Ibrahim Neya

Daniel Yamegueu
email: daniel.yamegueu@2ie-edu.org

Yézouma Coulibaly

Adamah Messan

Arnaud Louis

Sountong-Noma Ouedraogo

Impact of insulation and wall thickness in compressed earth buildings in hot and dry tropical regions

Keywords: thermal behaviour, tropical climate, energy model, experimental validation, thermal comfort

Outdoor climatic conditions such as sun radiation, air temperature and humidity, wind speed are the main factors that determine the thermal response of free-running buildings. However, the thermal behaviour of buildings can be regulated by a proper choice of suitable materials to maintain thermal comfort for the occupants. Through a validated energy model, this article evaluates the influence of insulation and thermal mass on the envelope of a compressed stabilised earth blocks test cell in a hot and dry tropical climate. The study assesses the impact of these parameters on building thermal performance. The effect of insulation is studied by considering different insulators made of glass wool or straw mixed with lime. The thermal inertia impact has been assessed by varying the wall thickness. The results show that insulation with 0.10 m glass wool thickness and 0.15 m straw mixed with 0.02 m lime have very close thermal performance. The study also shows that the appropriate wall thickness for adequate thermal comfort depends on the building insulation state. Without insulation, the wall thicknesses of 0.22 m and 0.35 m showed the best thermal performance. The corresponding decrement factors were respectively 30% and 17%. An insulated wall thickness of 0.14 m was

Introduction

The rapid growth of African population combined with a high urbanisation rate increase the need for decent dwellings with satisfactory comfort conditions for occupants [START_REF] Iepf | Efficacité Énergétique de la climatisation en région tropicale[END_REF]. In warms regions, cooling needs are especially high to adapt to current hot conditions. Therefore there is a real interest in low energy consumption houses in these regions where air conditioners ownership is around 0.06 units per household [START_REF]Africa Energy Outlook: World Energy Outlook Special Report[END_REF]. In Africa, people use widely ecological lowcost building materials such as earth, wood, straw and bamboo. However, the potential of these materials to time-shift and dampen the peak thermal loads have not been sufficiently investigated. This phenomenon known as thermal inertia effect characterises the building ability to store the daytime heat and release it in nighttime. The impact of the building envelope thermal inertia consists in providing a 'passive thermoregulation cooling' [START_REF] Guglielmini | The Influence of the Thermal Inertia of Building Structures On Comfort and Energy Consumption[END_REF]. This leads in improving the building indoor thermal conditions without any energy consumption.

Verbeke and Audenaert [START_REF] Verbeke | Thermal inertia in buildings: A review of impacts across climate and building use[END_REF] highlighted the discrepancies of thermal inertia effect in terms of cooling and heating loads reduction. The low indoor temperature observed in medieval churches show the practical benefits of thermal inertia. Some studies on dwellings made of earth [START_REF] Ip | Thermal behaviour of an earth-sheltered autonomous building -The Brighton Earthship[END_REF], stone [START_REF] Medjelekh | A field study of thermal and hygric inertia and its effects on indoor thermal comfort: Characterization of travertine stone envelope[END_REF] and concrete [START_REF] Givoni | Effectiveness of mass and night ventilation in lowering the indoor daytime temperatures. Part I: 1993 experimental periods[END_REF] proved that thermal inertia ensure the thermal stability of building indoor environment. Contrary to this general observation, some authors pointed out that the net cooling demand of air conditioned buildings increases with thermal inertia in warms regions. This was noticed for example in the mediterranean climate of Italy [START_REF] Ferrari | Building envelope and heat capacity: re-discovering the thermal mass for winter energy saving[END_REF] and hot desert climate of Las Vegas, USA [START_REF] Zhu | Detailed energy saving performance analyses on thermal mass walls demonstrated in a zero energy house[END_REF]. In fact, in air-conditioned buildings, energy is required to cool down the additional thermal mass related to thermal inertia. The methods used in the different constructions in the Swiss continental climate through experiments. The indoor temperature fluctuates less in the building with high thermal inertia, which improved indoor thermal stability. The indoor temperature was also up to 3 °C less in the higher thermal inertia building.

However, the experimental methodology remains tedious and requires a lot of time, money and expertise to analyse all the different scenarios affecting the impact of thermal inertia. It is also difficult to distinguish with acceptable accuracy the thermal inertia effect from other influencing parameters impacts. Therefore a mix of simulation and experimental approaches could be a good compromise to analyse the thermal inertia effect.

The combination of these two methods is well known as empirical validation, and consists firstly in comparing measured and simulated data through building energy programs to assess the model ability to reproduce the building thermal behaviour. Secondly, when the numerical model precision is acceptable, the sensitivity analysis is performed and the influence of different parameters involved is found with acceptable accuracy. Toure et al. [START_REF] Toure | Influence of envelope thickness and solar absorptivity of a test cell on time lag and decrement factor[END_REF] investigated the influence of envelope thickness and solar absorptivity on time lag and decrement factor using this approach. They found that increasing wall thickness improve the thermal inertia effects as decrement factor and time lag. The study was performed in a test cell of 1m 3 made of compressed earth bricks stabilised with cement. The small size of the cell reduced the influence of the complex physical heat exchange phenomena as conduction and radiation heat gains through windows.

The present study aims to use the empirical validation approach to investigate the influence of thermal insulation and thermal mass on full-scale building thermal inertia. The novelty of this research stands in using local available materials such as compressed stabilised earth blocks and straw to reduce overheating in dwellings. Some previous studies pointed out the good performance of compressed earth blocks to offer better durability than adobe materials [START_REF] Adegun | Review of economic and environmental benefits of earthen materials for housing in Africa[END_REF][START_REF] Omar Sore | Stabilization of compressed earth blocks (CEBs) by geopolymer binder based on local materials from Burkina Faso[END_REF] and offer same or better thermal response than concrete in warms regions [START_REF] Adegun | Review of economic and environmental benefits of earthen materials for housing in Africa[END_REF][START_REF] Yézouma | Climat et confort thermique[END_REF][START_REF] Jannot | Economie d'énergie et confort thermique dans l'habitat en zone tropicale[END_REF][START_REF] Hema | Vernacular housing practices in Burkina Faso: representative models of construction in Ouagadougou and walls hygrothermal efficiency[END_REF]. Other works [START_REF] Toguyeni | Study of the influence of roof insulation involving local materials on cooling loads of houses built of clay and straw[END_REF][START_REF] Pritchard | Evaluation of Strawbale Building: Benefits and Risks[END_REF][START_REF] Samuel | Temperature and moisture storage in crop-based materials: Modelling a straw bale wall subject to a thermal shock[END_REF][START_REF] Douzane | Hygrothermal performance of a straw bale building: In situ and laboratory investigations[END_REF][START_REF] D'alessandro | Straw bale constructions: Laboratory, in field and numerical assessment of energy and environmental performance[END_REF] highlighted the benefits of using straw in building construction. These materials are attractive alternatives to concrete and conventional insulators which are usually more expensive and less ecologically friendly. Tiskatine et al. [START_REF] Tiskatine | Thermo-physical analysis of low-cost ecological composites for building construction[END_REF] investigated thermal performance of cement stabilised red clays regarding incorporation of insulators like sawdust, petiole, straw, argan shells, and palm fibres. They found that the best thermal insulation performance is achieved with straw. Pritchard and Pitts [START_REF] Pritchard | Evaluation of Strawbale Building: Benefits and Risks[END_REF] presented straw as an abundant, ecological, inexpensive good thermal and sound insulator even though like each material, it has some drawbacks. Quagliarini and Lenci [START_REF] Quagliarini | The influence of natural stabilizers and natural fibres on the mechanical properties of ancient Roman adobe bricks[END_REF] examined the influence of straw as natural binder used in ancient adobe bricks of Roman and concluded that straw influences both plasticity, breaking and shrinkage of adobe blocks. Aouba et al. [START_REF] Aouba | Predicting thermal performance of fired clay bricks lightened by adding organic matter: Improvement of brick geometry[END_REF] showed that incorporating wheat straw in fired clay bricks reduce their thermal conductivity by 35%.

The case study facility is a free-running compressed earth test cell built in a hot and dry tropical climate country. First, the study proposes experiments of the test building. Then, the energy model of the building is validated through an empirical validation approach. The passive strategies are thus examined using the validated numeric model of the building. Finally, the results are discussed and some recommendations are made.

Methodology 2.1 Description of the building

The experimental platform is located on the site of the International Institute for Water and Environmental Engineering (2iE) in Burkina Faso (12.5 ° north, 1.5 ° west). A test building was built on this site, with 0.14 m thick Compressed Stabilised Earth Brick (CEB) walls. This material results from the stabilisation of laterite, a local abundant material mixed with 8% of cement Portland CEMII. The use of cement improves the durability and mechanical strength of this earth-based material. Fig. 1 shows the test cell and its architectural plans. The test cell is a 3.06 m wide, 4.06 m long and 4.33 m high building. The size is representative of most buildings used by low-income population in rural and suburban areas of the country. A recent study conducted by Rincón et al. [START_REF] Rincón | Improving thermal comfort of earthen dwellings in sub-Saharan Africa with passive design[END_REF] in this location used an adobe building of similar size to assess thermal comfort in earthen buildings. Other authors used similar test cells to investigate thermal performance of building in locations such as Mexico [START_REF] Rojas | Thermal performance of two envelope systems: Measurements in non air-conditioned outdoor test cells and simulations[END_REF], France [START_REF] Kuznik | Experimental assessment of a phase change material for wall building use[END_REF] and Switzerland [START_REF] Manz | Series of experiments for empirical validation of solar gain modeling in building energy simulation codes-Experimental setup, test cell characterization, specifications and uncertainty analysis[END_REF]. Their work showed that test cells represent practical and efficient means to gather high quality data for empirical validation. They are a good compromise between laboratory and large-scale building experiments [START_REF] Strachan | Model validation using the PASSYS Test cells[END_REF].

The test cell building considered in the present study is oriented east - west with two identical 3 mm single glazing windows of 1.00 m wide and 1.20 m high. The windows are located on the north and south facades. The door of 0.85 m wide and 2.20 m high is made of metal and glazing identical to the windows in its upper part. It is on the south facade. The floor is a 0.10 m concrete slab. The roof of the test building is of 1.5 mm metal sheet. This is the most used roof material in low-income communities. The roof benefits from natural ventilation through five openings of 0.10 m diameter on the main facades. The ceiling is made of 5 mm plywood.

The thermophysical properties of the materials used for the building envelope are given in Table 1. The model also includes the windows and other openings thermal gain calculation. To do so, their materials thermal properties were taken from the EnergyPlus database. To characterise the thermal response of the test cell regarding outdoor climatic conditions, the building was kept closed and in free-running mode during the experiments.

Data Collection

The temperature was recorded using a Pt 100 of range -20 °C to 85 °C with an accuracy of 0.12 °C. The sensor was set at a height of 1.1 m from the ground in the centre of the room. The outdoor weather parameters of the study site were recorded using a Vaisala HydroMet weather station located on the experimental site (Fig. 2). The measured parameters are the dry temperature, the relative humidity, the global solar irradiation, the diffuse solar irradiation, the wind speed and direction.

Modelling and simulation of the building 3.1 Model development

The model was implemented in the dynamic simulation engine EnergyPlus 9.0.1, released in October 2018. EnergyPlus is one of the most advanced and most used energy-simulation programs. EnergyPlus is commonly used to model and analyse the dynamic thermal behaviour related to energy and provides accurate temperature and comfort prediction [START_REF] Gerber | EnergyPlus Energy Simulation Software[END_REF][START_REF] Crawley | EnergyPlus: DOE's Next Generation Simulation Program, Energy Efficiency and Renewable Energy[END_REF][START_REF] Crawley | Energy plus: energy simulation program[END_REF][START_REF] Crawley | EnergyPlus: a new-generation building energy simulation program[END_REF].

The thermal conduction of the model is evaluated with the Conduction Transfer Functions (CTF) recommended in [START_REF] Yang | Evaluation of Different Thermal Models in EnergyPlus for Calculating Moisture Effects on Building Energy Consumption in Different Climate Conditions[END_REF] for the hot and dry climate. Considering the CTF model, the heat flux at one surface is linearly related to the prevalent and some of the past temperatures at both the interior and exterior surface as well as some of the past flux values at the other surface as shown by the Eq. 1-2 [37]. The CTF is solved in EnergyPlus using the basic state space method with finite difference variables as described in [37]. In the resolution using Conduction Transfer Functions method, nz and nq are respectively the number of CTF temperature and flux coefficients. They are constant and depend on the construction type. The Thermal Analysis Research Program from ASHRAE is used for both external and internal convective heat exchange [37,[START_REF] Walton | Thermal Analysis Research Program Reference Manual[END_REF]. Outdoor global coefficient (Eq. 3) is split into forced component and natural component, respectively evaluated in Eq. 4 and Eq.5. Indoor convective coefficient is calculated here using natural convection equation (Eq.5).

" = - , - , + , + , + Φ , " (1)
" = - , - , + , + , + Φ , " (2)
ℎ = ℎ + ℎ (3)
Where hc, hf and hn are respectively global convective, forced convective and natural convective coefficients.

ℎ = 2.537 & ' ( )* + , /. (4)
Where:

Wf is the wind direction multiplier, Vz is the wind speed at height above ground of the surface centroid, A is the surface area of the surface P is the perimeter of the surface Rf is the surface roughness multiplier For natural convection:

• When ΔT = 0 or a vertical surface ∆T, the temperature difference between the surface and air Σ, the surface tilt angle Air infiltration was evaluated using the model of effective leakage area [START_REF]ASHRAE handbook: fundamentals[END_REF]. The infiltration was assessed according to that handbook method as mentioned in Eq.6:

;<=>? @A >7< = B C DEFGHE + I 1000 JK C ∆ + K L &><MNOPPM ² (6)
Where:

Fschedule is a value from a user-defined schedule,

AL is the effective air leakage area in cm2

Cs is the coefficient for stack-induced infiltration ΔT is the absolute temperature difference between zone air and outdoor air,

Cw is the coefficient for wind-induced infiltration

WindSpeed is the local wind speed.

Thermal Model Validation

The empirical validation of the model consists in comparing the temperatures predicted (Tsim) by the model with the measured ones (Tmeas) in the test cell. Two main statistical indicators for model validation are used. The first one is the average absolute difference between measured and simulated data [START_REF] Mousa | Simulations and quantitative data analytic interpretations of indoor-outdoor temperatures in a high thermal mass structure[END_REF] (Eq. 7). The second one is the linear correlation coefficient R² (Eq. 8).

In Eq. 3-4, the indices i refer to single record and n to the total number of records.

+vg. abs. error °C

= ∑ ]T _`a,`-T abc_,`] d ` n (7)

Inertia and insulation effect on buildings

The building envelope thermal inertia and insulation characterise the envelope capacity to regulate indoor climate by dampening and shifting outdoor thermal loads. Two main regulation

R ² = 1 - ∑ gT _`a,`-T abc_,`h . d `
∑ gT abc_,`-T abc_,i jjjjjjjj h . d ` [START_REF] Ferrari | Building envelope and heat capacity: re-discovering the thermal mass for winter energy saving[END_REF] effects are commonly used to assess the building performance in this regard. These are the time lag and the decrement factor. The two indicators are evaluated between the outdoor and indoor ambiance temperatures as mentioned in [START_REF] Stéphan | Experimental assessment of thermal inertia in insulated and non-insulated old limestone buildings[END_REF].

The decrement factor is calculated as the temperature amplitudes ratio between their indoor values and outdoor values (Eq. 9). The decrement factor express the building potential to dampen the heat flux transfer due to external thermal solicitations as solar radiation and outdoor temperature.

The time lag expresses how long it takes to the outdoor temperature to reach the interior of the building (Eq. 10). The thermal time lag expresses the building capacity to delay the thermal loads impact on indoor temperature to keep the building cool in warms periods.

= =

,klm -,k ,klm -,k

With T: temperature, i: indoor, o: outdoor, max: maximum, min: minimum and t: time

Empirical validation 4.1 Experimental results

Data considered for the analysis in the present study are those for April, the hottest month of the country and therefore the most uncomfortable. The monitoring was performed in the year 2018. For illustrative purpose, all the following figures except Fig. 6 will cover only the first week of April as the representation of the whole month may hide some gaps between data.

However, the data analysis and discussion cover the whole month of April to draw conclusions representative of the overheating reduction of the alternatives considered.

The experiments were achieved during clear sky conditions and absence of precipitations. The daily peak irradiance values are between 850 W•m -² and 1120 W•m -². They are observed at The quick rise of indoor temperature with outdoor temperature during the daytime is probably due to the high solar radiation. Therefore it is suitable to limit heat transfer from outdoor to indoor ambiance using insulation. It is also possible to increase the envelope thermal mass to absorb the solar gains received from the walls, openings and the roof. The absence of solar radiation during nighttime explains the low difference between indoor and outdoor temperature extrema. The natural ventilation during nighttime can accelerate the building cooling process because of the fresh outdoor nighttime temperature.

∅ = o p,qrs -o t,qrs (10)

Model results and empirical validation

The measured and simulated buildings indoor temperatures are plotted in Fig. 5.

Fig. 5. Measured and simulated temperature of building indoor environment

The temperature measurement uncertainty was 0.12 °C. This uncertainty is too small to be visible on the graph and was not drawn. The measured temperature varies between 29 °C and 42 °C and the simulated ones between 28 °C and 43 °C. A fairly good agreement can be observed between model and experiment. A good linear relationship is observed between simulated and measured temperature with residues less than 2 °C (Fig. 6). The calculated mean absolute error value is 0.76 °C and the correlation coefficient is equal to 0.93.

The absolute mean difference is between 0.5 °C and 1 °C. This range is reasonable because of the measurement and calculation uncertainties [START_REF] Strachan | Whole model empirical validation on a full-scale building[END_REF]. The discrepancies could be explained by the uncertainties related to material properties taken in the literature. The R² value shows a strong fit between simulated and measured temperatures. Thus the building thermal model is acceptable for simulation cases assessment.

Simulation case studies

Simulation scenarios

The aim of this modelling is to set up a tool to help in the thermal design of houses in warms regions by assessing how indoor temperature can be reduced using various architectural effects and local building materials.

Building indoor temperature is a prerequisite parameter to assess the thermal comfort in freerunning mode. The following case studies intend to study the effect of wall insulation and block thickness on the indoor temperature of test cells. The two proposed options were combined in the last section in order to assess their combined effect on indoor temperature of test cells.

To

Influence of Insulation on the Cell Indoor Temperature

The insulation analysis aims in this case to compare the traditional glass wool material with the innovative use of a mixture made of lime and straw. The different insulation simulation cases are shown in Fig. 7. They are used to insulate the outdoor surface of walls and thus protect the indoor environment from the solar radiation and outdoor ambient air gains. The materials disposition ensures that the CEB is in contact with the building indoor environment. Such disposition improve the building thermal performance in all climate zones [START_REF] Jazaeri | Influence of building envelopes, climates, and occupancy patterns on residential HVAC demand[END_REF]. The glass wool thickness considered was 0.10 m and the mixture was 0.15 m of straw recovered with 0.02 m of lime. The thermophysical properties of these materials are given in Table 1.

Fig. 8 shows the simulation results of the two proposed insulation solutions. The results are compared to the baseline case without any insulation.

One can see that the two insulation cases have close thermal performance. Compared to the reference case, the use of insulation provides interesting indoor temperature reduction. The value of decrement factor in the baseline case, 0.61 decreases to 0.22 in the insulation cases.

The insulation therefore reduces the decrement factor by 64%. However, the time lag is reduced of 2.50 from baseline to insulation cases.

The outdoor temperature ranges between 23 °C and 43 °C. The indoor temperature varies between 27 °C and 41 °C for reference case; and 29 °C and 36 °C for insulation cases. The maximum daily daytime temperature reduction between insulation and reference case fluctuates between 2 °C and 6 °C. The mean daytime temperature reduction is evaluated at 2 °C. During nighttime, temperature in the reference case is lower than those of insulation cases. The mean temperature gain is 0.8 °C with a maximum value of 2.8 °C.

Influence of Wall Thickness on the Cell Indoor Temperature

The second option considered consists in using blocks of different thicknesses to assess their capacity to store the heat and thus better regulate the indoor thermal conditions. The 0. In fact, increasing thickness reduces the indoor temperature amplitudes (Fig. 10).

Compared to the baseline where the block thickness is 0.14 m, the daytime temperature reduction reaches 3 °C, 5 °C and 5 °C respectively for thickness 0.22 m, 0.35 m and 0.50 m.

The mean values of these reductions are 1.0 °C, 1.6 °C and 1.7 °C. During nighttime, the temperature in the baseline case is the lowest. The mean temperature gains are 0.9 °C, 1.2 °C and 1.3 °C respectively for 0.22 m thickness, 0.35 m and 0.50 m. One can notice that the results for 0.35 m and 0.50 m are close. This means that there is no interest to consider thickness more than 0.35 m for the case study. Table 2 shows temperature, decrement factor and time lag ranges and their mean values.

Combined influence of insulation and blocks thickness

The earlier sections study the separate effects of the insulation and thermal mass on building indoor temperature variation. They were found useful to dampen thermal waves of outdoor environment. This section aims to assess the combined effect of the two previous options on the building indoor temperature. As shown by the results obtained in the previous sections, insulation with 0.10 m of glass or 0.15 m of straw mixed with 0.02 m of lime have similar thermal performance. Hence, only the mixture of straw and lime is used for the following simulations. Therefore, the variation of indoor temperature is analysed through different wall thickness recovered with the same mixture of lime and straw (Fig. 11).

Simulation discussions

Here the time lag was expected to increase with insulation as referenced in [START_REF] Toure | Experimental determination of time lag and decrement factor[END_REF]. Such results

were found only for CEB 0.14 m and CEB 0.20 m where time lag increase a little with values between 4-5 h. However for other simulation cases, time lag values were less than 2 h. In fact, the more the thermal mass or insulation thickness, the less the heat conduction through the building wall. As mentioned [START_REF] Toure | Influence of envelope thickness and solar absorptivity of a test cell on time lag and decrement factor[END_REF] beyond 32 cm, the indoor environment is no longer influenced by the outdoor thermal flux through walls. This explains why the effect of thermal mass on thermal lag is more pronounced for thicknesses 0.14 m and 0.22 m; and not 0.35 m and 0.50 m. Because insulation and CEB 0.35 m and CEB 0.50m hinder heat conduction through walls, the low values of thermal lag obtained are related to direct daytime heat gains through the building's other components, especially openings and roof. In fact, the building air because of its low heat capacity is influenced by these heat gains and the indoor temperature keeps increasing until sunset. The maximum indoor temperature is thus reached and the building cooling begins through thermal radiation and convection heat exchanges. But in the CEB 0.14 m and CEB 0.22 m in thermal mass influence, because the walls have stored more energy during the daytime, they continue to increase the building indoor temperature until they reached equilibrium with the outside environment.

Insulation impact analysis shows that insulation lowers indoor temperature during the daytime.

In fact, insulation with the mixture of 0.15 m straw and 0.02 m lime or glass wool reduce the building indoor temperature up to 6 °C. In the nighttime, natural ventilation can cancel the reverse effects of insulation and provide better comfort conditions using outdoor fresh air.

Insulation also ensures better thermal stability. In fact, insulation reduces by two third the decrement factor when compared to the baseline scenario. This is mainly due to the insulation capacity to reduce the heat transfer through walls in the building indoor environment. Time lag of 2 h may be seen not enough, meaning that adequate thermal inertia is not obtained.

Nonetheless, insulation remains a very attractive solution as the low indoor temperature amplitude makes the heat exchange time less important.

For the wall inertia assessment, the higher the wall thickness, the lower the indoor temperature.

The decrement factor and time lag of CEB 0.14 m ( of wall thickness simulated offer slightly the same thermal performance, the insulation effect is dominant on the thermal mass impact. An optimal insulation layer can thus be investigated to take advantage of both thermal mass and insulation potential of the blocks thickness. Yet, because it requires the least material quantities, the CEB 0.14 m is the most advantageous when using typical insulation and material thicknesses. The different simulation scenarios show how insulation and thermal mass of building envelope walls influence the building thermal behaviour. Furthermore, improving indoor climatic conditions through dwelling envelope thermal enhancement is still possible by reducing the heat transmission through the building openings and roof; and also using nocturnal natural ventilation. Another investigation that could be addressed in future works concerns the possibility of storing the night freshness in building internal partitions to improve the cooling down of the whole structure.

Conclusion

The study aims to assess the thermal impact of the thermal inertia and insulation of a freerunning Compressed Earth Brick (CEB) test building. A building model was built on the leading software EnergyPlus and validated through multiple adequate statistical indicators that demonstrate the ability of the model to reproduce with acceptable accuracy the thermal behaviour of the building. Hence, simulation was performed to investigate the building wall capacity to regulate the indoor thermal conditions regarding hot climatic external conditions.

It is found on one hand that an insulation of walls with 0.10 m glass wool and a mixture of 0.02 m lime and 0.15 m straw give the same thermal performance, and, on the other hand, that wall thicknesses of 0.22 m and 0.35 m are acceptable in terms of performance, without any insulation. Results also show that a 0.14 m wall thickness is sufficient when an adequate insulation is used. The study contributes to fill the gap of information on the influence of earthen blocks thickness and insulation materials in harsh tropical climatic conditions. The use of straw, abundant in these regions, ecologically friendly and cheap, in contrast with glass wool, also contributes to the sustainable building approach. The practical thicknesses suggested are also important to avoid losing money on the basis that increasing wall thickness always augments building thermal inertial and therefore its comfort. The study weekly increase of temperatures in some experiments suggest that sequential inertia be part of this study. This will be one of the issues explored by the next study of the laboratory. Further investigation is underway and will provide in-depth insight on heat transmission reduction through openings and roof; and how passive strategies can be combined to ensure adequate thermal comfort conditions to low-cost houses in dry and hot climatic regions.

Fig. 1 .

 1 Fig. 1. (a) Test cell front view (b) monitoring sensor (c) top view and (d) front view

Fig. 2 .

 2 Fig. 2. Weather station located on the experimental building platform

  outdoor CTF coefficient Yj, the cross CTF coefficient Zj, the indoor CTF coefficient Φj, the flux CTF coefficient Ti, the indoor face temperature To, the outdoor face temperature q"ko = Conduction heat flux on outdoor face q"ki = Conduction heat flux on indoor face The subscript following the comma indicates the time period for the quantity in terms of the time step δ.

ℎ = 1 .

 1 31 |∆ | 2 (5.1) • For (ΔT < 0.0 on an upward facing surface) or (ΔT > 0.0 on a downward facing surface ℎ = 9.482 |∆ | 2 7.283 -|678 Σ| (5.2)• For (ΔT > 0.0 on an upward facing surface) or (ΔT < 0.0 on a downward facing surface

Fig. 3

 3 Fig.3presents a weekly time evolution of relative humidity and outdoor temperature. One can notice that the outdoor temperature fluctuates between 24 °C and 41 °C with a mean value of 33 °C while relative humidity varies between 6% and 70%. The outdoor air temperature maximum is observed around 3-5 PM and the minimum around 6-7 AM. During the daytime, outdoor temperature increases while relative humidity decreases. In night-time, outdoor temperature decreases while relative humidity increases.

Fig. 3 .

 3 Fig. 3. Weekly temperature and humidity from the weather station Fig. 4 compares indoor and outdoor measured temperatures. The measured indoor temperature varies between 29 °C and 42 °C with a mean value of 36 °C. The indoor temperature maximum occurs between 5 PM and 6 PM, and the minimum between 7 AM and 8 AM. The outdoor and indoor temperatures are closer during the daytime than nighttime. The differences between maximum outdoor and indoor temperatures are smaller than gaps between minimum indoor and outdoor temperatures.

Fig. 4 .

 4 Fig. 4. Weekly outdoor and indoor temperatures

Fig. 6 .

 6 Fig. 6. Fitting between measured and simulated data

  assess the typical performance of the test cell, the climatic data of the Station 655,030 (N 12° 21', W 1° 31'; 316 m above sea level) of Ouagadougou, representative of long-term period, were used. During the hottest month, April, dry bulb temperatures fluctuate in range 23-43 °C; and relative humidity in range 15-80 %. The global horizontal irradiation varies between 1053 W.m -2 during the same period. The maxima of temperature and global solar irradiation are observed respectively during 1-2 PM and 11 AM-1 PM. The baseline simulation case corresponds to the initial building model simulated with the climatic data file.

Fig. 7 .Fig. 8 .

 78 Fig.7. Insulation simulations (a) baseline case (b) CEB with straw and lime mixture (c) CEB with glass wool

  14 m and 0.22 m thicknesses are the commonly used thicknesses for compressed earth blocks in the country. The thickness of 0.35 m and 0.50 m are also used to further investigate the influence of wall thickness. The different simulation cases on wall thickness are shown in Fig. 9.

Fig. 9 .

 9 Fig. 9. Simulation cases of wall thicknesses (a) 0.14 m CEB (b) 0.22 m CEB (c) 0.35 m CEB (d) 0.50 m CEB The mean indoor temperature fluctuates around 34 °C with progressive reduction in amplitude up to thickness 0.35 m. The simulation shows how the block thickness influences the indoor temperature. In fact, increasing thickness reduces the indoor temperature amplitudes (Fig. 10).

Fig. 10 .

 10 Fig. 10. Influence of blocks thickness on the building thermal response

Fig. 11 .

 11 Fig. 11. Simulation cases of CEB with outside side straw and lime insulation of thicknesses (a) 0.14 m (b) 0.22 m (c) 0.35 m and (d) 0.50 m Table3summarises the statistical parameters as function of the blocks thickness.

Fig. 12 .

 12 Fig. 12. Combined influence of insulation and wall thickness on indoor temperature

Table 1 . Thermophysical properties of building materials conductivity (W m -1 K -1 ) density (kg m -3 ) specific heat (J Kg -1 K -1 )

 1

	CEB	1.02	986	1,935
	Concrete	1.4	2,240	840
	Wood	0.15	1,200	500
	Metal sheet	50	7,800	480
	Glass wool	0.04	200	1.21
	Straw	0.06	100	1,700
	Lime	1.2	1,600	1,000

Table 2 .

 2 Thermal performance of test cell for different wall thickness

		CEB 0.14 m CEB 0.22 m CEB 0.35 m CEB 0.50 m
	Temperatures
	Range (°C)	27-41	29-39	30-37	30-37
	Mean (°C)	34.0	33.9	33.7	33.5
	Decrement factor	0.61	0.30	0.17	0.21
	Time lag (h)	4.50	4.63	2.00	1.50

Table 3 .

 3 Thermal performance of insulated test cell according to wall thickness

		CEB 0.14 m CEB 0.22 m CEB 0.35 m CEB 0.50 m
	Temperatures
	Range (°C) 29° C-36°C 30° C-36°C 30° C-36°C 30° C-36°C
	Mean (°C)	32.7 °C	32.7 °C	32.7 °C	32.6 °C
	Decrement factor	0.22	0.22	0.23	0.24
	Time lag (h)	1.90	1.80	1.80	1.70
	The indoor temperature for the different cases of blocks thickness ranges between 29 °C and
	36 °C with decrement factor around 0.23 and a time lag of 1.80 h.
	The indoor temperatures are very close for the different blocks thicknesses (Fig. 12).

Table 2 )

 2 , respectively of 0.61 and 4.50 h are low for adequate thermal inertia when compared to values of 6 hours of time lag and 0.40 of decrement factor for sufficient thermal inertia[START_REF] Moschella | A Methodology for an Integrated Approach for Seismic and Energy Refurbishment of Historic Buildings in Mediterranean Area[END_REF]. Toure et al.[START_REF] Toure | Experimental determination of time lag and decrement factor[END_REF] found time lag values in the range 6.02 h -6.38 h and decrement factor in the range 0.38-0.43 by experimental analysis for a 1x1x1 m 3 test cell of 14 cm stabilised earth blocks with cement. The discrepancies with the present results may be mainly due to the test cell scale, difference in CEB thermophysical properties and air humidity that can impact the thermal properties. In fact, the CEB properties are dependent on the laterite properties that also depend on the quarry. The investigation of Asan and Sancaktar 1998 showed that thermal inertia effects depend on material thermal properties. Concerning air humidity, the study was achieved in the humid climate of Senegal as opposed to the dry climate of our case. Indeed, Shaik et al.[START_REF] Shaik | Influence of ambient air relative humidity and temperature on thermal properties and unsteady thermal response characteristics of laterite wall houses[END_REF] proved that ambient relative humidity, temperature and outdoor convection coefficient influence greatly the decrement factor and time lag of laterite material. As earth material is sensitive to water, this affects the thermal performance of buildings. Because of the good thermal stability obtained with CEB 0.22 m, CEB 0.35 m and CEB 0.50 m, they can be used to improve indoor

	thermal comfort. When block thickness is increased by 57% from CEB 0.14 m to get
	CEB 0.22 m, by 150% to get CEB 0.35 m, and by 257% to get CEB 0.50 m, the mean indoor
	temperature reduction is respectively 1.0 °C, 1.6 °C and 1.7 °C. Therefore the thickness of
	0.50 m is less attractive because of the higher mass increase with less thermal impact. Further
	investigations on economic and environmental issues are also suitable for optimal choice of
	blocks thickness.

Concerning the combination of the alternatives, for the different blocks thickness, the indoor temperature amplitude is about 6 °C. A good indoor thermal stability is observed with daily values of decrement factor below 0.30. The time lag values are very close. Because all the cases

Acknowledgments

The authors acknowledge the support of the German Academic Exchange Office (DAAD) for funding the research that allowed this research work to be carried out.


M.D Karen Benezery

M.D Lucile Montagne

M.D Ludovic Evesque

MsC Renaud Schiappa

Jean-Michel Hannoun-Levi

M.D Eric Francois

Brice Thamphya

Pr (Hon Jean-Pierre Gerard
email: jean-pierre.gerard@nice.unicancer.fr

; Jean-Michel

M.D Hannoun Levi

Brice Thamphya Msc

Clinical response assessment after contact X-Ray brachytherapy and chemoradiotherapy for organ preservation in rectal cancer T2-T3 M0: The time/dose factor influence

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

Introduction

A neoadjuvant treatment aimed at rectal preservation should achieve a clinical complete response.

This study comparing neoadjuvant treatment initiated with Contact X-ray (CXB) or External Beam radiotherapy (EBRT) is evaluating the influence of the time/dose parameter on clinical response during the first six months.

Materials and methods

This retrospective consecutive series included T2-3 rectal adenocarcinoma staged using digital examination (DRE), endoscopy, magnetic radiation imaging and/or endorectal ultrasound. All patients were treated with organ preservation intent. Treatment protocol combined CXB (80-110 Gy/ 3-4 fractions) and EBRT ± concurrent capecitabine. In tumor exceeding 3.5 cm treatment was often initiated using EBRT. Clinical response was assessed (DRE, proctoscopy ± imaging) at very close interval between 2 weeks and 6 months after treatment initiation.

Results

Between 2002-2017, 61 patients (T2: 31; T3: 30) M0 (median age: 76 years) were treated. Treatment was initiated in 40 patients (T2: 28, T3: 12) with contact X-ray and in 21 (T2: 4, T3: 17) with EBRT.

Using contact X-ray or EBRT first treatment, clinical complete (or near complete) response at week 14(±1) was respectively 88% [95CI:74-96] and 33% [95CI: . In multivariate analysis the treatment chronology was the most significant factor influencing cCR (OR: 7.53). At 6 months, with contact X-ray first all patients were in clinical complete response and five with EBRT remained in partial response. With 61 months median follow-up time, the local recurrence rate was 10% [95% CI: 6-16] at 5 years. T3 and fungating tumors were at higher risk of local recurrence. Organ preservation with good function was achieved in 95% of cases.

Conclusion

This non randomized study tends to show that in early T2-3 tumors, a strategy using upfront contact therapy, which is reducing the overall treatment time, is an option allowing a more favorable outcomes than EBRT first.

Key Words

Organ preservation, rectal cancer, neoadjuvant treatment, contact X-ray brachytherapy, Watch and Wait.

Introduction

Proctectomy, often combined with external beam chemoradiotherapy (EBCRT), is the standard treatment for T2-3 rectal cancer. Rectal preservation is a field of interest in clinical research to improve patient quality of life [START_REF] Heald | Report from a consensus meeting: response to chemoradiotherapy in rectal cancer -predictor of cure and a crucial new choice for the patient: on behalf of the Champalimaud 2014 Faculty for 'Rectal cancer: when NOT to operate[END_REF]. To achieve rectal conservation, a neoadjuvant treatment must achieve clinical complete response (cCR). Two strategies are used for this purpose: neoadjuvant EBCRT [START_REF] Habr-Gama | Local recurrence after complete clinical response and watch and wait in rectal cancer after neoadjuvant chemoradiation: impact of salvage therapy on local disease control[END_REF][START_REF] Martens | Longterm Outcome of an Organ Preservation Program After Neoadjuvant Treatment for Rectal Cancer[END_REF][START_REF] Renehan | OnCoRe project investigators. Watch-and-wait versus surgical resection for patients with rectal cancer -Authors' reply[END_REF][START_REF] Smith | Assessment of a Watch-and-Wait Strategy for Rectal Cancer in Patients With a Complete Response After Neoadjuvant Therapy[END_REF] or contact X-ray Brachytherapy (CXB) combined with EBCRT [START_REF] Gérard | Renaissance of contact x-ray therapy for treating rectal cancer[END_REF][START_REF] Dhadda | Organ Preservation Using Contact Radiotherapy for Early Rectal Cancer: Outcomes of Patients Treated at a Single Centre in the UK[END_REF][START_REF] Myint | Dose Escalation Using Contact X-ray Brachytherapy After External Beam Radiotherapy as Nonsurgical Treatment Option for Rectal Cancer: Outcomes From a Single-Center Experience[END_REF][START_REF] Gérard | Planned organ preservation for early T2-3 rectal adenocarcinoma: A French, multicentre study[END_REF]. The assessment of cCR remains a dilemma when using digital rectal examination (DRE), proctoscopy and imaging. cCR is defined as the disappearance of the rectal tumor opposed to partial response (PR) in which a persisting tumor is observed. A "grey zone" exists between cCR and PR called near clinical complete response (ncCR) [START_REF] Lynn | Organ-Preserving Strategies for the Management of Near-Complete Responses in Rectal Cancer after Neoadjuvant Chemoradiation[END_REF]. The optimal timing to assess this clinical response remains controversial [START_REF] Dossa | A watch-and-wait approach for locally advanced rectal cancer after a clinical complete response following neoadjuvant chemoradiation: a systematic review and meta-analysis[END_REF].

The goal of this study is to analyze the influence of the dose/time factor on the clinical response during the first six months after treatment initiation in a cohort of patients treated using CXB or EBCRT delivered first.

Material and methods

This retrospective study evaluated the clinical outcomes of patients presenting rectal cancer treated with organ preservation intent using neoadjuvant treatment initiated with either CXB or EBCRT.

Selection criteria for this strategy were: tumors, located in the distal or middle rectum, biopsyproven adenocarcinoma, T2-T3 not exceeding 5 cm in largest dimension and/or half rectal circumference, N0-N1, M0, any age, operable or inoperable patient. Work-up included colonoscopy, rectal imaging using endo-rectal ultrasound (ERUS) and/or magnetic resonance imaging (MRI).

General work-up used thoraco-abdomino-pelvic CT scan and biology tests. Tumors < 3 cm largest diameter were treated with CXB first. For larger tumors, treatment was often initiated with EBCRT.

Clinical tumor assessment at baseline (week 0).

This evaluation was performed by two experienced radiation oncologists (JPG, KB) using DRE and rigid proctoscopy with a patient in the knee-chest position. Objective tumor measurement was performed using data from DRE, initial colonoscopy, ERUS and/or MRI. Depending on MRI and/or ERUS, T3 tumors were sub-classified as T3a, b, c or d. Using all these examinations the tumor was defined as a half-sphere when mostly polypoid or as a cylinder (described as fungating when presenting exophytic edges with deep ulceration). Volume was calculated in cm 3 using 3D measurements and geometrical formula (half sphere: 4/3 π r 3 X 0.5; cylinder: π r 2 x thickness). For tumor length, MRI sagittal view was considered as the most reliable measure. For tumor thickness MRI or ERUS was used as the reference.

Treatments

Following the Papillon experience [START_REF] Papillon | Present status of radiation therapy in the conservative management of rectal cancer[END_REF], CXB was given first in 3 sessions over 4 weeks delivering a total dose of 80 to 90 Gy combined after the second or third session with EBRT. For EBRT technique, 3D conformal or IMRT was used into a restricted posterior pelvic volume with the upper limit of CTV below S2 or S1 and exclusion of most of the anal canal. Total dose over 5 weeks was 45 Gy or 50 Gy (with shrinking field after 44 Gy). Concurrent chemotherapy with capecitabine (800 mg/m2/BID) was given on radiation days and was omitted in frail patients. When tumor response was slow, a last session could be given 3 weeks after the end of EBRCT (total dose: 100-110 Gy/4 fr). EBRT (± capecitabine) was the initial treatment, mostly after 2013 when organ preservation became more popular among oncologists. CXB was initiated 3 to 5 weeks after completion of EBCRT. Depending on tumor response, CXB dose ranged between 60 Gy (after cCR) and 110 Gy delivered in 3 to 4 fractions [START_REF] Papillon | Present status of radiation therapy in the conservative management of rectal cancer[END_REF]. A transanal local excision (TLE) was done in some patients on an individual decision of the attending surgeon and/or multidisciplinary team (MDT) (Figure 1).

Clinical response evaluation (W2 to W25)

When treatment was initiated using CXB, clinical evaluation was performed at each CXB fraction on week 2 and 4 after first treatment. When it was initiated with EBCRT, clinical response was done at time of the first CXB fraction at week 8 (±1). In all cases this clinical response evaluation was performed by the radiation oncologist using DRE and rigid proctoscopy. On week 14 (±1) in all cases a response evaluation was performed using DRE and rigid proctoscopy often combined with MRI. MRI response was reported using the TRG score [START_REF] Nougaret | The use of MR imaging in treatment planning for patients with rectal carcinoma: have you checked the "DISTANCE[END_REF]. Diffusion weighting imaging (DWI) was frequently used and a diffusion restriction influenced the diagnosis toward PR. In case of cCR at week 14(±1) close surveillance was advised every 3 months (DRE, rigid proctoscopy ±MRI) for 2 years then every 6 months until year five. In case of ncCR at week 14 (±1), a new evaluation (DRE, proctoscopy ±MRI or PET-CT) was made every month until cCR was achieved. In case of PR depending on tumor response and/or patient context, a radical proctectomy or a new clinical evaluation one month later was proposed. For decision-making ncCR was considered as a cCR and no radical proctectomy was decided if ncCR was recorded. In a few frail patients, still with PR at week 25 (±2), a more prolonged surveillance was decided, with monthly evaluation.

According to RECIST criteria [START_REF] Eisenhauer | New response evaluation criteria in solid tumours: revised RECIST guideline (version 1.1)[END_REF], definitions of cCR, ncCR, partial response (PR) and stable disease are given in table 1.

Other study endpoints

When a surgery was performed pathological examination was recorded according to the Dworak classification [START_REF] Dworak | Pathological features of rectal cancer after preoperative radiochemotherapy[END_REF].

Local control was defined as no detectable tumor in the rectum or pelvis after 6 months.

Local recurrence was any tumor relapse in the rectum or pelvis after cCR or ncCR.

Distant metastases and survival (overall, and cancer specific) were evaluated.

Bowel function was recorded using the MSKCC score (in 4 categories) [START_REF] Minsky | Phase I/II trial of pre-operative radiation therapy and coloanal anastomosis in distal invasive resectable rectal cancer[END_REF] or since 2014 with the LARS score [START_REF] Emmertsen | Low anterior resection syndrome score: development and validation of a symptom-based scoring system for bowel dysfunction after low anterior resection for rectal cancer[END_REF].

Toxicity was scored using the common terminology criteria for adverse events (CTCAE) version 4.03.

Statistical analysis

Qualitative data, such as response rate, were presented as absolute frequency and relative frequency with a 95% confidence interval [95 CI]. These data were compared using Chi2 test or a Fisher exact test in case of failure to meet the Chi2 application rules.

Quantitative data were presented as mean, standard deviation, median and range. Quantitative data were compared using the Student T test or the Wilcoxon test in case of non-respect of the application conditions of the Student T test.

Clinical response was evaluated using the last observation carried forward methods (LOCF). As every patient was not evaluated every week neither at the same time, we used the LOCF method for imputation of missing data. LOCF consisted in completing the data at week n (if missing) with the data from week n-1. This imputation method is justified in this study as it does not increase the effect of the treatment.

For evaluation of the clinical response rate or the tumor volume and diameter, patients were censored at the time of Trans-anal Local Excision (TLE) if performed.

Survival distributions were estimated with the Kaplan-Meier method. Comparisons were performed using the log-rank test. Univariate and multivariate analysis was performed for prognostic factors.

The significant factors found in univariate analysis were introduced in a multivariate model, from which a final model was constructed using bachward stepwise regression. P-value and curves were estimated using logistic regression model. All analyses were performed at 5% alpha risk with bilateral hypothesis, using R software version 3.5.1.

Results

Baseline characteristics

Between 2002 and 2017, 168 patients presenting rectal cancer were treated at our institution using CXB (Figure 2). Among them 70 consecutive patients were treated with organ-preserving intent.

Three patients treated with short course EBRT (25G y/5) and six with CXB alone were excluded. The study cohort comprised 61 patients with median age 78 years. Classification was done using ERUS alone in 15 patients, MRI alone in 17 and ERUS with MRI in 29. T2 and T3 were reported respectively in 31 and 30 cases. Treatment was initiated respectively with CXB and EBCRT in 40 and 21 cases. The two groups were imbalanced with in EBRCT first more T3, larger diameters, more fungating appearance. Table 2 gives patients baseline characteristics and treatments description. Median follow-up time was 61 months.

Clinical tumor response during the first six months

When CXB was the first treatment, at week 4 (±1) at time of third CXB session, cCR or ncCR was observed in 33% of cases. When EBCRT was the first treatment, at week 8 (±1) at time of first CXB session, cCR or ncCR was observed in 14% of cases. Out of 23 T2-T3a ≤3 cm treated using CXB first, [START_REF] Maas | Assessment of Clinical Complete Response After Chemoradiation for Rectal Cancer with Digital Rectal Examination, Endoscopy, and MRI: Selection for Organ-Saving Treatment[END_REF] were in cCR (or ncCR) at week 4. Out of 7 T2-T3a ≤ 3cm with EBCRT first, two were in ncCR and 5 in PR at week 8(±1). At week 14(±1), three weeks after end of all radiotherapy treatments, cCR or ncCR was seen, respectively, in CXB and EBCRT group in 88% [95 CI : 74-96] and 32% [95 CI : 15-57] of cases (chi 2: p<0.001) (Figure 3) (suppl File fig 1). TLE was performed on 12 patients (CXB: 11, EBCRT: 1) between weeks 12 and 25 after treatment initiation. Eight patients were in cCR, 3 in ncCR and 1 in PR. Pathology showed ypT0 in 6, yp T1 in 4 and ypT2 in 2. All TLE were R0. One patient had a local recurrence at 7 years.

At week 20 to 25 (± 2), a cCR or ncCR was seen in all patients treated with CXB first. Five patients with EBCRT first were still in PR, four of these achieved cCR between month 6 and 8 and did not develop local recurrence. The other patient received palliative treatment and died without requiring a diverting stoma. When evaluating tumor volume or diameter during this 6-months period, the same difference in rapidity of response was observed in patients receiving CXB first. At week 14 (±1) mean volume or diameter for CXB-first patients was close to zero and was still measurable 4.94 cm 3 (SD 8.1) and 1.6 cm (SD 1.3)) for EBCRT-first patients (Figure 4).

When ncCR was reported, in both groups, between week 8 and 25, it involved ulceration in 70 % of cases, firm rectal wall using DRE in 20% and residual nodularity in 10%.

MRI was not included in this evaluation study but had little influence on the decision. MRI data will be analyzed in another paper.

Local control and local recurrence

At one year after treatment initiation, local control was observed in 59 out of 61 patients. One 3).

Survival and metastases

Overall and cancer-specific survival at 5 years were respectively 54% [95 CI : 41-71] and 90% [95 CI : 81-100]. Cumulative incidence of distant metastases at 5 years was 20% [95 CI : 8-31].

Prognostic factors

When treated with CXB first all 23 patients with polypoid tumors < 3 cm in diameter were in cCR (or ncCR) at week 11±1 (3 weeks after end of EBCRT) and none had local recurrence. One developed isolated distant metastasis.

Taking cCR + ncCR at week 14 as the end point in univariate analysis, in addition to treatment chronology, the following parameters were significant (for 60 evaluable patients): T stage : T2 87%

Toxicity

Main complication was rectal bleeding in 28 patients. Plasma argon coagulation was needed in 4 cases. Telangiectasia was described in 30 % of patients usually 1 or 3 years after end of treatment and was responsible for the rectal bleeding which stopped after 3 years. No patient required diverting stoma for toxicity. Bowel function was estimated as good or excellent in 85% of patients and none required diverting stoma for poor function.

Discussion

The main original finding of this study is to show the difference in speed of clinical tumor response when CXB is used as first treatment (with a high dose over a short time in a small well-targeted tumor volume) versus EBCRT (lower dose, longer time and larger volume). At week 14 (±1), 88% vs 32% of patients respectively, were evaluated as cCR or ncCR. When treating T2 < 3cm in diameter using EBCRT first, both cCR and ncCR were infrequently observed (28%) at week 8 (±1). On the opposite, with CXB first at week 4 the rate of cCR and ncCR was already 33%. As well stressed by Habr Gama [START_REF] Habr-Gama | Achieving a Complete Clinical Response After Neoadjuvant Chemoradiation That Does Not Require Surgical Resection: It May Take Longer Than You Think![END_REF], there is a need for a prolonged follow-up period even after 6 months since complete tumor regression can take a long time and proctectomy should not be performed too urgently. It is logical that tumor response is faster in T2 tumor and tumor with small size (than in T3 or large volume). More interesting is the prognostic relevance of a polypoid aspect for rapid response and good local control, as already mentioned by Papillon in the 1970s [START_REF] Papillon | Present status of radiation therapy in the conservative management of rectal cancer[END_REF]. When discussing treatment options for a T2 T3a < 3cm with a polypoid aspect it appears possible to propose a conservative treatment using CXB first in frail but also in fit patients. A rapid cCR observed at week 4 is a strong argument in favor of this initial option. Conversely, the use of EBCRT first is associated with a longer period of uncertainty for oncologists and of anxiety for patient during the first 6 months. The present outcome data may appear better than those published by institutions using a W-W strategy without intracavitary boost reporting a rate of cCR close to 25% with a rate of local relapse at 2 years approximating 20% [START_REF] Martens | Longterm Outcome of an Organ Preservation Program After Neoadjuvant Treatment for Rectal Cancer[END_REF][START_REF] Renehan | OnCoRe project investigators. Watch-and-wait versus surgical resection for patients with rectal cancer -Authors' reply[END_REF][START_REF] Smith | Assessment of a Watch-and-Wait Strategy for Rectal Cancer in Patients With a Complete Response After Neoadjuvant Therapy[END_REF]. In Habr Gama's experience the rates of cCR for T2 and T3 are respectively, 72% and 63% and the rates of local relapse 8% and 40% [START_REF] Habr-Gama | Achieving a Complete Clinical Response After Neoadjuvant Chemoradiation That Does Not Require Surgical Resection: It May Take Longer Than You Think![END_REF]. This difference is probably explained by the different strategies used: in the Nice experience early tumors are treated with high radiation dose with a planned organ preservation whereas in other institutions, more locally advanced tumors are treated with lower radiation dose leading to opportunistic preservation [START_REF] Gerard | Organ preservation for T2-T3 rectal cancer: opportunistic or planned strategy[END_REF]. The Montreal strategy using high dose endoluminal iridium brachytherapy is quite similar to the Nice approach and report similar results for cCR and organ preservation [START_REF] Garant | Image-guided Adaptive Endorectal Brachytherapy in the Non-Operative management of patients with rectal cancer[END_REF]. This study has many limitations. It is a monocentric retrospective analysis of only 61 patients. The main limitation is clearly a significant difference between the two groups regarding baseline tumors characteristics with more locally advanced tumors in the EBCRT group. Part of the difference in tumor shrinkage can be attributed to this imbalance. The ongoing OPERA trial (NCT 02505750) is designed to provide some answers on this question [START_REF] Gerard | Organ preservation for T2-T3 rectal cancer: opportunistic or planned strategy[END_REF]. Although performed throughout this study by the same two radiation oncologists, clinical description and response assessment remain inherently subjective and tumor size measurements whatever the tools used remain uncertain.

Tumor size measurements is difficult to assess and it is possible that the largest tumor diameter could be the most relevant measurement. MRI performed at week 14 and every 3 months subsequently is a standard recommendation but is outside the scope of this article. MRI may assist the decision-making but many experts recognize that a robust way for assessing cCR or local relapse is DRE and endoscopy [START_REF] Maas | Assessment of Clinical Complete Response After Chemoradiation for Rectal Cancer with Digital Rectal Examination, Endoscopy, and MRI: Selection for Organ-Saving Treatment[END_REF][START_REF] Appelt | High-dose chemoradiotherapy and watchful waiting for distal rectal cancer: a prospective observational study[END_REF][START_REF] Gollub | Pelvic MRI after induction chemotherapy and before long-course chemoradiation therapy for rectal cancer: What are the imaging findings?[END_REF].

Organ preservation for rectal cancer is still controversial. The definition of cCR may vary from one center to another [START_REF] Garant | Image-guided Adaptive Endorectal Brachytherapy in the Non-Operative management of patients with rectal cancer[END_REF]. There is a clear need for a common language to describe the clinical tumor responses with either DRE or endoscopy. The optimal time interval for assessing this response [START_REF] Dossa | A watch-and-wait approach for locally advanced rectal cancer after a clinical complete response following neoadjuvant chemoradiation: a systematic review and meta-analysis[END_REF] and appropriate management of ncCR are not standardized [START_REF] Wu | Modulating Both Tumor Cell Death and Innate Immunity Is Essential for Improving Radiation Therapy Effectiveness[END_REF]. Therefore it is possible to stress some potential benefits to be achieved by initiating treatment in early polypoid tumors using CXB first. As there is no need for long planning simulation, CXB treatment can be commenced within a day or a week following the decision. Overall treatment time can be reduced as EBCRT can be initiated after the second CXB session. The dose to the visible tumor (Gross Tumor Volume) can be higher. Taking advantage of a visible tumor, CXB targeting is improved which is not always the case when CXB is given after EBCRT. CXB first may also trigger a better immunological reaction [START_REF] Wu | Modulating Both Tumor Cell Death and Innate Immunity Is Essential for Improving Radiation Therapy Effectiveness[END_REF].

In summary cCR or ncCR are observed more rapidly when the neoadjuvant treatment is initiated with CXB. When selecting early polypoid T2 (T3a) N0 tumor < 3 cm in diameter, using upfront CXB is an option allowing a more favorable outcomes. This strategy can be adopted as the first treatment followed by EBCRT. This combination rapidly provides a high rate of cCR and enables long-term local control with little toxicity. This approach can be proposed as a planned conservative option in wellinformed patients. In all cases, prolonged and strict multidisciplinary surveillance is mandatory. Tables

  patient achieved only PR. On account of the advanced age of the population, 3 patients died during the first year with no detectable rectal tumor. One patient (T3b) after cCR presented a local recurrence 10 months after initiation of treatment and was treated with Hartman surgery. Local recurrence was diagnosed in 7 patients. At 5 years the cumulative incidence of local recurrence was 10 % [95 CI: 1 -18] and organ preservation was seen in 95% of patients. Two local recurrences were observed at year six and seven. The median occurrence time of the 7 local recurrences was 22 months. All these local recurrences were found on DRE and endoscopy (suppl File fig 2 Table

  Taking the cumulative rate of local recurrence at 5 years as the end point in univariate analysis two parameters were significant: T stage: T2 0% [95%CI 0-0]-T3 21% [95%CI 2-26]p-value <0.05 and clinical aspect : polypoid 0%[95%CI 0-0]-fungating 26% [95%CI : 3-44] p-value <0.05. Chronology had no influence : CXB first 6% [95% CI 0-13]-EBRT first : 19% [95% CI 0-36] p-value = 0.68.

FiguresFigure 1 :

 1 Figures

Figure 2 :

 2 Figure 2 : Consort diagram of 168 patients treated using CXB.

Figure 3 :

 3 Figure 3 : Rate of clinical response and time

Figure 4 : 20 Figure 1

 4201 Figure 4 : Tumor Volume and Diameter evolution with time

Table 1 : Tumour response classification

 1

	DRE : digital rectal examination; cCR: clinical complete response ; PR : partial response ; SD : stable
	disease ; TRG : tumor regression grade.

Table 2 : Baseline characteristics of 61 patients (Curative-conservative intent) and treatment

 2

	PS : performance status ; T : tumor; N: node; NK: not known.

In 2009 a grant of 564 868 € was given by the French ANR (Agence Nationale de la Recherche) (ANR-08-TECS-015) to the Centre Antoine-Lacassagne to support the development of the Papillon 50 system.

Highligts


Benoît Iung

Duc-Hanh Dinh

Phuc Do

Benoit Iung

Maintenance optimisation for multi-component system with structural dependence: Application to machine tool sub-system

Keywords: Maintenance, Optimisation, Disassembly

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

Introduction

Reliability is an important key performance indicator in manufacturing systems [START_REF] Colledani | Design and management of manufacturing systems for production quality[END_REF][START_REF] Do | Maintenance grouping for multicomponent systems with availability constraints and limited maintenance teams[END_REF][START_REF] Iung | Opportunistic maintenance based on multi-dependent components of manufacturing system[END_REF]. An accurate assessment of the system's reliability must prove functionality, efficiency, and safety. Reliability is also an appropriate decision indicator for production scheduling, spare parts management, and maintenance optimisation [START_REF] Goyal | Condition based maintenance of machine tools-A review[END_REF]. The reliability assessment becomes more complicated when the system is complex; that is, its many components are economically and structurally interdependent. Economic dependence means that joint (opportunistic) maintenance of several components can reduce cost. Structural dependence implies that component maintenance requires disassembly of obstructing components. Economic dependence was studied and successfully applied in maintenance optimisation [START_REF] Do | Maintenance grouping for multicomponent systems with availability constraints and limited maintenance teams[END_REF][START_REF] Iung | Opportunistic maintenance based on multi-dependent components of manufacturing system[END_REF]. Prior art rarely dealt with structural dependence in maintenance optimisation [START_REF] Iung | Opportunistic maintenance based on multi-dependent components of manufacturing system[END_REF][START_REF] Dao | Selective maintenance of multi-state systems with structural dependence[END_REF]. Most prior work assumed that disassembly would not impact component failure rates. This is not always true in practice.

Disassembly is categorised into three types: non-destructive, semi-destructive, and destructive disassembly [START_REF] Vongbunyong | Disassembly automation[END_REF]. Destructive disassembly deals with the partial or complete destruction of the obstructing components. The semi-destructive approach aims to destroy only connective components and leaving the main components with little or no damage. The non-destructive methods seek to leave components undamaged. These methods can cause undesired damage. The interaction between the faying surfaces of the components or between the components and the tool used to perform the disassembly may cause scratches, deformation, and more. [START_REF] Technologies | Mounting and dismounting of rolling bearings[END_REF]. Such damage increases the likelihood of failure, i.e., it reduces the reliability and operating performance of the affected components [START_REF] Santochi | Disassembly for recycling, maintenance and remanufacturing: state of the art and perspectives[END_REF][START_REF] Dinh | Modeling the impact of disassembly operations on the degradation process of multi-component systems[END_REF].

Component and system failure risk is underestimated if the impact of the disassembly operations on the failure rate of the components is ignored. An inaccurate reliability assessment and maintenance plan can then be expected. Our original approach starts with a model based on a connection matrix using the Proportional Hazard Model. It quantifies the impact of disassembly operations on the component failure rate. An opportunistic maintenance policy is then developed. It considers the impact of disassembly and the economic dependence between components, allowing a more realistic and efficient maintenance plan to develop, that is synchronised with the production plan.

We introduce the failure rate modelling integrating disassembly operations impact in section 2. Our opportunistic condition-based maintenance policy considering both economic and structural dependencies is discussed in section 3. Section 4 illustrates the application of the model and strategy proposed on the spindle of a milling machine. Conclusions and future work are presented in Section 5.

Failure rate modelling with impact of disassembly

System modelling and assumptions

A manufacturing system (i.e. machine tool) or sub-system (i.e. spindle) consists of n interdependent components connected in series, which are economically and structurally interdependent. Components form a hierarchical structure that is illustrated by a directed graph [START_REF] Zhou | Preventive maintenance modeling for multi-component systems with considering stochastic failures and disassembly sequence[END_REF]. (Sub)system components experience hard failure. The degradation alone does not lead to component failure but likely factors into it. The failure rates of component i (i = 1, 2… n) can be described by a Weibull baseline Proportional Hazard Model:

,

/ is the Weibull baseline hazard rate with shape and scale ; ԑ . , is a degradation signal and ԑ is regression coefficient quantifying the impact of degradation on the failure rate of component i. is assumed to follow a linear general path model, i.e., . In which, , and are the initial degradation, degradation rate, and degradation volatility of component i, respectively, B(t) is the standard Brownian motion. This model was extensively studied and successfully applied [START_REF] Hu | Predictive maintenance of systems subject to hard failure based on proportional hazards model[END_REF]. These parameters are either known or estimated based on historical data to model the impact of disassembly operations, reliability assessment, and maintenance optimisation.

The reliability of component i is defined as the probability that component i is still in functioning state at time t. It can be formulated as follows [START_REF] Dinh | Modeling the impact of disassembly operations on the degradation process of multi-component systems[END_REF]: exp ! ", " #" $ %

(2)

Disassembly operations and their impact

Disassembly operations are a process to separate one or several components from the system for offline maintenance [START_REF] Santochi | Disassembly for recycling, maintenance and remanufacturing: state of the art and perspectives[END_REF][START_REF] Hu | Predictive maintenance of systems subject to hard failure based on proportional hazards model[END_REF]. In manufacturing systems, components are inter-connected via connectors. The disassembly operation of a component is defined as a process to disconnect connections in sequence to remove the component from the system and later reassemble the component after maintenance. The connection matrix, & ' () * +, is used to represent the system's structure, whereas, rij indicates whether there is a connection between the two components i and j. The value of the element rij is "1" if a connection exists, and otherwise "0". Figure 1 shows a simple gearbox system with its connection matrix and directed graph. Node 0 represents the whole system, and the numbered nodes (1, 2, 3, and 4) represent the components. The line that connects the node in the upper layers and the node in the lower layer indicates that disassembly of the lower layer node needs disassembly of the upper node first. The arrow between the nodes of the same layer represents the disassembly sequence between the nodes. We assumed that disassembling the connection (i,j) between the two components i and j results in an amount of damage δij on the degradation level of the component i (δji denotes the damage on component j) to model the impact of that disassembly. δij depends on the following factors: -The strength of the connection between the two components, i.e., the more difficult it is to break the connection, the higher is the degree of impact on the component's degradation level. The connection matrix is herein extended to represent the strength of the connection, & ' ,-$,.$ (/ * +. Sij ≥ 0 is the strength of the connection between the two components i and j. / * is deterministic and can be acquired during the design stage. -The properties of the component, i.e., the damage on components made of stronger materials is lower than that of components made of weaker materials. -The method/process used to perform the disassembly. For example, using a mechanical process to dismount bearings impacts damage more than a hydraulic process [START_REF] Technologies | Mounting and dismounting of rolling bearings[END_REF]. The expertise of technicians also influences the impact of the disassembly, δij. The adjustment factor θij is used to reflect the technician's degree of expertise to perform the disassembly of the connection (i,j). θij is likely random and can be described by a normal distribution with mean 0 1 and standard deviation 0 1 . The expected value 0 1 reflects the impact of the disassembly performance of the connection (i,j). The uncertainty endowed with maintenance technician quality is characterised by the corresponding standard deviation 0 1 . δij is expressed in Eq. ( 3).

2 * / * . 3 * /4

Where, 4 5 0 is a factor related to the properties of the component i and is estimated from previous data, life testing, etc. δij follows a normal distribution with mean 7 1 / * . 0 1 /4 and variant 7 1 / * /4 8 0 1 . We assumed that 0 1 is rather small so that the probability for δij < 0 is likely zero. This assumption is valid when only qualified technicians are assigned to carry out complex disassembly operations.

The connections of other components on the disassembly path of the maintained components are also disconnected due to the structural dependence. The disassembly path for each component is assumed to be predefined due to technical constraints. The disassembly path of component h is represented by its disassembly matrix, 9 : (5)

Failure rate modelling with disassembly impact

Each component is subjected to both continuous degradation over time (own degradation) and the damage caused by disassembly operations. The total degradation signal of component i can then be expressed as:

K ∑ = @ A L $ J? (6)
Where N(t) is the number of maintenance events. The failure rate of the component i can be rewritten as: The impact modelling of disassembly operations allows investigating its effect on system reliability and maintenance optimisation.

, K ԑ . ∑ = @ A L $ J? % (

Maintenance policy

A condition-based maintenance policy (CBM) is herein implemented; both economic and structural dependencies between components are considered.

Description of the proposed maintenance policy

The system's components shall be inspected at regular intervals Tk=k.τ (k=1, 2…) with the inter-inspection interval τ that is a decision variable which needs to be optimised. At every inspection, the degradation level of each operating component is

(G k O ∅), component j, F ∉ & J is opportunistically maintained together with group G k if * R JS TR J , & J U V , W X V U 1 ,
Ro is also a decision variable to be optimised. The proposed maintenance policy is illustrated in Figure 3.

Reliability (Lifetime) prediction with disassembly impact

If at inspection event Tk, the component i is still functioning, the reliability of component i at the next inspection, Tk+1 = Tk + τ, will be [START_REF] Dinh | Modeling the impact of disassembly operations on the degradation process of multi-component systems[END_REF]:

R JS |R J exp Z ԑ ! " . " #" $ A[\ $ A ] ( 8
)
If a group G k is maintained at Tk, the reliability of component j is calculated with considering the impact of disassembly of the group G k (see Eq. ( 7) and Eq. ( 8)).

* R JS TR J , & J exp Z ԑ * ! * " * " = *@ A #" $ 1 A S$ 1 A ] ( 9
)

Cost structure and maintenance optimisation

The PM cost for component i can be expressed as: . 9 dE @ A (12) The maintenance duration of the group G k is:

_ W M W` M W M Wa (
b @ A b @ A a ∑ b c ∈@ A (13)
This duration is significantly reduced by a multi-maintenance team [START_REF] Do | Maintenance grouping for multicomponent systems with availability constraints and limited maintenance teams[END_REF]. After failure, when a CM is implicated on component i, it incurs a CM cost:

_ ' M '` M ' M 'a (14) Where, M '`, M ' and M 'a b c b a M 'a , are the corrective setup cost, specific cost and downtime cost, respectively. Three decision variables (τ, Rp, and Ro) need to be optimised. In maintenance optimisation framework, maintenance cost is usually used as the main criterion [START_REF] Do | Maintenance grouping for multicomponent systems with availability constraints and limited maintenance teams[END_REF][START_REF] Iung | Opportunistic maintenance based on multi-dependent components of manufacturing system[END_REF]. A maintenance cost model is herein developed named long-run maintenance cost rate model, and defined as:

_ e b, W , V lim $→e j k ^,l m ,l n $ $ onpq (15)
Where, C t (τ, Rp, Ro) and tdown are cumulative maintenance cost and downtime of the system within the period (0, t]. The long-run maintenance cost rate is rewritten with the renewal theory [START_REF] Ross | Stochastic process[END_REF] as: is the inspection cost; aVx. ∑ b @ A L J?

_ $ rqo b, W , V ∑ j s A Sj t A u Av\ $ rqo $ onpq
; and _ y J is the maintenance cost at the k th inspection. The optimal value of decision variables can be obtained by minimising the long-run maintenance cost rate.

Case study: spindle unit of a milling machine

It is now necessary to concretely illustrate the impact of disassembly operations on the system reliability and maintenance optimisation for a spindle unit of a milling machine [START_REF] Abele | Machine tool spindle units[END_REF][START_REF] Brecher | Developments for high performance machine tool spindles[END_REF]. The case was chosen as part of a collaboration with RENAULT on the maintenance of a 5-axis machine tool (but with anonymised data).

Description of the spindle unit

An internal motor driven spindle unit generally consists of six main components: spindle house, spindle shaft, front bearings, rear bearings, motor, and clamping unit [START_REF] Abele | Machine tool spindle units[END_REF] (Figure 4). The spindle unit is a structurally dependent system. The disassembly matrix of each component of the spindle is shown in Figure 5. The failure rate and degradation parameters of the components of the spindle unit are given in Table 1. The maintenance costs are provided in Table 2. All cost parameters are given in arbitrary units (arbitrary cost unit (acu)). The disassembly duration (in hours) of each connection and the mean and variation of the adjustment factor are presented in Figure 6.

Reliability assessment

With the inspection interval of τ=5, at the inspection Tk=30, the respective age of the components is J 30, 30, 10, 10, 30, 10

and the degradation level is { J 3.2, 2.8, 1.1, 1.0, 2.2, 0.9 .

Suppose that components 3 and 4 (front and rear bearings) are replaced at Tk. Figure 7 shows the predicted reliability of the system at the next inspection Tk+1. It underlines that the disassembly operations associated with the maintenance of components 3 and 4 have a significant impact on system reliability.

Impact of disassembly on the optimum maintenance policy

We assumed that the disassembly operations impact on the failure rate of the components is ignored to study the impact of disassembly operations on the optimum maintenance policy. It means that = *@ A 0 in the failure rate model presented in Eq. ( 6). In this case, the optimal decision parameters are τ* = 5.6 (months), Rp* = 0.67, and Ro* = 0.75. Then the values of these decision variables are applied to the system considering disassembly impact. Consequently, the long-run maintenance cost rate is now 106.6 acu. This is significantly higher than the cost determined in section 4.3 (7.37% increase). The reason is that in section 4.3, the disassembly impact is integrated in the optimisation process to find the optimum maintenance policy, while this is not the case in section 4.4 (the impact is considered after calculation of the optimal parameters). It implies that not regarding structural dependence between components in finding the optimal decision variables can lead to a sub-optimal maintenance policy with potential impact on production time.

Conclusions

Our maintenance model quantifies the impact of disassembly operations on the failure rate of the components with structural dependence. Several factors that influence the impact of disassembly operations can be considered, such as component properties, strength of the connections between components and more. An opportunistic maintenance policy considering both the impact of disassembly and economic dependence is proposed. The case study focused on the maintenance of the spindle unit of a milling machine. It proved that the maintenance plan is suboptimal if the impact of disassembly operations is ignored. We validated the model with real machine tool data to extend our findings to other industrial systems.

Fig. 1 .

 1 Fig. 1. (a)-a gearbox system (b)-its directed graph, and (c)-the corresponding connection matrix.

  (9 * : +, where, 9 * : 1 if connection between the two components (i and j) is on the disassembly path of component h; 9 * : 0 otherwise. The impact of disassembly of component h on the degradation level of component i can then be expressed as: exist among the disassembly paths of different components during the maintenance on a group G k of components. The disassembly path of the group G k should be defined as: 9 @ A 9 * ∪ 9 C ∪ … ∪ 9 E , F, G, … H ∈ & J . The impact of disassembly of group G k on component i is then: = @ A ∑ 2 * .

7 )

 7 Figure 2 (b) illustrates the correlation of the evolution of degradation signal and failure rate of system's components in a 3unit system, with the directed graph of the system shown in Figure 2 (a). The directed graph underlines that component 1 and component 2 are restricted by each other, and the disassembly of one component always means the disassembly of the other, while component 3 is structurally independent of the two other components. At time t1, component 1 is replaced. The degradation signal of component 2 jumps by an amount of δ21 due to the impact of the disassembly operation. The increase of degradation signal results in the increase of failure rate of component 2. Since components 3 is structurally independent from the two other components, the disassembly operations of the latter components do not affect the failure rate of component 3 and vice versa.

Fig. 2 .

 2 Fig. 2. (a)-directed graph and (b)-illustration of the evolution of degradation signal and failure rate of the system's components.

  measured. Each inspection incurs a cost M N . Component failure is self-evident. The maintenance decisions are: • If component i failed between (Tk-1, Tk), corrective maintenance (CM) is performed on component i at time Tk. • If at time Tk, component i is still operating, both preventive maintenance and opportunistic maintenance rules are applied based on the predicted reliability of the components. More precisely: -Preventive maintenance (PM) rule: if the reliability of the component at the next inspection (Tk+1), denoted as Ri(Tk+1|Tk), is less than the fixed preventive maintenance threshold, Ri(Tk+1|Tk)<Rp (Rp is also a decision variable to be optimised), the component is preventively replaced at Tk. -Opportunistic maintenance (OM) rule: if CM and/or PM are implemented on a group G k

Fig. 3 .

 3 Fig. 3. Illustration of the maintenance policy

  [START_REF] Zhou | Preventive maintenance modeling for multi-component systems with considering stochastic failures and disassembly sequence[END_REF] where M W` is the set-up cost for PM and can be shared if several components are maintained together (it represents the economic dependence between components [2]); M W is the specific PM cost of component i; M Wa b c b a . M Wa is the maintenance downtime cost with the PM downtime cost rate; M Wa , b c , and b a are the replacement and disassembly duration of components i. The disassembly duration of component i is calculated based on its disassembly path: Where, b dE is the disassembly duration of the connection (u, v).Similarly, disassembly duration of a group of components G k is:

  , ,.a w. b is the length of the first life cycle of the system; N is the number of inspections in the first life cycle; _ N J ∑ M N . ?

Fig. 4 .

 4 Fig. 4. a-A sketch of an internal motor spindle, b-its directed graph and c-its extent connection matrix.

Fig. 5 .

 5 Fig. 5. Disassembly matrix of spindle componentsTable 1. System parameters Parameters Components βi λi (months) Ԑi αi μi σi ki

Fig. 6 .

 6 Fig. 6. (a)-mean and (b)-variation of adjustment factor for each connection, (c)-disassembly duration of each connection

Fig. 7 .Fig. 8 .

 78 Fig. 7. System reliability with the disassembly impact

Table 1 .

 1 System parameters

	Parameters Components	βi	λi (months)	Ԑi	αi	μi	σi	ki
	1. Spindle house	5	60	0.15 0 0.09 0.02 1.8
	2. Spindle shaft	3	50	0.3	0 0.08 0.02 1.6
	3. Front bearings	2	12	0.4	0 0.01 0.03 0.8
	4. Rear bearings	2	12	0.4	0 0.01 0.03 0.8
	5. Motor	4	60	0.3	0 0.08 0.02 2.5
	6. Clamping unit	2	20	0.35 0 0.09 0.02 0.9

Table 2 .

 2 Maintenance cost parameters

	Parameters Components	M	W	M W` M Wa	M '	M '`	M 'a	M N	b c (hour)
	1. Spindle house 100			500			10	4
	2. Spindle shaft	120			600			25	5
	3. Front bearings 4. Rear bearings	60 60	50	20	300 300	200 100	15 15	1 1
	5. Motor	120			600			20	4
	6. Clamping unit 100			500			15	2


Dr Sara Romano-Bertrand
email: sara.romano-bertrand@umontpellier.fr

Ludwig-Serge Aho Glele

Bruno Grandbastien

Didier Lepelletier

Preventing SARS-CoV-2 transmission in rehabilitation pools and therapeutic water environments

Summary

SARS-CoV-2 is mainly transmitted by respiratory droplets and contact with contaminated surfaces. It can be retrieved in faeces but there is no evidence of faecal-oral transmission, which is the main route of contamination in recreational waters. Standard cleaning and disinfecting procedure, microbiologic control and health rules aim to prevent infectious risk regardless of the microorganisms. In the context of progressive lockdown exit and hospital activities recovery, we assessed the risk of SARS-CoV-2 transmission in rehabilitation pools and therapeutic water environments in order to provide specific recommendations to control the spread of SARS-CoV-2 while ensuring essential rehabilitation cares for patients.

Key-words: coronavirus; COVID-19; waterborne infection; oral-faecal transmission; viral pandemic SARS-CoV-2 is mostly transmitted by droplets and contact with contaminated surfaces but can also be retrieved in high load in feces [START_REF] Wang | Detection of SARS-CoV-2 in Different Types of Clinical Specimens[END_REF]. It is mainly responsible of both respiratory and gastrointestinal symptoms but there is no evidence of SARS-CoV-2 faecal-oral transmission to date [2]. A recent research letter suggested a possible cross-transmission of SARS-CoV-2 between 9 patients via bathing in a public bath centre [START_REF] Luo | Possible Transmission of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) in a Public Bath Center in Huai'an, Jiangsu Province, China[END_REF], underlining the need to implement specific measures to prevent this risk. In the context of progressive hospital activities recovery, we assessed the risk of SARS-CoV-2 transmission in rehabilitation pools and therapeutic water environments in order to protect patients and healthcare workers from COVID-19. To do so, we reviewed the current literature on SARS-CoV-2 sustainability in water environments. We also made an overview on risk and likely causes of viral cross-transmission in swimming pools. The different methods for swimming pool water disinfection in order to maintain its microbiological quality were described. According to this risk assessment strategy, we proposed pragmatic recommendations to control the risk of SARS-CoV-2 cross-transmission while preserving essential rehabilitation cares for patients.

SARS-CoV-2 sustainability in water environments

SARS-CoV-2 environmental sustainability is conditioned by the initial viral load, the type of support, the residual humidity, the temperature and the presence of biologic fluids. SARS-CoV-2 survival conditions in biologic fluids are not transposable to recreational water and there are no current data on SARS-CoV-2 stability in water environments such as swimming pools. However, coronaviruses seem instable in water environment and are very sensitive to chlorine [4]. Enveloped virus including influenza viruses and coronaviruses, are too sensitive in environment and too rapidly inactivated in water to be transmitted within swimming pools; this is converse to naked viruses such as adenoviruses, noroviruses, enteroviruses or hepatitis A virus, that are usually more resistant and able to survive several days in water, even when treated by biocides such as chlorine, ozone or bromide [START_REF] Rosa | Coronavirus in water environments: Occurrence, persistence and concentration methods -A scoping review[END_REF][START_REF] Bonadonna | A Review and Update on Waterborne Viral Diseases Associated with Swimming Pools[END_REF]. Accordingly, water from swimming pools does not appear favourable for survival of SARS-CoV-2.

Swimming pools and risk assessment of viral cross-transmission

Most outbreaks related to contaminated recreational waters are caused by oral-faecal transmission of enteric viruses [START_REF] Sinclair | Viruses in recreational water-borne disease outbreaks: A review[END_REF][START_REF] Barna | The risk of contracting infectious diseases in public swimming pools. A review[END_REF]. Investigating water-borne viral outbreaks is hampered by the requirement to sample very large volumes of water (1,000 to 2,000 L), which helps explain why the causative virus is identified in water in less than 28% of cases.

Viruses can contaminate swimming pools for various reasons including inadequate compliance with disinfection procedures due to technical failures or human factors (lack of, or incompetent, maintenance); lack of a warning system; or faecal soiling by infected users.

Although few specific data are available, the same risks apply to rehabilitation pools and therapeutic water environments.

Viruses are not able to replicate on inanimate supports out of host tissues and cells.

Consequently, the presence of viruses in water of swimming pools is directly linked with contamination by bathers that excreted biologic fluids such as saliva, mucus, vomit or faeces (http://www.who.int/iris/handle/10665/43336). Ingestion by the oral route remains the most frequent route of viral transmission in water, but the ocular mucosa may also be an important a portal of entry for SARS-CoV-2 [8,9], possibly contributed to by irritation caused by chemical products used for disinfecting water. Skin lesions (injury, barrier disruption) may also allow viral entry, possibly contributed to by the skin softening that occurs with prolonged immersion in water; however, this mode of transmission has not been demonstrated for SARS-CoV-2. wearing of goggles or face shield in case of close contact with patient # Disinfection of common surfaces at both opening and closure of pools, and disinfection of dressing rooms and high touch surfaces between patients. Recommended disinfectants are 0.5% bleach, 70° alcohol or usual disinfectant with virucidal activity according to the norm EN14464+A2 (July 2019). * by reviewing clinical record of patients. ° because it appears impossible to cough and sneeze in elbow when bathing, we recommend to use hands then immediately perform hand hygiene by washing hands with soap and water for at least 30 seconds as the use of hydro-alcoholic solution is not recommended on wet hands.

Table I : Prevention measures of SARS-CoV-2 transmission in rehabilitation pools and therapeutic water environments Specific recommendations

 I For technical staff Ensure the proper application of standard guidance from the French Public Health Code in order to prevent from microbiologic risks in pools • appropriate procedure of water disinfection using chlorine or other disinfecting product

		• •	monitoring physicochemical indicators monthly microbiologic control of water
		•	pool closing and maintenance operation in case of non-conformity frequent surfaces disinfection with appropriate product #
	For patients	Ensure the respect of hygiene and behavioral rules before entrance in pools • use individual dressing rooms • clothes storage on hangers in individual dedicate compartments • shower using soap and water (before and after bathing) • booth bath • wearing of swim cap • wearing of swimming goggles
		Avoid access to bathers suspect or affected of COVID-19 *
		Avoid or restrict access to bathers presenting respiratory and/or digestive symptoms *
		Ensure that bathers respect strictly barrier measures in order to prevent cross-transmission outside of pools • strict hand hygiene at the entrance in the building and in case of bathroom use • surgical mask wearing until reaching the dressing room and once dressed after bathing • physical distancing of at least one metre • sneeze and cough into hands then directly wash their hands with soap and water ° • avoid touching face, nose, mouth and eyes
	For healthcare workers	Ensure the strict respect of barrier measures in order to prevent cross-transmission outside of pools • surgical mask wearing • physical distancing of at least one metre • regular hand hygiene • avoid touching face and eyes •

Standards of cleaning and disinfection procedure in swimming pools

Strict standards apply for treating water and maintaining its quality in swimming pools. In both public and hospital swimming pools, the water must be filtered and disinfected, and must meet physical, chemical and microbiological qualities defined by the French Public Health Code [START_REF]Règles sanitaires applicables aux piscines[END_REF]. The Code also defines the required frequencies of monitoring of physicochemical and microbiological indicators, and the processes for pool closure and maintenance operations in case of non-conformity.

Disinfectant added to water must kill or inactivate microorganisms while preserving skin, eyes and mucosa integrity. Chlorine is usually used because of its cost-effectiveness, easy use and safety (https://www.cdc.gov/coronavirus/2019-ncov/php/water.html). Measures of cleaning and disinfecting must be accompanied by strict hygiene and behavioral rules for bathers, along with the respect of capacity limit of bathers, which cannot be higher than 3 per 2m [START_REF] Luo | Possible Transmission of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) in a Public Bath Center in Huai'an, Jiangsu Province, China[END_REF] of water in open-air recreational waters, and 3 per m 3 in covered swimming pools [START_REF]Règles sanitaires applicables aux piscines[END_REF].

Specific preventive measures regarding SARS-CoV-2 transmission

The first line of prevention of SARS-CoV-2 transmission is based on barrier measures including hand hygiene, physical distancing, and respiratory hygiene (wearing of a mask, covering the mouth and nose appropriately when coughing or sneezing). However, these precautions are difficult or impossible to apply by patients when bathing. We propose here a range of specific measures for pools used for rehabilitation care to protect bathers and healthcare workers from SARS-CoV-2 (Table I). Ensuring safety begins with reviewing clinical records to ensure that patients have no symptoms of COVID-19, followed by use of barrier precautions and social distancing, especially in dressing rooms. Indeed, the main risk of SARS-CoV-2 cross-transmission is through respiratory droplets and contact with contaminated surfaces, and strict application of barrier measures is the best way to prevent transmission. Hand hygiene measures include appropriate provision of hydro-alcoholic solution for use on dry hands, but also soap and water for washing wet hands.

All these recommendations are based on the guidelines issued by the French Society for Hospital Hygiene (https://www.sf2h.net/wp-content/uploads/2020/03/Avis-SARS-CoV-2-eteau-de-piscine-SF2H-09.03.2020.pdf) and are applicable to therapeutic pools and other therapeutic water environments. Meeting usual pool disinfection standards, together with appropriate individual behaviours in the pool should be sufficient to prevent a risk of waterborne transmission of SARS-CoV-2 (https://www.wef.org/news-hub/wef-news/thewater-professionals-guide-to-the-2019-novel-coronavirus/). These precautions must be accompanied by strict respect of barrier measures by both patients and healthcare workers outside of the pool. All these measures may also be applicable to public and private swimming pools in order to control the transmission of SARS-CoV-2 in the community.