L Fontana
email: lfontana@uniroma3.it

EXPERIMENTAL STUDY ON THE GLOBE THERMOMETER BEHAVIOUR IN CONDITIONS OF ASYMMETRY OF THE RADIANT TEMPERATURE

Keywords: Globe thermometer, Radiant temperature, Asymmetry Nomenclature

Heating and cooling systems based on the use of hot or cold floors or ceilings meet increasing favour.

In such systems, moreover, radiant temperature gains a far greater importance than in traditional systems; and therefore the importance of measurement and control techniques grow; but at the same time, in presence of these systems, unavoidably the radiant field tends to become asymmetrical.

In this work a theoretical study and an experimental check on the most common radiant temperature measurement tool, the globe thermometer, when used in conditions of asymmetrical radiant temperature are described. The results point out the necessity of a more complete definition of the features of the globe thermometers designed to operate in non symmetric radiative fields, especially with reference to covering material and thickness, to temperature sensor position and to radiative properties of the inner surface.

Introduction

Heating and cooling systems based on the use of hot or cold floors or ceilings are getting increasingly popular. In such systems moreover, radiative exchanges and radiant temperature gain greater importance than in traditional systems; the importance of measurement and control techniques of these properties grows accordingly; but at the same time, the radiative field tends to become asymmetrical.

Globe thermometer is the most common radiant temperature measurement tool. The methodologies so far suggested (e.g. the European Standard EN 27726-1993 [START_REF]Thermal Environments -Instruments and methods for measuring physical quantities[END_REF]) to deduce the mean radiant temperature from the globe temperature, stand on the assumption that the temperature at the center of the globe is equal to the average temperature of the globe surface. The presence of non uniformity and asymmetry of the radiant temperature, causes non-uniformity of the globe surface temperature, which in turn brings nonuniformity of the globe internal air temperature and consequently internal convective flows could arise: in particular the temperature value in the center of the globe could be different from any average of the surface temperatures, resulting in errors in average radiant temperature computations.

Aim of this work is an investigation on such theme.

Previous works and Standard references.

Since H.M. Vernon first proposed the usage of globe thermometer as a measurements tool for radiative heat exchanges between human bodies and environment [START_REF] Vernon | The measurement of radiant heat in relation to human comfort[END_REF], the interest in such a device has developed in multiple directions. On one side, the target has been to build a tool able to simulate the human body reactions to environmental conditions, so as to obtain a complete thermal environment meter. In this direction the papers by Bedford e Warner [START_REF] Bedford | The globe Thermometer in studies of heating and ventilation[END_REF], Botsford, [START_REF] Botsford | A wet globe thermometer for environmental heat measurement[END_REF] and later Kuehn et al. [START_REF] Kuehn | A single thermometer wet bulb globe temperature index meter[END_REF], who proposed devices sensitive to air humidity as well; Madsen [START_REF] Madsen | A new instrument for measuring thermal confort[END_REF], who proposed a tool that could simulate the human body answer to sensible heat exchanges, based on a human thermo-regulation model grounded on the Fanger theories; and eventually Mendes e Da Silva [START_REF] Mendes | Development of a new thermal environment meter responding both to sensible and latent heat fluxes[END_REF], who more recently proposed a device that could simulate the human body reactions to both sensible and latent heat exchanges.

On the other side, the globe thermometer has been further studied and perfectioned as a mean radiant temperature measurement tool. Research has meanly focused on topics such as accuracy [START_REF] Hey | Small Globe Thermometers[END_REF][START_REF] Graves | Globe Thermometer evaluation[END_REF],

promptness of results [START_REF] Eissing | Investigation and Improvement of the Adjustment time of the Globe thermometers, Klima, Kalte[END_REF][START_REF] Nikolopoulou | Improvements to the globe thermometer for outdoor use[END_REF], optimization of shape and size [START_REF] Graves | Globe Thermometer evaluation[END_REF][START_REF] Humpreys | The optimum diameter for a globe thermometer for use indoors[END_REF][START_REF] Dear | Ping-Pong Globe Thermometers For Mean Radiant Temperatures[END_REF]. Though the influence of radiative field non uniformity on comfort conditions is relevant and deeply investigated [START_REF] Fanger | Thermal Confort[END_REF][START_REF] Kahkonen | Draught, radiant temperature asymmetry and air temperaturea Comparison between Measured and Estimated Thermal Parameters[END_REF][START_REF] Sakoi | Thermal confort, skin temperature distribution, and sensible heat loss distribution in the sitting posture in various asymmetric radiant fields[END_REF], it was not possible to find papers dedicated to the behaviour of the globe thermometer itself in highly asymmetrical conditions; in particular, it is worthwhile investigating weather or not such conditions may cause measurements inaccuracies. This deficiency is present as well in standardization initiatives, that do ignore such problems.

The current standards [START_REF]Thermal Environments -Instruments and methods for measuring physical quantities[END_REF], with reference to radiant temperature measurement, give only the following essential definitions, prescriptions or instructions.

Shape of the globe thermometer

In appendix B the mentioned Standard suggests as best approximation of the shape of a standing human body, with reference to the view factors between the body itself and the various environment walls, a rotation solid (e.g. ellipsoid) with assigned values of the projected area factors (ratio between projected surface and total surface) equal to 0.08 for the vertical projection ( T PV A A / ), and 0.28 for the horizontal ( T PH A A / ) projection. Those two ratios are not independent from each other in the rotation ellipsoid. A / =0.28) are jointly respected by the cylinder with better approximation than the ellipsoid. For these reasons, this investigation has been referred to the cylindrical with flat bottoms shape.

Construction features

In Appendix B of the Standard the globe thermometer is described as a "black globe with a temperature sensor placed in the middle". A diameter not below 15cm is suggested, and the blackening of the outer surface of the globe is required, so as to realize emissivity values close to 0.95. A small thickness of the covering is recommended. No other constructive requirement is given about material to be used, internal emissivity, thickness , thermal conductivity of the covering.

Theoretical study

In a previous work [START_REF] Fontana | Studio sul comportamento di globotermometri in condizioni di asimmetria della temperatura radiante[END_REF] a theoretical study has been conducted, on the free convection inside a cavity with thin conductive covering, subject to convective and radiative thermal exchanges both on the outer and the inner surface.

Reference has been made to a cylindrical cavity with flat bottoms, for different values of the height to diameter ratio, placed vertically in a room with uniform air temperature and dissymmetry of the radiant temperature.

More precisely, it was supposed that:

 Each point of the upper bottom outside surface "sees" the same average temperature T RT , and each point of the lower bottom outside surface "sees" the same average temperature T RB ;

 Each point of the side surface "sees" the same radiant temperature, assumed equal to 2

RB RT RS T T T   .
With reference to the interior surface of the globe, it was supposed that:

 The surface has a grey and Lambertian behaviour.

 The fluid-dynamic field has axial symmetry.

 The expected maximum values of the Rayleigh number Ra turn out equal to about 6x10 6 . The flow has been therefore considered as laminar.

The mathematical model

The thermo-fluid-dynamic field inside the globe is described by the Navier-Stokes energy and continuity equations, with reference to a Boussinesq fluid (constant fluid properties except for the density in the buoyancy terms), laminar flow, cylindrical coordinates (r,z) and steady state.

The model is therefore described by the following equations: Momentum according to r:

                          2 2 2 2 2 1 1 z u r u r u r r u r p z u v r u u    (1a)
Momentum according to z:

g z v r u r v r r v z p z v v r v u                                2 2 2 2 2 1 1 (1b) Continuity: 0        z v r u r u (2)
Energy:

                      2 2 ) ( 1 1 z t r t r r r c r p z t v r t u P    (3)
The 1st type boundary conditions are:

On the bottom surfaces R r   0 : ) ( ) 0 , ( 0 r f r t  ; ) ( ) , ( r f H r t H  On the side surface H z   0 : ) ( ) , ( z f z R t R  (4)
The thermal field inside the covering is described in the hypothesis of negligible temperature changes through the thickness. Moreover, in the hypothesis of axial symmetry, the thermal field turns out to be one-dimensional, function of z in the side shell and of r in the two bottoms. The heat transfer through the covering slab is by conduction; on the two slab surfaces the convection and radiation heat exchanges are taken into account.

The thermal field is therefore described by the equations:

lower bottom:   RAD CONV RB LB A LB CE LB LB q q T T t t h dr dt r dr t d s        ) ( ) ( ) 1 ( 4 4 0 2 2    (5) upper bottom:   RAD CONV RT UB A UB CE UB UB q q T T t t h dr dt r dr t d s        ) ( ) ( ) 1 ( 4 4 0 2 2    (6) shell:   RAD CONV RS SS A SS CE SS q q T T t t h dz t d s       ) ( ) ( 4 4 0 2 2    (7)
and for each portion of the covering the boundary conditions are given by the temperature continuity.

In the (5-7) q CONV is the convective specific heat flux (outgoing) exchanged between the current surface element and the air inside the globe; q RAD is the net specific heat flux (outgoing) from the current surface element resulting from the radiative exchanges balance with the inner surface of the globe. The flux q RAD is evaluated with the radiosity method, in the hypotheses of grey and Lambertian behaviour for emission and reflection.

With the notations shown in Nomenclature, and being dA 1 the current surface element; dA 2 any internal surface element "seen" from dA 1 ; T, L and E the absolute temperature, the radiosity and the specific radiative incoming flux of dA 2 , the radiative balance for the generic element dA 1 is given by

1 2 2 1 dA dA S F dA L EdA     (8)
where S is the globe thermometer inner surface, and furthermore

4 0 ) 1 ( aT a E L     ; a E aT q RAD    4 0  (9)
The numerical investigation has been conducted studying two extreme cases: the black body ( 1   , simulating an inner surface painted with a high emissivity paint), and absence of radiative exchanges ( 0   , bare and bright metal inner surface).

The thermal and fluid-dynamic field in the air and the conductive field in the covering are matched through the q CONV , t UB , t LB , t SS variables. More precisely the system solution has been obtained by iteration. In any iteration, q CONV values were determined by the inner field, being valid the relations

upper bottom: H z CONV z t q       ) (  ; lower bottom: 0      z CONV z t q  ; side shell: R r CONV r t q       ) (  ; ( 10
)
with such values the thermal field is solved in the covering. The obtained temperatures act as boundary conditions for the thermal field in the inner air assuming:

) ( ) ( 0 r f r t LB  ; ) ( ) ( r f r t H UB  ; ) ( ) ( z f r t R SS  (11)
The procedure is iterated up to convergence.

The set of governing equations (1-7 and 10-11) has been solved through a control-volume formulation of the finite-difference method. A monomial interpolation scheme ("power-law") has been used for the diffusive-convective terms. The pressure-velocity coupling through the continuity equation is handled by the SIMPLE algorithm described in detail by Patankar [START_REF] Patankar | Numerical Heat transfer and fluid flow[END_REF].

The resultant algebraic equation system has been solved iteratively, line by line, with the Thomas algorithm. The non linear coefficients have been iteratively replaced with the dated values, applying under-relaxation criteria. The integration domain has been covered by a grid with uniform mesh-spacings except close the borders where the mesh was finer. The solution is considered to be fully converged when the maximum absolute values of both the mass source and the percent changes of the dependent variables at any grid-node from iteration to iteration are smaller than prescribed values, i.e., 10 -4 and 10 -6 , respectively.

For every height to diameter ratio, the dependence of the obtained results from the mesh pacing has been tested. Grids have been examined increasing by a pace of 3 the mesh number in the integration domain.

Then grid-size values representing a good compromise between solution accuracy and computational time required, were assumed as those over which further grid refinements did not produce material modifications (i.e. 0.1%) in the heat transfer rates and in the maximum and minimum shell temperature values. The used typical grid was therefore of about 21x21 meshes for the square configuration, and 18x27 for the slim.

The system of (8, 9) that expresses the radiative exchanges among elements of the internal surface has been expressed in discrete terms as well, with reference to plane concentric rings for the bottoms and circular cylindrical surfaces for the shell. Values of the view factors have been calculated by the relations in closed form available in any view-factors catalog, e.g. in [START_REF] Modest | Radiative Heat Transfer[END_REF].

Results of the theoretical model

The results are showed in Fig. 2 through the values of the ratio

R   /
where  is the difference between the highest and the lower values of the shell temperature, and  R is the difference among the extreme values assumed for the radiant temperature (

RT RB R t t    ). The R   /
values are reported as a function of ( s   ), assuming the other relevant variables (H, R, ) as parameters. Results show that, for some variable combinations, the temperature non-uniformity can turn out to be important, with The inner air temperature is moreover measured in the globe thermometer. The maximum non-uniformity of the air temperature inside the globe is equal to that of the covering, but the convective flows could attenuate it in the central zone, far from the walls. So the inner temperature measured in presence of a such surface temperature non uniformity could not correspond to the mean temperature of the shell surface; and therefore the radiant temperature value, obtained from the inner globe thermometer temperature measure, could be affected by an error.

The obtained fluid-dynamic fields can give an idea of the above, within the limits given by the hypothesis of axial symmetry.

In Fig. 3 some of the recurring configurations are showed. One or more frequently two superimposed recirculating cells appear, often moreover of non regular and different shape. Therefore it would seem favourable to make the temperature measurement strictly at the center of globe thermometer.

This behaviour moreover could turn out different in presence of geometrically different asymmetries of the radiant temperature, and cylinder positions other than vertical; this is a matter of the experimental study. Vice versa, the obtained results suggest that small enough non-uniformities may however be obtained:

 Realizing the covering in copper or silver and among 0.5 mm -1mm thick.



Using high-emissivity paints in the inner surface. Any not-electrically conductive paint could in practice be adopted, while it appears important not to leave naked the inner metal surface.



Not exceeding the dimension (15 cm) suggested by the Standard; strictly referring to the the surface non-uniformities, smaller dimension (about 10 cm) would be preferable.

Experimental study

Two cylindrical globe thermometers, one made of iron and one made of copper and a scale model of the indoor space, equipped for surface and air temperature measurement and control, have been realized as below described.

The environment model

A scale model (box shaped) has been realized, as sketched in Fig. 4.

The model scale dimensions, albeit small compared with the globe thermometer dimension, do not materially influence the convection heat transfer coefficients over the external globe surface.

All the relations in use and suggested by the standards e.g. [START_REF]Thermal Environments -Instruments and methods for measuring physical quantities[END_REF] to deduce the mean radiant temperature from the globe temperature are referred to free convection in still air, and do not take into account possible convection flows on a large scale, that could differ between the model and the real room scale, the latter being higher.

On the other hand, the globe thermometer gives reliable results when used in absence of significant convection flows (other than those due to the globe itself).

Besides, both the thermo-fluid-dynamic fields over the globe surface and on the model walls surfaces are of the boundary layer type, with thickness below 1 cm. In the model the distance between the globe thermometer and the wall surfaces is always bigger than 13 cm, so the boundary layers over the globe external surface and over the walls surfaces are far and do not interfere.

In these conditions, the convection coefficient h CE depends on the globe height H, that in the experimental model has been kept of the size suggested by the standards and of the commonly used globe thermometers, and on the difference between globe surface and air temperatures, that in the experimental test has been set on values comparable with the real ones.

The walls and the ceiling have been made using 0.5 cm plywood sheets, and a 2 cm layer of expanded polystyrene.

The surface temperatures are measured through 10 K-type thermocouples applied to each wall (Fig. 5).

Two additional K-type thermocouple, with polished joint, placed respectively at the level of the upper and lower bottom of the globe thermometer, and at a distance of 5 cm from the globe thermometer side surface, measure the inner air temperature.

A small fan equipped with an electrical heater lets an air flow of up to 7 vol/h, properly heated, be introduced in the box. This option has only been used for the globe thermometers calibration, as shown in section 5.2.

Heating floor

The heated floor is made of a nylon slab under which an heating element is inserted. Between the heating element and the nylon slab a copper sheet 0.5mm thick has been placed, in order to reduce the surface temperature non uniformity. The heater is electrically supplied by an autotransformer. On the upper nylon slab surface 16 K-type thermocouples have been applied.

A further thermocouple is inserted on the center of the upper surface. The signal of such thermocouple has been used for the floor thermal control; a temperature control within +-0.2 °C has been obtained. In the experimental study temperature in the range between 33°C and 55°C have been set.

The thermocouples applied to the walls and the floor are made up using wires 0.2 mm diameter. In order to minimize the thermal field perturbation produced by the thermocouple insertion, the wires run on the surface for length of various hundreds of diameters and the joint is stuck to the wall with an interposed disk of copper 0.2 mm thick and diameter 15 mm, as recommended in [START_REF] Jacob | Heat Transfer[END_REF].

Cold ceiling

The ceiling is realized in two equal parts, each made by a panel refrigerated by a cold fluid circulation.

The cold-water hydraulic circuit is embedded in a epoxy resin slab 6 mm thick, placed between two aluminium sheets 0.8 mm thick.

The hydraulic circuit is formed by a polyethylene pipe (external diameter 6 mm, internal 4 mm), disposed in plane-coil with going and return pipes running side by side (Fig. 4), so that the average couple temperature remains constant for the length of the coil.

To improve the ceiling temperature uniformity, a single aluminium slab 1.5 mm thick, having the ceiling dimensions, has been applied to the lower face of the two panels. Such slab is the ceiling surface; it has been painted with several black paint coats, and has been equipped with six thermocouples. A slab of expanded polystyrene 25 mm thick and a panel of plywood 6 mm thick have been stuck to the upper side.

Ceiling feeding and thermal control system

In the coil embedded in the ceiling panels flows a forced circulation of a water (60%) and ethil alcohols solution, refrigerated by a chiller. The required cooling power is of a small number of watt. Since a chiller of a so little power production doesn't exist, it was obtained from a modified domestic ice-cream-maker, as shown in Fig. 4.

A temperature control within +-0.2 °C has been obtained inserting in the pool of the cold solution an electrical heater regulated by a thermostat, equipped with a Pt100 type thermometer. The temperature values of the incoming water flow into the ceiling have been set at 8-14°C; the temperature difference between inlet and outlet/entrance and exit was of about 2-3 °C, thus obtaining ceiling surface temperature values between 10°C and 15°C.

Globe thermometers

Two cylindrical globe thermometers (15 cm diameter, 15 cm height) have been realized, with different materials; one has been realized with a mild steel sheet, the other with a copper sheet, both 0.4 mm thick.

Thermocouples have been arranged both on the covering and inside.

In both cases the thermocouples on the covering were of the so-called "intrinsic" type: for each thermocouple one of the two components was the covering material; the other one was formed by constantan wires (diameter 0.25 mm, with silicone insulation, all from the same spool). Therefore the thermocouples were iron-constantan in a case, and copper-constantan in the other.

In both cases, a thermocouple was realized with a thin strip of the metal sheet used for the covering, and a constantan wire from the above mentioned spool; such thermocouples have been submitted to careful calibration in the range 0÷100 °C.

Figure 6. Thermocouples arrangement inside and on the covering of the globe thermometer

Thermocouples on the side surface have been placed on three lines at a 120 degrees angular distance, and on each line, in three positions (1/6, 1/2 and 5/6 of the cylinder height).

Each bottom was ideally shared in three zones of equal area, a circle and two circular crowns. The thermocouples have been placed in the center of the circle and along three radial lines, on the circumferences which share the circular-crown zones in two parts of equal area.

Fig. 5,6 show the globe in the box, the thermocouple arrangement and the measurement circuit scheme.

Five inner thermocouples have been placed in an axial plan; one in the geometrical cylinder center, the others in four points distant 1.5 cm from the center and both in the parallel and normal directions to the cylinder axis. The K-type thermocouples have been realized with wires (0,2 mm diameter) arranged so as to be kept in tension and to ensure a good positioning and alignment of the thermocouples.

For each globe thermometer, different series of measurements have been done, with the internal surface naked and emery, or painted with two black paint coats.

Globe thermometers have been calibrated determining the globe temperature (temperature G AIR t measured by the thermocouple in the centre of the cylinder) in conditions such that both the floor heating system and the ceiling cooling one were inactive while a hot air flow was introduced. In such conditions the side walls, the floor and the ceiling were all at very close temperatures -and so in absence of asymmetry-but different from the environment air temperature of about 10°C.

The mean radiant temperature, obtained from the walls surfaces temperature measurements as described in 5.3, has then been compared with the mean radiant temperature value deducted from the globe temperature with the relations given in the Standard [START_REF]Thermal Environments -Instruments and methods for measuring physical quantities[END_REF]. The two values were in accordance in the range ±0,25°C.

Measurements and results -Comparison with the theoretical model

Measures of all the temperatures have been made for three different values of the floor temperature set up. For the chilled water the outlet temperature of 10 °C has been always set up. In such conditions it was not produced moisture condensation on the ceiling surface.

From the temperature values of the walls surfaces and of the globe thermometer surface, we have derived the: The view factors have been numerically computed. Each A K surface has been divided in smaller portions AK j (average dimension roughly 3 cm) and the temperature measured in the centre of A K has been attributed to each of them. Similarly, the various cylinder surfaces have been divided in A1 i portions. A cartesian coordinate system has been assumed as in Fig. 7, then the general formula as proposed in [START_REF] Eissing | Investigation and Improvement of the Adjustment time of the Globe thermometers, Klima, Kalte[END_REF] has been used. For instance, to compute the


R TOP t :             i Kj Kj i Kj Kj i Kj Kj i i i Kj i i Ki i i Kj j j i TOP A S R n z z m y y l x x n z z m y y l x x AK A S F K TOP 3 1 1 1 1 1 1 1 1 1 ] ) ( ) ( ) [( ] ) ( ) ( ) [( 1 1   where: 2 / 1 2 1 2 1 2 1 ] ) ( ) ( ) [( i Kj i Kk i Kj z z y y x x R      
and l,m,n are the direction cosines of the local surface perpendicular lines. , there is a fairly good agreement. The experimental values turn out lower (about 20%) than those given by the model; the trend of Fig. 8 b) shows that deviations are correlated (with reference both to the magnitude and the sign) to the difference between the surface temperature and the air temperature. This behaviour and the deviations magnitude are in accordance with the effect of "extended surface" caused by the thermocouples, evaluated as in [START_REF] Jacob | Heat Transfer[END_REF].

Referring to the air temperature values, the differences between air temperature at the center of the globe thermometer and surface average temperature are of the same order as the theoretical ones. The experimental values of the difference between the side and the centre values of the air temperature also appear to be close to the theoretical ones. Significant differences among the vertical and the inclined globe thermometer do not result.

Conclusions

The radiant temperature measurement is based on the assumption that the temperature at the center of the globe is equal to the average temperature of the globe surface. This assumption could be not verified in presence of non-uniformity of the radiant temperature, that could cause a globe thermometer surface temperature non-uniformity, with consequent growing convective flows inside the globe and temperature value in the center of the globe different from any average of the surface temperatures.

The study has pointed out the advisability of a more complete definition of the features of globe thermometers designed to work in radiative non uniform and asymmetric environments: particularly, the importance of thermal conductivity of the material used, covering thickness, temperature sensor position, inner surface radiative properties has been pointed out.

The experimental study has confirmed the reliability of the theoretical model, within the accuracy limits expected.

The theoretical model shows, in accordance with the experimental results, that the circulation of internal air can produce in the central zone an attenuation of non-uniformity and an alignment of the air temperature value to the surface average temperature value; however, the results of this study show that the difference between the air temperature value in the centre of the globe and the globe surface average temperature, could bring errors of some centigrade degrees °C in the radiant temperature measurement. In the case, for example, of a globe thermometer with a thin stainless steel covering (=20 W/m°C, thickness s= 0.25 mm) this error can achieve 2°C, and could be much bigger in the case of globe thermometers made of plastic as proposed in [START_REF] Dear | Ping-Pong Globe Thermometers For Mean Radiant Temperatures[END_REF].

However, the results also show that with simple constructive precautions (copper covering, thickness not lower than 0.5 mm, internal high-emissive surface) the surface temperature unevenness can be reduced to negligible values, and the related radiant temperature measurement error become unimportant.

Figure 1 .

 1 Figure 1. Projected area ratios for the ellipsoid and cylinder with flat bottoms

  Figure 2. Results of the theoretical model

5 .

 5 The non-uniformity increases as the product s   decreases, as H grows and as H/R ratio decreases.Fors   typical values for stainless steel (5÷25•10 -3 W/°C), with the dimensions required from the Standard (H = 15 cm), and the ratio H/R = 2 (the examined shape nearest to the spherical one), R   / values between 0.25 and 0.3 in case of black internal surface, and between 0.4 and 0.6 in absence of radiative internal exchanges, have been obtained. That means, with  R values of about 20 °C (it is the case in presence of a radiant floor), a globe surface temperature unevenness of about 10 °C. The situation is completely different in case of globe thermometers made of copper, (l•s=78÷385•10 -3 W/m): the ratio R   / takes values of about 0.05 for black inner surface and 0.1 in absence of radiative heat exchanges (corresponding to a surface temperature non uniformity of about 1 or 2 °C in the cited conditions).

Figure 3 .

 3 Figure 3. Examples of the inner thermal fields a) H=0.05m; R=0.0375m; s=0.25mm; =20W/mK

Figure 4 .Figure 5 .

 45 Figure 4. Sketch of the scale model (dimensions in cm) with the electrical feeding of the heating floor and the hydraulic feeding of the cold ceiling

Figure 7 .

 7 Figure 7. The surface subdivisionThe obtained values are shown in Tab. I.



  = 0.95 for the internal enclosure surfaces and the globe thermometer outer surfaces; for the internal globe thermometer surface, it has been assumed,  = 0.15 for the naked surface and  = 0.95 for the painted surface.- = 55 W/m°C for the iron;  = 385 W/m°C for the copper s = 0.4 mm for both the iron and the copper.

Fig. 8a )

 8a Fig. 8a) shows the experimental values of ( G MAX t -G MIN t ) and the values obtained in the same conditions,

Fig. 8

 8 Fig. 8 Theoretical and experimental results:

  Average temperature t CEY of the ceiling, t FLOOR of the floor and t SIDE of the side walls. Ceiling, floor and walls have been ideally divided into portions of A K area; in each portion centre the K

	thermocouple was placed. Then	t	FLOOR		FLOOR A 1	  FLOOR A A K	t	K	and so on.
			Mean radiant temperature (°C) respectively "seen" by the top bottom of the globe thermometer
	(	R TOP t ), by the lower bottom ( R BOT t	) and by the side shell (	t	R SIDE	) with:
	t	R TOP	( WALLS A       t	K		273	16 .	)	4	S F	TOP		 A K	   	25 . 0 .		273	16 .
	where	WALLS A		FLOOR A		CEY A		SIDE A	and furthermore	K A F  TOP S 	is the factor of view of the A K
	surface sight from the surface of the upper bottom, and so on.
			Maximum and minimum values of the globe thermometer surface temperature	t	G MAX t ,	G MIN	.
			Air temperature values inside the enclosure in the two described positions, t A1 , t A2 .
			Surface average temperature of the globe thermometer	t	G SAV	. The globe thermometer surface S G
	has been ideally divided into portions S K , and in the geometrical center of each portion the
	thermocouples were placed. Then			t	G SAV		G 1 S	  G S S	K	t	K	.
			Air Temperature value at the center of globe thermometer,	G AIR t .

Comparison between the experimental and the theoretical results -air temperature values- Iron globe thermometer

		t CEY	t FLOOR	G UNDER t	\	T UNDER t	G AIR t \ T AIR t	G OVER t \ T OVER t	G SIDE t 1 \ T SIDE t	G SIDE t 2
		°C	°C
					°C		°C		°C	°C	°C
		10.9	33.8		22.2\22.8		22.0\22.5	21.9\22.4	22.1\22.2	22.2
	Iron,black	13.0	41.0		26.2\26.7		26.2\26.5	25.9\26.4	26.3\26.1	26.2
		14.1	52.0		31.7\32.4		31.5\32.2	31.3\32	31.8\31.5	31,7
	Iron, metal	12.3	34.2		23.2\23.7		23.0\23.4	22.8\23.1	23.1\23.2	23.0
	bright	13.1	41.8		26.6\27.7		26.5\27.0	26.2\26.8	26.6\26.7	26.6
		15.1	51.6		31.7\35.6		31.5\34.8	31.3\34	31.8\33.2	31.6
	Tab. II T CEY	T FLOOR		t	G SAV		t	G AIR	t	G SAV	t	G AIR
		°C	°C
							°C, Globe upright	°C, Globe upright	°C, Globe tilted	°C, Globe tilted
			11		34		22.4		22.0	22.2	21.9
	Iron,black		13		41		26.5		26.1	25.8	25.4
			15		52		32.1		31.5	31	30.4
	Iron, metal		12		34		23.2		23.0	22.0	21.6
	bright		13		G AIR t obtained in case of vertical or tilted globe thermometer. 41 26.8 26.5 25.3 24.9
			15		52		32.0		31.5	29.5	29

t FLOOR = 41.8 °C; t CEY = 13.1 °C; t AIR = 26.7 °C Tab. II shows, for the iron globe thermometer and for different values of t FLOOR and t CEY , the values of the air temperature inside the globe thermometer (measured in five points as above described and shown in fig. 6), compared with the corresponding theoretical value. Lastly, Tab. III, for the various realized values of t FLOOR and t CEY , shows values of

Tab.III. Case of vertical or tilted Iron globe thermometer

  With reference to the globe thermometer surface temperature values, the experimental results confirm the predictions of the theoretical model and, in particular for the values of

	t	G MAX		t	G MIN


Antonino Uncini
email: uncini@unich.it

Claudia Manzoli

Francesca Notturno

Margherita Capasso

Prof Antonino Uncini

Pitfalls in electrodiagnosis of Guillain-Barré syndrome subtypes

Keywords:

Objective: To electrophysiologically classify an Italian Guillain Barré syndrome (GBS) population into demyelinating and axonal subtypes, to investigate how serial recordings changed the classification and to underline the pitfalls in electrodiagnosis of GBS subtypes.

Methods:

We applied two current electrodiagnostic criteria sets for demyelinating and axonal GBS subtypes in 55 patients who had at least two serial recordings in three motor and sensory nerves. Results: At first test electrodiagnosis was almost identical with both criteria: 65-67% of patients were classifiable as acute inflammatory demyelinating polyradiculoneuropathy (AIDP), 18% as axonal GBS, and 14-16% were equivocal. At follow-up 24% of patients changed classification: AIDP decreased to 58%, axonal GBS increased to 38 % and equivocal patients decreased to 4%. The majority of shifts were from AIDP and equivocal groups to axonal GBS and the main reason was the recognition by serial recordings of the reversible conduction failure and of the lengthdependent compound muscle action potential amplitude reduction patterns as expression of axonal pathology. Conclusions: Axonal GBS is pathophysiologically characterized not only by axonal degeneration but also by reversible conduction failure at the axolemma of Ranvier node. The lack of distinction among demyelinating conduction block, reversible conduction failure and length-dependent compound muscle action potential amplitude reduction may fallaciously classify patients with axonal GBS as AIDP. Serial electrophysiologic studies are mandatory for proper diagnosis of GBS subtypes and the identification of pathophysiological mechanisms of muscle weakness. More reliable electrodiagnostic criteria taking into consideration the reversible conduction failure pattern should be devised.

INTRODUCTION

Guillain-Barré syndrome (GBS) is divided in three major subtypes: acute inflammatory demyelinating polyradiculoneuropathy (AIDP), acute motor axonal neuropathy (AMAN) and acute motor and sensory axonal neuropathy (AMSAN).

AIDP is most frequent in Western countries whereas AMAN is common in China and Japan. [START_REF] Mckhann | Acute motor axonal neuropathy: a frequent cause of acute flaccid paralysis in China[END_REF][START_REF] Rees | Anti-ganglioside GM1 antibody in Guillain-Barré syndrome and their relationship to Campylobacter jejuni infection[END_REF][START_REF] Ho | Guillain-Barré syndrome in Northen China. Relationship to Campylobacter jejuni infection and anti-glycolipid antibodies[END_REF][START_REF] Hadden | Electrophysiological classification of Guillain-Barré syndrome: clinical associations and outcome[END_REF][START_REF] Ogawara | Axonal Guillain-Barré syndrome: relation to anti-ganglioside antibodies and Campylobacter iejuni infection in Japan[END_REF] AMAN and AMSAN have been associated with antecedent Campylobacter jejuni (C. jejuni) infection and autoantibodies to gangliosides especially to GM1 and GD1a. [START_REF] Rees | Anti-ganglioside GM1 antibody in Guillain-Barré syndrome and their relationship to Campylobacter jejuni infection[END_REF][START_REF] Ho | Guillain-Barré syndrome in Northen China. Relationship to Campylobacter jejuni infection and anti-glycolipid antibodies[END_REF][START_REF] Hadden | Electrophysiological classification of Guillain-Barré syndrome: clinical associations and outcome[END_REF][START_REF] Ogawara | Axonal Guillain-Barré syndrome: relation to anti-ganglioside antibodies and Campylobacter iejuni infection in Japan[END_REF][START_REF] Ho | Anti-GD1a antibody is associated with axonal but not demyelinating forms of Guillain-Barré syndrome[END_REF][START_REF] Yuki | Acute motor axonal neuropathy and acute motor-sensory neuropathy share a common immunological profile[END_REF] In AMAN and AMSAN the pathology is consistent with an antibody-mediated primary axonal damage at the Ranvier node. [START_REF] Feasby | Severe degeneration in acute Guillain-Barré syndrome evidence of two different mechanisms[END_REF][START_REF] Griffin | Guillain-Barré syndrome in Northen China: the spectrum of neuropathological changes in clinically defined cases[END_REF][START_REF] Griffin | Early nodal changes in the acute motor axonal neuropathy pattern of Guillan-Barré sindrome[END_REF][START_REF] Hafer-Macko | Acute motor axonal neuropathy: an antibody-mediated attack on axolemma[END_REF] AIDP, AMAN and AMSAN are difficult to distinguish on clinical grounds and electrophysiology plays a determinant role in GBS diagnosis, classification and in establishing the prognosis. AMAN is currently diagnosed by absence of demyelinating features and decrease of distal compound muscle action potential amplitude. [START_REF] Ho | Guillain-Barré syndrome in Northen China. Relationship to Campylobacter jejuni infection and anti-glycolipid antibodies[END_REF][START_REF] Hadden | Electrophysiological classification of Guillain-Barré syndrome: clinical associations and outcome[END_REF] However some GBS patients with IgG to gangliosides showed besides axonal features rapid resolution of conduction block (CB) and conduction slowing without development of temporal dispersion or restoration of F-waves without increased latency. [START_REF] Kuwabara | IgG anti-GM1 antibody is associated with reversible conduction failure and axonal degeneration in Guillain-Barré syndrome[END_REF][START_REF] Kuwabara | Axonal involvement at the common entrapment sites in Guillain-Barré syndrome with IgG anti-GM1 antibody[END_REF][START_REF] Kuwabara | Isolated absence of F waves and proximal axonal dysfunction in Guillain-Barré syndrome with antiganglioside antibodies[END_REF][START_REF] Hiraga | Patterns and serial changes in electrodiagnostic abnormalities of axonal Guillain-Barré syndrome[END_REF] These findings were thought to be incompatible with demyelination and remyelination and indicated that AMAN is characterized not only by axonal degeneration but also by "reversible conduction failure" possibly induced by anti-ganglioside antibodies at the axolemma of the Ranvier node. [START_REF] Kuwabara | IgG anti-GM1 antibody is associated with reversible conduction failure and axonal degeneration in Guillain-Barré syndrome[END_REF][START_REF] Hiraga | Patterns and serial changes in electrodiagnostic abnormalities of axonal Guillain-Barré syndrome[END_REF] The aim of this study was to electrophysiologically classify an Italian GBS population according to the current criteria, to investigate how serial recordings changed the initial classification and to underline the possible pitfalls in electrodiagnosis of GBS subtypes.

METHODS

Patients

We reviewed the clinical and electrophysiological records of patients discharged with the diagnosis of GBS from the University Hospital of Chieti between January 1995 and June 2009 and selected patients with progressive weakness of more than one limb with or without sensory symptoms or signs, who had at least two electrophysiological recordings in at least three motor and three sensory nerves. Fifty-five patients fulfilled these requirements. All patients signed an informed consent for utilization of personal data, storage and assay of biological materials for research purposes.

Electrophysiology

Motor conduction studies were performed by a Nicolet Viking IV machine (Nicolet, USA). Amplitude and duration of negative peak of compound muscle action potential (CMAP) from distal (dCMAP) and proximal (pCMAP) stimulation, conduction velocity (CV), distal motor latency (DML) and minimal F-wave latency were measured. Sensory studies were performed antidromically in median and ulnar nerves, orthodromically in sural nerve. Amplitudes of sensory nerve action potentials (SNAPs) were measured baseline to negative peak. For DML, CV and F wave latency we defined the upper and lower limit of normal as the mean ±2.5 SD of control values of our laboratory. For CMAP and SNAP amplitude the lower limit of normal was calculated as the mean ±2.5 SD of the logarithmically transformed amplitudes of the controls. Electrophysiological findings in patients were expressed as percentages of upper and lower limits of controls. In serial recordings of the same patients dCMAP amplitude was considered significantly increased when higher than 50% of the value found at the first study. Electrophysiology was performed in each patient at least twice in the same motor and sensory nerves. The total number of tests was 170. The first test was performed within 15 days from onset of symptom (mean 9 days; range 2-15 days) and the results employed for the electrodiagnosis at first study. When a patient had more than one follow-up test the recording which we considered most informative was utilized for the final electrodiagnosis. The mean interval between disease onset and the most informative test was 28 days (range: 7-70 days). EMG of biceps brachialis, first dorsalis interosseous, quadriceps femoralis and tibialis anterior was performed in at least one follow up test and spontaneous activity was graded semi-quantitatively as absent, mild, moderate and abundant.

Electrodiagnostic criteria

In Table 1 are reported the electrodiagnostic criteria sets employed at initial test. In the Ho's criteria evidence of "unequivocal temporal dispersion" is enclosed among the parameters to assess demyelination. [START_REF] Ho | Guillain-Barré syndrome in Northen China. Relationship to Campylobacter jejuni infection and anti-glycolipid antibodies[END_REF] As how much temporal dispersion of CMAP should be considered "unequivocal" was not defined we used an increased duration of negative peak of pCMAP ≥30% compared to dCMAP. [START_REF] Albers | Sequential electrodiagnostic abnormalities in acute inflammatory demyelinating polyneuropathy[END_REF] Hadden and colleagues replaced unequivocal temporal dispersion with CB defined as a pCMAP/dCMAP amplitude ratio less than 0.5. [START_REF] Hadden | Electrophysiological classification of Guillain-Barré syndrome: clinical associations and outcome[END_REF] AMSAN was diagnosed by absence of demyelinating features, as in the Ho's criteria, and reduction of sensory nerve action potential amplitude <50% of lower limit of normal in at least two nerves. [START_REF] Feasby | Severe degeneration in acute Guillain-Barré syndrome evidence of two different mechanisms[END_REF][START_REF] Rees | Campylobacter Jejuni infection and Guillain-Barré syndrome[END_REF] Patient not fulfilling the criteria for AIDP, AMAN and AMSAN were classified as equivocal. The reasons for classification changes at follow-up are reported in the results section.

C. jejuni serology and definition of antecedent C. jejuni infection

Sera from 51 of 55 patients were tested for the presence of IgA and IgG against C. jejuni by enzyme-linked immunosorbent assay (ELISA). [START_REF] Caporale | Susceptibility to Guillain-Barrè is associated to polymorphisms of CD1 genes[END_REF] Subjects were considered to have had an antecedent C. jejuni infection if they had a positive stool culture for C. jejuni or a high optical densities for both IgA and IgG classes at dilution of 1:200 and 1:2000 and a definite history of a diarrheal illness within the previous 3 weeks before disease onset.

Anti-ganglioside antibody testing

Serum IgG and IgM to gangliosides GM1, GD1a, GD1b, were tested in acute phase sera by ELISA. [START_REF] Caporale | Susceptibility to Guillain-Barrè is associated to polymorphisms of CD1 genes[END_REF] Serum was considered positive when showing antibody of IgM and IgG or only IgG class with titre ≥ 1:400.

Statistical analysis

Patients were grouped according to final electrodiagnosis, presence or not of antecedent C. jejuni infection, and presence or not of anti-ganglioside antibodies.

Comparative analyses were made with Fisher's exact test. Results were considered significant if p < 0.05.

RESULTS

Electrodiagnosis at first test

At the first neurophysiologic test 37 of 55 patients (67%) fulfilled the Hadden's criteria for AIDP, 10 patients (9 AMAN, 1 AMSAN) (18%) for axonal GBS and 8 (14%) were equivocal. According to Ho's criteria 36 patients (65%) were classified as AIDP, 10 as axonal GBS (9 AMAN, 1 AMSAN) (18%) and 9 (16%) were equivocal (Fig. 1).

Follow-up and reasons for changes of electrodiagnosis

Thirty patients initially classified as AIDP according to both criteria did not change classification at follow-up. Two patients, initially classified according to both criteria as equivocal, developed definite demyelinating features and were reclassified as AIDP. Fourteen of 32 patients (23%) with final diagnosis of AIDP developed mild to moderate spontaneous activity in at least one muscle. The ten patients initially classified as axonal GBS showed at follow-up dCMAPs which substantially unchanged or further reduced, with some nerves becoming inexcitable, without the development of any demyelinating features and confirming a motor axonal degeneration pattern (Figs. 2A,4A). All ten patients developed moderate to abundant spontaneous activity at EMG. Therefore none of these subjects changed the initial electrodiagnosis. Two patients according to Hadden's criteria and three patients according to Ho's criteria classified at the first study as equivocal developed amplitude reduction of dCMAPs and in one patient of SNAPs and were finally diagnosed as axonal subtypes. All three patients showed moderate to abundant spontaneous activity at EMG.

Three patients showed at the first study a progressive CMAP amplitude reduction along the nerve length (Fig. 2B) fulfilling in some segments the criterion for CB in at least one nerve. According to the Hadden's criteria, two patients were classified as AIDP whereas the other was classified as equivocal. According to Ho's criteria one patient was classified as AIDP and the other two were equivocal. Serial recordings showed that dCMAP amplitudes decreased becoming comparable to the pCMAPs with the disappearance of CB without development of excessive temporal dispersion or other features of demyelination (Fig. 2B). All three patients showed abundant spontaneous activity at EMG. We interpreted this length-dependent CMAP amplitude reduction as due to progressive loss of excitability in fibres undergoing axonal degeneration and these patients were finally classified as axonal GBS. [START_REF] Brown | The electrophysiological changes in the acute "axonal" form of Guillain-Barré syndrome[END_REF][START_REF] Lugaresi | Acute motor axonal neuropathy with high titer IgG and IgA anti-GD1a antibodies following Campylobacter enteritis[END_REF][START_REF] Uncini | Acute motor conduction block neuropathy followed by axonal degeneration and poor recovery[END_REF] Partial motor CB was found in intermediate nerve segments in at least two nerves in four patients and in one nerve in other two patients. CB was localized in six ulnar nerves of four patients in the segment across the elbow with slow CV (range 24-38 m/s) (Figs. 2D,3). In five of these six patients DMLs were prolonged in 11 nerves (mean 122% of ULN, range 110-147%) reaching the cut-off for demyelination (Fig. 4B). Four of these six patients were classified on the basis of the first study according to both criteria as AIDP and two patients as equivocal. At serial recordings partial CB rapidly resolved without development of excessive temporal dispersion of dCMAPs or pCMAPs in all nerves (Figs. 2D,3) and CV improved returning to the normal values in parallel with resolution of CB (Fig. 3). In 17 nerves dCMAP amplitude promptly increased with a mean of 141% (range 67-350%) within a mean interval between the first study and follow-up of 9 days (range 6-17 days) (Figs. 2C,4A). DMLs, when prolonged, returned to normal values within 3 weeks (Fig. 4B). The time course of electrophysiological abnormalities in the nerves of these six patients was clearly different from what found in nerves of patients with AIDP and AMAN with axonal degeneration (Figs. 2,4). Only two of six patients developed mild spontaneous activity at EMG. These six patients were finally classified as axonal GBS with reversible conduction failure. [START_REF] Kuwabara | IgG anti-GM1 antibody is associated with reversible conduction failure and axonal degeneration in Guillain-Barré syndrome[END_REF][START_REF] Kuwabara | Axonal involvement at the common entrapment sites in Guillain-Barré syndrome with IgG anti-GM1 antibody[END_REF][START_REF] Kuwabara | Isolated absence of F waves and proximal axonal dysfunction in Guillain-Barré syndrome with antiganglioside antibodies[END_REF][START_REF] Hiraga | Patterns and serial changes in electrodiagnostic abnormalities of axonal Guillain-Barré syndrome[END_REF]

Final electrophysiological classification

Because of the of better definition of electrophysiologic abnormalities at follow-up, the recognition of the reversible physiologic conduction failure and of the length-dependent CMAP reduction patterns as expressions of axonal pathology 13 subjects (24%) changed classification (Fig. 1). Overall 32 patients (58%) were finally classified as AIDP, 21 (38%) as axonal GBS (18 AMAN, 3 AMSAN) and two (4%) remained equivocal (Fig. 1). In the AIDP subtype 56% of patients had pain, 73% had paresthesias and 64% sensory loss. In AMAN subtype 38% of patients had pain, 16% had paresthesias and none sensory loss. All three AMSAN patients had paresthesias and sensory loss; pain was present in one patient.

Relations between final electrodiagnosis, antecedent C. jejuni infection and antiganglioside antibodies

Twenty-one of 51 (41%) GBS patients had antecedent C. jeuni infection. Sixteen of 19 patients (84%) with axonal GBS and 5 of 30 patients (17%) with AIDP had antecedent C. jeuni infection. The difference was highly significant (p=0.000004).

The two patients who remained equivocal at follow-up did not have antecedent C. jeuni infection.

Antibody to GM1 was present in eight AIDP and 12 axonal GBS (2 with reversible conduction failure). Antibody to GD1a was present in five AIDP and 13 axonal GBS (three with reversible conduction failure). Antibody to GD1b was present in six AIDP and eight axonal GBS (three with reversible conduction failure). Overall at least one antibody to gangliosides GM1, GD1a or GD1b was present in 28 of 55 (51%) GBS patients, in 19 of 21 (90%) axonal GBS and in 9 of 32 (28%) AIDP patients. The difference was highly significant (p=0.000007). Eight of 10 patients who were classified as axonal GBS at first test and did not change classification at follow-up had antibodies to gangliosides. The three patients with the length-dependent CMAP amplidute reduction pattern and the six patients with the reversible conduction failure pattern had antibodies to gangliosides. The two patients who remained equivocal at follow-up did not have anti-ganglioside antibodies.

Fifteen of 19 (79%) patients with axonal GBS had antecedent C. jejuni infection and at least one anti-ganglioside antibody. On the other hand only 4 (13%) of 30 AIDP patients had antecedent C. jeuni infection and at least one of anti-ganglioside antibodies. The difference was highly significant (0.000002)

DISCUSSION

The percentages of patients with demyelinating and axonal GBS vary substantially in different series. [START_REF] Ho | Guillain-Barré syndrome in Northen China. Relationship to Campylobacter jejuni infection and anti-glycolipid antibodies[END_REF][START_REF] Hadden | Electrophysiological classification of Guillain-Barré syndrome: clinical associations and outcome[END_REF][START_REF] Kalita | Neurophysiological criteria in the diagnosis of different clinical types of Guillain-Barré syndrome[END_REF][START_REF] Kushnir | Evolving pattern of Guillain-Barré syndrome in a community hospital in Israel[END_REF] This may be due to genetic susceptibility, different triggering factors, electrophysiological criteria used and whether the electrodiagnosis was based on a single or serial studies. Ho and colleagues in 129 Chinese patients, classified by a single test, found 65% AMAN, 24% AIDP and 11% unclassifiable patients. [START_REF] Ho | Guillain-Barré syndrome in Northen China. Relationship to Campylobacter jejuni infection and anti-glycolipid antibodies[END_REF] Hadden and colleagues applied their criteria to 369 GBS patients from 11

Western countries examining the results of two electrophysiologic tests performed approximately four weeks apart. [START_REF] Hadden | Electrophysiological classification of Guillain-Barré syndrome: clinical associations and outcome[END_REF] At first test, 69% of patients met the criteria for AIDP and 3% the criteria for AMAN; the remaining patients being equivocal or showing inexcitable nerves. At second test, although the final proportion of AIDP and AMAN were similar, many subjects changed classification. More recently in 51 Indian patients applying the Ho'criteria to the results of a single test 86 % of patients had AIDP and 14% axonal GBS whereas in 41 patients from Israel, using the results of two studies performed within 4 weeks from onset, the percentage of AIDP was 63 % and of axonal GBS 37%. [START_REF] Kalita | Neurophysiological criteria in the diagnosis of different clinical types of Guillain-Barré syndrome[END_REF][START_REF] Kushnir | Evolving pattern of Guillain-Barré syndrome in a community hospital in Israel[END_REF] In the GBS series we report electrodiagnosis was almost identical at the first test with both criteria but at follow-up 24% patients changed classification. The main shifts being from AIDP and equivocal groups to the axonal group which resulted more than doubled. The principal reason was the individuation of CBs rapidly resolving without the development of dispersed CMAPs due to remyelinating, slow conducting, desynchronized components which are characteristic of the evolution of CB due to segmental demyelination. [START_REF] Saida | Antiserum-mediated demyelination: relationship between remyelination and functional recovery[END_REF][START_REF] Uncini | Tellurium-induced demyelination: an electrophysiological and morphological study[END_REF][START_REF] Clouston | Quantitative analysis of the compound muscle action potential in early acute inflammatory demyelinating polyneuropathy[END_REF] This feature, denominated reversible conduction failure, has been described in some Japanese AMAN patients and in a GBS subtype named acute motor conduction block neuropathy (AMCBN) and ascribed to an antibody mediated impaired physiological conduction at the axolemma of nodes of Ranvier. [START_REF] Kuwabara | IgG anti-GM1 antibody is associated with reversible conduction failure and axonal degeneration in Guillain-Barré syndrome[END_REF][START_REF] Kuwabara | Axonal involvement at the common entrapment sites in Guillain-Barré syndrome with IgG anti-GM1 antibody[END_REF][START_REF] Kuwabara | Isolated absence of F waves and proximal axonal dysfunction in Guillain-Barré syndrome with antiganglioside antibodies[END_REF][START_REF] Hiraga | Patterns and serial changes in electrodiagnostic abnormalities of axonal Guillain-Barré syndrome[END_REF][START_REF] White | Multifocal motor neuropathy with conduction block and Campylobacter jejuni[END_REF][START_REF] Sugie | A case of acute multifocal motor neuropathy with conduction block after Campylobacter jejuni enteritis[END_REF][START_REF] Susuki | Rapid resolution of nerve conduction blocks after plasmapheresis in Guillain-Barré syndrome associated with anti-GM1b IgG antibody[END_REF][START_REF] Capasso | Acute motor conduction block neuropathy. Another Guillain-Barré syndrome variant[END_REF] The pathophysiology of AMAN with axonal degeneration, AMAN with reversible conduction failure and AMCBN can be explained by the experimental model of axonal GBS. In the rabbit the immunopathologic cascade starts with IgG deposit at the axolemma of Ranvier nodes, is followed by complement activation with the final formation of the membrane attack complex, disruption of nodal sodium channel clusters, detachment of paranodal myelin terminal loops and lengthening of the nodal region. [START_REF] Susuki | Anti-GM1 antibodies cause complement-mediated disruption of sodium channel clusters in peripheral motor nerve fibers[END_REF] All these changes lower the safety factor for impulse transmission and when transposed to humans suggest that at an early stage the immunologic reaction at nodal axolemma may induce a potentially reversible conduction failure. If the immune reaction progresses with the formation of membrane attack complex pores and calcium entry in the axon a process of cytoskeletal degradation and mitochondrial injury develops with axonal damage and Wallerian-like degeneration. To support a continuum between reversible conduction failure and axonal degeneration a reversibly reduced safety factor for impulse conduction has been documented by threshold tracking technique and refractory period studies in nerves of AMAN patients and one patient with AMCBN who progressed to axonal degeneration was reported. [START_REF] Kuwabara | Differences in membrane properties of axonal and demyelinating Guillain-Barré syndromes[END_REF][START_REF] Kuwabara | The refractory period of transmission is impaired in axonal Guillain-Barré syndrome[END_REF][START_REF] Rajabally | Acute motor conduction block neuropathy followed by axonal degeneration and poor recovery[END_REF] The above considerations explain why AMAN patients do not necessarily have poor prognosis and may improve faster or slower according to the shares of axonal degeneration and reversible conduction failure, being the patients with AMAN with reversible conduction failure or AMCBN the ones with the best prognosis and complete recovery. [START_REF] Capasso | Acute motor conduction block neuropathy. Another Guillain-Barré syndrome variant[END_REF][START_REF] Kuwabara | Indicators of rapid recovery in Guillain Barré syndrome[END_REF][START_REF] Hiraga | Recovery patterns and long term prognosis for axonal Guillain-Barré syndrome[END_REF] An objection to the not demyelinating nature of reversible conduction failure might come from the observation that CV was slow at the site of CB in some nerves of patients we finally diagnosed as axonal GBS with reversible conduction failure. In these patients CV slowing was present from the first recording when CB was at maximum, CV rapidly increased with the decrease of CB and returned to normal range when CB had disappeared. Conduction slowing at CB sites may be a factitious phenomenon due to preferential block of large diameter fastest conducting fibres. The same explanation can be applied to the nerves showing prolonged DMLs which in sequential recordings quickly normalized in parallel with increased dCAMP amplitude. Alternatively sodium channel dysfunction, which is hypothesized to be at the basis of reversible conduction failure, may be responsible for conduction slowing.

In human poisoning by tetrodotoxin slow CVs, increased DMLs and reduced dCMAP amplitudes recover in few days without temporal dispersion possibly because of an uniform involvement of all fibers in the nerve resulting in synchronous slowing of impulse conduction. [START_REF] Oda | Nerve conduction study of human tetrodoxication[END_REF] Two patients were initially classified as AIDP because of progressive CMAP amplitude reduction along the nerve length fulfilling in some segments the criterion for CB. At follow up the dCMAP amplitude decreased and equalized the proximal CMAP without the development of temporal dispersion. This pattern was named by van der Meché and colleagues "length-dependent CMAP amplitude reduction" and initially thought to be due to demyelinating lesions scattered along the nerve followed by axonal degeneration. [START_REF] Van Der Meché | Patterns of conduction failure in the Guillain-Barré syndrome[END_REF] However this pattern is also consistent with an immune-mediated primary axonal degeneration with progressive loss of excitability in fibres undergoing axonal degeneration. [START_REF] Brown | The electrophysiological changes in the acute "axonal" form of Guillain-Barré syndrome[END_REF][START_REF] Lugaresi | Acute motor axonal neuropathy with high titer IgG and IgA anti-GD1a antibodies following Campylobacter enteritis[END_REF][START_REF] Uncini | Acute motor conduction block neuropathy followed by axonal degeneration and poor recovery[END_REF][START_REF] Van Der Meché | Axonal damage in Guillain-Barré syndrome[END_REF] The dCMAP is initially greater than the pCMAP because the injured axons are inexcitable above the lesion site whereas they remain excitable distally. The inexcitability progresses over few days distally till it reaches the nerve terminals. Other possible explanations are that CB may be due to an axonal dysfunction, as in reversible conduction failure, which progresses to axonal degeneration or imputable to an adjunctive distal axonal involvement. In any case the damage should be considered axonal in nature.

Because of the recognition of reversible conduction failure and length dependent CMAP amplitude reduction patterns a total of 7 patients shifted from the AIDP and equivocal groups to axonal GBS and none from axonal GBS to AIDP. In the study by Hadden and colleagues six of ten patients initially classified in the axonal group were later reclassified as demyelinating, three equivocal and only one remained in the axonal group. Of the original demyelinating group 4% become axonal and 5% inexcitable. [START_REF] Hadden | Electrophysiological classification of Guillain-Barré syndrome: clinical associations and outcome[END_REF] This study was published in the same year of the paper on reversible conduction failure in axonal GBS and we think that, at least in part, the differences in results may be due to the lack of recognition of reversible conduction failure pattern. [START_REF] Hadden | Electrophysiological classification of Guillain-Barré syndrome: clinical associations and outcome[END_REF][START_REF] Kuwabara | IgG anti-GM1 antibody is associated with reversible conduction failure and axonal degeneration in Guillain-Barré syndrome[END_REF] In the series we report antecedent C. jejuni infection and anti-ganglioside antibodies are more frequent in axonal GBS than in AIDP. Overall 79% of axonal GBS but only 13% of AIDP had antecedent C. jejuni infection and anti-gangliosides antibodies.

These results confirm that the three conditions: axonal GBS (including reversible conduction failure), antecedent C. jeuni infection and IgG to gangliosides GM1, GD1a, or GD1b are closely associated. [START_REF] Ogawara | Axonal Guillain-Barré syndrome: relation to anti-ganglioside antibodies and Campylobacter iejuni infection in Japan[END_REF] Hiraga and colleagues advanced the hypothesis that anti-ganglioside antibodies are associated to axonal degeneration or reversible conduction failure but not to true AIDP. [START_REF] Hiraga | Patterns and serial changes in electrodiagnostic abnormalities of axonal Guillain-Barré syndrome[END_REF] In our series all patients who shifted to the axonal group had antibodies. However 28% of patients finally classified as AIDP have anti-ganglioside antibodies. Reversible conduction failure is thought to be due to a transient attack of antibodies and complement limited at the excitable axolemma of Ranvier node but it is conceivable that an immunologic process, although specific, cannot have the "surgical" precision to completely spare the paranodal region. As a matter of fact detachment of terminal loops of paranodal myelin and lengthening of the nodal region has been shown in AMAN patients and in the experimental model. [START_REF] Griffin | Early nodal changes in the acute motor axonal neuropathy pattern of Guillan-Barré sindrome[END_REF][START_REF] Hafer-Macko | Acute motor axonal neuropathy: an antibody-mediated attack on axolemma[END_REF][START_REF] Susuki | Anti-GM1 antibodies cause complement-mediated disruption of sodium channel clusters in peripheral motor nerve fibers[END_REF] This feature, although the primary pathology is on the axonal side, mimic paranodal demyelination and may explain the "grey zone" of patients with anti-ganglioside antibodies and some de-remyelinating features at electrophysiology fulfilling the criteria for AIDP.

This study demonstrates that in the early phase of GBS the distinction between AIDP and axonal GBS may be difficult or even impossible in some patients. Theoretically the Ho's criteria including excessive temporal dispersion but not CB should avoid the pitfalls due to reversible conduction failure and length-dependent CMAP amplitude reduction resulting more specific than Hadden's criteria for AIDP. However the fact that reversible conduction failure can also transiently slow CV and increase DML eliminates the advantage making the two criteria substantially equivalent. Hadden et al.1998[4] At least one of the following in each of at least two nerves, or at least two of the following in one nerve if all others inexcitable and dCMAP≥10% LLN:

In conclusion in GBS only

Motor conduction velocity<90%LLN (<85% if dCMAP<50%LLN) Distal motor latency >110 %ULN (>120% if dCMAP<100% LLN) pCMAP/dCMAP ratio< 0.5 and dCMAP ≥20%LLN F-response latency>120% AMAN c) Ho et al. 1995 [START_REF] Ho | Guillain-Barré syndrome in Northen China. Relationship to Campylobacter jejuni infection and anti-glycolipid antibodies[END_REF] No evidence of demyelination as defined in a dCMAP<80% LLN d) Hadden et al. 1998[4] None of the features of demyelination in any nerve as defined in b (except one demyelinating feature allowed in one nerve if dCMAP<10%LLN) dCMAP<80% LLN in at least 2 nerves AMSAN e) Feasby et al. 1993[8], Rees et al. 1995 [START_REF] Rees | Campylobacter Jejuni infection and Guillain-Barré syndrome[END_REF] No evidence of demyelination as defined in a dCMAP<80% LLN in at least 2 nerves SNAP <50% LLN in at least 2 nerves LLN: lower limit of normal; ULN: upper limit of normal; dCMAP: amplitude of compound muscle action potential after distal stimulation; pCMAP amplitude of compound muscle action potential after proximal stimulation; SNAP sensory nerve action potential. On day ten there was a partial CB across the elbow which improved on day 20 and resolved at day 27 without the development of excessive temporal dispersion. The patient had IgG anti-GM1, anti-GD1a and anti-GD1b. E) Acute inflammatory demyelinating neuropathy pattern. Ulnar nerve. On day two all conduction parameters were normal. On day 14 all CMAPs were dispersed, distal CMAP amplitude was greatly reduced (1 mV), distal motor latency was increased (5.7 ms), the CMAP amplitude ratio between below-elbow and wrist stimulation was 0.2 and conduction velocities were reduced (20 m/s in the below-elbow wrist segment and 26 m/s across the elbow). On day 40 the CMAP amplitude ratio between below-elbow and wrist stimulation was 0.5 but all CMAPs were still reduced in amplitude and dispersed, DML was further increased (7.2 ms) and conduction velocities reduced (19 m/s in the below-elbow wrist segment and 16 m/s across the elbow). The patient did not have anti-ganglioside antibodies. C) CMAPs recorded from the extensor digitorum brevis muscle after stimulation of peroneal nerve at ankle, below-fibular head and above-fibular head in a patient with antibodies to GD1b. On day six DML is prolonged and dCMAP amplitude reduced (1.6 mV). On day 12 DML is slightly prolonged and dCMAP amplitude is 106 % increased. On day 25 DML is in the normal range and dCMAP amplitude is 150 % increased compared to day six.

TABLE 1 .

 1 serial electrophysiological studies allow the identification of pathophysiological mechanisms of muscle weakness and the correct classification in subtypes. More reliable electrophysiological criteria taking into consideration the reversible conduction failure pattern should be devised and validated in large populations. CRITERIA FOR ELECTROPHYSIOLOGICAL CLASSIFICATION AIDP a) Ho et al.1985[3] Patients must have one of the following in two or more nerves during the first 2 weeks of illness: Motor conduction velocity<90%LLN (<85% if dCMAP<50%LLN) Distal motor latency >110 %ULN (>120% if dCMAP<100% LLN) Evidence of unequivocal temporal dispersion F-response latency>120% b)

Figure 1 .

 1 Figure 1. Electrodiagnosis of GBS patients at first study and after serial

Figure 2 .

 2 Figure 2. Patterns of motor conduction abnormalities.

Figure 3 .

 3 Figure 3. Serial electrophysiologic findings in ulnar nerves of two patients with

Figure 4 .

 4 Figure 4. Serial electrophysiologic findings in patients with axonal GBS and

FUNDING

This study was supported by a grant from Ministero della Salute (Ricerca Corrente 2006).

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COMPETING INTERESTS

This study was not sponsored by any company. Prof. Uncini received research support from Kedrion and payement for lectures by Pfizer.