H Guo

T Kooyman

P Sciora

L Buiron

Application of Minor Actinides as Burnable Poisons in Sodium Fast Reactors

Keywords: burnable poison, minor actinides, reactivity control

The reduction of the initial excess reactivity in fast reactor cores would enhance their inherent safety level as it would reduce the impact of a control rod withdrawal accident and lower the requirements on the absorption ability of control rods design. Compensation for burn-up reactivity loss is considered as a possible solution to limit initial excess reactivity. Minor actinides challenge the long-term nuclear waste management. Minor actinides can be transmuted from "absorber" isotopes to "fissile" isotopes, which show the possibility of their application as burnable poisons.

Two loading modes of minor actinides as burnable poisons are considered in this paper: the first one, denominated homogenous mode, mixes minor actinides with all the fuel and the second one, denominated hybrid mode, packages minor actinides in independent pins in the fuel assemblies. The content of americium or neptunium in these two designs is considered with regards to current technological feasibility, including burn-up, cladding stress, decay heat and the neutron source of the assemblies considered here. Both these two modes are able to compensate for the reactivity loss of an industrial power core and thus reduce excess reactivity at the beginning of cycle. The application of these designs in the cores with higher reactivity loss will be considered in next step work.

The impact of minor actinides loading on the core characteristics, including power distribution, material balance and feedback coefficient, are considered from the assembly level to the core level. The hybrid mode shows better management feasibility while the use of neptunium exhibits lower impacts on the current fuel recycling.

Key words: fast reactor,

Introduction

In our previous paper, boron carbide coupled with moderator is applied as burnable poison (BP) in a sodium fast reactor (SFR) to reduce core excess reactivity at the beginning of an equilibrium cycle (BOEC) and thus to reduce the effect of an inadvertent control rod withdrawal (CRW) [START_REF] Guo | Improvement of sodium fast reactor control rods calculations with APOLLO3[END_REF]. Now we seek to investigate a new burnable poison design.

As discussed in the previous paper [START_REF] Guo | Improvement of sodium fast reactor control rods calculations with APOLLO3[END_REF], the candidates for the burnable poison should have a negative contribution to the chain reaction at the beginning of irradiation and this negative contribution must be reduced under irradiation or even be converted into positive contribution. The contribution to chain reaction of isotope i can be defined by plutonium equivalence w i as [START_REF] Bussac | Traité de neutronique: physique et calcul des réacteurs nucléaires avec application aux réacteurs à eau pressurisée et aux réacteurs à neutrons rapides[END_REF]:

𝑤 𝑖 = σ 𝑖 + -σ U 238 + σ Pu239 + -σ U 238 +
Where σ 𝑖 + is defined as 𝑣σ 𝑖 fission -σ 𝑖 absorption . In a classical SFR using plutonium based mixed oxide (MOX) fuel, 239 Pu and 238 U are chosen as the reference fissile and fertile isotopes because they are the principal contributors to the chain reaction.

As plutonium is re-used in a closed fuel cycle, long-term behavior of nuclear waste is driven by minor actinides (MA) [START_REF] Kooyman | A comparison of curium, neptunium and americium transmutation feasibility[END_REF], which challenges the recycling process and long-term underground storage because of their long half-life, high activity and important decay heat. The main minor actinides from current spent fuel are 237 Np, 241 Am and 243 Am.

The evolution chain of actinides is shown in Fig. 1 with their plutonium equivalence calculated for an oxide SFR neutron spectrum (See Section2.1). The evolution of plutonium equivalence of interesting isotope and their by-products under irradiation of fast spectrum is shown in Fig. 2 in which the fluence 6.010 23 n/cm 2 is corresponding to 3000 days irradiation of 2.4×10 15 n/cm 2 /s. The isotopes 237 Np, 241 Am and 243 Am can be considered as "absorbers" in SFR due to their negative contribution to the chain reaction in fast spectrum. After neutron irradiation and decay, they can be transmuted into isotopes that have a positive contribution or "less negative" contribution to the chain reaction.

This transmutation from absorber isotopes to "fissile" isotopes reveals the possibility to use minor actinides as burnable poison in SFR. Therefore, this paper is aimed at studying the application of minor actinides as burnable poisons in fast reactors. The loading of minor actinides in the cores, the performance for the burnable poison objective and the impact on the core characteristics will be investigated.

Section 2 presents the calculation methods and the cores used here for the application of minor actinides as burnable poisons. The options used to load minor actinides in the core are discussed in Section 3.1 along with the various minor actinides feed available for use as burnable poisons. The burnable poisons designs are descripted in Section 3.3. The reactivity compensation ability of these designs is presented in Section 3.4, which demonstrates the capacity of minor actinides to be used as burnable poisons. Then, the design of these assemblies is analyzed to verify their feasibility with regards to current technological requirements (See Section 3.5). Finally, the impact of minor actinides loading on the core behavior is discussed in Section 3.6.

Methodologies

Reference core: SFR-V2B

A core similar to the one described in our previous paper [START_REF] Guo | Improvement of sodium fast reactor control rods calculations with APOLLO3[END_REF] and known as SFR-V2B SFR-V2B (3600 MWth) has been chosen as the target core in this work to apply minor 4 actinides as burnable poison. This core has been deeply studied to achieve objectives defined for Generation-IV reactors [START_REF] Mignot | Studies on french SFR advanced core designs[END_REF]Sciora et al., 2009). The objective of the burnable poison studied in the following is to reduce the reactivity loss for SFR-V2B to zero.

As shown in Fig. 3, SFR-V2B has 267 inner core assemblies and 186 outer core assemblies. After one cycle irradiation (410 Equivalent Full Power Days), 1/5 th of the core is refueled. The fuel assembly residence time in the core is 2050 EFPD and the average discharge burn-up is around 100 GWd/t. SFR-V2B has two independent control rods systems: CSD (Control Shutdown System) and DSD (Diverse Shutdown System). We recall that the reference SFR-V2B core has 1177 pcm of excess reactivity at BOEC of which 427 pcm are reserved for the burn-up reactivity loss while 750 pcm are reserved for operation margin and uncertainty margin. CSD2 (control rod at the interface inner and outer core) are inserted 25 cm at BOEC and be withdrawn slowly to compensate for burn-up reactivity loss.

Calculation scheme

Accurate and high performance neutronic simulation is the key for the evaluation of these innovative designs. The complex geometries of heterogeneous assemblies and the complete depletion chains for various isotopes should be considered for their depletion calculation. After careful consideration of the advantages and drawbacks of various tools, the recent deterministic code APOLLO3 [START_REF] Coquelet-Pascal | APOLLO3®: A common project of CEA, AREVA and EDF for the development of a new deterministic multi-purpose code for core physics analysis[END_REF] is chosen for the neutronic simulations carried out in this paper.

The calculation scheme includes two steps [START_REF] Guo | Improvement of sodium fast reactor control rods calculations with APOLLO3[END_REF]: lattice calculation to generate homogenized/collapsed cross-sections libraries and core calculation. The TDT (Three Dimensional Transport solver, coupling Collision Probability Method and Method of Characteristic) [START_REF] Archier | Validation of the Newly Implemented 3D TDTMOC Solver of APOLLO3 Code on a Whole 3D SFR Heterogeneous Assembly[END_REF] based lattice calculation is able to simulate complex geometries with exact geometrical description and thereby compute accurate spatial self-shielding effects. A multi-group cross-section library tabulated with burn-up information of the calculated assembly is produced in the lattice step. Then, the S N solver MINARET [START_REF] Moller | Minaret, a deterministic neutron transport solver for nuclear core calculations[END_REF] is used for 3D complete core simulation. The tabulated cross-section scheme improves significantly the accuracy of depletion calculation because it is able to transfer the variations in self-shielding from the lattice step to the core step, which is necessary for materials with significant change in absorption ability such as minor actinides and boron carbide. Such a scheme was already used and qualified in [START_REF] Guo | Improvement of sodium fast reactor control rods calculations with APOLLO3[END_REF] for the design of innovative control rod designs.

Results and discussion

Minor actinide loading modes

There are different approaches to load these minor actinides in the core. The minor actinides can be loaded in special target assemblies located at the core periphery, which is the so-called heterogeneous transmutation mode. These special target assemblies can have flexible cycle length and limit the negative impacts of minor actinide loading on the fuel cycle since they can be recycled separately from the core fuel. Since the flux level at the core periphery is insufficient to ensure high transmutation performances, the addition of moderators has been proposed to accelerate transmutation [START_REF] Grouiller | Minor actinides transmutation scenario studies with PWRs, FRs and moderated targets[END_REF][START_REF] Kooyman | A comparison of curium, neptunium and americium transmutation feasibility[END_REF]. However, this loading mode would not be considered for burnable poison objective because the impact of minor actinides is limited by the low flux level. Moreover, the absorbers consumption and generation of fissile materials at the core periphery would increase the neutron leakage, which would reduce the positive contribution to the reactivity from the transmutation of minor actinides.

The homogeneous mode, which involves mixing minor actinides directly within the fuel, is also considered to take advantage of the high flux level in the core center. This approach would not modify the power distribution but would have a potential negative effect on the core feedback coefficients such as the sodium void worth and the Doppler constant [START_REF] Palmiotti | Impact of the Core Minor Actinide Content on Fast Reactor Reactivity Coefficients[END_REF]. Due to the important decay heat, activity, neutron source of minor actinides, this would increase the complexity of the entirety of the fuel cycle. These two modes to load minor actinides have been investigated in depth for transmutation purpose (OECD, 2012).

This work discusses a third option in which minor actinides are loaded in dedicated pins inside all fuel assemblies in the core as shown in Fig. 4. These pins with minor actinides are irradiated in a high flux environment and could theoretically be separated from other fuel pins before dissolution. However, their impact on the "safety" performances of the core should be considered with care. As this loading mode separates minor actinides from the other fuel pins (as in the heterogeneous) mode but load minor actinides in all the fuel assemblies (as homogeneous mode), it will labelled as "hybrid" mode in the following. This hybrid mode is investigated for burnable poisons objective in this paper to limit the reactivity swing of a fast reactor. Regarding the significant experience in MOX fuel manufacturing, the hybrid mode relies on the use of uranium oxide (UOX) as a matrix to incorporate the minor actinides in the oxide form, UAmO 2 or UNpO 2 . In the present study, the hybrid mode substitutes only 6 MOX pins with minor actinide pins for a first step of investigation.

The sensitivity study to the number of UAmO 2 or UNpO 2 pins is currently ongoing. Moreover, this hybrid mode enables independent pins to improve local neutronic characteristics such as MgO-and ZrO 2 -based fuel [START_REF] Ronchi | Thermophysical properties of inert matrix fuels for actinide transmutation[END_REF] or even the use of local moderator materials, which will be investigated in the future.

Both the homogeneous and hybrid approaches burnable poison performances will be investigated in this work.

Minor actinides content for different loading modes

This section will discuss the acceptable content of neptunium and americium in MOX matrix (corresponding to the homogeneous mode) or in UOX matrix (corresponding to the hybrid mode) to meet technological requirements on SFR fuel. The fuel of SFR-V2B, with 15 %wt plutonium recycled form PWR MOX fuel (See Table 1) in uranium oxide is taken as reference MOX fuel. According to [START_REF] Coquelet-Pascal | APOLLO3®: A common project of CEA, AREVA and EDF for the development of a new deterministic multi-purpose code for core physics analysis[END_REF], the neptunium is considered as 100 % 237 Np while americium is considered as 75 % 241 Am and 25 % 243 Am in the following work. Beside depleted uranium and reference SFR MOX, several minor actinide oxides are tested as independent pins in SFR-V2B fuel assembly using the APOLLO3-TDT solver [START_REF] Schneider | APOLLO3: CEA/DEN deterministic multi-purpose code for reactor physics analysis[END_REF] and DARWIN-2.3 code [START_REF] Tsilanizara | DARWIN: An Evolution Code System for a Large Range of Applications[END_REF] to evaluate their characteristics under irradiation in a typical SFR neutron environment and during cooling in the fuel reprocessing stage. There are multiple criterions that should be considered during the life of a fuel assembly from fabrication, irradiation, in-site cooling, transport, reprocessing to waste storage [START_REF] Chabert | Impact of minor actinide transmutation options on interim storage and geological disposal: The French Case[END_REF].

The main gases released from reference SFR MOX fuel are gaseous fission products in the form of Kr, Xe and I 2 . Oxide fuel requires closed pin design and thus the gas production must be limited to avoid over-pressurization of the pin. The gas release is not a significant issue to limit content of neptunium compared to decay heat. However, significant helium production will occur in the long transmutation chain of 241 Am, mainly due to the decay of short-lived 242 Cm, which is produced by capture on 241 Am. In order to comply with the maximal cladding stress (i.e. 120 MPa Tresca stress), the americium content is limited to 2.3 %wt in MOX matrix and 5.9 %wt in UOX matrix. The pressure allowance can be increased by extending the expansion room and adapting pins size, while this option is not considered in this paper.

After irradiation, the main technological requirements are related to decay heat, activity and neutron source limitations at the reprocessing stage. In the SFR-V2B case, the spent fuel is first moved to internal storage positions in the reactor vessel 15 days after the core shutdown. Then the spent fuel is cooled in the reactor vessel for about one fuel cycle, which is around 450 days including some operation time. Finally, it is washed and moved to a cooling pool for 5 years before being transported to the reprocessing plant. The decay heat per gram of fuel is used to consider not only global heat removal for fuel assembly but also local effect on special pins such as for the hybrid mode [START_REF] Chabert | Impact of minor actinide transmutation options on interim storage and geological disposal: The French Case[END_REF]:

 A 0.25 W/g (40 kW per assembly) limit for assembly handing inside the reactor vessel (15 days cooling)  A 0.047 W/g (7.5 kW per assembly) limit for removal of the residual sodium in the assembly before it can be stored under water (operated after 450 days cooling in vessel, which is one SFR-V2B fuel cycle combined with refueling outage time) The neptunium and americium mass content in UOX matrix (hybrid mode) is limited respectively to 16.3 %wt and 5.2 %wt by the 7.5 kW requirements for out-of-vessel removing. Their content in MOX matrix (homogenous mode) is further limited to 9.5 %wt for neptunium and 3.0 %wt for americium. These requirements could be lessened by improving fuel handing technologies or increasing the cooling time before operation.

The limitations on the activity and neutron source strongly depend on the industrial approach considered and the associated data is generally proprietary. The neutron source will not challenge the neptunium case, but it would be the most limiting factor in the 243 Am case due to the high intrinsic neutron source of accumulated 244 Cm, which is produced by capture on 243 Am.

One advantage of the hybrid mode discussed here is that the UNpO 2 or UAmO 2 pins can be recycled separately in dedicated plants, which would minimize the impact on the fuel cycle especially for activity and neutron source aspects.

In summary, as shown in Table 2, the neptunium content is limited to 9.5 %wt for homogeneous mode (MOX matrix) and 16.3 %wt for hybrid mode (UOX matrix). The americium content is limited to 2.3 %wt for homogeneous mode and 5.2 %wt for hybrid mode. The most limiting requirement is the decay heat removal that requires improvement on the fuel cooling technologies. This discussion is based on loading minor actinides in UOX or MOX to satisfy current technological requirements that vary with designs and technological options. Therefore, this discussion gives only coarse estimations and it is necessary to carry out several calculations assess the feasibility of detailed designs in Section 3.5. Remarks: DH means that this content is limited by decay heat; GR means that this content is limited by gas release.

Design description

Using the loading modes detailed in section 3.1, this paragraph presents 6 burnable poison designs with minor actinides that will be investigated in the following sections. These designs are based on depleted uranium oxide with different content in plutonium or minor actinides. Table 3 summarizes the designs of fuel assembly in the inner core. The plutonium content is adjusted to obtain the same end of equilibrium reactivity as for the reference case that is about 750 pcm to cover uncertainty and operation margin. For each burnable poison design, the outer core is also loaded with burnable poisons but with a higher plutonium content to optimize power distribution. In the reference core, the ratio of plutonium content between outer core and inner core is 1.19. Since the minor actinides are loaded in the entire core and only lead to small differences on plutonium content from the reference core, all burnable poison designs keep the same ratio to optimize power distribution.

MABP1 and MABP2 are related to the homogeneous mode to load neptunium while MABP3 and MABP4 load americium. The 0.77 %wt content is chosen to enable MABP1 with enough ability to compensate for the reactivity loss for SFR-V2B (See Section 3.4). MABP3 load the same content in americium for comparison purpose. MABP4 loads the maximal content (2.32 %wt) of americium to show the maximal potential reactivity compensation ability. Current technologies enable higher content of neptunium, but only the conservative loading is considered in MABP2 for comparison purpose with americium.

MABP5, MABP6 and MABP7 use hybrid mode with 6 independent pins in maximal content of minor actinide. The characteristics of all these fuel pins are investigated in this paper to assess their feasibility within the current industrial limitations (See Section 3.5).

Reactivity compensation ability

The reactivity at BOEC and EOEC (both with the control rods parked at the top of fissile zone) of the reference case and different designs with burnable poisons are listed in Table 4 in which the minimal excess positive reactivity of core is set at about 750 pcm by adjusting the plutonium content. The reactivity variation is defined as the difference of reactivity between EOEC and BOEC. The compensation ability, the key parameter to evaluate the capability of burnable poisons, is the difference in the reactivity variation compared to reference case.

For the reference case, the core reactivity decreases from 1177 pcm to 750 pcm. This reactivity loss is compensated by withdrawing the CSD2 from 25 cm insertion to the top of the fissile zone. The MABP1 is an ideal burnable poison design for SFR-V2B, because its negative reactivity contribution decreases at the same rate as the excess positive reactivity of the core is depleted. There is no excess positive reactivity during all the cycle. For MABP1, SFR-V2B requires no control rods movement to compensate for the burn-up reactivity loss.

The core reactivity of MABP2, MABP3 and MABP4 increases with its burn-up. As self-breeder core, the initial SFR-V2B design becomes breeder core when a large amount of MA is introduced. These three designs are not adequate for fine tuning purpose regarding the low reactivity swing of SFR-V2B. However, this kind of solution could be interesting for a larger reactivity swing in case of plutonium quality change or core design adaptation (start-up core, fleet deployment stage, etc.). For instance, these burnable poison configurations could be tested for the ASTRID core for which the reactivity loss is around 1400 pcm per cycle [START_REF] Chenaud | Status of the ASTRID core at the end of the pre-conceptual design phase 1[END_REF]. MABP5, MABP6 and MABP7 configurations are less "efficient" compared to MABP1, but they also reduce the BOEC excess reactivity. For these hybrid modes, the minor actinides content is limited unless improvement on the fuel handing and reprocessing technologies can be achieved. However, the number of UAmO 2 or UNpO 2 pins could be increased to improve their compensation ability. This option requires further investigation. Firstly, as shown in Fig. 1, 241 Am, which as a plutonium equivalence of -0.35, has a more negative contribution to the chain reaction than 237 Np for which the plutonium equivalence is -0.29. The one-group capture cross-section for 241 Am and 237 Np are respectively 1.85 barn and 1.61 barn. Moreover, the capture product of 241 Am is 242 Am which has a plutonium equivalence of 2.19 while the production of 237 Np is 238 Pu, which the plutonium equivalence is 0.66. Consequently, americium has better compensation ability than neptunium if the same quantity is loaded. However, a higher content of neptunium is allowed due to the issues on the gas release, decay heat and neutron source. As discussed in Section 3.2, the maximum content is 10 %wt for neptunium using homogeneous mode while it is only 3 %wt for americium. Therefore, with the current technological limitations, neptunium has equivalent or even better compensation ability compared to americium.

With 0.77 %wt addition of neptunium in all the fuel assemblies, the reactivity variation for SFR-V2B case is close to zero. A 2.32 %wt addition of americium in all the fuel shows compensation ability about 1500 pcm. With 6 fuel pins (among 271) substituted by U 0.82 Np 0.18 O 2 or U 0.94 Am 0.06 O 2 pins, the hybrid mode shows a large compensation ability. Among designs investigated in this paper, the homogeneous mode shows a better compensation ability than the hybrid mode. However, hybrid approach is more efficient than homogeneous approach in terms of compensation ability per unit of minor actinides loaded. For instance, the quantity of neptunium in the hybrid mode with 6 independent pins (MABP6) is only 55 % of that the homogeneous mode with 0.77 %wt addition in all the fuel (MABP1), but the compensation ability of MABP6 is 87 % of that with MABP1.Moreover, the high content of minor actinides in independent pin would reduce the manufacturing constraints and give additional flexibility to adjust the quantity of minor actinides.

Technological feasibility of fuel assemblies

Section 3.2 has discussed preliminarily the expected minor actinide content in homogeneous mode or hybrid mode. In this section, the characteristics designs in Table 3 are analyzed under neutron irradiation and during cooling to investigate their technological feasibility in current industrial background. Beside the reference fuel pin, only the pins with addition of minor actinides from MABP2, MABP4, MABP6 and MABP7 are investigated in the following because their technological feasibility is currently not guaranteed.

The characteristics of fuel assembly of these designs are calculated with APOLLO3 TDT solver in an infinite lattice from 0 GWd/t to 150 GWd/t at 50 watts per gram of heavy nuclei which is equivalent to the average value in the reference core. The compositions of irradiated materials 100 GWd/t are fed to DARWIN for the long-term cooling performance analysis.

Flux and power distribution in assembly

The flux and power distribution in the reference SFR fuel assemblies are quite flat during the whole irradiation time. The homogeneous mode has no influence on the spatial flux and power distribution because the minor actinides are added into every fuel pin. However, the hybrid mode adds significant amounts of minor actinides in selected pins, which will influence the power distribution in the assembly. Therefore, this section is devoted to compare the flux and power distribution in MABP6 and reference fuel assembly.

The Fig. 5 shows the spatial distribution of the discrepancy in flux between MABP6 assembly and reference assembly i.e.

𝑣 𝑀𝐴𝐵𝑃6 -𝑣 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑣 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 × 100. The independent pin with 18 %wt

237 Np increase has no significant influence on the flux distribution at different burn-up level.

The average linear heat rating in the pins of the reference designs or the designs with homogeneous mode is around 299 W/cm. However, for the fuel pin as 18 %wt Np in UOX matrix (MABP6), the linear heat rating increases from 140 W/cm at 0 day to 334 W/cm at 2000 days. Similarly, the linear heat rating increases from 92 W/cm to 266 W/cm for the fuel pin with 6 %wt Am content in UOX matrix (MABP7). The linear heat rate in the burnable poisons pins appears as acceptable compared to the maximal heat rate in the core. The impact of pins with minor actinides on its neighboring fuel pins is not significant. The loading of additional independent pins with minor actinides is feasible but may require some design modifications in order to limit their linear power rate variation during irradiation

Characteristics under irradiation

Based on current fuel technological limitations, the designed average burn-up for SFR-V2B is about 100 GWd/t while maximal burn-up is 150 GWd/t. The local burn-up of a fuel pin and of a minor actinide bearing pin at a similar position in the core is compared in Fig. 7. The burn-up of fuel pins with minor actinides in homogeneous mode varies almost the same as reference fuel pin because the power distribution is flat in all the fuel assembly for homogeneous mode. Yet, the burn-up of U 0.82 Np 0.18 O 2 or U 0.94 Am 0.06 O 2 pin in the hybrid mode is lower than that the one of reference pins although the power in these pins increases significantly along the irradiation.

Fig. 7. Evolution of burn-up under irradiation

As shown in Fig. 8, the fuel centerline temperature for U 0.82 Np 0.18 O 2 or U 0.94 Am 0.06 O 2 pin increases significantly with irradiation but remains always lower than the melting temperature. Finally, the melting margin for the fuel assembly of MABP6 is reduced 200 K compared to reference fuel assembly, which require future works to improve the heat transfer or to limit linear heat rating in the pins with minor actinides. Reference MOX MOX + 2.32% Np (MABP2) MOX + 2.32% Am (MABP4) UOX + 18% Np (MABP6) UOX + 6% Am (MABP7)

The gas pressure in these pins is presented in Fig. 9. The pressure for the cases with addition of americium is 20 % higher than the one that of reference pin, but still close to maximal allowance, because of helium released from 242 Cm decay.

Consequently, for the criterions of burn-up, margin to temperature and gas release, these designs satisfy current technological requirements under irradiation of neutrons until a 150 GWd/t maximal burnup.

Characteristics during cooling

After irradiation in the core, the depleted fuel cools down during the recycling processes in which several requirements must be followed to ensure that the designs discussed here are compatible with the current industrial background. The key characteristics during cooling, i.e. decay heat, activity and neutron source are obtained using the DARWIN2.3 code with a fuel composition corresponding to the discharged fuel with a 100 GWd/t burnup.

The decay heat from irradiated americium is higher but decreases quickly with time because the main contribution is from 242 Cm which has a half-life of 142 days. As shown in Fig. 10, except for the two hybrid designs with americium, all design satisfies current technological requirements on the decay heat removal i.e. 0.25 W/g after 15 days cooling and 0.047 W/g after 450 days cooling (See Section 3.2). The decay heat for these two hybrid designs is very close to the limit threshold. The cooling time can be adjusted to satisfy current requirements. For instance, MABP7 with 6 %wt Am in UOX matrix needs additional 15 days before in-vessel fuel handing and 50 days before removal to water storage. MABP6, with18 %wt Np in UOX matrix, requires additional 150 days before it can be moved to water storage, which can be achieved within 2 cycles of in-vessel storage. The activity and neutrons source of these fuel pins are presented prospectively in Fig. 11 and Fig. 12. Regarding activity, these designs have no significant impact on the fuel recycling processes because their levels are very close to the reference MOX fuel. Neutrons source for the hybrid approach with americium is about 6 times as the reference MOX, but this would not be an issue because there are only 6 pins with addition of americium among 271 fuel pins in each fuel assembly. The neutron source for the homogeneous loading of americium is about 3 times as the reference MOX. Neutron sources hazard source is related to dose rates at transportation, storage and reprocessing stages. These potential issues should be investigated in the future.

The neptunium addition increases decay heat in long term while the americium addition increases both decay heat and neutron source. It appears that all these designs either satisfy current technological requirements or could be handled in foreseen fuel cycles facilities if a slightly extended cooling time is considered.

The spatial flux and power distribution for the hybrid design investigated in this section, shows no significant impact regarding the main technological criteria. The evolution of the main characteristics under irradiation (burn-up, fuel temperature and gas release) and during the cooling (decay heat, activity and neutron source) proves that these burnable poison designs satisfy current fuel technologies.

Influence on the core

This section will study the impact of burnable poisons with minor actinides on the core performance including the materials balance, power distribution and feedback coefficients.

Core material balance

The objective of these burnable poison designs is to compensate for the reactivity, but it is also interesting to evaluate the core mass balance. The mass difference (of uranium, plutonium, americium and neptunium) between EOEC and BOEC for each design is shown in Table 5. The reference core is in the self-breeding option in which a large quantity of uranium is consumed but without significant plutonium production. Nevertheless, the reference core design produces 53 kg americium and 8 kg neptunium at each equilibrium cycle.

With addition of minor actinides, an increase on the plutonium production is observed thereby less plutonium inventory in the new fuel is required. Furthermore, all the homogeneous loading cases and the neptunium hybrid loading case are net consumer of minor actinides.

The MABP7 corresponding to 6 UOX pins with 6 %wt americium, does reduce by 14 kg the core americium production but cannot achieve a net consumption of americium, therefor the hybrid mode requires 20 ~ 30 such pins to realize zero production of americium in SFR-V2B core. However, the addition of americium would increase the product of curium. In summary, these designs show an interesting capability to reduce production even consume minor actinides, which should be investigated in the future. 3.6.2. Core power distribution For the reference SFR-V2B, the control rods CSD2 is inserted about 25 cm into fissile zone at BOEC which is reserved for the reactivity compensation function. However, the MABP1 core does not need this insertion of control rods to compensate for the reactivity loss. Consequently, the comparisons is drawn here between the BOEC of the reference core with rods 25 cm inserted, while the burnable poisons cases are considered without rod insertion.

The discrepancy in power distribution between the MABP1 core and the reference core varies between -8.0 %wt and +6.6 %wt at BOEC (See Fig. 13). As shown in Table 6, the maximal linear heat rating of reference design and MABP1 are respectively 445 and 449 W/cm at BOEC. The main impact is located close to the position of control rods because of the change in control rods insertion.

The power density decrease forms the core center to the core periphery. After one cycle irradiation, CSD2 in the reference core is withdrawn to the top of fuel, which helps to increase the linear heating in the core periphery. However, MABP1 compensate for reactivity loss by using minor actinide and thus lacks of such power tuning from the control rods. Consequently, the linear heating in the periphery of MABP1 is lower than the reference core. The maximal linear heat rating of reference design and MABP1 are respectively 419 and 430 W/cm at EOEC.

The MABP5, MABP6 and MABP7 have similar influence on the core power distribution by comparison with MABP1. The influence of MABP2, MABP3 and MABP4 on the power distributions are not considered because they are overqualified to compensate for the reactivity loss in SFR-V2B. The influence on the power distribution is origin from the position of control rods and is limited. 7). The loading of americium or neptunium to achieve burnable poison objective has only slight influence on the sodium void worth. On the other hand, both americium and neptunium weaken the Doppler Effect.

The core transient behavior can be analyzed based on these parameters. However, it appears that the impact of these burnable poison designs on the core safety performance is limited. These designs are applied for the burnable poison objective in this paper, but they do help transmutation of minor actinides. The impact on the core power distribution is limited and is origin from the position of control rods to compensate for the reactivity loss. These designs have little influence on the sodium void effect, but they weaken the Doppler Effect.

Conclusions

This paper studies the application of minor actinides as burnable poisons in the sodium fast reactors. Two loading modes of minor actinides is considered: the homogeneous one mixes minor actinides in all fuel and the hybrid one packages minor actinides in UOX matrix as independent and limited pins in fuel assembly. The maximum minor actinides content in these two loading modes are discussed by considering current technological limitations. Finally, the results of seven designs with minor actinides are presented.

Both homogeneous and hybrid loading modes show a satisfactory capability to compensate for the reactivity loss. For SFR-V2B core design considered in this study, the reactivity compensation ability of homogeneous modes studied in this paper vary from 415 pcm to 1525 pcm. If the reactivity compensation ability of hybrid modes is lower, it could show a good potential if more pins with minor actinides have to be used and/or if alternative matrix to UOX, such as zirconium, can be used. Moreover, this hybrid mode facilitates the management of minor actinides. The independent pins reduce the impact on the manufacture and the recycling stage. The loading mass can also be adjusted by mean of content or the pin number tuning.

Americium has better compensation ability than neptunium if same quantity is loaded. However, neptunium has less issues on the gas release, decay heat and neutron source, which enable quantitatively more a high content than americium.

Finally, the feasibility of these designs has been investigated both at assembly and core level. These designs meet current technological requirement on fuel pin design (thermomechanical behavior, constraints on fuel back end, etc.) and show only limited influence on the core performances. However, future studies, such as behavior under accidental transients and the fuel reprocessing scenario are required to assess the industrial viability of theses designs.

Fig. 1 .

 1 Fig. 1. The actinides burnup chain marked with plutonium equivalence in MOX SFR spectrum

Fig. 3 .

 3 Fig. 3. The radial Layout of SFR-V2B core (left) and its standard fuel assembly (right)

Fig. 4 .

 4 Fig. 4. Radial layout of the hybrid mode fuel assembly with 6 independent pins with minor actinides

Fig. 5 .Fig. 6 .

 56 Fig. 5. The discrepancy in flux between MABP6 and reference fuel assembly at 0 GWd /t (left) and at 100 GWd /t (right)

Fig. 8 .

 8 Fig. 8. Evolution of centerline temperature under irradiation

Fig. 9 .

 9 Fig. 9. Evolution of gas pressure in fuel pin under irradiation

Fig. 10 .

 10 Fig. 10. Evolution of decay heat in fuel pin during cooling

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Evolution of activity in fuel pin during cooling

Fig. 13 .

 13 Fig. 13. The discrepancy in power distribution between MABP1 core and reference core (Units: %)

Table 1 . Isotopic compositions of plutonium recycled form PWR MOX fuel

 1

	Isotopes	238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 241 Am
	Content ( %wt) 3.6	47.4 29.7	8.2	10.4	0.8

Table 2 . Maximal content of minor actinides in homogeneous and hybrid loading mode

 2

		Homogeneous mode (MOX matrix) Hybrid mode (UOX matrix)
	237 Np	9.5 %wt (DH)	16.3 %wt (DH)
	241 Am 0.75 243 Am 0.25	2.3 %wt (GR)	5.2 %wt (DH)

Table 3 . Description of burnable poison designs

 3 : Pu is plutonium recycled form PWR MOX fuel as shown in Table1; Np is 237 Np; Am is 75 % 241 Am and 25 % 243 Am; Homo is the homogenous loading mode.

	Design	Mode	Inner fuel assembly	Pu (kg) Am (kg) Np (kg)
	Reference		271 (14.431 %wt Pu) pins	12656	0	0
	MABP1 Homo 271 (0.77 %wt Np + 14.254 % Pu) pins	12500	0	607
	MABP2 Homo 271 (2.32 %wt Np + 14.2 %wt Pu) pins	12453	0	1822
	MABP3 Homo 271 (0.77 %wt Am + 14.17 %wt Pu) pins 12430	619	0
	MABP4 Homo 271 (2.32 %wt Am + 13.99 %wt Pu) pins 12267	1857	0
	MABP5 Hybrid	6 depleted UOX pins 265 (14.60 %wt Pu) pins	12521	0	0
	MABP6 Hybrid	6 (18.00 %wt Np) pins 265 (14.58 %wt Pu) pins	12507	0	333
	MABP7 Hybrid	6 (6.00 %wt Am) pins 265 (14.49 %wt Pu) pins	12429	113	0

Remark

Table 4 . Reactivity compensation ability (Unit: pcm)

 4

	Design	BOEC EOEC	Reactivity Variation	Compensation Ability
	Reference 1177	750	-427	--
	MABP1	850	838	-12	415
	MABP2	729	1092	363	789
	MABP3	760	1011	252	678
	MABP4	536	1634	1098	1525
	MABP5	925	748	-177	250
	MABP6	882	817	-65	362
	MABP7	859	732	-127	299

Table 5 . Mass balance at the equilibrium cycle (Unit: kg)

 5

	Design	Np	U	Pu	Am	Cm
	Reference	+8	-1716	+59	+53	+13
	MABP1	-59	-1691	+102	+52	+15
	MABP2	-188	-1619	+161	+51	+14
	MABP3	+9	-1710	+106	-16	+30
	MABP4	+9	-1671	+168	-148	+58
	MABP5	+8	-1731	+74	+52	+15
	MABP6	-28	-1710	+90	+52	+15
	MABP7	+8	-1733	+86	+39	+18

Table 6 . Maximal linear heat rating different cores (W/cm)

 6 Feedback coefficientThe feedback coefficients, i.e. sodium void worth and Doppler constant, are compared for different cores (See Table

		BOEC	EOEC
	Ref	445	419
	MABP1	449	430
	3.6.3.

Table 7 . Core feedback coefficient at the end of equilibrium cycle (Unit: pcm)

 7

	Design	Sodium void worth Doppler constant
	Reference	2123	-916
	MABP1	2141	-887
	MABP2	2253	-783
	MABP3	2083	-895
	MABP4	2080	-800
	MABP5	2092	-912
	MABP6	2121	-883
	MABP7	2106	-896


Didier Le Ray
email: leray@lnf.cnrs-mrs.fr

François Clarac

Daniel Cattaert

Integration of Sensory Inputs in Motor Neurons

INTRODUCTION

The role of sensory information, especially proprioceptive feedback [START_REF] Sherrington | Flexion-reflex of the limb, crossed extension reflex stepping and standing[END_REF], in the organization of motor output has been studied extensively in a variety of different preparations, invertebrate and vertebrate alike (Barnes and Gladden 1985).

Proprioceptive inputs may be integrated at different levels of the motor command. The simplest interactions consist of direct contacts between proprioceptive sensory afferents and motor neurons (MNs). More complex integrations involve one or several interneurons. For example, in the cat spinal cord, Ia afferents evoke monosynaptic excitatory postsynaptic potentials (EPSPs) and Ib afferents evoke disynaptic inhibitory postsynaptic potentials (IPSPs) in homonymous MNs (Eccles 1964). Polysynaptic connections also exist both in insect [START_REF] Bässler | The femur tibia control system of stick insects. A model system for the study of the neural basis of joint control[END_REF]; [START_REF] Burrows | Positive feedback loops from proprioceptors involved in leg movements of the locust[END_REF][START_REF] Büschges | Nonspiking local interneurons in insect leg motor control. I. Common layout and species-specific response properties of femur-tibia joint control pathways in stick insect and locust[END_REF] and in crustacea [START_REF] Clarac | Interneuronal control of a walking leg reflex in an in vitro crayfish preparation[END_REF]Le Ray and Cattaert 1997). Recent intracellular studies have shown that simple neuronal network activity depends upon connectivity, and endogenous properties of component neurons [START_REF] Harris-Warrick | Dynamic biological networks: The stomatogastric nervous system[END_REF]. Therefore sensory-motor integration may imply more complex dynamic processes.

However, studies of sensory-motor interactions mainly concern simple reflexes. Among these, a great amount of data concerns the vertebrate stretch reflex: it is a negative feedback loop in which stretching the muscle spindle evokes activation of homonymous MNs [START_REF] Eccles | The physiology of nerve cells[END_REF][START_REF] Granit | Receptors and sensory perception[END_REF][START_REF] Matthews | Mammalian muscle receptors and their central actions[END_REF]. For the last 40 years, physiological studies of this reflex have demonstrated that most of the excitatory connections between sensory afferents and MNs are monosynaptic [START_REF] Burke | Handbook of Physiology. The nervous system[END_REF][START_REF] Redman | Junctional mechanisms at group Ia synapses[END_REF]. In arthropods, the monosynaptic connections between primary afferents from proprioceptors and MNs is a widespread phenomenon too. In all cases, these connections support resistance reflexes, comparable to the vertebrate stretch reflex, in which MNs respond to counteract the imposed movement. In insect, the monosynaptic connections have been demonstrated for the femoral chordotonal organs of the locust [START_REF] Burrows | Parallel processing of proprioceptive signals by spiking local interneurons and motor neurones in the locust[END_REF]). In the crustacean walking leg, Blight and Llinás (1980) described monosynaptic connections in the thoraco-coxal muscle receptor organ (TCMRO). More recently, in the crayfish walking legs, afferents from the coxo-basipodite chordotonal organ (CBCO) were demonstrated to make direct excitatory synapses onto levator (Lev) and depressor (Dep) MNs: stretch-sensitive sensory fibers connect Lev MNs and release-sensitive fibers connect Dep MNs [START_REF] El Manira | Monosynaptic connections mediate resistance reflex in crayfish (Procambarus clarkii) walking legs[END_REF].

Although systematic analysis of the coding of movement parameters have been extensively performed (Bush 1965a, b;Le Ray et al. 1997;[START_REF] Matheson | Responses and locations of neurones in the locust metathoracic femoral organ[END_REF]), the organization of the reflex responses, and particularly the role of a given sensory information in this organization, remains unclear. The sensory-motor loop involving the CBCO in the crayfish thoracic in vitro preparation gives us the possibility to unravel this question: only around 20 sensory afferents connect less than ten Dep MNs (Le Ray and Cattaert 1997). In an associated work, we performed the complete classification of the CBCO release-sensitive fibers and of the Dep MN reflex responses (Le Ray et al. 1997).

In this paper, we have analyzed what type of information each identified Dep MN received from the CBCO during imposed movements. A functional wiring diagram is established, and the role of EPSP characteristics in the integration of the MN response is analyzed using a compartment model simulation.

METHODS

Preparation.

performed on adult male and female crayfish, Pacifastacus leniusculus and Procambarus clarkii. Animals were maintained in aquarium at 18°C and fed once a week.

The in vitro preparation consisted in the last three thoracic ganglia and the two couples of antagonistic motor nerves innervating the two proximal joints of the 5 th leg (Promotor/Remotor and Depressor/Levators). The CBCO, which encodes the vertical movements of the leg, was dissected out together with its sensory nerve. The preparation was pinned down dorsal side up in a Sylgard-covered Petri dish and superfused with oxygenated crayfish saline.

Stimulations / Recordings.

Extracellular recordings were performed using pin platinum electrodes contacting the nerves, isolated from bath with petroleum jelly (Vaseline), and directed to a 4-channel differential AC amplifier (A-M Systems). Single and paired intracellular recordings from Intracellular and extracellular recordings were digitized at 20 kHz and written to disk.

A homemade puller controlled mechanical stimuli characterized by cyclic stretch and release of the CBCO strand, according to a sinusoidal (Fig. 1C) or a ramp protocol (Fig. 4).

Movement stimulations were performed from the most released position of the CBCO strand, and total movement amplitude was one third of the released CBCO strand length (1 mm -1.8 mm). The movement control voltage traces were visualized on the oscilloscopes and stored on both tape and computer.

Salines.

Vaseline wall was used to superfuse separately the CBCO and the thoracic ganglia.

The CBCO was superfused with saline which contains (in mM) 195 NaCl, 5 KCl, 13 CaCl 2 , 2 MgCl 2 . The thoracic ganglia was superfused with saline where divalent cation concentration was increased [(in mM) 34 CaCl 2 , 6.4 MgCl 2 , with the sodium concentration reduced accordingly], in order to raise the activation threshold of all central neurons without affecting the CBCO sensory inputs. It allowed to unmask the monosynaptic reflex response from MNs [START_REF] Berry | Criteria for distinguishing between monosynaptic and polysynaptic transmission[END_REF]. Moreover, in experiments where intracellular current pulses were delivered into the CBTs, the high divalent cation concentration saline did not affect the monosynaptic EPSP produced in the post-synaptic Dep MN (Fig. 5B). Saline solutions were buffered with 3 mM N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (HEPES) and pH adjusted at 7.7 at 15°C.

Analysis.

Physiological signals were analyzed with the CED SPIKE2 program. Data and traces were acquired using scripts running with the SPIKE2 program. The SPIKE2 "Wave Marker" tool allowed to identify extracellular CBCO units from the neurogram. Subsequently, it was possible to determine which sensory unit connected a given intracellularly recorded assistance (A MN) or resistance (R MN1 and 2) Dep MN (Fig. 1C, 1 and 2).

Circular statistics were used to analyze the distribution of identified CBCO EPSPs recorded from a given MN during imposed sine wave movements. The phase occurrence of each sensory unit over several movement cycles (starting of the release phase being chosen as zero) was figured by a unit vector  v i . The resulting vector  R was calculated as the sum of all (n) unit vectors  v i divided by n (Fig. 1, C3, left), for each identified CBCO unit:

  R v n i n   ,  R R R x y   2 2 ,         ArcTan R R y x ,
with R x and R y representing the x and y coordinates of the resulting vector  R . The resulting vector length (  R ) has a value between 0 and 1, and is a measure for the mean distribution of spikes within a stimulus cycle: a value of zero would indicate that the spikes were evenly distributed; a value of one would indicate that all spikes occurred at the same phase. In Statistical analysis and fittings were performed with the GraphPad Prism statistic programs.

Simulations.

Spatial and temporal integration of EPSPs produced at different locations of MN dendrites, was simulated with a compartment model (program SWIM, Ekeberg et al. 1991).

The model allows construction of arbitrarily complex dendritic trees. The simulation model used 60 compartments. The main neurite, from which intracellular recordings are usually performed in real MNs, was composed of 20 compartments each 20 µm long and 10 µm in diameter. In addition, two primary branches, one composed of 15 compartments (length: 20 µm; diameter: 2 µm) the other composed of 7 compartments (length: 20 µm; diameter: 10 µm), and two secondary branches composed of 8 compartments (length: 20µm; diameter: 2µm) were simulated too. In real crayfish MNs, input synapses are likely to be located on primary and secondary neurite branches. Because no active spike propagation occurs in crayfish MN neurites, only passive electrical properties were simulated:

The intra-compartment potential E is described by the differential equation

dE dt I I I I cm leak core ch syn     (equation 1)
I leak models passive leakage through the cell membrane. It is

I E E G leak leak leak   ( ).
where the parameters E leak and G leak are the equilibrium potential and the leak conductance respectively. I core is the electrical coupling to neighboring compartments summed over all neighbors

I E E G core c c neighbors core     ( ).
The parameter G core denotes the core conductance from the compartment in question to the neighboring compartment. (area is the membrane surface of the compartment, C m is the specific capacitance).

All compartments had the same membrane resistivity R m that was adjusted to 4000 or 8000 .cm 2 . All computations were carried out assuming a specific capacitance C m of 1µF/cm 2 and a cytoplasmic resistivity R i of 75 .cm.

Synaptic excitatory input was modeled with a conductance in the postsynaptic compartment, and an activation level of the postsynaptic channel, s, which is 0 if the synapse is "closed" and 1 if it is fully "opened". The maximum conductance G syn is fixed, but the value of the actual conductance G syn s varies with s; the kinetic of s is controlled by two parameters: the duration and the decay time. The synaptically induced current that enters the postsynaptic compartment is calculated by

I E E G s syn syn synapses syn    ( ).
in which E syn is the equilibrium potential for EPSPs.

RESULTS

In a previous work, Le Ray and Cattaert (1997) In order to find out the type and number of CBCO afferents that project onto a given MN, we performed systematic intracellular recordings from all Dep MNs in single experiments, and used the procedure described in figure 1C to identify the different CBCO units from the sensory nerve. In some experiments, we determined the number of postsynaptic Dep MNs that received monosynaptic EPSPs from a given sensory unit. We focused exclusively upon resistance Dep MNs, using both extracellular and intracellular approaches. Figures 3 and4 show two examples of the results obtained with both methods. In experiments where sinusoidal movements were applied to the CBCO strand, we impaled successively the different postsynaptic Dep MNs and extracellularly recorded the CBCO units. the way to reproduce a phasico-tonic pattern (Fig. 6B2). In these conditions, the post-synaptic

Dep MN response resembled the phasico-tonic type of reflex response, i.e. the membrane potential did not return to its resting value between each 40-Hz bursts, but was gradually depolarized in relation with the CBT tonic frequency. Thus, the control of the firing of only one presynaptic CBT was sufficient to transform the Dep MN phasic reflex response into a phasico-tonic-like reflex response.

Figure 7A shows the normal resistance reflex of a phasico-tonic Dep MN in response to the application of a ramp stimulation to the CBCO strand (only the release phase of the stimulation is presented). In the absence of movement (Fig. 7B), in order to reproduce a phasico-tonic sensory firing, we injected depolarizing current pulses (+12 nA, [100 Hz, 0.5 s],

response resembled the physiologic one, i.e. great phasic EPSP bursts added onto a graded tonic depolarization of the membrane (Fig. 7B1). The firing pattern of the single presynaptic CBT was modified in order to reproduce a phasic CBT discharge (Fig. 7B2) by intracellular injection of depolarizing current pulses (+12 nA, 3 ms, 100 Hz) delivered in trains (0.5-s duration, 2-s interval). Consequently, the postsynaptic Dep MN response was transformed in a purely phasic reflex response.

High frequency EPSP summations in phasic and phasico-tonic Dep MNs.

In Simulation experiments were performed to analyze the integration processes of the afferent signal in the postsynaptic MN. The simulated MN is restricted to a main neurite, two primary and two secondary branches in which the conduction is passive. The input synapses can be located in different parts of the postsynaptic MN (to match more to reality, synapses were only located on primary and secondary branches). Then, it is possible to simulate the spatial and temporal integration of one or several sensory inputs.

A first set of simulations was performed in order to analyze the role of spatial arrangement of synapses, and of geometry of the postsynaptic compartments in the shape of the centrally recorded EPSP (Fig. 9). One possibility could be that the shape of the EPSP is the same (possibly with various amplitude) whatever the compartment in which it is produced, but because of passive propagation in dendrites, its temporal characteristics change and could give rise to the whole range of EPSP shapes recorded from the main neurite (see figure 3).

Moreover, during a high frequency train of EPSPs, the amplitude, time to peak and duration of each EPSP should be responsible for dissimilarities in the amount of depolarization (Fig. 8).

The shape of EPSPs depends upon the amount of membrane that has to be charged in the postsynaptic compartment. Therefore, we simulated large (20 µm in diameter) and small (1µm in diameter) postsynaptic compartments (Fig. 9A). On the other hand, the amplitude of EPSPs recorded in the main neurite depends upon the diameter of compartments that are in between the synapse and the recording electrode. In order to maximize the low filtering effects of passive propagation in dendrites, compared to reality, 1 µm-diameter and 300 µm-length branches were used. Because membrane resistivity (R m ) is a parameter difficult to measure in real dendrites, four R m values were tested (4000, 8000, 12000 and 20000 .cm 2 ) in both large and small postsynaptic compartment configurations. The results are presented in graphs of figure 9B: in each case, measurements were made in the main neurite. Peak amplitude, time to peak and time constant of the propagated EPSP were increased with increasing R m . Simulated synaptic inputs in large postsynaptic compartments (filled squares) induced EPSP of smaller amplitude, longer time to peak and larger time constant than in small postsynaptic compartments (filled circles). By comparison, between both postsynaptic compartment configurations, more proximally generated EPSPs (unfilled symbols) did not show as marked differences as distally generated EPSPs (filled symbols). Moreover, proximally generated EPSP presented shorter time to peak and smaller time constant than distally generated one.

The parameters involved in the evolution of trains of EPSPs were studied using the same models. We studied effects of R m values of 4, 8, 12 and 20 k.cm 2 , but figure 10 between proximally and distally generated compound EPSPs were more marked than in the small postsynaptic compartment configuration (1 µm in diameter, Fig. 10 A,C). The proximally generated compound EPSP changed very little (less than 1 % of the normalized single EPSP) from one configuration to the other; the main difference resulted in the distally generated compound EPSP which amplitude varied from 2% (when R m was 4 k.cm 2 ) to more than 50 % (when R m was 20 k.cm 2 ) of the normalized single EPSP.

Although the geometry of the postsynaptic neuron seems to be able to determine the shape of the response recorded from the main neurite, the weak variability observed between the two extreme postsynaptic compartment configurations are unable to explain the great differences observed among the EPSPs that can be recorded from real MNs (see figure 3 5C),. it seems that properties of synapses between sensory afferents and MN are also determinant for the development of phasico-tonic reflex responses in some Dep MNs.

DISCUSSION

In vitro and in vivo CBCO strand movements.

In this study, imposed movements corresponded to the angular range covered during locomotion. We could argue that more CBCO afferents normally project onto MNs, especially during extreme downward movements of the leg. Consequently, some MNs classified as nonresponding would perhaps respond to these larger movements. However this is unlikely because electrical stimulation of the CBCO nerve failed to activate monosynaptically these silent MNs (data not shown). Anatomical studies have demonstrated that the CBCO nerve contains 38-41 axonal profiles (diameter ranging from 1 µm to 17 µm) (Cattaert, unpublished observations), likely equally divided into release and stretch-sensitive fibers. During release movements, up to 14 distinct release-sensitive CBCO afferents could be identified from the CBCO neurogram (Fig. 3). Therefore, there exist around six release-sensitive CBCO fibers that were not identified during sine wave movements. Possibly, these units could be activated by release movement starting from extreme stretched positions, and thus not involved during locomotion or posture. Another possibility is that these units were activated by the imposed movements but could not be identified due to their identical shapes in the CBCO neurogram.

Nevertheless, if this is the case, the results presented in figure 2 would have been roughly the same (although there would exist more sensory units, the resulting vectors would remain identical). Therefore, this study is very representative of the connections involved in the monosynaptic resistance reflex pathways, during walking or resting activities in crayfish.

Functional consequences of sensory-motor wiring.

Contrary to the cat spinal cord, in which Ia afferent fibers have been demonstrated to project onto most (65 to 80%) of the homonymous MNs [START_REF] Nelson | Projection of single knee flexor Ia fibers to homonymous and heteronymous motorneurons[END_REF][START_REF] Scott | Individual EPSPs produced by single triceps surae Ia afferent fibers in homonymous and heteronymous motoneurons[END_REF], in crayfish half of the release-sensitive CBCO fibers project onto only one

Dep MN (Fig. 3). This would indicate some specific input-output connections. However, this

does not seem to be the case since each Dep MN receives several (from two to five) CBCO afferents coding different angular sectors, and therefore integrates a compound sensory signal.

However, none of the MNs realizes the same proprioceptive integration. These integration processes result in the different Dep MNs being sequentially activated during passive levation of the leg (Fig. 2). By comparison of the results obtained in other preparations, convergence of proprioceptive inputs is a widespread phenomenon also described in the crayfish terminal abdominal ganglion [START_REF] Newland | Parallel processing of proprioceptive information in the terminal abdominal ganglion of the crayfish[END_REF] as well as in the stick insect [START_REF] Sauer | Distributed processing on the basis of parallel and antagonistic pathways simulation of the femur-tibia control system in the stick insect[END_REF] as in the locust [START_REF] Burrows | Parallel processing of proprioceptive signals by spiking local interneurons and motor neurones in the locust[END_REF]) and as in the leech [START_REF] Lockery | Distributed processing of sensory information in the leech. I. Input-output relations of the local bending reflex[END_REF].

However, in these cases, proprioceptive afferents mainly project onto spiking or non-spiking interneurons which decide of the motor response (shape, strength and direction). Surprisingly, convergence of direct connections from proprioceptive afferents onto MNs are a shared feature of resistance reflex in crayfish and stretch reflex in vertebrates [START_REF] Eccles | The convergence of monosynaptic excitatory afferents on to many different species of alpha motoneurones[END_REF].

This common characteristic would lead to a very rigid reflex behavior that is avoided by the mean of presynaptic inhibition of central origin in both cases [START_REF] Cattaert | Direct evidence for presynaptic inhibitory mechanisms in crayfish sensory afferents[END_REF][START_REF] Eccles | Presynaptic inhibition of the spinal monosynaptic reflex pathway[END_REF].

In opposition to the convergence of CBCO inputs onto resistance Dep MNs (about five CBCO units per MN), divergence is quite heterogeneous (from one to eight MNs connected by a single CBCO fiber; see figure 3). This characteristic would allow differential regulation of the sensory-motor connections: presynaptic inhibition of sensory afferent that connect all resistance reflex Dep MNs would affect all Dep MN responses, whereas presynaptic inhibition of sensory fiber connecting only one Dep MN would only affect this MN response.

Such differential reflex responses have been demonstrated in the thoraco-coxal joint [START_REF] Skorupski | Heterogeneity and central modulation of feedback reflexes in crayfish motor pool[END_REF], that could be supported by specific sensory-motor projections such as the one presented here. Functional analysis of divergence of sensory inputs remains a question difficult to unravel. So far, the crayfish thoracic in vitro preparation is one of the rare models which appear to be adapted to solve this problem. Nevertheless, we must keep in mind that results obtained in vitro are oversimplified compared to intact animal in which more neurons would be active, and modulation from central or peripheral origin would be capable of rebuilding neuronal networks [START_REF] Meyrand | Construction of a pattern-generating circuit with neurons of different networks[END_REF].

Role and interpretation of EPSP shape.

This study has demonstrated that EPSPs from a given CBCO afferent onto different Dep MNs displayed different shapes (time to peak from 0.7 to 1.3 ms, decrease time constant from 2.14 to 12.44 ms, amplitude from 0.07 to 0.5 mV). Because of the geometry of the MN dendritic trees, EPSP generated on small distant branches would elicit smaller and slower centrally recorded events than the same EPSP generated on proximal branches [START_REF] Rall | Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input[END_REF][START_REF] Rall | Dendritic location of synapses and possible mechanisms for the monosynaptic EPSP in motoneurons[END_REF]. In order to test this assertion, we have simulated propagation of EPSPs in a compartment model (Fig. 9A). It appeared that temporal characteristics of the propagated EPSP also depends upon the geometrical characteristics of the postsynaptic compartment in which it has been produced: the EPSP duration is directly related to the membrane resistivity, but inversely related to the diameter of the postsynaptic compartment (Fig. 9B). Therefore, in electrophysiological recordings, the variability in the shape of the EPSPs recorded from distinct MNs could be due to MN morphological differences. However, recording different EPSP shapes from the same MN would likely indicate different synaptic locations (see differences between proximally and distally generated EPSPs in figure 9B). Then the summation properties of EPSPs in synapses located at various places within the MN dendritic tree, was studied in different conditions of membrane resistivity for both small and large postsynaptic compartment configurations (Fig. 10): here again, the difference between proximal and distal synapses was more pronounced in the large postsynaptic compartment configuration (Fig. 10B cf. A and D cf. C). Except the case of low membrane resistivity (R m = 4 k.cm 2 ), the simulated frequency stimulation affected the postsynaptic depolarization amplitude in a way very similar to reality (cf. Fig. 8). On the basis of these simulation studies, we propose a functional interpretation of synapse location, that matches to physiological observations: proximal synapses would produce fast, large amplitude EPSPs involved in the MN phasic firing; in opposite, distal synapses would not produce enough depolarization to give rise to an immediate MN discharge, but rather contribute to a slow graded depolarization that would increase the neuron excitability (see complete fusion of distally generated EPSPs, in figure 10B). However, synapse location is not the only way to account for the variety of EPSP shapes: time to peak, duration and decay time are characteristics that could be specified at the synapse itself. Such parameters would thus depend upon neurotransmitter release probabilities, diffusion coefficient, and uptake/degradation functions that can vary from one synapse to the other [START_REF] Laurent | Single local interneurons in the locust make central synapses with different properties of transmitter release on distinct postsynaptic neurons[END_REF][START_REF] Redman | Amplitude fluctuations in synaptic potentials evoked in cat spinal motoneurones at identified group Ia synapses[END_REF].

Functional implications of the resistance reflex design.

In an associated paper, we described that, in the angular sector studied, movements imposed to the CBCO strand activated the release-sensitive sensory units in a greater number than stretch-sensitive ones. Moreover, although their coding was not so specific, these sensory units were activated in a sequential way (Le Ray et al. 1997). Here, we demonstrated that Dep MNs were also activated sequentially (Fig. 2). In both sensory coding and MN response, the angular sector eliciting the strongest neuronal activation is comprised between the full release (corresponding to the leg contacting the dorsal thoracic carapace) and about 60 degrees in the stretching direction (corresponding to the basipodite around the horizontal position). Although these results were obtained from an isolated nervous system in high Ca 2+ -high Mg 2+ saline, it is likely that the same sensory-motor pathways are involved in the intact animal; the monosynaptic connections from CBCO afferents onto Dep MNs would then operate to uphold the body in the most commonly observed posture.

In this study, all intracellularly recorded Dep MNs displayed phasic or phasico-tonic responses to CBCO strand ramp stimulation (Figs. 6 and7). The absence of purely tonic MN response is the consequence of the absence of purely position-coding CBCO afferent (Le Ray et al. 1997). Because they receive several release-sensitive CBCO afferents (Fig. 3), all coding for release movements, all resistance Dep MNs presented larger reflex responses during movement than during maintained position (Figs. 4,6 and 7). This mainly dynamic feedback would therefore operate as a zero-velocity servo control: it is not the position but the movement that is detected in order to maintain a constant position. We could have think that the resistance reflex, mainly involved in posture, would have been based on the position coding. In contrary, the crayfish walking network chose a more "simple" system which does not need to compare permanently to precise position-coding references. Moreover, a system only based upon position-coding would require an incompressible integration time to take into account, and counteract, changes in position. The strategy adopted in the crayfish sensorymotor system allows faster dynamically-adapted responses. Therefore, in resting animal, the resistance reflex pathway would only be activated if a perturbation occurs. How this neuronal pathway, here involved in purely negative feedback, would work during more complex motor behaviors in intact animal remains to be determined. The time constant () of the repolarizing phase of each CBCO-related EPSP was calculated by one-phase exponential decay fitting: although distributed between two extreme values (2.5 ms and 12.5 ms), the mean EPSP  value was 6.5 ms. Only the extreme conditions are presented: A: Small postsynaptic compartments and Rm of 20 k.cm 2 ; B: Large postsynaptic compartments and Rm of 20 k.cm 2 ; C: Small postsynaptic compartments and Rm of 4 k.cm 2 ; D: Large postsynaptic compartments and Rm of 4 k.cm 2 . Physiological compound EPSPs were found between these extreme simulations (see text for details).

  CBTs and Dep MNs (Fig. 1, A and B) were realized with thin-walled glass micro-electrodes filled with a potassium chloride solution (3M) and having a 25-to 30-M resistance. The signals were amplified by an Axoclamp 2B (Axon Instruments). Intracellular current pulses were controlled by an 8-channel digital stimulator (A.M.P.I.). All signals were monitored on a eight channel oscilloscope, a four channel digital oscilloscope (Yokogawa DL 1200) and stored on D.A.T. tapes (BioLogics digital tape recorder) and digitized on a PC-based computer through an A/D interface (from Cambridge Electronic Device, CED 1401PLUS).

Fig. 1 -

 1 Fig. 1-C3, the right circular diagram illustrates distribution of the resulting vectors of the three

I

  ch and I syn , in equation 1, model the flow of ions through active channels and synapses respectively. The parameter cm describes the capacity of the compartment cm C area m  .

  described the Dep MN monosynaptic reflexes elicited by ramp movements imposed to the CBCO strand. They demonstrated the existence of three types of Dep MN response: Three Dep MNs did not present any monosynaptic response, one displayed an assistance reflex response (i.e. depolarizations during the stretch of the CBCO), and eight Dep MNs produced a resistance response (i.e. depolarizations during the CBCO release). Moreover, in an associated work, we did an extensive analysis of the release sensory coding, and demonstrated the existence of two distinct resistance responses: one characterized only by phasic EPSP bursts related to release ramps; the other characterized by both phasic bursts of EPSPs and a graded membrane depolarization during the release phase of the movement (Le Ray et al. 1997). The present study aimed at analyzing the transfer of information from CBCO fibers to monosynaptic output Dep MNs. I-Projections of CBCO units onto the Dep MNs -Extracellular and intracellular studies.

  figure presents the resulting vector of each of the CBCO afferents that connect the MNs (thin

  Figure 3 presents one of these experiments in which 14 different CBCO units were identified and the eight postsynaptic resistance Dep MNs were impaled two by two successively. Most of the recorded CBCO units elicited EPSPs in only a few number of postsynaptic Dep MNs: ten of the sensory afferents do not project upon more than one or two different Dep MNs. Nevertheless, some CBCO units elicit monosynaptic EPSPs in several resistance Dep MNs (from three to eight distinct postsynaptic Dep MNs); there exists one CBCO afferent that produce EPSPs in each of the eight resistance Dep MNs. It is noticeable that the same CBCO afferent is able to produce different shape and amplitude EPSPs in the different postsynaptic Dep MNs (see the averaged EPSPs in Fig. 3). Thus, there exist both a divergence and a convergence of the sensory informations onto the different Dep MNs. In some experiments, ramp movements were applied to the CBCO strand and successive paired intracellular recordings were performed from a given CBT and several resistance Dep MNs. In figure 4, while a phasico-tonic release-sensitive CBT was intracellularly recorded, we impaled successively all 12 Dep MNs. The phasico-tonic releasesensitive CBT connected monosynaptically five different resistance Dep MNs (distinguished with their different extracellular spikes), and produced EPSPs of different shape and size (see averaged EPSPs in the right part of Fig. 3). These results confirmed the divergence of one sensory information onto different Dep MNs. II-"Manipulation" of the signal transmission.In order to confirm that the MN response to ramp stimulation of the CBCO strand was due exclusively to the temporal characteristics of the sensory inflow (since the associated paper demonstrated that MN properties were not involved), we analyzed the effect of a single sensory input onto the MN reflex response. We therefore performed paired intracellular recordings from both a CBT and a Dep MN. Injection of depolarizing current pulses at high frequency rates (30 to 200 Hz) into the CBT were then used to study the properties of sensorymotor synapses in high Ca 2+ and high Mg 2+ saline. In such experiments, high frequency stimulations evoked sustained depolarizations in Dep MNs (Fig.5A), and each presynaptic spike was capable of producing an EPSP in the postsynaptic Dep MN (Fig.5B). As presented in figure3, CBCO-related EPSPs displayed different time constants. The graph in figure5Cpresents the plot versus time of the relative exponential decay of repolarizing phase from six representative EPSPs. Each one-phase exponential decay fitting allowed us to calculate the time constant () for each CBCO-related EPSP: the extreme  values ranged from 2.5 ms up to 12.5 ms, but most of the Dep MN EPSPs had a  value between 6 and 7 ms. Modification of the Dep MN responses by controlling the CBT firings. An associated paper showed the existence of several kinds of CBCO unit firings and two types of resistance reflex responses in Dep MNs (Le Ray et al. 1997). By using various combinations of stimulation frequencies, it was possible to mimic the different CBT activities recorded during ramp movements and, consequently, to analyze the different Dep MN monosynaptic responses (results presented from six experiments). Figures 6 and 7 present the normal and modified reflex responses of both phasic and phasico-tonic Dep MNs in high Ca 2+ and high Mg 2+ saline.

Figure

  Figure6Ashows the normal resistance reflex of a phasic Dep MN in response to the

  paired intracellular recording experiments (n=9), we compared the different postsynaptic Dep MN responses produced by high-frequency stimulation of a single CBT. During high frequency CBT stimulations, summation of EPSPs evoked in the Dep MN resulted in a sustained depolarization (Fig. 5A). This effect was progressive, the rate of depolarization depended upon the stimulation frequency and the stimulated CBT. Graphs representing the rates of depolarization for both phasic and phasico-tonic Dep MNs are shown in figure 8. The responses obtained in a phasic Dep MN with the same CBT for 50 and 200 Hz stimulations are presented in figure 8A (top). The maximum depolarization amplitude was four time higher and was reached four time faster for 200 Hz stimulation frequency than for 50 Hz stimulation frequency. Therefore, the rate of EPSP summation was strongly frequencydependent for that CBT. However, great differences were observed among the CBTs that connect a single Dep MN, since the same stimulation frequency (200 Hz) could produce motoneuronal responses of quite different amplitudes (one to four folds, Fig. 8A bottom). Nevertheless, each of these CBTs evoked frequency-dependent motoneuronal response comparable to that shown in figure 8A (top). Similar results were found with a postsynaptic phasico-tonic Dep MN. The amplitude of the depolarization was frequency-dependent (Fig. 8B, top). The maximum depolarization amplitude was three time higher for 200 Hz stimulation frequency than for 50 Hz stimulation frequency, but was reached nearly at the same time (50 ms). Here again, great differences were observed among the CBTs that connect a single Dep MN, because the same stimulation frequency (100 Hz) could produce motoneuronal responses of quite different amplitudes (one to three folds, Fig. 8B bottom). III-Simulation of the sensory-motor synapse.

  only presents the results obtained for R m values of 4 k.cm 2 (right) and 20 k.cm 2 (left), for clarity. In order to compare in each case the evolution of membrane potential during EPSP trains, all single simulated EPSPs (distal and proximal) were normalized to the same amplitude (100%). Three presynaptic spike frequencies (50, 80 and 140 Hz) were tested on each postsynaptic configuration at distal and proximal synapse locations. For both R m examples, fittings of summations are presented on graphs for 50 Hz 80 Hz and 140 Hz stimulation frequencies (left: distal synapses; right: proximal synapse); the corresponding simulated raw data are presented for 50 and 140 Hz stimulation frequencies (left: distal; right: proximal). With increasing frequencies, the depolarization amplitude increased and the rise time of the depolarization decreased. In each case, the distal synapse-induced EPSP summation was always of greater amplitude than the proximal one. Moreover in the large postsynaptic compartment configuration (20 µm in diameter, Fig. 10 B, D), differences

LEGENDSFig. 1 :

 1 Fig. 1: Diagram of the experimental procedure -Methodology.

Table 1 :

 1 Connections between sensory fibers and Dep MNs.On the basis of the results obtained with circular statistics from several experiments, we classified the CBCO units that connected the Dep MNs according to their reflex response (: non-responding; A: assistance; R: resistance, in the first column). The number of afferents and their specificity to movement (release, non-specific and stretch) are indicated for each Dep MN.

Fig. 2 :

 2 Fig. 2: Temporal distribution of sensory-motor connections.

Fig. 3 :

 3 Fig. 3: CBCO-related EPSPs in the resistance Dep MNs.

Fig. 4 :

 4 Fig. 4: Intracellular demonstration of the sensory input divergence.

Fig. 6 :

 6 Fig. 6: Phasic Dep MN response to high frequency stimulations of a single CBT.

Fig. 7 :

 7 Fig. 7: Phasico-tonic Dep MN response to high frequency stimulations of a single CBT.

Fig. 8 :Fig. 9 :

 89 Fig. 8: Time course of compound EPSPs elicited by train-stimulation of a single CBT.

Fig. 10 :

 10 Fig. 10: Simulation of trains of EPSPs.

Table 1

 1

summarizes the results obtained in several experiments. In our conditions, the assistance Dep MNs received about five exclusively stretch-sensitive sensory units. The resistance Dep MNs received an averaged number of six CBCO units (from three to eight) in sine wave movement conditions. Resistance Dep MNs seemed to receive inputs from a larger variety of CBCO units than the assistance Dep MN: The organization of CBCO afferent projections onto the Dep MNs is given in Table

1

. Although all of the impaled resistance Dep MNs mostly received release-sensitive CBTs, some (17 Dep MNs) received also inputs from non-specific CBCO units, and in some cases (four Dep MNs) from stretch-sensitive CBCO units.

  ), or observed among the Dep MN reflex responses elicited by CBCO release (see Le Ray et al.

	1997). Some other simulations were performed to study the importance of the synapse
	temporal characteristics. It appeared that long lasting synapses, i.e. synapses with a long decay
	time, produced EPSPs with long time constant that were able to much more summate than
	short time constant EPSPs (not shown). Although these EPSPs with long time constant are

rarer than short ones (see graph in Fig.