 topological descriptors were considered. After the BMLR analysis, the following three-parameter regression in Eq. 3 was selected as the one presenting the most important correlation regarding its level of parameterization.

-ΔH = -1385.4 + 142.0 0 χ + 953.4 1 IC avg -31.8 1 IC (Eq. 3)

where 0 χ is the Randic index (order 0), 1 IC avg is the average information content (order 1) and 1 IC is the information content (order 1).

The interpretation of the topological descriptors was more difficult since they mainly represent the shape of molecules. In the cases of biological effect, they are very likely understood as representing a molecular feature that interacts with biological receptors. In the case of impact sensitivity, subjacent mechanism is very different and does not issue from such steric interaction. If these descriptors also characterize the size of molecules, which is globally connected to the quantity of energy available for the decomposition, such direct interpretation was not evidenced since none of these descriptors was related to the chemical mechanisms involved in the decomposition of nitro compounds.

The performances of this model were less good than the previous one (Eq. 2), in terms of correlation (R²=0.78) and robustness (Q² LOO =0.71). Nevertheless, the Y-randomization test exhibited no chance correlation and predictions, once considering the applicability domain of the model appeared satisfactory (R² IN =0.82).

It has to be noticed that R² EXT value was lower (0.46) due to the large error in the prediction for the nitrobenzene molecule (more than 300 kJ/mol in error) which was not included into the AD of the model. This shows the importance of taking into account the applicability domain in the evaluation of the predictive power.

The slight increase of values between R² and R² IN (0.04) could be considered in the present case as due to the use of small sets of data for both the training and the validation sets. However, both correlation and predictivity are significant.

Model based on both constitutional and topological descriptors

In a last step, the whole set of 88 constitutional and topological descriptors was used to derive the final four-parameter model, which associated the best correlation regarding its number of descriptors among the regressions issued from BMLR analysis:

-ΔH = 153.5 + 386.4 n NO2 -78.9 n CH3 + 131.2 1 χ v -327.7 0 IC avg (Eq. 4)

where n CH3 is the number of methyl groups, 1 χ v is the Kier and Hall index (order 1), 0 IC avg is the average information content (order 0).

If n CH3 , 1 χ v and 0 IC avg are not directly interpretable in terms of chemical mechanism, the number of nitro groups was satisfactory included (like for the constitutional-based model) since it is in agreement with the general statements recognized on the decomposition process of nitro compounds. Besides this descriptor was the most significant in the model when considering its t-test value (9.30).

The correlation of this model was also high with R²=0.85 and stable among the series of computed cross validation (Q² LOO =Q² 5CV =0.76, Q² 10CV =0.74). It did not issue from a chance correlation as demonstrated by the 500-iteration Y-randomization test (R² YS =0.13, SD YS =0.08). Finally, the predictive power calculated for the 11 molecules of the validation set was also good (with R² EXT =0.81). When considering the only compounds that were included in the AD of the model, R² IN value (0.87) was slightly higher than R² but, regarding experimental uncertainties (5-10%) and the size of the dataset, the difference between R² IN and R² (0.02) was not significant. Moreover, both R² and R² IN values were particularly remarkable.

Discussion

The three models developed in this study respect the OECD principles of validation for regulatory uses. Indeed, these models were defined starting from heats of decomposition obtained from an unique original reference to ensure that data were obtained using a single protocol. The algorithms of the models are simple and entirely defined on constitutional and topological descriptors. They are applicable for nitrobenzene derivatives that present no substituent in ortho position to the nitro group in an AD simply defined on the values of the descriptors included in the models. The detailed ranges of values for each descriptor in each model are available in supporting information (Table S4). Performances were revealed from internal and external validation tests: fitting evaluation for the molecules of the training set, LOO and LMO cross-validations, Y-randomization, predictions on an external validation set.

From the three developed models, the ones presenting the best performances are those integrating constitutional descriptors (Eqs. 2 and 4). Indeed, they do not only propose significant predictivity in their applicability domains (R² IN =0.81 and 0.87, for Eqs. 2 and 4 respectively) but they are also satisfactory in terms of fitting and robustness (with R²=0.84-0.85 and Q² LOO =0.76-0.79). Moreover, these two models include the number of nitro groups that is directly related to the energy released during decomposition. The topological model (Eq. 3) presents globally inferior performances in particular in terms of correlation and robustness (R²=0.78 and Q² LOO =0.71). Moreover, no straightforward interpretation is evidenced for any of the constituting topological descriptors.

It has to be noticed that the n NO2 descriptor introduced in models of Eqs. 2 and 4 was already included in the decision tree developed in our previous work [START_REF] Fayet | Predicting the thermal stability of nitroaromatic Compounds using Chemoinformatic Tools[END_REF]Fayet, Rotureau, Joubert, & Adamo, 2011) for the prediction of the heat of decomposition of nitroaromatic compounds. Moreover, descriptors influenced by the presence of NO 2 groups were also selected in the MLR model obtained for the only non-ortho substituted nitroaromatic compounds (Fayet, Rotureau, Joubert, & Adamo, 2011, which Globally, the performances of these two new models remain very interesting in view of predictions, with nearly similar capabilities and less computer times than our previous model, which needed prior quantum chemical calculations. In particular, the constitutional-based model (Eq. 2) is very simple with high performances and represents the best compromise between performances and practical complexity for final users to obtain predicted data.

Conclusion

In this paper, new multilinear QSPR models were developed to predict the heats of decomposition of nitroaromatic compounds. In particular, the target molecules were nitrobenzene derivatives not substituted in ortho position to the nitro group. These models were derived from a series of constitutional and topological descriptors with the aim to achieve reliable predictions without any time expensive calculations. Three models were computed according to the OECD principles for validation for regulatory use from a dataset of 42 compounds using constitutional and/or topological descriptors. As a consequence, they can be used in a regulatory framework like REACH.

High performances were exhibited in terms of correlation, robustness (including leave-many-out cross validations), absence of chance correlation (by Y-randomization) and predictive power for the two models including constitutional descriptors (Eqs. 2 and 4). Moreover, these two models were based on the number of nitro groups that is recognized to be linked to the energy released during the decomposition process. Finally, they present performances close to the ones of the previous quantum chemical model and the advantage to be easier to apply (without any time expensive preliminary calculations). [START_REF] Ando | Analysis of differential scanning calorimetric data for reactive chemicals[END_REF]

Figure 1 -

 1 Figure 1 -Distributions of the experimental values in the training and validation sets.

Figure 2 -

 2 Figure 2 -Experimental vs. predicted heats of decomposition (in kJ/mol) of nitroaromatic compounds based on Eq. 2.

Figure 3 -

 3 Figure 3 -Correlation of the models issued from Y-randomisation (R² random ) vs. level of randomisation, as estimated by the correlation between the randomised and experimental values (R²(Y random /Y exp )).

  the gravitation index, WPSA1 the weighted positive surface area, Q max the maximal partial charge in the molecule and RPCS the relative positive charged surface area. This model was well correlated (R²=0.90), robust (Q² LOO =0.86), and presented remarkable predictive power for an external validation set (R² EXT =0.84), in particular in its applicability domain (R² IN =0.86).Compared to this model including quantum chemical descriptors(Fayet, Rotureau, Joubert, & Adamo, 2011), the two new models (Eq. 2 and 4) are slightly less fitted, for the molecules of the training set (R²=0.84-0.85). Moreover, a slight decrease in accuracy is observed from the predictions computed for the molecules of the validation set for the first model (R² IN =0.81 in this paper vs. R² IN =0.86 in our previous work). Nevertheless, the last model (Eq. 4), including both constitutional and topological descriptors, presents similar predictive ability (R² IN =0.87).

		represent the only
	previous quantitative model to have been externally validated to predict the heat of decomposition
	of nitroaromatic compounds.
	-ΔH = 0.8 G -3.8 WPSA1 -4255.1 Q max + 26.8 RPCS -251.2	(Eq. 5)
	where G is

Table 2 -

 2 Performances of the previous and new QSPR models

		constitutional	topological	both	previous model a
		Eq. 2	Eq. 3	Eq. 4	Eq. 5
	R²	0.84	0.78	0.85	0.90
	MAE TR (%)	17	18	16	12
	Q² LOO	0.79	0.71	0.76	0.86
	Q² 10CV	0.80	0.71	0.76	-
	Q² 5CV	0.78	0.71	0.74	-
	R² YS	0.13	0.10	0.13	-
	SD YS	0.08	0.07	0.08	-
	R² EXT	0.81	0.46	0.81	0.84
	Q² EXT	0.81	0.42	0.81	-
	MAE EXT (%)	18	32	19	18
	R² IN	0.81	0.82	0.87	0.86
	Q² IN	0.81	0.81	0.87	-
	MAE IN (%)	18	15	13	17
	a (Fayet, Rotureau, Joubert, & Adamo, 2011)

The model based only on constitutional descriptors was particularly interesting since it was very easy to use for prediction to any user without needing any complex calculations.

Table 1 -Experimental and predicted heats of decomposition (in kJ/mol) of nitroaromatic compounds from new QSPR models (Eqs. 2-4) compared to the previous one (Eq. 5 (Fayet, Rotureau, Joubert, & Adamo, 2011)


INERIS Candice Lagny
email: candice.lagny@ineris.fr

The emissions of gases from abandoned mines: role of atmospheric pressure changes and air temperature on the surface

Keywords:

Intrinsic parameters influence abandoned mine gas emissions. Independently of the presence or not of noxious gas in mine voids, meteorological factors influenced directly the gas outflow or inflow. Measurement stations were installed in the exits located in abandoned mines of the iron Lorraine basin, the Lorraine and the North East France coal basins to enhance the gas flow behaviour. Closure methods of the mines and exits from the abandoned mines are quite different. For the first, shafts are associated with adits. Some of them are closed with bars to avoid people entrance into abandoned mine workings but gas flow is enabled. For the second, there are essentially shafts which are secured. Some of them are equipped with a vent to enable outflow of the mine gas in specific conditions. Mine gas parameters were measured. Besides, external parameters like temperature and atmospheric pressure were monitored. Gas flow can be influenced mainly by the temperature difference between external atmosphere and mine workings (in iron mines, which can be considered as an open system) while atmospheric pressure influences gas flow in the coal mines, which can be considered as closed systems. Modelling has confirmed the differential pressure value measured that exceeds friction losses.

Key words Mine gas emission . Atmospheric pressure . Air temperature on the surface

Introduction

Some underground abandoned mines may continue to be vented to the atmosphere through wells, portals or shafts...Some, which are not mechanically ventilated, can contain noxious gas. Noxious gas emissions can occur when gas migrates to the surface through cracks and fissures in the strata covering the abandoned mine. The following factors influence abandoned mine gas emissions:

-time since abandonment [START_REF] Pokryszka | Gas migration from closed coal mines to the surface risk assessment methodology and prevention means[END_REF]; -gas content and adsorption characteristics of coal for coal mines; -gas flow capacity of the mine; -mine flooding; -presence of vent holes and; -mine seals... Independently of these intrinsic parameters that directly induced the composition and the quantity of noxious gas produced and the emitted gas location, factors external from the abandoned mine such as temperature on the surface, atmospheric pressure, speed and direction of the wind have also effects on mine gas outflow or atmospheric gas inflow. The aim of this paper is not to evaluate mine gas intensity. It is to enhance the understanding of these external parameters on gas outflow from underground mine voids that can contain or not noxious gas. Scientific publications show that gas outflows from abandoned mines or gas inflows are influenced by various external factors. [START_REF] Pokryszka | Emissions gazeuses à partir des vides miniers dans le basin ferrifère lorrain[END_REF] highlighted the link between external temperature as well as direction and intensity of gas flow in the Moyeuvre iron ore lorain mine. The atmospheric pressure does not have any significant influence on gas flow. On the contrary, [START_REF] Burrel | The influence of minewater recovery on surface gas and water discharges in the Yorkshire Coal Field[END_REF], [START_REF] Strakos | The problems of underground gas flowing into areas with closed coal mining activity. 10 th[END_REF] and Senovsky & Trunecek (2001) have written that noxious gas could flow out after an atmospheric pressure drop. The role of atmospheric pressure on noxious gas emission in firedamp mines has been studied for a long time: [START_REF] Lagrange | Notes: Les mines diamantifères de Kimberley, les dégagements gazeux et la pression atmosphérique[END_REF], [START_REF] Harries | On the relationship between barometric pressure changes on the emission of firedamp[END_REF], Carter and Durst (1995). To understand the problematic, some exits in different abandoned mines (iron mines in Lorainne, coal mines in Lorraine and in North East France) were equipped with specific devices. Several parameters were monitored and the results were analysed. A modelling is also proposed to evaluate the flow strength in different cases. These measurements are important to do because it will be shown, in some cases, that no gas will be detected even if there is some noxious gas in the abandoned mines.

Studied sites

The Lorraine coal basin Coal extraction was made using shafts due to the occurrence of the coal seams (depth more than one hundred meters). This basin presents variations in surface altitude (from 200 to 400 m NGF [Nivellement Général de la France that is to say , height when positive or depth when negative relatively to the sea level which is considered to be equal to 0 m NGF] in different sectors of the mine called "La Houve". At the end of exploitation, in early 2000's, dewatering was stopped and the exits were closed (with concrete plug or concrete slab). Some were equipped with a vent to enable gas exit in specific conditions. A vent or a venting borehole (when not put on a shaft) or a flare is a pipe in connection with the old mine workings. It is equipped with a flame arrestor and a check and relief valve. The check and relief valve should inhibit any intake of atmospheric air and is set to only open if the difference in pressure between inside of the pipe and outside exceeds 220 Pa (for Lorraine coal basin). Two exits which were not under gas capture stations influence were equipped with measurement stations: one shaft (Barrois) and one venting borehole (SDEC OUEST 1). Coal extraction was made using the shafts due to the depth of the coal seams' occurrence. The shafts were numerous (about 150 in the Eastern part of the basin, which is not under gas capture influence). Some venting boreholes were equipped with specific monitoring system in this part. This basin does not present significant variations in altitude.

The Lorraine iron basin

This basin is divided into three main parts (the northern-one, the central-one and the southern-one), separated by the faults. The access to the mines was with shafts and adits. Shafts are located usually on the tops of the hills while adits are located on the hillsides. Iron ore extraction has begun with scrapings on the hillsides. This basin presents variation in surface altitude (in the northern part, from 355 to 440 m NGF for the shafts and from 210 to335 m NGF for the adits). Some exits are closed by a grated gate to prevent from entering into old mining workings but gas entrance and exit are enabled. Several exits (see

Materials and methods

A monitoring system was installed on several exits in order to understand gas flow mechanisms and to evaluate mine gas composition in time for various abandoned mines. Several parameters were measured:

External parameters such as atmospheric pressure and air temperature on the surface. Gas parameters such as gas velocity and flow direction, O 2 , CO 2 , and CH 4 gas content, radon volumetric activity, gas temperature, differential pressure. Fig. 3 shows a typical measurement and monitoring station.

Fig. 3 Measurement and monitoring station

Results and discussion

Lorrain coal basin

A monitoring station was installed at Barrois shaft in October 2007. The recorded measurements are shown on Fig. 4. A differential pressure build-up was observed with a gas outflow: CH 4 content is close to 100 % volume, CO 2 content is almost 3% volume and radon volumetric activity is about 2000 Bq/m 3. The variations in differential pressure (P diff ) are opposite to the variations in atmospheric pressure, but there is no relation with the external temperature. This behaviour is typical and has already been observed in other coal basins where the mine voids represent a significant volume and where exits between mine and surface are closed shafts out of gas capture influence (gas drainage station exits in the mid-part of the basin but its influence (represented by negative The North and Pas-de-Calais coal basin

It was observed for all exits equipped or not with a vent and for venting boreholes that the differential pressure shows variations that are the opposite of those of the atmospheric pressure [START_REF] Lagny | Modélisation de la pression du réservoir post-minier et des debits de gaz passant par les exutoires du secteur Est du bassin houiller du Nord et du Pas-de-Calais[END_REF]. The decrease or the increase of the atmospheric pressure induced variations of P diff which are varying and can be included for example between -550 Pa and +2000 Pa (see Fig. 5 for S11 borehole located at the Vieux Condé mine). The impact of air temperature on the surface is smaller: temperature variations comprised between 8 and 25°C induce pressure variation less than 300 Pa (relation observed on the S15 venting borehole at the Raismes concession but not on the S11 venting borehole).

The Lorraine iron basin CO 2 volume gas content presents seasonal variations as do radon volumetric activity and oxygen content.

According to the season and for each exit, it is observed that gas flow direction changes due to the variations of air temperature on the surface. No relation is observed between gas flow direction and atmospheric pressure (Fig. 6).

Modelling

The Lorraine iron basin When the internal temperature (which is quite constant and equal to 11-12°C) is larger than the external one, massive thermal venting induces colder external air (heavier) to enter through the low openings while, the warmer mine gas (lighter) flows out through the upper openings.

As mine gas temperature is almost constant, the variation of the air temperature on the surface value will induce change in the direction of the flow. The pressure induced (or the push) can range from -5 to 25 Pa (which is in the order of magnitude of the differential pressure measured in situ at Algrange adit for example) with a difference of temperature between -5 to 25°C, a blow speed equal to 0 and a height difference of 30 meters [START_REF] Axley | Application of natural ventilation for U.S. commercial buildings[END_REF]. The push, , is the driving force and counterbalances the entrance (or exit) air losses.

where : = volumic mass of the external gas (kg/m 3 ); = volumic mass of the internal gas (kg/m 3 ); = gravity acceleration (m 2 /s); = height difference (m). The North and Pas-de-Calais coal basin A numerical simulation was made [START_REF] Lagny | Modélisation de la pression du réservoir post-minier et des debits de gaz passant par les exutoires du secteur Est du bassin houiller du Nord et du Pas-de-Calais[END_REF] for the eastern part of North and Pas-de-Calais coal basin.

In particular, a decrease in atmospheric pressure like those observed on S11 (Taffin) borehole was simulated and the differential pressure was calculated.

Assumptions were taken concerning: initial pressure in mining voids; a flooding time of mine voids of 24 years; a desorption capacity which decreases linearly with time; some average characteristics for the 150 shafts and the venting boreholes located in this basin's part;

the use of perfect gases law for calculation of mol number in the mining voids at each calculation step; a voids volume of 62.4 Mm 3 which decreases linearly with flooding and with time; an initial pressure in the borehole equal to 1016 hPa; a mine gas density closed to 0.8; 150 shafts whose intrinsic permeability is around 10 -10 m 2 , the diameter is taken equal to 3 m, the average depth of the upper exploited level is 145 m; mine gas exit through the recovery is neglected.

The flow (in m 3 /s) in a venting borehole is described by the equation which links it to the pressure drop and to the differences of the square of the pressure. The differential pressure calculated is clearly similar to those registered in January 2005 (Fig. 5). Atmospheric pressure variations induce differential pressure variations which are opposite.

Discussion

The abandoned mine voids, which consist of a closed system (shafts closed off and/or filled-in like in the coal mines previously presented) operate as follows:

The variations in atmospheric pressure lead to fairly significant differential pressure. So, the atmospheric pressure serves as the main parameter driving mine gas. In the iron basin, natural thermal convection plays a major role in the creation of the flow between old mine workings and the surface. This phenomenon is due to the difference between the air temperature on the surface and the temperature in the voids. Thermal convection is facilitated by a surface topography difference and by the methods of closing the exits.

Conclusions

The results of the present study clearly show that the main motor of gas migration from the old mining works towards the surface is not the same in the various basins which were analysed. In one case (abandoned mines defined as an open system), the external temperature is the main parameter; in the other case (when the abandoned mines are defined as a closed system) the atmospheric pressure variations are then the crucial parameter.

The present results should improve the interpretation of the gas measurements made at abandoned mines exits and boreholes. Atmospheric conditions and abandoned mines configurations should be taken into account to understand data obtained in various contexts. It is especially important to take care of these observations because, in some cases, measurements made in specific atmospheric conditions will show that no gas is emitted from abandoned mines although mines voids could contain noxious gases which could be emitted in others atmospheric conditions. This could induce mistakes on gas emission level estimation or on the detection and location of abandoned shaft by infrared thermo graphic method [START_REF] Donnely | The location of abandoned mine workings using thermal techniques[END_REF], or on the measurement of radon volumetric activity which value depends, notably, on atmospheric conditions (see IRSN (Institut de Radioprotection et de Sûreté Nucléaire) publications) or on the behaviour of venting boreholes connected with abandoned mines...

Fig. 1

 1 Fig. 1 Photographs of the venting borehole SDEC OUEST 1 (left) and Barrois shaft with a vent (right) (Lorraine coal basin)

  Fig 2 for example) were equipped with a measurement and monitoring station (see § Materials and methods).

Fig. 2

 2 Fig. 2 Algrange adit and François shaft (Lorraine iron basin)

Fig. 4

 4 Fig. 4 Data recorded at Barrois shaft from 9/10/2007 to 10/10/2007 (Lorraine coal basin)

Fig. 5

 5 Fig. 5 Atmospheric pressure, differential pressure and air temperature on the surface over the time (recorded during ten days) on the S11 venting borehole at the Vieux Condé mine (Eastern part of the North and Pas-de-Calais coal basin)

Fig. 6

 6 Fig. 6 Radon volumetric activity, atmospheric pressure and air temperature on the surface registered at Algrange adit (Lorraine iron basin)Similar results (Fig.7) were observed in G37 adit, which has been equipped with a monitoring station more than ten years ago and which is located in Moyeuvre town, in the low part of North iron basin. Gas flow direction is induced by the air temperature on

Fig. 7

 7 Fig. 7 Data registered on G37 adit (Moyeuvre-Grande town) from April 2000 to April 2008 (Lorraine iron basin)

Fig 8

 8 Fig 8 shows the value of the driving force (black curves) which includes wind (v r ) and thermal (T o ) effects. Fig. 8 Driving force due to wind and thermal effects[START_REF] Axley | Application of natural ventilation for U.S. commercial buildings[END_REF]

Fig. 9

 9 Fig. 9 Differential pressure calculated before, during and after an atmospheric pressure drop

Acknowledgments This work was supported by the ministry in charge of mines and GISOS (Groupement de recherche sur l'Impact et la Sécurité des Ouvrages Souterrains) -Research Group for the impact and safety of underground cavities.


Jean-Luc Garden

Hervé Guillou

Jacques Richard

Comment regarding "On the theoretical determination of the Prigogine-Defay ratio in

Keywords:

Generally, experimentally determined values of the Prigogine-Defay (PD) ratio are different from unity. This can be explained if one considers that more than one single order parameter are involved in the thermodynamics of the glass transition process. Against the consensual view, Tropin et al. demonstrated that PD ratios can be different from unity even if one single order parameter is involved. This "Comment" aims to discuss fundamental mistakes leading to this conclusion in the recent article "On the theoretical determination of the Prigogine-Defay ratio in glass transition" [

In a recent paper by Tropin et al. "On the theoretical determination of the Prigogine-Defay ratio in glass transition" [1], several important errors are made that invalidate the principal conclusions. Since some of these errors are systematically reproduced in several papers published these last years by the same group, we feel obliged to draw attention to them. [2][3][4] In the seminal papers of Davies and Jones on the irreversible approach to equilibrium in glasses [5], or on the thermodynamic and kinetic properties of glasses [6], the notion of structural order parameter ξ was used to describe the non-equilibrium behavior of systems undergoing a glass transition. Particularly, it is nowadays admitted that, since the experimentally determined values of the Prigogine-Defay (PD) ratio at the glass temperature are generally different from unity, then more than one structural order parameter are involved in the thermodynamics of the glass transition [6].

Against the consensual view, Tropin et al. demonstrated that PD ratios can be different from unity even if one single order parameter is involved. Although we do not discuss on the eventuality of such a conclusion, we argue that the expression of the PD ratio under which the authors based their reasoning is inexact. Firstly, we argue that this expression is not a PD ratio. Secondly, we state that this expression cannot be related to the glass transition, because important contributing terms are missing. Furthermore, we demonstrate that the alternative approach proposed in the last part of Ref. [1], allowing comparison between theory and experimentally determined values of the PD ratio, is also erroneous. Such as originally demonstrated by Garden et al. [7], and published recently [8], a general expression can be derived when the configurational contributions of the three thermodynamic coefficients C p , α p and κ T , are used in order to define a non-equilibrium configurational PD ratio:

Π conf = 1 V T C conf p κ conf T α conf p 2 (1)
= ∂H ∂ξ p,T ∂V ∂ξ T,p + dA dp T ∂V ∂ξ T,p A + ∂H ∂ξ p,T -T dA dT p ( 2
)
where A is the affinity, ∂H and dA dT p are the temperature and pressure derivatives of the affinity at constant temperature and constant pressure respectively. This expression above, and the associated exact calculations have only been recently used by Tropin and co-workers [4], and shown again in the Ref. [1]. Unfortunately, the authors systematically neglected the temperature and pressure derivatives of the affinity dA dp T and dA dT p as compared to their neighboring terms. Consequently, the following expression that the authors identified to a PD ratio is:

Π = ∂H ∂ξ p,T A + ∂H ∂ξ p,T (3)
This approximated expression was originally provided ad hoc in previous works because at this time the two affinity derivative contributions were simply omitted [2,3,[START_REF] Gutzow | The Vitreous State[END_REF]. No proof is given in Ref. [1] and in previous works that suggest neglecting the two affinity derivatives in Eq. ( 2) to yield to Eq. (3). Actually, this assumption cannot be related to the glass transition since the expression (3) corresponds to a glass transition process occurring at constant affinity (dA = 0). On the contrary, Garden et al. demonstrated recently that the two affinity-derivative contributions are of fundamental importance in the phenomenological description of the glass transition (see Fig. (5) and Fig. [START_REF] Gutzow | The Vitreous State[END_REF] in Ref. [START_REF] Garden | [END_REF]). They are both involved in the thermodynamics describing the temperature and pressure behaviors of the coefficients C p , κ T , and α p and thus in their changes at T g [START_REF] Garden | [END_REF]. For non-equilibrium systems (A = 0), it is obvious that the expression (3) above is different from unity. The question now arises whether this departure from unity has something in common with the classical question on measured PD ratios of glasses such as claimed by the authors. The departure from unity of such expression (3) is very small and has nothing to do with the classical problem of glass science on the nonunity of measured PD ratios (such as for example shown in Fig. 3 of Ref. [1] with only few percent of departure from unity).

In a further step, Tropin et al. proposed an alternative approach of the non-unity of the PD ratio [1]. This way was totally different from the previous one although the authors claimed that it reconfirmed previous conclusion. Indeed, the authors based now their demonstration on exact expressions relying on equilibrium properties of the system under consideration, i.e. now A = 0, in total contradiction with the PD ratio defined by the expression (3) above. Indeed, in the first part they attributed the departure from unity on the departure from equilibrium of the system. Now, in the paragraph IV, the authors used the fundamental equation (90) of Ref. [1]:

Π(T g ) = - ∂H ∂ξ p,T T ∂V ∂ξ T,p ∂ξe ∂p T ∂ξe ∂T p (4)
considering, this time, equilibrium transformations only, to allow comparison between the theory and experimentally determined values of the PD ratio. In a first step, they used the lattice-hole model of liquid to demonstrate that Π(T g ) = 1 (see paragraph IV.B: "Application to model systems: First example"). Next, in the same paragraph, the authors derived a new expression for the PD ratio (Eq. ( 100)). This time, the temperature and pressure dependence of the model parameters ∆E 0 (p, T ) and v 0 (p, T ) were taken into account to discuss on the departure from unity of the PD ratio. As they did not know explicitely this temperature and pressure dependence, a very crude approximation was used in the following paragraph (see paragraph IV.C: "Application to model systems: Second example") leading to an other expression of the PD ratio containing the Clausius-Clapeyron equation (Eq. ( 104)). The authors wanted to convince us that their approximate expressions (102) were in fact rather equivalent to the exact expressions (97) and (98) for the temperature and pressure derivatives of the equilibrium order parameter. We point out that using too rough expressions (102), a wrong value for Π(T g ) is achieved. To demonstrate that, it is sufficient to calculate the expressions ∂ξe ∂p T and ∂ξe ∂T p independently of the model used. Nevertheless, we agree that the parameters ∆E 0 and v 0 can be temperature and pressure dependent. Starting from the total differential of affinity (Eq. ( 5) of Ref. [1]), considering equilibrium only (i.e A = 0; dA = 0; ξ = ξ e ), we then obtain the model independent expressions for the pressure and temperature derivatives of the equilibrium value of the order parameter (see for example Eq. (19.14), p. 293 of Ref. [START_REF] Prigogine | Chemical Thermodynamics[END_REF]):

∂ξ e ∂p T = ∂V ∂ξ T,p ∂A ∂ξ T,p , ∂ξ e ∂T p = - ∂H ∂ξ p,T T ∂A ∂ξ T,p (5)
Substituting these expressions into (4) yields to unity. The question is: how these approximate expressions (102) can lead to Π(T g ) = 1, while the exact expressions above lead to Π(T g ) = 1 ? The answer is that the expressions (102) are truly too approximate and consequently this alternative second approach is also irrevelant.

In conclusion, the exact general expression (2) is not a classical PD ratio [7,8]. Therefore, the expression (3) does not represent a classical PD ratio. More importantly, if it can be demonstrated that the general expression ( 2) is related to experimentally determined PD ratios (which has not been demonstrated by the authors), the expression (3) cannot be used, because important thermodynamic contributions are arbitrarily neglected. Eventually, the alternative approach based on equilibrium properties of the system allowing comparisons with experiments is also wrong.

Finally, at the present time it has not been demonstrated by Tropin et al. that, if only one single underlying order parameter is supposed to be involved in the thermodynamics of the glass transition, then the Prigogine-Defay ratio should be very different from unity like in experiments.