L Barelli
email: barelli@unipg.it

G Bidini

C Buratti

R Mariani

DIAGNOSIS OF INTERNAL COMBUSTION ENGINE THROUGH VIBRATION AND ACOUSTIC PRESSURE NON -INTRUSIVE MEASUREMENTS

Keywords: I.C.E. Diagnosis, I.C.E. vibration analysis, I.C.E. acoustic pressure analysis

The present study proposes a diagnosis methodology for internal combustion engines (I.C.E.) working conditions, by means of non invasive measurements on the cylinder head, such as acoustic and vibration, related to the internal indicated mean effective pressure. The experimental campaign was carried out on the internal combustion engine of the cogeneration plant at the Faculty of Engineering -University of Perugia (Italy), for different values of the engine load. Results show that both the vibration and acoustic signals measured on the cylinder head are strictly related to the phenomena inside the cylinder, depending on the engine load and the combustion frequency. Some vibration and acoustic indexes were introduced, in order to evaluate the working regimen of the engine. Their values, obtained for different engine loads, constitute the reference values; when the methodology was implemented , the evaluation of such indexes allows to estimate the combustion quality, comparing measured and reference values.

Introduction

The condition monitoring of diesel engines has been the aim of many research approaches. Most of them are based on the acquisition of signals, which can be the cylinder pressure, the engine vibration, the crankshaft acceleration. The processing of the acquired signals and the comparison with threshold values allows to discriminate between regular and faulty engine running condition [START_REF] Daniere | Effective vibration analysis of IC engines using cyclostationarity. Part II -New results on the reconstruction of the cylinder pressures[END_REF]. Among these approaches, vibration and acoustic measurements offer a great potential due over all to the non -intrusive nature of the measurements. The sound generation of a diesel engine can be modelled based upon the combustion process, and time -frequency analysis can be used to reveal the underlying characteristics of the sound waves [START_REF] Ball | The condition monitoring of diesel engines using acoustic measurements. Part 1: Acoustic characteristic of the engine and representation of the acoustic signals[END_REF][START_REF] Ball | The condition monitoring of diesel engines using acoustic measurements[END_REF].

The aim of the present paper is to develop a diagnosis methodology for internal combustion engines (I.C.E.) quality, by evaluating macroscopic working parameters measured with non invasive instruments [START_REF] Barelli | Design of the measurements validation procedure and expert system architecture for a cogeneration internal combustion engine[END_REF]. The study was carried out considering the internal combustion engine of the cogeneration plant at the Faculty of Engineering -University of Perugia (Italy).

Measurements were carried out considering both Caterpillar CAT G3516 LETA, working until September 2004, and a new unit, CAT G3516B, substituting the former due to serious failure.

The diagnosis methodology is based on the characterization of the working conditions by means of acoustics and vibrations measurements and relating data to the indicated mean effective pressure inside the cylinder. Some indexes were introduced, in order to evaluate the working regimen of the engine. The mean indicated cycle and the intake and exhaust valve lift law of CAT G3516 LETA for different values of the produced electric power were related to the vibration measurements on the cylinder head and, for CAT G3516B, to the acoustic pressure levels in a close frequency band. Some parameters were proposed, in order to relate data to the indicated mean effective pressure in the monitored cylinder, which indicates the working state of the engine. A reliable methodology to evaluate the internal combustion engines quality was finally developed.

The Faculty of Engineering Cogeneration Plant -University of Perugia

The experimental activity was carried out on the I.C.E. of the cogeneration plant installed at the Faculty of Engineering (University of Perugia, Italy).

Measurements were carried out both on the Caterpillar CAT G3516 LETA Engine and the new unit, CAT G3516B LE, installed for substituting the first one for serious failure.

Both engines CAT G3516B LE and CAT G3516 LETA have 16 cylinders V disposed and are characterized by costant low rotation velocity (1,500 r.p.m.), natural gas fuelling, controlled ignition, turbocharging with aftercooling. The main characteristics of both engines are listed in Table 1.

A heat recovery, both in winter and summer, is carried out for the Faculty air conditioning plant; heat is recovered at high (exhaust gases) and low (engine cooling) temperature. In summer the recovered heat is employed in a Water -Lithium Bromide absorption chiller (thermal power 2MW t ). The electric energy, produced by the engine working at a constant load of 950 kW (just a little below than the maximum value), is used to satisfy the Faculty demand. The exceeding part is sold to the National Electric Grid, while electric energy is taken when the engine is not working. The electric energy exchange is regulated by means of suitable contracts.

Fig. 1 shows a scheme of the plant: the three-way valve (5) sets the water flow rate for the engine cooling and the parallel auxiliary circuit, according to the temperature of the engine cooling fluid; if higher than 85 °C, part of the flow rate is sent to the auxiliary heat exchanger [START_REF] Daniere | Effective vibration analysis of IC engines using cyclostationarity. Part II -New results on the reconstruction of the cylinder pressures[END_REF] where it is cooled by the water from the evaporative tower (2). The on-off three -way servocontrol valve (9) sends gases from the turbocharging turbines directly to the exhaust and to the high temperature shell and tube heat exchanger [START_REF] Li | Engine failure diagnosis with sound signal using wavelet transform[END_REF], in order to guarantee the temperature variation of the hot water.

In the scheme of fig. 1 the auxiliary chillers and boilers, utilized in the case of heat recovering not present or insufficient, are not indicated. Also the flow rate circulating in winter conditions for the user is not present; it is controlled by a three -way valve proportional to the water temperature at delivery.

Indicated cycle survey as a function of engine operation regime and main parameters evaluation

Instrumentation and measurement methodology

The engine indicated cycle represents the thermodynamic cycle followed by a working fluid in the engine combustion chamber; it could be experimentally obtained using a pressure sensor pointed out in the combustion chamber.

The preliminary work involved an experimental acquisition of the intake and exhaust valves lift law. To this aim, taking as reference the fly-wheel at the engine head, it was possible to relate the lift of the intake and exhaust valves to the crankshaft angle. Figure 2 shows the obtained cams profiles on CAT G3516 LETA engine.

The employed equipment was composed by: -Tektronix TDS 420 A oscilloscope; -magnetic pick-up; -Kistler Type 6055BB Pressure sensor (piezoelectric sensor, sensitivity 20 pC/bar, maximum measurement temperature 400°C), characterized by an accuracy <= ±0.5% of the full scale value and a calibrated range of 0-100 bar.

The pressure sensor was placed in correspondence of the monitored cylinder top dead centre (TDC); a magnetic pick-up was positioned on the damped wheel even in correspondence of the TDC, in order to associate to each pressure value measurement the corresponding crank angle value (and also the value of the combustion chamber volume). Moreover, a further pick -up was placed in correspondence of the flywheel at the engine head.

Signals surveyed from the two magnetic picks-up and from the pressure sensor were acquired by the oscilloscope, with a 25 kHz sampling frequency and a wave shape of 30,000 points, corresponding to a total sampling time of 1.2 s.

Tests were carried out on CAT G3516 LETA in three different load settings:

-650 kW; -450 kW; -Without load (min.).

Measurements results

Considering 1,500 rpm speed engine and a sampling time of 1.2 s, 15 engine cycles and consequently 30 passages to the TDC were acquired.

The pressure sensor takes the pressure difference, so measured data must be corrected considering the absolute pressure relative to the engine inlet manifold. This value (Tab. 2, col. 2) was acquired for all the different load settings of the test, using the Caterpillar DDT diagnostic module, that allows to read the engine pressure sensor placed on the inlet manifold.

The indicated cycle describes the pressure variation inside the combustion chamber as a function of the variation of the chamber volume; therefore the pressure trend must be related to the combustion chamber volume as a function of the crankshaft angle, by means of the following equation [START_REF] Ferrari | Motori a combustione interna, edizioni il capitello[END_REF].

Λ - Λ - - Λ + + - = θ θ 2 2 sin 1 1 cos 1 1 2 1 1 1 r V V c (1)
where:

-V c is the unitary displacement; -r is the compression ratio; -is the ratio between connecting rod length and crank radius; -is the crankshaft angle.

The mean indicated cycle relative to the tested load settings was evaluated according to the described methodology; results are illustrated in figure 3.

The indicated mean effective pressure (IMEP) is the pressure value applied constantly on the pistons during the only expansion phase; it yields the work produced by a complete engine cycle.

The IMEP could be consequently calculated as the ratio between the indicated work produced per mean indicated cycle and the displacement [START_REF] Ferrari | Motori a combustione interna, edizioni il capitello[END_REF]:

tot i V W IMEP = (2)
where:

-V tot is the total displacement; -W i is the indicated work produced per engine cycle.

The indicated work associated to one cylinder could be calculated starting from the mean indicated cycle by integrating the infinitesimal work in all the cycle. In Tab. 2, col. 3, the IMEP values are summarized at the load variation.

Measurement of the cylinder head vibration conditions, varying engine operation regime

Instrumentation and measurement methodology

The correlation between vibration measurements acquired by an accelerometer placed on the cylinders head and engine fundamental parameters, such as cam profiles and inside cylinder pressure, is interesting to analyze the operational condition of internal combustion engine for diagnostic purposes.

To such aim, the necessary data were acquired at the same time. In particular vibration measurements were carried out by employing PCB Piezotronics 353B17 accelerometers (sensitivity 1.02 mV, measurement step ± 4,905 m/s 2 pk) and a signal conditioner PCB 442C04, as showed in figure 4.

Accelerometers were placed at 4 points on engine head upper surface; inside the same cylinder the indicated cycle was acquired. Vibration measurements, carried out following the same sampling parameters previously described, were performed on CAT G3516 LETA engine in correspondence of three load settings: 650 kW, 450 kW, minimum load and on engine CAT G3516B at 950 kW.

Results of measurements. Definition and evaluation of characteristic indices

Figure 5 shows the vibration signal state as a function of the crankshaft angle, varying load conditions. Superimposing the vibration signals obtained from CAT G3516 LETA for the three load settings, it can be noted that they are strongly related to the operation engine and in particular to the inside cylinder pressure. In fact there are greater vibration signal peaks as load increases .

Then it can be asserted that vibration signal acquired on the engine cylinder head is a good indicator of the combustion phenomena being in an I.C.E., and in particular of the pressure signal characteristic of the indicated cycle at the different loads.

Subsequently the acquired vibration signals were elaborated in frequency through the Fourier discrete transform, DFT (fig. 6). The amplitude value trend (expressed in Volt rms), at the frequency variation, strongly decreases with increase in frequency; in the three load settings the most part of signal energy is in the frequency range within 2,000 Hz, to confirm that mechanical solicitations, that occur mostly at low frequencies, represent the main part of the force globally transmitted at the cylinder head.

Figure 7 shows DFT of vibration signal acquired on CAT G3516 LETA; it can be noted that the signal presents a fundamental frequency at 12.5 Hz, corresponding to the combustion frequency.

Vibration measurements on Caterpillar CAT G3516B were executed only at 950 kW load.

The agreement between cylinder head state of vibration of CAT G3516 LETA and G3516B engine is shown in fig. 7, where the vibration signal is plotted in the frequency domain. The comparison of the DFT trend of the cylinder head vibration signal between CAT G3516 LETA and CAT G3516B shows load influences on the vibration transmitted to the structure; vibration value measured on the new engine at the load of 950 kW is constantly higher than the value measured on the I.C.E. previously installed.

It is therefore suitable to find vibration signal characteristic parameters; with such aim in mind the RMS value, or vibration effective value, supplies a good indication of its intensity [START_REF] Ferrari | Motori a combustione interna, edizioni il capitello[END_REF], in fact: ( ) ( )

t q t q 2 i rms i = (3)
with q i (t) vibration instantaneous value.

Experimental results. Typical index definition and its evaluation

Figure 8 shows the acoustic pressure trend in the frequency domain, for the load configuration of 950 kW and 650 kW. The measured acoustic pressure also depends on the load, values at 950 kW load are always higher than the ones at 650 kW. Such as in vibration measurements, the signal peaks correspond to the combustion harmonic frequency (12.5 Hz). The very high value of the recorded signal at 950 kW near the 112.5 Hz frequency is probably caused by the room second resonance frequency (115 Hz) contribution, calculated according to the engine room dimensions.

In the frequency domain, for acoustic signal so as for the vibration one, the mean of the peaks related to the first 100 harmonics of the combustion basic frequency were evaluated; the index was named I fa (Table 4).

Comparison between the experimental results and the proposed diagnostic methodology validation

Correlation between inside cylinder pressure (IMEP) and vibration cylinder state (RMS, I fv )

Figure 9 shows the vibration trends recorded on the cylinder of CAT G3516 LETA engine and the valves lift law calculated with the methodology explained in the first paragraph; it is possible to remark that the valve opening and closing contribute to the vibration generation. The pressure variation in the intake duct at the moment of the valve opening, together with the impact due to the valve closing, contributes highly to the cylinder vibration. These vibrations are superimposed to the ones generated by the pressure variation due to combustion, so that the generated global signal depends only on the internal cylinder pressure. The variation on the vibration signal, recorded in correspondence of the valve opening and closing, is more evident if its inverse value is calculated, as shown in figure 10. Figure 11 shows a correlation between the signal value in terms of its amplitude and the position of the valves, which cause a vibration peak at each opening and closing phase. Moreover the energy distribution is prevalent in low -frequency. From the values in table 3 it is possible to note that both the characteristic parameters of the vibration signal (RMS, I fv ) depend on the I.C.E. load. Moreover comparable reductions of such parameters take place at the load decrement.

Finally, as remarked in the time signal analysis, also in the frequency domain there is a load dependence. In fact as the load increases, the DFT amplitude increases in correspondence of the basic frequency and its harmonics. So the vibration phenomenon in the cylinder upper area is proportional to the internal pressure and it depends on the I.C.E. load. From the recorded values it is possible to obtain the cylinder internal pressure trend or, more easily, the correspondence IMEP using as input data the vibration intensity; this is possible because there is a correlation between the IMEP and the RMS vibration value, as shown in table 5. In the time domain the signal analysis gives a good tool to evaluate, at a fixed load, the engine operation conditions and the combustion quality through the comparison between measured RMS values and the reference ones.

Correlation between the single cylinder vibrational state and the single cylinder pressure level

A comparison between vibration and acoustic power in the same frequency range was carried out in the 950 kW configuration load (fig. 12). Values of I f and of its percentage variation for CAT G3526B at 950 and 650 kW load, calculated for both vibration and pressure level, are reported in tab. 6; the percentage variation has approximately the same values, due to a strict correlation between the two parameters.

Results show that the combustion quality could be evaluated without distinction from RMS, Ifv or Ifa values; they are in fact all related to the indicated mean effective pressure inside the cylinder.

Diagnostic methodology

Pressure or vibration signals could be employed without distinction to detect phenomena in the combustion chamber. If I f , calculated from acoustic or vibration measurements, is not congruent with a correct engine functioning, an irregular combustion and a consequent anomalous value of the IMEP are possible.

This methodology could point out misfire and elastic band seal problems. Misfire, as an example, produces a shift of the fundamental frequency of the combustion, with a consequent lower value of the index, while if seal problems occur in a cylinder, the corresponding IMEP diminishes and with it also RMS and I fv values.

Conclusions

Monitoring working conditions and combustion quality in an internal combustion engine often requires intrusive techniques. Therefore the study of alternative diagnosis methodologies is desirable; in the present research a non intrusive methodology is proposed, based on vibration and pressure level measurements on the cylinder heads. Both signals are strictly related to the phenomena inside the cylinder, depending on the combustion frequency.

In the analysed internal combustion engines, at a constant rotation velocity (1,500 r.p.m.), a strict correlation among these parameters and the indicated mean effective pressure inside the cylinder was found.

Both vibration and pressure level signals were characterized by the internal load of the cylinder and by the combustion frequency (12.5 Hz).

In order to develop a valid methodology based on these signals, a graphic analysis was carried out; it showed that the signals amplitude is maximum at frequencies lower than 2 kHz; this is therefore the useful range for the development of alternative diagnosis methodologies.

A new index was proposed, calculated as the mean value of the first 100 harmonics of the combustion frequency of both the vibration (I fv ) and the pressure level signal (I fa ), together with the RMS value of the vibration vs. time.

The proposed indexes, obtained for different values of the engine load, allow to evaluate the indicated mean effective pressure inside the cylinder and to estimate the combustion quality, comparing measured and reference values.

Vibration and acoustic pressure levels could be employed without distinction: in particular, if the I f value (calculated indifferently from vibration or pressure level measurements) is not congruent with the reference one, the combustion inside the cylinder in which measurement is carried out could be irregular, with a consequent anomalous value of the IMEP inside the same cylinder; it could happen when misfire or elastic band seal problems occur.

CAT G3516B

CAT

Tab. 3 , 4 .

 34 col. 2, summarizes the RMS values at the load variation for the CAT G3516 LETA engine and at the load of 950 kW for CAT G3516B. The RMS value of the signal noticed on CAT G3516B engine is equal to 0.055 Volt, approximately 4 times higher than the value calculated for the old engine CAT G3516 LETA at 650 kW, and it confirms what previously stated. Then, to correlate the IMEP to the vibration signal in frequency domain acquired on the engine cylinder head, attention was focused on the definition of a suitable indicator; the best result, as reported in the next paragraph, was obtained by employing an indicator named I fv . Such indicator is defined as the mean of the frequency peaks relative to the first hundred harmonics of the fundamental frequency; the choice of considering only those harmonics is justified by the characteristic of the signal, that quickly decreases in amplitude over 1,500 Hz. In Tab. 3, col. 3, the I fv values for CAT G3516 LETA and CAT G3516B are shown. The parameter suitability and all hypotheses previously assumed are demonstrated for CAT G3516B operating at 950 kW by a value higher than the one realtive to CAT G3516 LETA at the load of 650 kW. This parameter verifies once again the correlation between inside cylinder pressure and vibration acquired on the cylinder head, and allows to link results obtained for CAT G3516 LETA engine with CAT G3516B. Acoustic pressure level observation near a cylinder 4.1 Experimental apparatus and measurement methodology Acoustic pressure measurements were carried out near the investigated cylinder, in order to obtain an acoustic characterization of the combustion inside it [6, 7, 8]. The experimental apparatus was constituted by: -a spectrum analyzer Symphonie, by 01 dB -Stell: it answers to precision class 1 according to IEC 651 and IEC 804, digital filters (class 0) are in compliance with IEC 1260; dynamic range 20-135 dB; weighting A, B, C and Lin; -a ½" Random Incidence microphone by G.R.A.S. (Sound & Vibration): it complies with the requirements in IEC 1094 part 4; Nominal Open Circuit Sensitivity at 250 Hz 50 mV/Pa; Frequency response ±2 dB (3.15 Hz -12.5 kHz), ±1 dB (12.5 Hz -8 kHz); Upper limit of Dynamic Range 148 dB (ref. 20 Pa), Lower limit of Dynamic Range 16 dBA (ref. 20 Pa); -a ½" condenser preamplificator (PRE12H) by 01 dB -Stell: frequency scale 1 -20 kHz, Gain, Typical -0.035 dB, max -0.050 dB; Noise measured with 15 pF equivalent capacity: weighted A typical 2.5 V, linear 22 Hz -22 kHz typical 10 V; -a CAL 01 calibrator, by 01 dB -Stell: according to IEC 942; typical sound pressure level 74, 94, 114 dB; stability of sound pressure level ±0.1 dB; Acoustic pressure tolerance ±0.3 dB; frequency 1kHz ±20 Hz; stability of frequency > 0.5%. The acoustic signal was recorded for a period of 30 s in the frequency range 0 Hz -20 kHz and postprocessed by means of a suitable software, dBFA32. The signal elaboration was made by a narrow -band analysis through a Hanning FFT with a 6.25 Hz step. Measurements were carried out on CAT G3516 B engine in 950 kW and 650 kW load configuration .

  The recorded vibration signal was analyzed together with the measured pressure values on CAT G3516 LETA and the valves lift law trend through a 3D visualization of the DFT. The vibration signal spectrograph was obtained as a load function for the CAT G3516 LETA and CAT G3516 B engine; the spectrograph is a DFT signal visualization as a function of the acquisition time. In this case an engine complete cycle was considered.The DFT value is visualized through a chromatic scale and it is possible to analyze the DFT amplitude variation with frequency . For example, figure11shows the CAT G3516 LETA engine spectrograph at the 450 kW load (red corresponds to the signal amplitude peacks) together with the valves lift law; to calculate the DFT, a Hanning window with 56 samples width was considered.

Figure 1 -Figure 2 -Figure 3 - 2 )Figure 4 -

 12324 Figure 1 -Cogeneration plant layout

Figure 5 -Figure 6 -Figure 7 -Figure 8 -Figure 9 -Figure 10 -Figure 12 -

 567891012 Figure 5 -Vibration signal state in fuction of the cranckshaft angle with engine load variation

Table 1 -

 1 Mean CAT G3516B and CAT G3516 LETA technical data relative to standard conditions and after coolerwater inlet temperature of 25 °C

	G3516 LETA

Table 2 -

 2 Absolute pressure values in the engine inlet manifold and IMEP values as a load function

		Load (kW)	RMS (Volt)	I fv (Volt)
		650	0,013645	0,001801
	CAT G3516 LETA	400	0,012093	0,000907
		Lowest	0,006403	0,000488
	CAT G3516B	950	0,055000	0,004570

Table 3 -

 3 Vibration RMS values and I fv index as a load function related to CAT G3516 LETA and CAT G3516B engine

	Load (kW)	I fa (Pa 2 )
	950	0,114283
	650	0,038532

Table 4 -

 4 CAT G3516B engine: Index I fa

	Load (kW) IMEP (bar) Difference (%) RMS (Volt) Difference (%) I fv (Volt) Difference (%)
	650	0,013645	11%	9,7612564	34%	0,001801	50%
	400	0,012093	47%	6,4062634	83%	0,000907	46%
	Lowest	0,006403	-	1,0947554	-	0,000488	-

Table 5 -

 5 Correlation between the IMEP and the RMS vibration values

	Load (kW)	I fv (Volt)	Difference (% )	I fa (Pa 2 )	Difference (%)
	950 650	0,0045724 0,0018010	61%	0,114283 0,038532	66%

Table 6 -

 6 CAT G3526B engine: I fv and I fa indeces and percentage difference

Acknowledgements

Authors wish to thank Dr Fabio Bonucci for his collaboration in the measurements campaign.


G Maggio

L G Gordeeva

A Freni

Yu I Aristov

G Santori

F Polonara

G Restuccia

Simulation of a solid sorption ice-maker based on the novel composite sorbent "lithium chloride in silica gel pores"

Keywords: Adsorption cooling, Solar ice-maker, Lithium Chloride in silica gel pores, Activated carbon, Dynamic simulation

In this paper, a novel composite sorbent "lithium chloride in silica gel pores" is proposed for application in solar-powered adsorptive ice makers. A mathematical model was used in order to calculate the performance of an ice-maker using this material as adsorbent and methanol as adsorbate. The results of the model showed that a maximum solar Coefficient Of Performance (COPs) of 0.33 and a maximum Daily Ice Production (DIP) of 20 kg m -2 can be obtained for an ice-maker equipped with a solar collector area of 1.5 m 2 and 36 kg of adsorbent material. Such performance are noticeably higher than those obtained using commercial activated carbon, that is the adsorbent mostly proposed till now.

Nomenclature

A i (i=1-5, 9) Heat transfer surface, m 2 c Specific heat, J kg -1 K -1 COPs Solar Coefficient Of Performance DIP Daily Ice Production, kg I β Available solar radiation @ β=30°, W m -2 K i (i=1-3) Flag: 0 or 1 (see Eqs. ( 2) and ( 9)) L a Adsorbate latent heat of condensation/evaporation J kg -

Introduction

A solar-powered adsorptive ice-maker consists of a small size adsorbent reactor connected to a solar collector, for regeneration of the sorbent material during the day, and connected to an evaporator, for ice production during the night [START_REF] Dieng | Literature review on solar adsorption technologies for icemaking and air-conditioning purposes and recent developments in solar technology[END_REF][START_REF] Li | A solar powered ice-maker with the solid adsorption pair of activated carbon and methanol[END_REF]. Different prototypes were realized, showing the potentiality of this technology [START_REF] Li | A solar powered ice-maker with the solid adsorption pair of activated carbon and methanol[END_REF][START_REF] Sumathy | Experiments with solar-powered adsorption ice-maker[END_REF][START_REF] Li | Experimental study on dynamic performance analysis of a flat-plate solar solid-adsorption refrigeration for ice maker[END_REF][START_REF] Anyanwu | Design, construction and test run of a solid adsorption solar refrigerator using activated carbon/methanol, as adsorbent/adsorbate pair[END_REF].

In particular, Sumathy and Li [START_REF] Li | A solar powered ice-maker with the solid adsorption pair of activated carbon and methanol[END_REF][START_REF] Sumathy | Experiments with solar-powered adsorption ice-maker[END_REF] designed and tested in Hong Kong a solar adsorption ice-maker with a single flat-plate collector (0.92 m 2 exposed area), based on activated carbon/methanol pair. Their experiments showed that this system can produce 4.3-5.4 kg m -2 day -1 of ice, with a solar COP of 0.10-0.12. These values are in good agreement with those reported by M. Li [START_REF] Li | Experimental study on dynamic performance analysis of a flat-plate solar solid-adsorption refrigeration for ice maker[END_REF] for a similar flat-plate ice-maker tested in Shanghai: 4.7-6.7 kg m -2 day -1 of ice and a COP of 0.12-0.15, for a solar collector of 0.75 m 2 . Anyanwu and Ezekwe [START_REF] Anyanwu | Design, construction and test run of a solid adsorption solar refrigerator using activated carbon/methanol, as adsorbent/adsorbate pair[END_REF] designed, constructed and tested in Nsukka, Nigeria, a flat-type solar adsorption refrigerator using activated carbon/methanol, with effective exposed area of 1.2 m 2 . They obtained a maximum solar COP of 0.02, but this low value was attributed to the "non-selective collector plate surface coating used".

Recently, Khattab [START_REF] Khattab | Simulation and optimization of a novel solar-powered adsorption refrigeration module[END_REF] proposed and tested an innovative modular ice-maker with the adsorbent (granular carbon bonded with blackened steel) placed in a glass container, positioned between reflector panels. This system, using methanol as adsorbate, provided a COP of 0.16 and a daily ice production of 9.4 kg m -2 day -1 . S.G. Wang and R.Z. Wang [START_REF] Wang | Recent developments of refrigeration technology in fishing vessels[END_REF] reported a COP of 0.18 for a sophisticated two-bed adsorption prototype ice-making machine operating with heat and mass recovery and based on activated carbon/methanol pair.

Several authors estimated the performance of adsorption ice-makers by mathematical modelling [START_REF] Li | Heat and mass transfer in a flat plate solar solid adsorption refrigeration ice maker[END_REF][START_REF] Dai | Heat and mass transfer in the adsorbent of a solar adsorption cooling system with glass tube insulation[END_REF][START_REF] Passos | Simulation of an intermittent adsorptive solar cooling system[END_REF][START_REF] Hu | Simulation and sensitivity analysis of an intermittent solar powered charcoal/methanol refrigerator[END_REF][START_REF] Boubakri | Adsorptive solar powered ice-maker: experiments and model[END_REF][START_REF] Leite | Performance of a new solid adsorption ice maker with solar energy[END_REF]. The solar COP and the DIP calculated by simulations ranged between 0.10-0.12 and 4-10 kg m -2 day -1 , respectively. Such results are in good agreement with those obtained by testing experimental prototypes.

It must be pointed out that most of the ice-makers presented in literature use conventional activated carbon as adsorbent. The adsorption capacity of activated carbons is rather low and usually does not exceed 30-40 wt.%.

The utilization of novel adsorbent materials with improved methanol sorption ability can be an efficient way to increase the performance of the system. Recently, the Boreskov Institute of Catalysis, Novosibirsk, Russia in collaboration with the CNR-ITAE, Messina, Italy, developed a new class of methanol composite sorbents [START_REF] Yu | Sorption Equilibrium of Methanol on new composite sorbents "CaCl 2 /Silica Gel[END_REF][START_REF] Gordeeva | Composites "lithium halides in silica gel pores": methanol sorption equilibrium[END_REF].

This new class of sorbents is directly derived by the SWSs (Selective Water Sorbents;

i.e. a composite materials consisting of "inorganic salts confined to porous matrices"), that have already been proposed for water vapour sorption [START_REF] Yu | A family of new working materials for solid sorption air conditioning systems[END_REF]. The synthesised composite sorbents demonstrated a strong affinity to methanol. Indeed, the maximal amount of methanol sorbed w max =75-80 wt.% exhibited by some composites is much higher that the methanol sorption capacity of conventional activated carbons [START_REF] Gordeeva | A new family of methanol sorbents for adsorptive air conditioning driven by low temperature heat[END_REF]. This great enhancement of adsorptivity is due to the high contribution of methanol absorption by the salt embedded in the silica gel porous matrix (see [START_REF] Gordeeva | Composites "lithium halides in silica gel pores": methanol sorption equilibrium[END_REF] for details).

Among the different composites synthesised, the sorbent "Lithium Chloride in mesoporous silica gel" (2-50 nm pore diameter) appeared to be the best candidate for sorption cooling driven by a low temperature energy source [START_REF] Gordeeva | Influence of characteristics of methanol sorbents "salt in mesoporous silica" on the performance of adsorptive air conditioning cycle[END_REF].

The aim of this paper is to evaluate the performance of a solar-powered adsorptive icemaker using the novel composite "Lithium Chloride in mesoporous silica gel" by applying the simulation tool presented in Ref. [START_REF] Vasta | An adsorptive solar ice-maker dynamic simulation for north Mediterranean climate[END_REF].

The model makes it possible to calculate the performance of the unit in terms of solar Coefficient Of Performance (COPs), Daily Ice Production (DIP) and equivalent Daily Ice Production (DIP eq ). The obtained performance are compared with those corresponding to the commercial adsorbent activated carbon AC35. In the first part of the paper, the main features of the composite sorbent and of the simulated adsorptive unit are presented. Then, performance of the adsorptive ice-maker are calculated.

Main features of the composite sorbent "Lithium Chloride in mesoporous silica gel"

The composite sorbent "Lithium Chloride in mesoporous silica gel" (salt content 29.5 wt.%) was synthesised by impregnation of silica gel Grace Davison 8926.02 (average pore diameter d av = 15 nm, specific surface S sp = 326 m 2 g -1 , pore volume V p = 1.5 cm 3 g -1 ) with an aqueous solution of Lithium Chloride. More details on the synthesis procedure were presented by Gordeeva et al. [START_REF] Gordeeva | Composites "lithium halides in silica gel pores": methanol sorption equilibrium[END_REF]. Figure 1 shows the basic thermodynamic cycles for an adsorption air conditioner (T ev =10 °C, T c =T ads =35 °C, T des =80 °C) and an ice-maker (T ev =-2 °C, T c =T ads =30 °C, T des =80 °C) using the composite "Lithium Chloride in mesoporous silica" and the commercial activated carbon AC35.

The cycles are plotted over an isosteric diagram that was obtained from the experimental equilibrium data presented in Refs. [START_REF] Gordeeva | Composites "lithium halides in silica gel pores": methanol sorption equilibrium[END_REF][START_REF] Restuccia | Performance of sorption systems using new selective water sorbents in[END_REF] (only the significant isosters are plotted). It is evident that this novel composite sorbent presents an outstanding variation of methanol uptake per cycle ( w= 46 wt.% and 18 wt.% for air conditioning and ice-making, respectively), which is much larger than those of the conventional carbon AC35 ( w= 11 wt.% and 9 wt.% for air conditioning and ice-making, respectively). This is a convenient feature, because the performance of adsorptive machines increase when the amount of cycled working fluid increases [START_REF] Gordeeva | A new family of methanol sorbents for adsorptive air conditioning driven by low temperature heat[END_REF].

The stability of adsorbent is of primary importance for evaluation of practical potential.

Study on the phase composition, porous structure, and sorption properties of both the fresh and tested composites showed that no significant change, in composite structure and sorption ability, occurs during the cycling. Further details can be found in [START_REF] Freni | Composite sorbent of methanol "lithium chloride in mesoporous silica gel" for adsorptive cooling machines: performance evaluation[END_REF].

Furthermore, the stability to the cyclic treatment has been verified for this typology of materials [START_REF] Restuccia | An advanced solid sorption chiller using SWS-1L: performance analysis and hydrothermal cycling stability of the sorbent bed[END_REF]. A stability of the porous structure of the solid adsorbent, identical to the material studied in this paper, has been evidenced, even after thousands of cycles.

Description of the ice-maker

The scheme of the solar-powered adsorptive ice-maker is presented in Fig. 2. It consists of the following components: a solar collector, in which the adsorbent material is embedded; a condenser for the methanol condensation and the heat rejection to the ambient during the day; a "cold chamber", containing the evaporator for the methanol evaporation and the liquid water to be frozen during the night.

We selected a flat planar panel because the proposed working pair is able to efficiently work with this type of solar collector. Moreover, the niche application for this system (ice production in remote areas) asks for employment of cheap components.

During the day, the solar energy received by the collector produces the desorption of methanol from the sorbent bed. Methanol vapour flows to the condenser, condenses, and then is collected inside the receiver. During this phase the valves V 1 and V 2 are closed (see Fig. 2). In the late afternoon the valve V 1 is opened, and the liquid methanol flows from the receiver to the evaporator. Then, V 1 is closed and V 2 is opened for the whole night, allowing adsorption of methanol by the sorbent layer. The evaporation of methanol inside the cold chamber cools down the liquid water, which is converted into ice.

The adsorbent/adsorbate working pair follows the typical adsorptive cycle, consisting of four phases [START_REF] Cacciola | Reversible adsorption heat pump: a thermodynamic model[END_REF]: I) isosteric heating until the pressure reaches p c ; II) desorption at high temperature and pressure of condensation; III) isosteric cooling until the pressure decreases down to p ev ; IV) adsorption at low temperature and pressure of evaporation.

During this last phase, three sub-steps may occur: IVa) cooling of the liquid water inside the cold box, IVb) freezing of the liquid water, IVc) under-cooling of the ice.

Modelling

The model is of dynamic type and is based on energy and mass balances for the adsorbent reactor and the connected components. The main governing equations are:

Solar collector: Adsorbent bed:

( ) ( ) ( ) amb m O C s m m m m eff T T A U T T A U dt dT c m I n - + - + =
( ) ( ) ( ) dt dw w H m K dt dT c wm c m T T A U s s a s s s s m ∆ - + = - 1 2 2
(2), with K 1 =0 for isosteric phases and K 1 =1 for isobaric phases. Further supplementary equations are reported in a previous paper [START_REF] Vasta | An adsorptive solar ice-maker dynamic simulation for north Mediterranean climate[END_REF].

The accompanying initial conditions and starting values are: Depending on the phase of the thermodynamic cycle, only a certain number of the previous equations ( 1)-( 6) is applied and the relative coefficients/parameters assume a different form (see [START_REF] Vasta | An adsorptive solar ice-maker dynamic simulation for north Mediterranean climate[END_REF] for details).

( ) ( ) ( ) ( ) ( ) = = = =
The end phase conditions are the following:

Phase I: This definition of solar COP is identical to that reported in other literature works (see, in particular, Refs. [START_REF] Anyanwu | Design, construction and test run of a solid adsorption solar refrigerator using activated carbon/methanol, as adsorbent/adsorbate pair[END_REF] and [START_REF] Luo | Year round test of a solar adsorption ice maker in Kunming, China[END_REF]).

The Daily Ice Production (DIP) and its equivalent value (DIP eq ), which accounts for the

Results and comments

Results of a base-case

A base-case was assumed considering an adsorption ice-maker with a solar collector In Figs. 4 and5 the calculated temperatures of the adsorbent material and of the condenser are presented for the activated carbon AC35 and the "LiCl silica gel" sorbent, respectively. Figure 4 shows that the maximum daily temperature reached by the activated carbon is 78°C (on May the 2 nd ), while the lowest daily temperature is 57°C, due to the unfavourable conditions on May the 6 th . The condenser temperature was always slightly higher than the ambient temperature.

The temperature evolution calculated for the composite sorbent "LiCl in silica gel" is rather different (see Fig. 5). Indeed, the sorbent maximum daily temperature is lower, ranging from 47°C to 57°C. This effect can be explained considering that a big part of the incoming radiant energy is required for rejection of the high amount of methanol sorbed by the composite. Besides, the higher content of methanol inside the adsorbent bed leads to higher thermal capacity, which contributes to increase the sensible heat of the system.

Correspondingly, the methanol uptake variation per day, ∆w, ranged from 9 to 20 wt.%, for the case of AC35, and from 20 to 35 wt.%, for the case of the composite sorbent "LiCl in silica gel". This confirms the better sorption properties for the proposed sorbent with respect to the commercial carbon.

Figures 6,7 show the calculated values of the temperature of methanol inside the evaporator and the mass of water converted into ice, inside the cold chamber. It can be observed that the system based on activated carbon (Fig. 6) is not able to produce 20 kg (i.e. 13.3 kg m -2 ) of ice every day, and the corresponding temperature is higher than -5

°C. On the contrary, the system based on "LiCl in silica gel" (Fig. 7) demonstrated a capability of Daily Ice Production of 20 kg and a lower evaporation temperature (-10 °C is the minimum). Only for the first day the DIP is lower than 20 kg (18.6 kg, i.e.

12.4 kg m -2 ); this is due to the low adsorbent temperature (see Fig. 5) and the corresponding high uptake, that are affected by the weather conditions of the previous (not represented) days. The temperature of the water in the cold chamber is almost coincident with that of evaporation, due to the good thermal contact between liquid methanol and water.

Inspection of Fig. 7 shows that, in the case of the system based on "LiCl in silica gel", the evaporator is significantly under-cooled after the production of 20 kg of ice.

Subsequently, it can be argued that this system could be able to produce a further amount of ice (i.e., more than 20 kg day -1 =13.3 kg m -2 day -1 ). Therefore the potentiality of this material, for ice-making applications, deserves a deeper investigation that is described in the next paragraph.

Calculation of performance

The performance were calculated considering an ice-maker with the same design of the above described base-case and different amounts of liquid water to be frozen. The Daily Ice Production (DIP), its equivalent value (DIP eq ) and the daily Coefficient Of Performance (COPs), were calculated according to Eqs. ( 9)- [START_REF] Hu | Simulation and sensitivity analysis of an intermittent solar powered charcoal/methanol refrigerator[END_REF]. Afterwards, the average values of these parameters ( DIP , eq DIP and COPs ), corresponding to the whole period considered for simulations, were determined. day -1 of ice, due to the limited adsorption capacity of the carbon. Furthermore, this value decreases when the amount of liquid water in the cold chamber increases, due to the higher liquid water sensible heat.

Thus the optimum amount of liquid water to put in the cold box is about 19 kg for the AC35-CH 3 OH pair. This value is much higher (about 37 kg of water) for the LiCl-CH 3 OH pair, with a corresponding maximum of 20 kg m -2 day -1 of ice production. This is evidently due to the higher adsorption capacity of the composite sorbent.

Figure 9 reports the COPs calculated for the two adsorbents. It results that the average solar COP corresponding to the system using activated carbon is equal to 0.17, independently on the liquid water mass. This result, which is coherent with the values reported by other authors [START_REF] Khattab | Simulation and optimization of a novel solar-powered adsorption refrigeration module[END_REF][START_REF] Wang | Recent developments of refrigeration technology in fishing vessels[END_REF][START_REF] Passos | Simulation of an intermittent adsorptive solar cooling system[END_REF][START_REF] Boubakri | Adsorptive solar powered ice-maker: experiments and model[END_REF], confirms that the use of activated carbon cannot ensure the design of a highly performing adsorption ice-maker. Differently, the COPs of the system based on Lithium Chloride increases when liquid water mass increases, and reaches a noticeable value of 0.33, which is almost twice the maximum value obtained for AC35.

These results clearly demonstrate that the outstanding methanol sorption properties of the composite sorbent "LiCl in silica gel" make possible the realization of an adsorption ice-maker which performs much better than the units previously proposed in literature and that is potentially attractive for the niche-market of the solar cooling in remote areas.

The COP and DIP values previously reported in literature for activated carbon/methanol systems represent a preliminary validation of the proposed model, which should be definitely accomplished when the measured performance parameters of a prototype, based also on the other adsorbent/adsorbate pair, will be available. This will be done in a following paper.

Conclusions

This study evidences that the utilization of innovative adsorbent materials with high sorption ability can improve the performance of adsorptive cooling systems. In particular, it was shown that the novel composite sorbent "Lithium Chloride in silica gel pores" makes it possible to design highly efficient solar-powered adsorptive ice-makers.

Indeed, mathematical modelling demonstrated that a maximum solar Coefficient Of Performance (COPs) of 0.33 and a maximum Daily Ice Production (DIP) of 20 kg m -2

  equal to C U 1 or O U 1 for heating and cooling phases, respectively.

  Water/ice heat and mass balances:

  where p ev is calculated from the initial evaporator temperature, w 2 is calculated from the initial temperature and pressure of the adsorber, t 1 is the time of the end of Phase I (and start of Phase II), t 3 is the time of the end of Phase III (and start of Step IVa), t 4a is the time of the end of Step IVa (and start of Step IVb) and 0 , ev T is the initial evaporator temperature.

  Phase II: I <100 W m -2 or w≤ 2%; Phase III: ev s p p = ;Step IVa: T w =0 or t=24 h; Step IVb:w ice m m = or t=24 h; Step IVc: t=24 h.Furthermore, for each day, the corresponding solar Coefficient Of Performance (COPs) is calculated as:where K 2 =0 and/or K 3 =0 when Step IVb and/or IVc does not occur.

  equivalent mass of ice corresponding to the possible under-cooling of the ice, are given by The model equations were numerically solved by using a commercial software (Mathematica ® 4.0 by Wolfram Research) for ordinary differential equation (ODE) systems, based on a function which automatically switches between stiff (Gear) and non-stiff (Adams) integration methods [25].

area n=1.5 m 2 ,

 2 mass of adsorbent material m s = 36 kg, mass of liquid water inside the cold chamber m w =20 kg. The simulations were carried out for a long period, considering as adsorbent material the activated carbon AC35 and the composite sorbent "lithium chloride in silica gel pores". Results are here presented for a few days of an intermediate season. Figure 3 shows the values of the dynamic data (useful solar radiation I β and ambient temperature T amb ) for the six-day period considered for simulations (May 1-6, 2005). The data were recorded by a meteo-station installed at the CNR-ITAE in Messina, Italy (38° 12' N). From this figure, it results that the daily ambient temperature ranges from 13.7 °C to 23.6 °C; while the daily average useful solar radiation is about 500 W m -2 , with a maximum daily radiation ranging from 970 W m -2 to 1055 W m -2 . The third day, i.e. May 3, 2005 showed the lowest ambient temperature, but the day that exhibits the most instable climatic conditions is May 6, 2005.

Figure 8

 8 m -2 ) calculated for the two adsorbents. The values of ice production calculated for the system based on activated carbon/methanol pair (7.5-11 kg m -2 day -1 ) are in good agreement with the values reported in literature for this configuration[START_REF] Wang | Recent developments of refrigeration technology in fishing vessels[END_REF][START_REF] Boubakri | Adsorptive solar powered ice-maker: experiments and model[END_REF][START_REF] Leite | Performance of a new solid adsorption ice maker with solar energy[END_REF]. It is evident that the adsorption ice-maker based on AC35 provides a maximum of 11 kg m-2

Figure 1 :

 1 Figure 1: Comparison between the composite sorbent "Lithium Chloride in mesoporous silica gel" and the activated carbon AC35, in terms of air

Figure 2 :

 2 Figure 2: Scheme of the solar-powered adsorptive ice-maker.

Figure 3 :

 3 Figure 3: Ambient temperature and solar radiation recorded in May 1-6, 2005.

Figure 4 :

 4 Figure 4: Condenser and adsorbent temperature, calculated for activated carbon and 20 kg of liquid water.

Figure 5 :

 5 Figure 5: Condenser and adsorbent temperature, calculated for LiCl in silica gel and 20 kg of liquid water.

Figure 6 :

 6 Figure 6: Evaporator temperature and mass of ice calculated for activated carbon and 20 kg of liquid water.

Figure 7 :

 7 Figure 7: Evaporator temperature and mass of ice calculated for LiCl in silica gel and 20 kg of liquid water.

Figure 8 :

 8 Figure 8: Equivalent Daily Ice Production vs. liquid water mass, calculated for the two adsorbents.

Figure 9 :Figure 1 Figure 2 ACCEPTEDFigure 9

 9129 Figure 9: Average Solar Coefficient Of Performance vs. liquid water mass, calculated for the two adsorbents.

can be obtained for an ice-maker using a solar collector area of 1.5 m 2 and 36 kg of "Lithium Chloride in silica gel pores" sorbent. Such performance are more than 80% higher than those obtained using common activated carbon.


Hubert Blain
email: h-blain@chu-montpellier.fr

Audrey Jaussent

Eric Thomas

Jean-Paul Micallef

Anne-Marie Dupuy

Pierre L Bernard

Denis Mariano-Goulart

Jean-Paul Cristol

Charles Sultan

Michel Rossi

Marie-Christine Picot

Appendicular skeletal muscle mass is the strongest independent factor associated with femoral neck bone mineral density in adult and older men

ABSTRACT

The relationship between bone mass and muscle mass may be due to the site-specific effects of loading on bone in adults and to lifestyle, nutritional, and hormonal factors. Another hypothesis is that the maintenance with aging of both appendicular muscle and bone mass may be determined by factors independent of all these previous factors, including genetic factors. In 160 healthy men aged 20 to 72 years, we recorded femoral neck bone mineral density (FN BMD), relative appendicular skeletal muscle mass [RASM; appendicular skeletal muscle mass (kg) /height (cm)], age, body mass, maximum grip and knee extension strength, lifetime physical activities, calcium intake, tobacco smoking, and serum parathyroid hormone (PTH), estradiol (E2), free testosterone, dehydroepiandrosterone sulphate (DHEAS), insulin-like growth factor (IGF-I), sex hormone-binding globulin (SHBG), calcium, 25(OH) vitamin D, albumin, and creatinine clearance. The correlation between FN BMD and RASM (that includes upper and lower limb muscle mass) was of slightly greater magnitude than that between FN BMD and the relative upper limb muscle mass and between FN BMD and the relative leg muscle mass (r = 0.39; p < 0.001 versus r = 0.36; p < 0.001 and r = 0.34; p < 0.001, respectively). The stepwise multiple linear regression model showed that FN BMD was significantly associated with RASM (15% of FN BMD variance, p<0.0001), age (10% of FN BMD variance, p < 0.0001), physical activities from age 11-20 years (5% of FN BMD variance, p < 0.01), and blood PTH, IGF-I, and creatinine clearance, (2%, 2%, and 1% of FN BMD variance, respectively, p < 0.05). These results show that RASM, with ASM measured by DXA, is the strongest factor associated with FN BMD in men. It remains to be determined whether assessing RASM by anthropometric methods would help screening adult men at risk of low FN BMD. Furthermore, since RASM is associated with FN BMD independently of appendicular skeletal loads and other lifestyle, nutritional, and hormonal factors, this suggests that common factors, possibly genetic factors, might also influence the coupled maintenance of appendicular muscle mass and FN BMD in adult men.

Key words: population studies -femoral neck bone mineral density -muscle strengthmen -aging

A C C E P T E D

M A N U S C R I P T 1.

1. 1.

Introducti Introducti Introducti Introduction on on on

At least one third of hip fractures occur in men [START_REF] Jones | Symptomatic fracture incidence in elderly men and women: the Dubbo Osteoporosis Epidemiology Study (DOES)[END_REF], resulting in increased debility and increased mortality [START_REF] Trombetti | Survival and potential years of life lost after hip fracture in men and age-matched women[END_REF]. Low femoral neck bone mineral density (FN BMD), reflecting in part low thickness of femoral neck cortices, is one of the main risk factors for hip fracture in men [START_REF] Rivadeneira | Femoral neck BMD is a strong predictor of hip fracture susceptibility in elderly men and women because it detects cortical bone instability: the Rotterdam Study[END_REF]. Age of men experiencing hip fractures tends to increase in most countries, suggesting the necessity to investigate factors that might be able to prevent FN BMD loss in adult and older men [START_REF] Looker | Prevalence and Trends in Low Femur Bone Density Among Older US Adults: NHANES 2005-2006 Compared with NHANES III dagger[END_REF][START_REF] Leslie | Osteoporosis Surveillance Expert Working Group. Trends in hip fracture rates in Canada[END_REF].

After reaching peak bone mass at about the age of 20 to 30 years, men maintain a stable bone density, before experiencing substantial age-related decrease in FN BMD [START_REF] Wishart | Effect of age on bone density and bone turnover in men[END_REF].

Acquisition of the skeletal mass in men seems strongly determined by genetic and ethnic factors [START_REF] Seeman | Do genetic factors explain associations between muscle strength, lean mass, and bone density? A twin study[END_REF], and by hormonal and lifestyle factors, including tobacco, alcohol consumption, and physical activity [START_REF] Deng | Characterization of genetic and lifestyle factors for determining variation in body mass index, fat mass, percentage of fat mass, and lean mass[END_REF][START_REF] Gallagher | Appendicular skeletal muscle mass: effects of age, gender, and ethnicity[END_REF][START_REF] Pettersson | A comparison of bone mineral density and muscle strength in young male adults with different exercise level[END_REF]. Indeed, load-bearing exercises in boys are able to increase muscle mass and muscle strength and to have a positive and sustained influence on peak bone mass at the hip [START_REF] Gunter | Impact exercise increases BMC during growth: an 8-year longitudinal study[END_REF], suggesting that bone mass and architecture of teenage males is in part physiologically adjusted to control the strains produced by mechanical loading [START_REF] Frost | Changing views about "osteoporoses", a 1998 overview[END_REF][START_REF] Parfitt | Perspective. Attainment of peak bone mass: what is the relationship between muscle growth and bone growth ?[END_REF]. The capacity of the skeleton to adapt to mechanical stress remains significant in adults also [START_REF] Ma | Long-term leisure time physical activity and properties of bone: a twin study[END_REF], but it tends to decrease with aging [START_REF] Frost | Changing views about "osteoporoses", a 1998 overview[END_REF].

A few studies have shown that the appendicular skeletal muscle mass (ASM), more than leg muscle mass, is associated with FN BMD in adult and older men, suggesting a possible musclebone unit at the appendicular level [START_REF] Szulc | Low skeletal muscle mass is associated with poor structural parameters of bone and impaired balance in elderly men--the MINOS study[END_REF][START_REF] Baumgartner | Associations of fat and muscle masses with bone mineral in elderly men and women[END_REF][START_REF] Pluijm | Determinants of bone mineral density in older men and women: body composition as mediator[END_REF]. Since muscle strength and other possible confounders were not measured altogether in these studies, it remains to be determined whether the relationship between the relative ASM

A C C E P T E D M A N U S C R I P T

(RASM; ASM/body height) and bone mass observed in adult and older men is the reflection of the effect on the femoral neck of strains exerted by muscles, the influence of lifestyle, nutritional, and hormonal factors, or is in fact independent of all these factors, thus lending support to the growing evidence of an underlying genetic component in the senescence of the muscle-bone unit in men [START_REF] Karasik | Genetics of the musculoskeletal system: a pleiotropic approach[END_REF].

To explore this issue, we assessed the relationship between FN BMD and RASM in healthy men with a wide range of ages, taking into account grip and maximum quadriceps strength, body mass, and past and current physical activities, considered as markers of skeletal loading, and adjusted our analyses for numerous hormonal and lifestyle factors known to influence bone and muscle mass in men.

Materials and methods

Participants

The present study included healthy men aged 20 to 72 years whose mother or grandmother had been included in the EPIDOS (Epidemiology of Osteoporosis) study in Montpellier in Southern France. The EPIDOS study was a cohort of women aged 75 and over, recruited using voter-registration rolls and enrolled in 1992-1993 in a multicenter prospective study on hip fracture risk factors [START_REF] Dargent-Molina | Fall-related factors and risk of hip fracture: the EPIDOS prospective study[END_REF].

Inclusion criteria in the present study were Caucasian individuals in apparent good health, non-institutionalized, and functionally independent. Subjects were excluded if they met any of the following criteria: (i) known metabolic bone disease, (ii) rheumatoid arthritis and/or physician-diagnosed osteoarthritis, (iii) ischaemic heart disease, (iv) previous joint surgery or

A C C E P T E D M A N U S C R I P T
cerebral disease affecting the lower limb, (v) or medication known to affect the musculoskeletal system (corticosteroids, anti-osteoporotic drugs, androgens or anti-androgen drugs, in particular).

All subjects included in the present study gave their written informed consent to participate in the study, which was approved by the Human Subjects Research Committee of our University Hospital.

Based on the results of the literature [START_REF] Szulc | Low skeletal muscle mass is associated with poor structural parameters of bone and impaired balance in elderly men--the MINOS study[END_REF][START_REF] Baumgartner | Associations of fat and muscle masses with bone mineral in elderly men and women[END_REF][START_REF] Pluijm | Determinants of bone mineral density in older men and women: body composition as mediator[END_REF], we expected a correlation coefficient of 0.3 between RASM and FN BMD in our sample. With an alpha risk of 0.05 and a power equal to 0.90, with a bilateral hypothesis, a sample size of 112 healthy men was sufficient to assess the significance of the relationship between RASM and FN BMD. The present study included 160 healthy men.

Osteodensitometric Parameters

BMD at the right femoral neck (FN BMD), lean mass (excluding bone mineral content), and fat mass for the whole body and specific regions were measured by dual-energy X-ray absorptiometry (DXA) (Hologic QDR-1500 device, Hologic, Waltham, MA, USA). The coefficient of variation for our device during measurement on a standard phantom is less than 3%

for FN BMD and whole body fat and lean mass. Appendicular skeletal muscle mass (ASM) was calculated as the sum of the lean soft tissue in both the right and left arms and legs measured by DXA, as described previously [START_REF] Szulc | Low skeletal muscle mass is associated with poor structural parameters of bone and impaired balance in elderly men--the MINOS study[END_REF], and the relative skeletal muscle mass index (RASM) was calculated as ASM (kg) /body height (cm).

A C C E P T E D M A N U S C R I P T

Muscle strength assessments

Strength measurements were performed once, at the same time of day to minimize any effect of diurnal variation. After a warm-up session, maximum strength performance was examined in the same order for all subjects: maximum grip strength and then isometric maximum knee extension strength (KES).

The right isometric KES was assessed using a load-cell recording device (Captels, St Mathieu de Tréviers, France) firmly attached to the metal framework of a chair and connected to a simple software sampling at 80 Hz. During assessment, subjects were seated on the chair with the back and thigh well supported (hip angle at 90°), hands resting on their thighs, the feet free, and the knee passively drawn into a 60° flexion. A soft cuff, attached via an adjustable nonelastic metal cord to the 500-kg load cell, was fitted with velcro just above the right ankle. Patients were asked to extend their right knee as forcefully as they could for five seconds, and the maximum KES in kilograms was recorded. The length of the test lever arm was measured from the knee joint center to the midpoint of the soft cuff (the distance between the soft cuff and the right ankle was similar for every subject at every session), with the direction of pull being in line with the force transducer. The results of the maximum KES measurements were expressed as the mean knee extension torque obtained by multiplying maximum KES by the lever arm length for each subject and expressed in kilograms × meters. Scores were the mean of the three maximum trials.

Grip strength was measured using the JAMAR (Smith and Nephew, Memphis, TN) dynamometer, calibrated as described previously [START_REF] Bohannon | Accuracy of spring and strain gauge hand-held dynamometers[END_REF], and used according to the recommendations of the American Society of Hand Therapists [START_REF] Fess | Grip strength[END_REF]. The second

A C C E P T E D M A N U S C R I P T
handle setting was used for all participants [START_REF] Firrell | Which setting of the dynamometer provides maximal grip strength?[END_REF]. For each visit, we recorded three maximal trials, and scores were the mean of the three peak grip strength values recorded in kilograms.

In 97 subjects aged 23-90, different from those included in the present study, KES and grip strength were measured in triplicate on three occasions separated by one week. Under the same conditions as those used in the present study, the intraclass correlation coefficients for grip strength and KES were more than 0.95 and the intrarater coefficients of variation were less than 10% (Blain et al., 2006).

Assays

Fasted morning blood samples were collected. Serum concentrations of E2 were measured using an enzyme immunoassay sandwich method with a final fluorescent detection (ELFA-Vidas, Biomerieux SA, France). The lower limit of detection of our E2 assay was 9 pg/ml (32 pmol/L). IGF-I (Diagnostic systems Laboratories, Webster, USA) and intact PTH (Diasorin, Ctillwater, MN) were determined by immunoradiometric assay. Free testosterone (non-extraction method, Diagnostic Systems Laboratories, Texas, USA), SHBG (CIS Bio International, France), DHEAS (Beckman Coulter, USA), and 25(OH) vitamin D (IDS RIA, France) were determined by RIA (intra-assay variation between 6.3 to 7.1%, inter-assay variation between 3.4 to 13.5%).

A standard colorimetric dry chemistry assay was used to measure serum creatinine and albumin (Synchron CX5 Automate, Beckman Coulter, Villepinte, France).

Other Variables

The subjects were weighed with an electronic scale to the nearest 0.1 kg, and their height was measured to the nearest 0.1 cm at the time of muscle strength assessment. Dietary calcium intake

A C C E P T E D M A N U S C R I P T
was estimated with a food-frequency self-administered questionnaire [START_REF] Fardellone | Evaluation of the calcium content of diet by frequential selfquestionnaire[END_REF], assessing intake of 20 common foods rich in calcium over the past week. The mean values were expressed in milligrams per day. Tobacco smoking was recorded in two categories: smokers (current and past, one year or more) and non-smokers. Subjects were divided into two categories on the basis of their alcohol consumption: light drinkers (daily consumption of less than onequarter liter of wine or beer, or less than one glass of liquor) and heavy drinkers (daily consumption of more than one-quarter liter of wine or beer, or more than one glass of liquor).

The recent and past physical activities were assessed using the QUANTAP system, a standardized and structured computer-assisted interview tool designed to assess lifetime physical activity [START_REF] Vuillemin | A computer-assisted assessment of lifetime physical activity: reliability and validity of the QUANTAP software[END_REF], converted into metabolic equivalents (METs) per week [START_REF] Ainsworth | Compendium of physical activities: an update of activity codes and MET intensities[END_REF].

Statistical Analyses

The characteristics of the men entered in the present study were described with proportions for categorical variables and with means and standard deviation values for continuous variables.

The distributions were tested with Shapiro-Wilk statistics. The relationships between FN BMD and RASM with independent variables were assessed using Pearson or Spearman's rank correlation coefficient when the continuous variables were normally or not normally distributed, respectively, and using Student's t-test for categorical ones. The linearity of the relation between FN BMD and the continuous variables was verified. The collinearity of variables and RASM was also analyzed. To determine factors independently associated with FN BMD, variables significantly associated with FN BMD in the univariate analysis (p < 0.1) and not collinear with RASM were entered in a multivariate analysis using a linear regression model. A forward

A C C E P T E D M A N U S C R I P T
selection was used to enter the variables in the model. R² criterion was used to select each one.

As appendicular skeletal muscle mass but not FN BMD was adjusted for body size, the same analyses were performed when entering body size in the final model and when studying the relationship between FN BMD/body height and RASM. The statistical software SAS (1) version 9.1 was used for this analysis.

Results

The characteristics of the 160 men participating in the study are displayed in Table 1. When body height was introduced into the multivariate linear regression analysis, the relationship between RASM and FN BMD also remained significant (p value < 0.0001). The relationship between FN BMD/body height and RASM was also significant in the univariate analysis (Pearson correlation coefficient = 0.32; p < 0.0001) and in the multivariate linear regression analysis (data not shown).

Discussion

The main result of the present study is that RASM is the strongest factor associated with FN BMD in healthy adults aged 20 to 72 years. Since this relationship appears to be independent of age, indices of appendicular skeletal loading, and numerous lifestyle and hormonal parameters, the present study supports the growing evidence that other common factors, including genetic factors, may influence the maintenance with aging of both appendicular skeletal muscle mass and femoral neck BMD in adult men [START_REF] Karasik | Genetics of the musculoskeletal system: a pleiotropic approach[END_REF].

In children, the gain in height precedes the gain in muscle mass, that precedes the gain in bone mass, suggesting a physiological adaptation of bone to muscle in the growing skeleton [START_REF] Rauch | The 'muscle-bone unit' during the pubertal growth spurt[END_REF]. If bodily growth and consequently bone mass accrual are to a great extent determined by genetic factors [START_REF] Parfitt | Perspective. Attainment of peak bone mass: what is the relationship between muscle growth and bone growth ?[END_REF], active children have a greater total body BMD than their inactive peers [START_REF] Bailey | A six-year longitudinal study of the relationship of physical activity to bone mineral accrual in growing children: the university of Saskatchewan bone mineral accrual study[END_REF] and an increased hip peak bone mass [START_REF] Gunter | Impact exercise increases BMC during growth: an 8-year longitudinal study[END_REF], suggesting a sustained osteotrophic effect of physical activity during growth. Our results are in line with this hypothesis, since physical activity performed during the age of 11-20 years is significantly associated with FN BMD in healthy grown-ups and older men, explaining about 5%

of the variance of their FN BMD.

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Appendicular muscle mass is significantly associated with FN BMD in men aged 50 years or older, and this relationship is independent of physical activity, body mass, and other covariates, suggesting a systemic component of the relationship between RASM and FN BMD [START_REF] Szulc | Low skeletal muscle mass is associated with poor structural parameters of bone and impaired balance in elderly men--the MINOS study[END_REF]. Since muscle strength and other possible confounders were not measured in this study nor in others, the authors could not conclude as to whether the relationship between ASM and FN BMD can be explained by the strains exerted by appendicular muscles or by other factors, independent of the habitual appendicular skeletal loading. Melton et al. showed that changes in habitual load (estimated by body mass, appendicular muscle mass, and habitual physical activities) and change in bone strength at the femoral neck in men younger or older than 50 years are not parallel, suggesting that reduced skeletal loading may not be a strong determinant of agerelated bone loss in men [START_REF] Melton | Does reduced skeletal loading account for age-related bone loss?[END_REF]. In addition, the age-related decline of lean mass observed in men seems in part independent of the age-related decline of muscle strength (Morley et al., 2001) and physical activity [START_REF] Proctor | Relative influence of physical activity, muscle mass and strength on bone density[END_REF]. A plausible hypothesis is therefore that the relationship between RASM and FN BMD in adult men is independent of skeletal loading, which may explain why the effects of various exercise regimens on BMD, although not negligible, have often been found to be weak in healthy adult subjects [START_REF] Suominen | Muscle training for bone strength[END_REF].

Several results in the present study support this hypothesis. RASM that includes upper and lower limb muscle mass was found to be slightly better correlated with FN BMD than was the relative upper limb muscle mass or the relative leg muscle mass, suggesting that the relationship between muscle mass and FN BMD may not only be due to a site-specific effect of skeletal loading in healthy adult men but may involve systemic factors influencing both appendicular bone and muscle mass.

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Furthermore, we found that the relationship between RASM and FN BMD was independent of markers of habitual skeletal loads, including current and long-term leisure time physical activities, knee extension and grip strength, and other possible confounders. The relationship between FN BMD and RASM was also found to be independent of body height, suggesting that this relationship was not due to differences in skeletal size. Taken together, these results suggest that common factors, other that age, body height, skeletal loading, and hormonal and lifestyle factors measured herein may be involved in the maintenance of both FN BMD and RASM in adult men.

Several hypotheses may explain the present results. Genetic factors account for most of the correlation between bone mass and muscle mass in adolescents [START_REF] Schoenau | The "muscle-bone unit" in children and adolescents[END_REF] and in twins [START_REF] Seeman | Do genetic factors explain associations between muscle strength, lean mass, and bone density? A twin study[END_REF]. This has been interpreted as an effect of natural selection to ensure that bone strength is closely matched to the strains developed by muscles [START_REF] Parfitt | Perspective. Attainment of peak bone mass: what is the relationship between muscle growth and bone growth ?[END_REF].

The results presented herein suggest that this so-called "muscle-bone unit" may persist after growth has ceased in healthy men of a wide range of ages, supporting the concept of a persistent "evolutionary adaptation" of bone mass to muscle mass in adult men, independently of the "physiologic adaptation" of bone and muscle strength to skeletal loading [START_REF] Frost | Changing views about "osteoporoses", a 1998 overview[END_REF]. The role of genes in the relationship between RASM and FN BMD is plausible since the resemblance of FN BMD between adult sons and their parents has been shown to be mediated in part by the resemblance of their lean mass, and this, independently of shared lifestyle habits, including physical activity (Blain et al., 2006). The fact that genes encoding for the androgen receptor and the estrogen receptor alpha may influence both bone mass and body composition in male mice (Callewaert et al., 2009a;Callewaert et al., 2009b) supports this hypothesis. Factors other than those taken into account in the present study might also be involved in the relationship between

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RASM and FN BMD. These factors include inflammatory factors since the age-related increase in pro-inflammatory cytokines is associated with sarcopenia [START_REF] Schaap | Inflammatory markers and loss of muscle mass (sarcopenia) and strength[END_REF] and bone resorption [START_REF] Lauretani | Correlates of bone quality in older persons[END_REF] in older men. Nutritional factors, other than those measured herein, such as protein intake, or the intake of fatty acids for example, might also be involved in the relationship between RASM and FN BMD in adult men [START_REF] Coin | Predictors of low bone mineral density in the elderly: the role of dietary intake, nutritional status and sarcopenia[END_REF].

The present study shows that age (which explains 10% of FN BMD in our model), serum IGF-I and PTH (which explain 2% of FN BMD variance), and serum creatinine (which explains 1% of FN BMD variance) were significantly associated with FN BMD in our sample of adult men. These results are in line with those of previous studies supporting the role of IGF-1 and PTH in FN BMD maintenance in men [START_REF] Blain | Age-related femoral bone loss in men: evidence for hyperparathyroidism and insulin-like growth factor-1 deficiency[END_REF][START_REF] Cheung | Determinants of bone mineral density in Chinese men[END_REF]. Our results suggest, however, that the effect of IGF-I and PTH is of low magnitude when muscle mass, age, muscle strength, lifestyle factors, and other biomarkers are included in the multivariate model. In accordance with previous studies conducted in healthy and well-nourished men with a moderate consumption of alcohol and tobacco, none of the hormonal factors assessed in the present study (neither E2, free testosterone, SGHG), nor vitamin D, calcium intake, or alcohol and tobacco consumption were significantly associated with FN BMD in the final model [START_REF] Cheung | Determinants of bone mineral density in Chinese men[END_REF].

In our study, we measured the main hormonal factors known to be significantly involved in the muscle-bone unit (Zofkova et al. 2008). It remains to be determined whether other hormonal factors such as insulin production and sensitivity, for example, are also involved in the relationship between RASM and FN BMD [START_REF] Fernández-Real | The relationship of serum osteocalcin concentration to insulin secretion, sensitivity, and disposal with hypocaloric diet and resistance training[END_REF].

Although our final model includes muscle mass, age, muscle strength, and numerous lifestyle factors and biomarkers, it accounts for only 35% of the variance in FN BMD. Because

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heritability estimates may explain more than 60% of the variance of appendicular lean mass and hip bone mass [START_REF] Peacock | Sex-specific and non-sex-specific quantitative trait loci contribute to normal variation in bone mineral density in men[END_REF][START_REF] Hsu | Heritability of body composition measured by DXA in the diabetes heart study[END_REF], a significant part of the 65% that remains unaccounted for in the present study may be ascribed to genetic factors. However, further studies are required to assess whether taking into account nutritional factors, inflammatory parameters, and hormonal factors other than those measured herein would improve the prediction of FN BMD in men. In addition, measurements of maximum knee extension and grip strength should only be considered as indirect measures of potential mechanical loading by muscles on the hip since the muscles involved in these measurements do not have attachments to the femoral neck.

It remains therefore to be determined also whether a better assessment of loads usually applied on the hip in men would improve the prediction of FN BMD in men.

Three potentially important messages can be drawn from the present study. First, our results support the hypothesis that promoting physical activity during hip bone accrual and implementing measures to prevent renal failure, low levels of IGF-I, and hyperparathyroidism during adulthood may help to maintain FN BMD in adult men. Second, RASM measured with DXA in the present study was found to be the strongest factor associated with FN BMD in our sample of adult men, explaining 15% of the variance of FN BMD. RASM measured by DXA can be predicted when measuring calf circumference [START_REF] Rolland | Sarcopenia, calf circumference, and physical function of elderly women: a cross-sectional study[END_REF], mid-upper-arm muscular circumference and arm muscle area (which are derived from the mid-upper-arm muscular circumference and the triceps skinfold) [START_REF] Frisancho | Anthropometric standards for the assessment of growth and nutritional status[END_REF], or when using a more complex equation based on body mass, body height, hip circumference, and grip strength for example [START_REF] Baumgartner | Epidemiology of sarcopenia among the elderly in New Mexico[END_REF]. Further studies are necessary to determine whether RASM, assessed by anthropometric methods, would be useful in the screening of adult men at risk of low FN BMD. Third, since the relationship between RASM and FN BMD seems to be in great part The main strength of the present study is that several indices of appendicular skeletal loading, including grip and maximum knee extension strength, body mass, and lifetime physical activity, and numerous possible hormonal and lifestyle confounders have been measured to adjust the relationship between RASM and FN BMD in a relatively large sample of well-characterized healthy men with a wide range of ages.

Some limitations of our results should be noted, and several questions remain to be answered.

Our study is cross-sectional, reflecting associations but not revealing causes and effects.

Isometric knee extension strength, body mass, and physical activity are only surrogate estimates of the strains applied on the hip. We have confidence in our results since the questionnaire we used to quantify physical activities was sufficiently sensitive to show a relationship between physical activities exerted over the age range of 11-20 years and FN BMD, and failed to show any significant relationships between FN BMD and physical activities exerted over the past five and ten years before entering the study. Besides, maximum quadriceps strength and grip strength are considered as good and reproducible indicators of aberrant loads that may have an influence on the maintenance of the skeleton [START_REF] Lanyon | Postmenopausal osteoporosis as a failure of bone's adaptation to functional loading: a hypothesis[END_REF]. There is a potential for selection bias in the current study, as healthier subjects are more likely to respond and participate in this type of study. Our results are therefore only valuable for a Caucasian population of healthy men. For ethical reasons, patients with osteoarthritis that were considered by their physicians to be sufficiently symptomatic to possibly influence their maximum extension strength were not included in the present study. In addition, osteoarthritis has a complex and specific influence on

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hip bone density. Indeed, if a reduction in physical activities is most often associated with a loss of proximal femur BMD, subjects with symptomatic osteoarthritis have marked loss of muscle mass and strength but an increased BMD at the proximal femur [START_REF] Suetta | Muscle size, neuromuscular activation, and rapid force characteristics in elderly men and women: effects of unilateral long-term disuse due to hiposteoarthritis[END_REF][START_REF] Chaganti | Bone mineral density and prevalent osteoarthritis of the hip in older men for the Osteoporotic Fractures in Men (MrOS) Study Group[END_REF]. Since elderly men with osteoarthritis at the lower limbs represent a large population, further studies are needed to determine whether our results are applicable to men with osteoarthritis. Another limitation is the accuracy of the evaluation of ASM by DXA, which might underestimate the age-related decrease of the muscle mass [START_REF] Proctor | Comparison of techniques to estimate total body skeletal muscle mass in people of different age groups[END_REF]. However, measurement errors of ASM may have underestimated the correlation between RASM and FN BMD in our sample of men with a wide range of ages.

In conclusion, the present study shows that RASM, with ASM measured by DXA, is the strongest factor associated with FN BMD in men of a wide range of ages, suggesting that RASM estimates by anthropometric methods may help screening men at risk for low FN BMD. Since the relationship between RASM and FN BMD is independent of indices of appendicular skeletal loading and numerous estimators of hormonal status and lifestyle, the present study suggests that common factors, including possibly genetic factors, may be involved in the coupled maintenance with aging of RASM and FN BMD in adult and older men.

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  and loading indices, here again further studies are needed to better understand which factors, including genetic ones, are involved in the coupled RASM-FN BMD maintenance in adult men.

Table 2

 2

displays non-adjusted correlations of FN BMD and RASM with the different covariates. The correlation between FN BMD and RASM (that includes upper and lower limb muscle mass) was of slightly greater magnitude than that between FN BMD and the relative upper limb muscle mass and between FN BMD and the relative leg muscle mass (r = 0.39; p < 0.001 versus r = 0.36; p < 0.001 and r = 0.34; p < 0.001, respectively). Factors associated with FN BMD in the univariate analysis (with p < 0.1), except body mass and body lean mass, that were found to be collinear with RASM, and body height, that was used for the calculation of RASM, were proposed to explain FN BMD in the multiple linear regression model.

Factors associated with FN BMD in the multiple linear regression model are reported in

Table 3 .

 3 RASM remains significantly associated with FN BMD, independently of age, indices of skeletal loading (physical activities, and grip and knee extension strength) and other tested , respectively). On the whole, the present model explains 35% of FN BMD variance.

	variables, explaining 15% of FN BMD variance. The other variables independently associated
	with FN BMD were age (10% of FN BMD variance), physical activities between 11-20 years
	(5% of FN BMD variance), and blood PTH, creatinine, and IGF-I (2%, 1%, and 2% of FN BMD

variance

Table 1 .

 1 Characteristics of the study population(n = 160)

	Mean ± SD

Table 2 .

 2 Correlations of RASM and FN BMD with different variables : FN BMD, femoral neck bone mineral density; METs, metabolic equivalents; E2, 17 beta-estradiol; DHEAS. dehydroepiandrosterone sulfate; IGF-I, insulin-like growth factor-1; SHBG, sex hormone-binding globulin. * Values are Pearson or Spearman's rank correlation coefficients between FN BMD (or RASM) and continuous variables or mean FN BMD (or RASM) ± SD in each subgroup for alcohol consumption and tobacco smoking. ** P corresponds to the level of significance of the correlation A C C E P T E D M A N U S C R I P T coefficients between FN BMD or RASM and continuous variables or to the t-test used to compare means FN BMD (or RASM) between subgroups for alcohol consumption and tobacco smoking.

	Variable (units)	FN BMD		RASM
		Correlation	p value**	Correlation	p value**
		Coefficient or		Coefficient or
		mean ± SD*		mean ± SD*
	Age (years)	-0.355	<0.0001	-0.030	0.7004
	FN BMD (g/cm²)	-	-
	Relative appendicular skeletal muscle mass (kg/cm)	0.390	<0.0001	-	-
	Height (cm)	0.161	0.0418	0.283	0.0003
	Body mass (kg)	0.209	0.0080	0.735	<0.0001
	Lean mass (kg)	0.338	<0.0001	0.890	<0.0001
	Fat mass (kg)	0.001	0.9314	0.418	<0.0001
	Calcium intake (mg/day)	0.073	0.3554	0.164	0.1434
	Tobacco smoking (mean ± SD)
	Current/past smokers (n = 105)	0.854 ± 0.121	0.3270	0.149 ± 0.016	0.5260
	No smokers (n = 55)	0.876 ± 0.141		0.151 ± 0.017
	Alcohol consumption (mean ± SD)
	Light (n = 92)	0.833 ± 0.111	<0.0010	0.149 ± 0.016	0.4400
	Heavy (n = 68)	0.900 ± 0.140		0.151 ± 0.017
	Knee extension strength (Nm)	0.177	0.0247	0.375	<0.0001
	Grip strength (Nm)	0.159	0.0440	0.368	<0.0001
	Physical activities (1-10 first years) (METs per week)	0.248	0.0016	0.088	0.2678
	Physical activities (11-20 first years) (METs per week)	0.216	0.0060	0.0463	0.5614
	Physical activities over the past five years (METs per	0.021	0.7848	0.124	0.1159
	week)
	Physical activities over the past ten years (METs per	0.003	0.9677	0.159	0.0442
	week)
	Serum calcium (mmol/L)	-0.026	0.7681	-0.084	0.2908
	Serum 25(OH) vitamin D (nmol/L)	0.131	0.0991	0.068	0.3913
	Serum creatinine (mmol/L)	0.144	0.0687	0.128	0.1063
	Serum albumin (g/L)	0.019	0.8146	-0.043	0.5847
	Serum PTH (pg/ml)	-0.248	0.0010	0.014	0.8578
	Serum E2 (pmol/L)	0.104	0.1897	0.143	0.0718
	Serum free testosterone (ng/ml)	0.045	0.5705	-0.179	0.0230
	Serum DHEAS (mg/ml)	0.163	0.0394	0.100	0.2083
	Serum IGF-I (ng/ml)	0.172	0.0292	0.114	0.1526
	Serum SHBG (nmol/L)	-0.135	0.0879	-0.243	0.0019

Abbreviations

Table 3 .

 3 Multiple linear regression model with variables associated with FN BMD in the univariate analysis

	Variables	β	SE (β)	Cumulative R²	p value
	Appendicular skeletal muscle mass /height	0.00283	0.000523	0.15	<0.0001
	Age (years)	-0.00356	0.000725	0.25	<0.0001
	Physical activities (11-20 first years) (METs	0.00001	0.000003	0.30	0.0020
	per week)
	Serum PTH (pg/ml)	-0.00220	0.001104	0.32	0.0480
	Serum creatinine (ng/ml)	0.00163	0.000734	0.33	0.0282
	Serum IGF-I (ng/ml)	-0.00026	0.000128	0.35	0.0402

Acknowledgements

Funding for this research was provided by the French Ministry of Health (Projet Hospitalier de Recherche Clinique, 1998, UF-7606). The authors acknowledge Ms. Muriel Fernandez, Ms.

Claire Belloc, Dr. Rachida Louahem, and Dr. Claude Jeandel, for help in data collection, and Sharon Lynn Salhi, PhD, for editorial assistance.

Funding for this research was provided by the French Ministry of Health (Projet

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