K Medjaher
email: kamal.medjaher@ens2m.fr

A K Samantaray

B Ould Bouamama

Bond Graph Model of a Vertical U-Tube Steam Condenser Coupled with a Heat Exchanger

Keywords: Vertical steam condenser, Heat exchanger, Bond graph

A simulation model for a vertical U-tube steam condenser in which the condensate is stored at the bottom well is developed in this paper. The U-tubes carrying the coolant are partially submerged in the stored condensate and thus the bottom well acts as a heat exchanger. The storage of hydraulic and thermal energies is represented using a coupled pseudo-bond graph model. Advection effects are modelled by considering reticulated segments of the tubes carrying coolant, over which condensation takes place. The developed model is of intermediate complexity and it is intended for use in observer based real time process supervision, which works by comparing the process behaviour to the reference model outputs. The simulation results obtained from the bond graph model are validated with experimental data from a laboratory set-up.

Introduction

Modern process engineering plants are designed to reuse the material and energy for improving the process efficiency and also to reduce production costs. The process dynamics of such systems is usually complex and consequently designing them for optimal utilisation of resources requires a well-developed simulation model. However, each component's model must not be too complex because the component's model is not only used for simulation of the single process component's behaviour, but also used to predict the overall steady state and dynamic response of the process. Furthermore, process models are being increasingly used for online monitoring, diagnosis of process faults, and fault tolerant control; and this requires real time computations of the model output for comparison with the actual process behaviour. Therefore, one needs faster numerical computation using a simplified, but accurate process model.

In this paper, model of a vertical U-tube steam condenser coupled with a heat exchanger is developed and the model complexity is limited to the intermediate level.

Steam condensers are integral part of any nuclear and thermal power plant utilising steam turbines, distillation industries using water as a solvent, etc. System-level modeling of steam condensers has to consider both mass and energy balances in two control volumes, namely steam and condensate, and energy balance in further two control volumes, namely tubes and the coolant flowing through them. That is why bond graph modelling as a multi-energy domain approach is a suitable tool for representing such systems [START_REF] Karnopp | Systems Dynamics: A Unified Approach[END_REF][START_REF] Thoma | Introduction to Bond Graphs and their Application[END_REF][START_REF] Mukherjee | Bond Graph in Modeling, Simulation and Fault Identification[END_REF][START_REF] Breedveld | Physical Systems Theory in terms of Bond Graphs[END_REF][START_REF] Borutzky | Bond Graphs -A Methodology for Modelling Multidisciplinary Dynamic Systems[END_REF]. Furthermore, the conservative nature of junction structure in a bond graph model ensures that the material and energy balances are correctly represented in each step.

The literature on bond graph modeling of heat exchangers is pervasive [START_REF] Hubbard | Pseudo bond graphs of circulating fluids with application to solar heating design[END_REF][START_REF] Shoureshi | Analytical and experimental investigation of flow-reversible heat exchangers using temperature-entropy bond graphs[END_REF][START_REF] Shoureshi | Modeling and dynamics of two-phase flow heat exchangers using temperature -entropy bond graphs[END_REF][START_REF] Delgado | Bond graph modeling and simulation of a water cooling system for a moulding plastic plant[END_REF][START_REF] Thoma | Modelling and Simulation in Thermal and Chemical Engineering: Bond Graph Approach[END_REF]. They are based on pseudo-bond graph representations of thermo-fluid transport and heat exchange developed in [START_REF] Karnopp | Pseudo bond graphs for thermal energy transport[END_REF][START_REF] Karnopp | State variables and pseudo-bond graphs for compressible thermo-fluid systems[END_REF][START_REF] Karnopp | Pseudo bond graphs for generalised compartmental models in engineering and physiology[END_REF][START_REF] Bouamama | Bond graph Approach as Analysis Tool in Thermo-fluid Model Library Conception[END_REF]. Thoma [START_REF] Thoma | Introduction to Bond Graphs and their Application[END_REF][START_REF] Thoma | Modelling and Simulation in Thermal and Chemical Engineering: Bond Graph Approach[END_REF] has even introduced the term 'HEXA', as a generic nomenclature, for the bond graph sub-model of a heat exchanger.

On the other hand, very few works on bond graph modeling of condensers are reported in literature. Some of the works on bond graph modeling of condensation phenomena assume bulk condensation (similar to cloud formation and its saturation) and base the analysis on the relative humidity [START_REF] Tylee | Pseudo bond graph representation of PWR pressurizer dynamics[END_REF][START_REF] Nebot | Simulation of heat and humidity budgets of Biosphere 2 without air conditioning[END_REF] in the control volume. Other bond graph formulations for storage and transport of two-phase mixtures (water and steam mixture, here) may be consulted in [START_REF] Brown | Simulating distributed-parameter multiphase thermodynamic systems using bond graphs[END_REF][START_REF] Brown | Non-iterative evaluation of multiphase thermal compliances in bond graphs[END_REF]. Bond graph representations of film condensation on vertical tubes were developed in [START_REF] Thoma | Modelling and Simulation in Thermal and Chemical Engineering: Bond Graph Approach[END_REF][START_REF] Ould Bouamama | Bond graph modelization of steam condensers[END_REF][START_REF] Bouamama | Supervision of an industrial steam generator. Part I: Bond graph modelling[END_REF]. However, the film condensation models developed therein are inaccurate because they assume the entire segments of the tube to be at uniform temperature. In this paper, we consider the temperature variation in the tube by considering several small and finite segments. This approach for bond graph modeling of distributed-parameter multiphase thermodynamic systems has been developed in [START_REF] Brown | Simulating distributed-parameter multiphase thermodynamic systems using bond graphs[END_REF] by using convection bonds. Further note that a pseudo-bond graph model of a U-tube steam generator (boiler) has been developed in [START_REF] Tylee | Bond graph description of U-tube steam generator dynamics[END_REF] by using one-dimensional finite-element modeling concept, which is similar to the one followed in this paper.

Modelling

Steam condensation involves both convection and conduction [START_REF] Nusselt | Die oberflächenkondensation des wasserdampfes[END_REF][START_REF] Chapman | Heat Transfer[END_REF]. In process engineering systems, it is simpler to use enthalpy flow instead of entropy flow to model heat convection using pseudo-bond graph representation [START_REF] Thoma | Modelling and Simulation in Thermal and Chemical Engineering: Bond Graph Approach[END_REF][START_REF] Karnopp | Pseudo bond graphs for thermal energy transport[END_REF][START_REF] Karnopp | State variables and pseudo-bond graphs for compressible thermo-fluid systems[END_REF][START_REF] Karnopp | Pseudo bond graphs for generalised compartmental models in engineering and physiology[END_REF][START_REF] Bouamama | Bond graph Approach as Analysis Tool in Thermo-fluid Model Library Conception[END_REF]. In this paper, pressure and temperature are considered as the generalised effort variables, and mass flow rate and enthalpy flow rate are taken as the generalised flow variables. The convection heat transfer due to mass flow is represented using inter-domain couplings presented in [START_REF] Bouamama | Supervision of an industrial steam generator. Part I: Bond graph modelling[END_REF]. Note that a simpler model for this type of condenser has been developed in [START_REF] Bouamama | Supervision of an industrial steam generator. Part I: Bond graph modelling[END_REF] for fault detection.

Description of the condenser

The schematic diagram of the coupled U-tube condenser and heat exchanger system is given in Fig. 1. The steam enters from the top and is condensed over the outer surface of vertical tubes carrying low temperature liquid coolant. There are a number of U-tubes of equal length; only one of them is shown in Fig. 1.

The condensate film thickness grows as it flows down because of further condensation of steam on film's surface. The condensate is stored at the bottom of the condenser. The stored condensate is referred to as a pool and its level is controlled, i.e. kept within a range about a set point, by using an on-off controller acting on the discharge valve. Parts of the U-tubes carrying the coolant are submerged in the pool and there is further heat transfer from stored condensate in the pool to the cooling tubes. The rate of condensation of steam can be controlled by adjusting the pool level set point, which adjusts the tube surface area exposed to the steam. Such flexibility in controlling the rate of condensation, which consequently controls the steam flow rate, makes this type of condensers suitable for use in variable load installations.

Modelling assumptions

To develop an intermediate complexity model, the following assumptions are made:

1. Non-condensable gases degrade the efficiency of condensers operating in subatmospheric vacuum pressure. Therefore, non-condensable gases are regularly vented out, usually from the boiler. We assume that the input steam is saturated and pure.

2. Usual Nusselt's assumptions [START_REF] Nusselt | Die oberflächenkondensation des wasserdampfes[END_REF][START_REF] Rohsenow | Handbook of Heat Transfer Fundamentals[END_REF][START_REF] Churchill | Laminar film condensation[END_REF] are made:

a. The steam temperature is assumed to be homogenous in the vapour phase.

b. The wall temperature in each finite-reticule used in the model is uniform.

c. The condensate flow is laminar.

d. The maximum film thickness is small when compared to the tube's diameter.

3. The liquid phase is assumed to be incompressible.

4.

It is assumed that the condenser is well insulated and heat loss to environment is negligible.

5. The condensation/evaporation over/from the pool surface is neglected.

Problem formulation

The variables, used in the analysis and model, are given in Table 1. The values for geometric parameters correspond to an experimental set-up, which is discussed later in this paper.

We assume that the bent of the U-tubes is always submerged in the pool. The two sections of a U-tube above the pool are each divided in to i number of finite elements which are enumerated starting from the coolant entry point (see Fig. 2). The submerged part of a U-tube is considered as a single finite element. Therefore, the total number of finite elements used to model a tube is 2i+1.

.05×10 -4 kg m -1 s -1 λ Thermal conductivity of condensate 0.675 J m -1 s -1 K -1 L v Latent heat of vaporisation (function of pressure) - J kg -1 X Steam quality - - C d Valve's overall coefficient of discharge 9×10 -5 kg s -1 Pa -
J kg -1 K -1 c pm Specific heat of tube's metal 419 J kg -1 K -1 ρ m Density of tube's metal 7850 kg m -3 λ m Thermal conductivity of tubes metal 46.73 J m -1 s -1 K -1 s m ɺ , s H ɺ
Mass and enthalpy flow rates of steam -Kg s -1 , J s Condensation occurs in elements 1 to i and also in elements i+2 to 2i+1. The heat, withdrawn from the steam due to condensation and also due to further sub-cooling of the flowing condensate from each section, is directly transferred to the metallic body of that section of the U-tube. This heat is then transferred from the metallic body to the flowing coolant. The condensate fluid film thickness grows as it flows downwards to the pool, i.e. in paths 1→2→...i and 2i+1→2i →...i+2. The fresh condensate enters the pool in sections i and i+2.

We apply Nusselt's condensation formulae [START_REF] Nusselt | Die oberflächenkondensation des wasserdampfes[END_REF] in each segment of the tube. In each section, the initial fluid film thickness is determined from the maximum fluid film thickness obtained from the segment which is geometrically just above the concerned section. The differential equation for film thickness [START_REF] Chapman | Heat Transfer[END_REF][START_REF] Rohsenow | Handbook of Heat Transfer Fundamentals[END_REF], δ, as a function of coordinate z (see Fig. 2) is given as

( ) (
),

' 3 wj s v v T T g L dz d - - = ρ ρ ρ λµ δ δ
where T wj is the tube wall temperature in j th section and ( )

wj s p v v T T c XL L - + = 68 . 0 ' .
In the top most sections, i.e. sections 1 and 2i+1, the initial conditions are δ(0)=δ(2i+2)=0. We use reticulated segments of tubes and then the film thickness, δ j , at the bottom of j th section is given by

( ) ( ) , 4 4 1 ' 4 0         - - + = s v v wj s j l g L T T ρ ρ ρ λµ δ δ (1)
where

     + + ∈ ∈ = + - ]. 1 2 , 2 [ for ], , 1 [ for 1 1 0 i i j i j j j δ δ δ
The length of each segment of tube in contact with steam is calculated dynamically from ( )

, 2 and , i l l L l l s c t = Φ - = (2)
where Φ c is a complex non-linear function, which determines the length of the U-tubes submerged in the pool. Note that due to the bent of the U-tube and also non-linear geometry at the bottom of the condenser, it is very difficult to obtain a symbolic equation for this function and usually it is evaluated using interpolations from a calibrated table of experimental data for a specific condenser.

The mass flow rate of condensate into the pool is calculated at the sections in contact with the pool, i.e. in i th and (i+2) th section. Consequently, the total condensate flow is given by ( ) ( )

3 2 3 3 + + - = i i v t c g D n m δ δ µ ρ ρ ρ π ɺ . ( 3
)
The heat transferred from the steam phase to the tube's wall in each section, j, per unit mass is given by ) ( 68 . 0

' wj s p v v T T c XL L - + =
in which the amount of heat withdrawn for condensation is L v and the rest is due to sub-cooling of the condensate. The actual sub-cooling is about 10 to 20% higher than the theoretically calculated value [START_REF] Rohsenow | Handbook of Heat Transfer Fundamentals[END_REF]. Thus the amount of heat, Q cj , conducted to the tubes in each section, j, is given by

( ) ( ) (
)

wj s p v j v t cj T T c XL g D n Q - + - = 68 . 0 . 3 3 α δ µ ρ ρ ρ π , ( 4
)
where α is a correction factor (between 1.0 to 1.2). Without sub-cooling, the condensate temperature would be the saturated liquid temperature, i.e. T s . Thus the amount of heat stored in unit mass of condensate is given by

) ( 68 . 0 wj s p s p T T c T c - - α .
(5) Then the total enthalpy flow into the pool from sections i and i+2 is given by

( ) ( ) ( ) ( ) ( ), ) ( 68 . 0 ) ( 68 . 0 3 ) 2 ( 3 2 3 + + - - + - - - = i w s s i wi s s i v p t c T T T T T T g Dc n H α δ α δ µ ρ ρ ρ π ɺ (6)
where T wi and T w(i+2) are respectively the tube wall temperatures in sections i and i+2.

These formulations are used in the following sections to construct the bond graph model of the condenser. Note that the formulations described in this section are simple and more accurate formulations are available in literature (see [START_REF] Churchill | Laminar film condensation[END_REF][START_REF] Denny | Nonsimilar solutions for laminar film condensation on a vertical surface[END_REF] for extended Nusselt's formulation, [START_REF] Botsch | A model to describe the steady-state and dynamic behaviour of vertical condensers fed by mixtures[END_REF] for Maxwell-Stefan equation based formulations for mixtures, [START_REF] Maheshwari | Investigation on condensation in presence of a noncondensable gas for a wide range of Reynolds number[END_REF] for effect of non-condensable gases, [START_REF] Park | Effects of a wavy interface on steam-air condensation on a vertical surface[END_REF][START_REF] Park | Condensation of pure steam and steam-air mixture with surface waves of condensate film on a vertical wall[END_REF] for effect of wavy interface, etc., and the references therein for further details). The pseudo-bond graph model of the vertical condenser-heat exchanger system is given in Fig. 3. The bonds and signals with a circle over them are vectors [START_REF] Thoma | Modelling and Simulation in Thermal and Chemical Engineering: Bond Graph Approach[END_REF]. Thick perpendicular lines are used to decompose vector bonds and signals to their scalar forms and vice versa.

graph model of condenser

The thermo-fluid coupling is represented using CETF (coupling element for thermo-fluid) [START_REF] Bouamama | Supervision of an industrial steam generator. Part I: Bond graph modelling[END_REF] in Fig. 3. The structure of this element is defined in Fig. 4.

( ) p p c s V V V dt d V ɺ ɺ - = - =
, where V p is the volume of condensate in the pool. Note that V p is a function of the differential pressure due to pool head.

The outputs from the field element C s are pressure and temperature in the steam phase, which are calculated by iteratively solving the following relation:

), ( ), ( ) 1 ( ) ( ), ( ) 1 ( ) ( s PT s s l s s m l l s s p c m P T P h X P Xh m H h P X P X m V V Φ = - + = = - + = - = υ υ υ (7)
where c V , p V , m υ and m h are respectively internal volume of condenser, volume occupied by the stored condensate in the pool, specific volume and specific enthalpy of the steam in the condenser, and s υ , l υ , l h and PT Φ are thermodynamic functions which return respectively the specific volume of dry saturated steam, the specific volume of saturated liquid, the specific enthalpy of saturated liquid, and the temperature of saturated steam, at any given pressure. From Eq.( 7), the steam quality (X) and steam pressure (P s ) are solved iteratively using bisection method and the result is then used to calculate steam temperature (T s ). An alternative way of modelling storage of mixtures, which does not involve an iterative solution and uses different set of state variables, is given in [START_REF] Brown | Non-iterative evaluation of multiphase thermal compliances in bond graphs[END_REF].

The condensate storage in the pool is represented by the bond graph element C h for hydraulic energy and element C t for thermal energy. In this case, it is possible to separate the hydraulic and thermal energy storage by assuming that the condensate is incompressible and is in an under-saturated state.

Element C h produces the differential pressure head (P l ) or pool level (L), defined by the following relations:

( ) ( ) , dt m m P l c p l ∫ - Φ = ɺ ɺ ( 8
)
where l m ɺ is the rate of condensate discharge and P Φ is a function, which depends on the geometry of the condenser (it is usually obtained using experimental calibration). In the simplest case, assuming a cylindrical condenser, Eq.( 8) may be rewritten as

( ) ( ) dt m m C P l c h l ∫ - = ɺ ɺ 1 , where . g A C c h =
The storage of thermal energy in the pool liquid is modelled using modulated bond graph element C t . Its constitutive relation is given by ( )

( ) ( ) ( ) l p p l c l c p l c l P c dt H H dt m m c dt H H T 1 - Φ - = - - = ∫ ∫ ∫ ɺ ɺ ɺ ɺ ɺ ɺ , (9)
where l H ɺ is the rate of enthalpy flow with condensate discharge and T l is the pool temperature. Assuming a cylindrical condenser, Eq. ( 9) can be rewritten as

(

)dt

H H C T l c t l 1 ∫ - = ɺ ɺ
, where .

l c p t P g A c C         = ( 10
)
The condensate discharge, represented by bond graph element R V and the enthalpy flow associated CETF element are given as

( ) , , , l p l l d s l d v l T c m H P P P u C m ɺ ɺ ɺ = - + Φ = (11)
where u is the controller signal, ) ,

( u C d v Φ
is a function that determines the overall discharge coefficient of the valve, which depends on the constructional features of the valve and its characteristics (linear, quadratic, quick opening, equal percentage, etc.). Note that at junction 1 b , the upstream pressure is sum of differential pool pressure and the steam pressure. The pool level controller, represented by block element LC, is defined as follows: [START_REF] Karnopp | State variables and pseudo-bond graphs for compressible thermo-fluid systems[END_REF] where . g

     ≤ ≥ = , for , 0 , for , 1 min max L L L L u p p
P L l p ρ =
The condensation phenomena, given by Eq. ( 1), Eqs. [START_REF] Mukherjee | Bond Graph in Modeling, Simulation and Fault Identification[END_REF][START_REF] Breedveld | Physical Systems Theory in terms of Bond Graphs[END_REF] and Eq.( 6), are represented by elements R nj for the j th section. The inputs are the steam temperature (T s ), pool level (calculated from P l and used to determine l s from Eq. ( 2)) and the wall temperature T wj . The outputs are the heat flowing from steam to condensate (Q ci ), the mass and enthalpy flow rates of condensate ( c c H m ɺ ɺ and ), and the maximum fluid film thickness δ j , which is used in Nusselt's relation of section that is vertically below the considered section.

The heat capacity of the tube in j th section is represented by element C tj , whose value is determined as follows:

( )

2 2 4 d D l c n C j m pm t tj - = π ρ , ( 13
)
where l j is the length of j th section. For j =1..i and j =(i+1)..(2i), l j = l s . For the section submerged in the pool, i.e. j = i,

s j il l l 2 - =
. Likewise, the heat capacity of the coolant in j th section is represented by element C cj and its value is determined from

. 4 2 d l c n C j p t cj π ρ = (14)
Element R tj_k represents longitudinal heat transfer resistance between j th and k th (consecutive) sections of the metal tube. Transverse heat transfer resistance between the metal tube and the coolant in j th section (depends on the coolant flow rate) is represented by element R ctj . Convection heat transfer coefficient h ml is obtained experimentally. Heat transfer resistance between liquid and the metal tube submerged in the pool is represented by element R tl . Heat transfer resistance between topmost segments of the tube and the un-modelled external segments exposed to the environment is modelled by element R to . The values for these elements are obtained as follows:

( ) ( ) 2 2 _ 2 d D n l l R m t k j k tj - + = πλ , j m t ml s t ctj l n d d D h dl n R πλ π 2 2 ln 1       + + = , ( )
s m t tl il l n d D D R 2 2 2 ln -       + = πλ , ( ) . 2 2 2 d D n l R m t s to - = πλ (15)
Junctions 0 Qi and 0 Qo are used to sum the total heat transferred to the tubes from steam in the coolant inlet side and the coolant outlet side of the tube, respectively, i.e.

∑ = = = i j j cj cin Q Q 1 ,

and

. ,

1 2 2 co cin c i j i j cj co Q Q Q Q Q + = = ∑ + = + =
Modulated sources MSf i and MSf o model the condensate mass and enthalpy flow rates (in vector form), respectively from i th and (i+2) th sections to the pool. Their relations are given by Eq. (3) and Eq.( 6). Junction 0 c is used to sum MSf i and MSf o . In steady state, the condensate flow rate is assumed to be equal to the rate of condensation. Thus, these mass and enthalpy flow rates represent the transfer of mass and energy from steam phase to the pool.

Note that the liquid phase is considered incompressible and all those elements whose relations involve the pool level L (alternatively, volume V p and pressure P l ) are in fact modulated (e.g. C tj , R ctj , C cj , for j=1...2i+1). These modulations are not shown in the model to maintain clarity of presentation.

The rest of the elements in the bond graph model given in Fig. 3 are simple and selfexplanatory.

Simulation and experimental validation

The steam generator installation [START_REF] Bouamama | Supervision of an industrial steam generator. Part I: Bond graph modelling[END_REF] at LAGIS (Laboratoire d'Automatique, Génie Informatique et Signal) was used for experimental validation of the model. The vertical condenser-heat exchanger component, shown in Fig. 5, is positioned after the loading circuit (a steam expansion system mimicking a turbine) to condense the steam generated by a boiler. The initial conditions for the states were calculated from steady-state process measurements. As an example, the initial conditions for states of the C s -field are given as

( ) ( ) ( ) ( ) ( ) T s s p c s s s s p c s P m V P h P m V q       - - = / , / 0 0 0 0 0 0 υ ρ υ ρ , ( 16
)
where P s0 is the initial steam pressure and m p0 is the initial mass of liquid in the pool. For the pool, initial conditions for states corresponding to elements C h and C t are given as q h = m p0 and q t0 = m p0 c p T p0 , where T p0 is the initial temperature of liquid in the pool. Initial conditions for other state variables are calculated likewise. For each tube, the length exposed to steam, i.e. the length over which condensation takes place, is obtained from the mass (or volume) of condensate in the pool using experimental calibration as follows:

( )

. 2 / , 98 . 4 / 56 . 1 i l l q q l l s h h c t = - = Φ - = (17)
Since it is a small condenser, we have taken i =2, i.e. a total of five sections. Additional data used in simulation, besides those given in Table 1, are given in Table 2. The value of α was chosen iteratively to produce best match with experimental results. It corrects the heat transfer by 15%, which is in accordance with the maximum correction factor of 20% suggested in [START_REF] Rohsenow | Handbook of Heat Transfer Fundamentals[END_REF]. This takes care of the uncertainties in estimating parameters such as the heat transfer coefficients, which are extremely sensitive to the surface roughness [START_REF] Park | Effects of a wavy interface on steam-air condensation on a vertical surface[END_REF][START_REF] Park | Condensation of pure steam and steam-air mixture with surface waves of condensate film on a vertical wall[END_REF] of the inside and outside of the tubes, etc. There are some recent researches into finding good correlations for film condensation [START_REF] Chun | Assessment of the new and existing correlations for laminar and turbulent film condensations on a vertical surface[END_REF], but it is not easy to apply them in a physical model.

The computational model was developed using ModelBuilder [START_REF] Bouamama | Model builder using functional and bond graph tools for FDI design[END_REF], which is specifically designed to handle thermo-fluid system models. ASME steam tables [START_REF] Meyer | ASME steam tables: Thermodynamic and transport properties of steam[END_REF] were used to obtain thermodynamic properties. The coolant flow rate and entry temperature were taken as constants as given in Tables 1 and2, respectively; the specific enthalpy and mass flow rate of the input steam, which enters from a pressure (consequently temperature) controlled boiler after isenthalpic expansion through a valve, were taken as 2772.2 kJ/kg and 0.004673 kg/s (average steady-state experimental data), respectively. From the simulation, the evolution of steam pressure (P s ), pool temperature (T l ) and coolant temperature at exit (T e ) are plotted in Fig. 6.

Fig. 6. Simulation results

Comparisons of the simulation results with experimental results for steam pressure and pool level are given in Fig. 7(a) and Fig. 7(b), respectively. These results show good agreement between the model and the real process. However, there is a phase shift between the results, which can be attributed to actuator dynamics. In the real process, the control valve used to discharge pool liquid does not immediately respond to the command given from the on-off controller. Therefore, the pool level slightly exceeds the upper threshold due to the condensation during the delay in opening the valve and it significantly falls below the lower threshold due to the extra discharge from the pool during the delay in closing the valve.

Simulation results for coolant temperature at the exit and the pool temperature are compared with their corresponding experimental results in Fig. 8. The results show that the simulation model is able to provide good estimates of the actual values. Minor discrepancies in the values can be attributed to un-modelled heat transfers, external disturbances, and variations in the inputs (Note that we have assumed constant steam flow rate at constant specific enthalpy, constant coolant flow rate and constant coolant inlet temperature).

Conclusions

Pseudo-bond graph model of a vertical U-tube steam condenser is developed in this paper. The equations for elements in the model can be changed to accommodate complex heat transfer and condensation rate formulations, while the model structure remains the same. The model presented is suitable for system level dynamics studies and can serve as a template for development of more accurate solutions. Simulation results obtained from the model with an empirical correction factor of the heat transfer coefficient are then compared to the output from an experimental condenser in a steam generator installation and the results show acceptable prediction of process behaviour.

Fig. 1 .

 1 Fig.1. The coupled condenser-heat exchanger system

  Fig. 2. (a) Exaggerated view of sections of the tube and (b) representation of temperature profile in one section (not to scale)

Fig. 3 .

 3 Fig. 3. Pseudo-bond graph model of the condenser-heat exchanger system

Fig. 4 . 1 T

 41 Fig.4. Expanded form of CETF element The relationship between the efforts (temperatures 1 1 T e = and 2 2 T e = ) and flows (enthalpy flows H f ɺ = 1

4 .Fig. 5 .

 45 Fig.5. Condenser-heat exchanger component in an experimental steam generator set-up

7 .Fig. 8 .

 78 Fig. 8. Comparison of simulation and experimental results for coolant and pool temperatures

Table 1

 1

	. Model variables

Table 2 .

 2 Additional parameters used in simulation

	Data	Description	Value	Unit
	s P	0	Initial steam pressure	3.0× 10 5	Pa
	m p0 T p0 T w0	Initial pool mass Initial pool temperature Initial temperature of tube walls 125 3.5 50	kg o C o C
	T in α		Inlet temperature of coolant Heat transfer correction factor	44 1.15	o C -


The S receptor kinase is inhibited by thioredoxins and activated by pollen coat proteins

To investigate the phosphorylation status of SRK during the self-incompatibility reaction, we labelled pistils from self-incompatible S 3 homozygous Brassica oleracea plants with 32 P-orthophosphate, and phosphorylation of the receptor was monitored during a self-pollination time course. Physiological studies have shown that pollen hydrates 30-90 min after its deposition on the stigmatic papillae [START_REF] Dickinson | Dry stigmas, water and self-incompatibility in Brassica[END_REF] . Figure 1a shows that SRK was phosphorylated about 60 min after self-pollination, but as with pollen hydration, the time course of SRK phosphorylation varied between 45-60 min depending on the experimental conditions. No phosphorylation of SRK was detected up to 90 min following compatible pollination (data not shown). Only a fraction of the SRK protein was phosphorylated in vivo (compare Fig. 1a with Fig. 1b left panel).

Stigmatic papillae are able to discriminate between a self and a cross pollen deposited on the same cell [START_REF] Sarker | Control of pollen hydratation in Brassica requires continued protein synthesis and glycosylation is necessary for intraspecific incompatibility[END_REF] , indicating that the SI reaction is highly localised at the subcellular level. Our data are consistent with SRK being activated only within regions of the stigma papillar cells that contact the pollen grains.

In contrast to these results obtained in vivo, recombinant SRK, expressed in a baculovirus-insect cell expression system, was constitutively active in vitro [START_REF] Giranton | The integral membrane Slocus receptor kinase of Brassica has serine/threonine kinase activity in a membranous environment and spontaneously forms oligomers in planta[END_REF] (Fig. 1b). This difference was not due to overexpression because SRK was also constitutively active in microsomes isolated from stigmas (Fig. 1b). One possible explanation for these conflicting results was the existence of an inhibitory factor in vivo that was absent from the microsome fraction used in the in vitro assay. To test this hypothesis, different amounts of a soluble stigma extract were added to recombinant SRK in an in vitro phosphorylation assay. Under these conditions, SRK phosphorylation decreased in a dose dependant manner (Fig. 2a) suggesting that the soluble stigma extract contained a negative regulator of SRK phosphorylation. A similar result was obtained when stigmaextracted SRK was used instead of recombinant SRK (data not shown). The inhibitory effect of the soluble stigma fraction was lost when it was boiled or treated with trypsin but not following treatment with denatured trypsin, indicating that the active component was a protein (data not shown). We tested soluble extracts from stigmas of Brassica lines carrying different S haplotypes and extracts from different tissues. All extracts had an inhibitory effect although the various tissue extracts varied in their ability to inhibit SRK activity, despite the fact that equal amounts of protein were added (Fig. 2b). These experiments showed that the inhibitory activity was present in a wide range of tissues, albeit at different concentrations, and was not haplotype-specific.

Although phosphatase inhibitors were used in the phosphorylation buffer, it was nonetheless possible that the observed activity might be the result of a non-inactivated phosphatase. To test this hypothesis, the soluble stigma extract was added either immediately or 30 min after the beginning of the phosphorylation reaction (at which point SRK is already phosphorylated, see Fig. 1b) and the reactions were incubated for an additional 30 min. As shown in Fig. 2c, inhibition of SRK activity occurred only if the soluble extract was added at the beginning of the reaction indicating that it prevents SRK phosphorylation rather than dephosphorylates this protein.

To test whether the decrease in SRK activity was due to direct binding of the inhibitor to SRK, we performed competition experiments in an in vitro phosphorylation reaction. To the phosphorylation reaction medium, we added an excess of an inactive recombinant form of SRK ( m His), together with the functional recombinant HA-tagged SRK, and soluble stigma extract. Figure 2d shows that when the m His competitor was added in a 3.6 fold excess, SRK-HA kinase activity was not inhibited by the stigma extract. This experiment indicated that the inhibitor bound to both the wild-type and mutant forms of SRK in a stoechiometric and phosphorylation-independant manner. ARC1 (Arm Repeat Containing 1) interacts specifically with the cytoplasmic domain of SRK [START_REF] Gu | Binding of an arm repeat protein to the kinase domain of the S-locus receptor kinase[END_REF] , but it was unlikely to correspond to the inhibitor because it interacts only with the phosphorylated form of SRK and is expressed specifically in stigmas.

Furthermore, reduced levels of ARC1 in transgenic plants are correlated with an attenuation of the SI response [START_REF] Stone | A breakdown of Brassica selfincompatibility in ARC1 antisense transgenic plants[END_REF] . Two other proteins, THL1 and THL2 (Thioredoxin-hlike), were better candidates because they bind the cytosolic domain of SRK in a phosphorylation-independant manner [START_REF] Bower | Two members of the thioredoxin-h family interact with the kinase domain of a Brassica S locus receptor kinase[END_REF] . Moreover, in mammals, thioredoxin (TRX) binds and regulates the activity of cytosolic kinases such as ASK1 (Apoptosis Signalregulating Kinase 1) 10 and p38 MAP Kinase [START_REF] Hashimoto | Thioredoxin negatively regulates p38 MAP kinase activation and IL-6 production by tumor necrosis factor-alpha[END_REF] .

We looked at the possible regulatory effect of thioredoxin on SRK activity by adding purified Spirulina thioredoxin (SpTRX) to SRK phosphorylation assays. SpTRX mimicked the effect of the stigma extract (Fig. 3a). DTT, which can be used by thioredoxins as an electron donor, is necessary for the inhibitory effect of TRX on ASK1 [START_REF] Saitoh | Mammalian thioredoxin is a direct inhibitor of apoptosis signalregulating kinase (ASK) 1[END_REF] . Figure 3b shows that SpTRX lost its inhibitory activity when DTT was omitted from the buffer or when SpTRX was treated with H 2 O 2 . SRK phosphorylation was not affected by these treatments when SpTRX was omitted (data not shown). The effect of DTT was dose dependant but excess DTT (5 mM) suppressed the action of SpTRX, possibly by preventing disulphide bridge formation between the enzyme and SRK.

Moreover, specific depletion of thioredoxins from the stigma extract by repeated incubation with Thiobond TM resin abolished the inhibitory effect of the soluble stigma extract (Fig. 3c upper panel). Inactivated resin did not deplete the inhibitory activity.

The S Locus Glycoprotein (SLG, a soluble glycoprotein expressed in stigmas [START_REF] Kandasamy | The S-locus specific glycoproteins of Brassica accumulate in the cell wall of developing stigma papillae[END_REF] ) was not significantly depleted from the extract, indicating that loss of inhibitory activity was not due to a general depletion of protein (Fig. 3c, lower panel). Taken together, these results indicated that the inhibitory effect of the stigma extract was due to the activity of a thioredoxin.

We confirmed that THL1 is capable of inhibiting SRK activity by adding a recombinant form of THL1, expressed in Escherichia coli, to phosphorylation reactions in vitro (Fig. 3d). To get further insight into the mechanism of action of this enzyme, we produced two mutated forms of THL1 in which one or both of the catalytic cysteines were replaced by serines (THL1 C45S and THL1 C45S/C48S ). These mutations suppress thioredoxin activity of the enzyme by impairing its catalytic mechanism [START_REF] Meyer | Plant thioredoxins and glutaredoxins: identity and putative roles[END_REF] . The two mutant forms of THL1 did not inhibit SRK phosphorylation in vitro, suggesting that the catalytic activity of THL1 is necessary for it to act as an inhibitor.

In Brassica, the male component of the SI response is a PCP [START_REF] Stephenson | The male determinant in self-incompatibility in Brassica oleracea is located in the pollen coating[END_REF] . When PCPs extracted from S 3 or S 15 pollen were added to recombinant SRK in the presence of the inhibitor, SRK was phosphorylated in a dose dependant and haplotype-specific manner (Fig. 4a). This result indicates that PCPs are capable of activating SRK in the presence of the inhibitor. In animal receptor kinases, ligands activate their receptor by inducing their oligomerisation and transphosphorylation [START_REF] Heldin | Dimerization of cell surface receptors in signal transduction[END_REF] . This activation can be mimicked by the addition of bivalent antibodies that create bridges between receptor molecules [START_REF] Spaargaren | Antibody-induced dimerization activates the epidermal growth factor receptor tyrosine kinase[END_REF] .

Interestingly, in the presence of the antibody anti-SRK 3 N-ter, recombinant SRK was phosphorylated in a dose-dependant and saturable manner (as expected for an antigen/antibody interaction) mimicking the action of PCPs (Fig. 4b). Similar results were obtained with stigma extracted SRK (data not shown). By analogy with the studies carried out on animal receptors, these data suggest that the activation of SRK by PCPs involves receptor oligomerisation. This is consistent with a previous study carried out in our group, which demonstrated transphosphorylation between SRK molecules 6 . To our knowledge, this is the first demonstration that a plant receptor-like kinase is phosphorylated in response to a specific stimulus.

Taken together, the data presented here strongly support a model in which THL1 (and THL2) interacts in a reversible manner with SRK in stigmas and prevents spontaneous activation of the SI signalling pathway. In this model, SRK thioredoxin inhibition is released by PCPs following self-pollination. In the absence of this regulation, it is probable that the SI system would be constitutively active, blocking both self and cross-pollinations and hence preventing seed set.

Methods

Extraction and analysis of stigma and recombinant SRK. Insect cell microsomes expressing recombinant, HA-tagged and kinase-inactive (K553R), 6His-tagged SRK 3 proteins have been described [START_REF] Giranton | The integral membrane Slocus receptor kinase of Brassica has serine/threonine kinase activity in a membranous environment and spontaneously forms oligomers in planta[END_REF] . Crude stigma extracts, plant microsomes and soluble fractions from B. oleracea lines were prepared as described [START_REF] Delorme | Characterization of the S locus genes, SLG and SRK, of the Brassica S 3 haplotype: identification of a membrane-localized protein encoded by the S locus receptor kinase gene[END_REF] , except that extraction buffer used for microsome preparation was 50 mM Hepes pH7.4, 0.5 M Sucrose, 1 mM DTT, 10 mM EDTA, 10 mM NaF, 5 mM b-Glycerophosphate plus a protease inhibitor cocktail (Boehringer). After ultracentrifugation, the microsome pellet was resuspended in 50 mM Hepes pH7.4 and stored, with soluble fraction (supernatant), at -80°C before use. Proteins were separated through a 7.5 % SDS-PAGE gel, electroblotted and analysed by autoradiography or immunodetected with anti-SRK 3 N-ter (MAb 85-36-71) as described [START_REF] Delorme | Characterization of the S locus genes, SLG and SRK, of the Brassica S 3 haplotype: identification of a membrane-localized protein encoded by the S locus receptor kinase gene[END_REF][START_REF] Gaude | Expression of a self-incompatibility gene in a self-compatible line of Brassica oleracea[END_REF] .

Immunoprecipitation of SRK. SRK was immunoprecipitated in 1 ml of TBST buffer (20 mM Tris pH8, 150 mM NaCl, 0.05% w/v Tween 20) complemented with 10 mM EDTA, a protease inhibitor cocktail (Boehringer) and phosphatase inhibitors (5 mM Orthovanadate, 10 mM b-Glycerophosphate, 10 mM NaF). Immunoprecipitation was carried out with monoclonal anti-SRK 3 N-ter (MAb 64-32-30) [START_REF] Gaude | Expression of a self-incompatibility gene in a self-compatible line of Brassica oleracea[END_REF] or monoclonal anti-HA (MAb 12CA5, Boehringer) and Protein G Agarose (Tebu) according to the instructions of the manufacturer.

In vivo radioisotope labelling. Pistils from S 3 homozygous Brassica oleracea plants were radiolabelled at room temperature in a microplaque well in 10 mM MES pH6, complemented with 25 µCi per pistil of 32 P-orthophosphate (ICN, specific activity 285 Ci/mg, 1.25 µCi/µl). After a 4 h incubation, incubation buffer was replaced by 10 mM MES buffer pH6 and pistils were self-pollinated. SRK was immunoprecipitated from crude protein extracts as described above.

Phosphorylation in vitro. Typically, stigma microsomes or insect cell microsomes expressing SRK (10 µg protein) were labelled for 30 min at room temperature using 5 µCi of g 32 P-ATP (4 µCi/µl, Amersham-Pharmacia, specific activity 3,000 Ci/mmol) as described [START_REF] Giranton | The integral membrane Slocus receptor kinase of Brassica has serine/threonine kinase activity in a membranous environment and spontaneously forms oligomers in planta[END_REF] . For stigma microsomes, ATP was removed at the end of the reaction by desalting on a hand made column containing 600 µl of P6DG Gel (Biorad) equilibrated in 20 mM Tris pH8, 2.5% SDS. SRK was immunoprecipitated prior to SDS-PAGE analysis. PCPs added to phosphorylation reactions were prepared as described [START_REF] Doughty | Interaction between a coating-borne peptide of the Bassica pollen grain and S (incompatibility)locus linked stigmatic glycoproteins[END_REF] .

Bacterial and recombinant stigma thioredoxins. Spirulina thioredoxin (Sigma) was resuspended in microsome extraction buffer and incubated for 30 min on ice. For the redox experiments (Fig. 3b) DTT was omitted, added at different concentrations or replaced by H 2 O 2 . THL1 was amplified from a B. oleracea stigma cDNA library [START_REF] Giranton | The S locus receptor kinase gene encodes a soluble glycoprotein corresponding to the SKR extracellular domain in Brassica oleracea[END_REF]

  Cabrillac, J. Mark Cock, Christian Dumas & Thierry Gaude * Reproduction et Développement des Plantes, UMR 5667 CNRS-INRA-ENSL-UCBL Ecole Normale Supérieure de Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France The self-incompatibility (SI) response in Brassica allows recognition and rejection of self-pollen by the stigmatic papillae. The transmembrane S locus receptor kinase (SRK), a member of the receptor-like kinase (RLK) superfamily in plants, mediates recognition of self-pollen on the female side 1 , whereas the S locus cysteine-rich protein (SCR) is the male component of the SI response 2 . SCR is presumably located in the pollen coat and is thought to be the SRK ligand 2,3 . Although many RLKs have been isolated in plants, the mechanisms of signal transduction mediated by these molecules are largely unknown. Here we show that SRK is phosphorylated in vivo within one hour following self-pollination. We also demonstrate that, in vitro, autophosphorylation of SRK is prevented by the stigma thioredoxin THL1 in the absence of a ligand. This inhibition is released in a haplotype-specific manner by addition of pollen coat proteins (PCPs). These data indicate that SRK is inhibited by thioredoxins and activated by PCPs.

LEGENDSFIGURE 1 .FIGURE 2 .b

 12 FIGURE 1. SRK is phosphorylated 60 min after self-pollination in vivo, but is constitutively active in vitro. a Time course of SRK phosphorylation in vivo. SRK was immunoprecipitated from extracts of radiolabelled stigmas and detected either by autoradiography (upper panel) or immunodetection (lower panel). b SRK is constitutively active in vitro. In vitro phosphorylation reactions were carried out with stigma microsomes containing SRK (left panel) and with microsomes from insect cells expressing either functional, HA-tagged SRK (HA) or kinase-inactive, His-tagged SRK ( m His) (right panel). Rec.SRK=Recombinant SRK.

FIGURE 3 .

 3 FIGURE 3. Thioredoxin inhibits SRK phosphorylation in vitro. a Spirulina thioredoxin (SpTRX, 20ng) has the same inhibitory effect as soluble stigma proteins (0.6µg). b The inhibitory activity of Spirulina thioredoxin is redox dependant. SpTRX (0.6µg) was pretreated with redox compounds as indicated. NT = Not Treated. c Depletion of thioredoxin from the stigma extract by functional Thiobond TM resin abolishes the inhibitory activity of the extract. d In vitro phosphorylation of SRK is inhibited by 15ng of Brassica THL1 (C-C), but

FIGURE 4 .

 4 FIGURE 4. SRK is phosphorylated following addition of an agonist in the presence of thioredoxin. a Following inhibition of SRK phosphorylation in the presence of soluble stigma extract, addition of S 3 , but not S 15 , PCPs induces SRK kinase activity. b Under the same conditions, addition of a bivalent antibody (anti-SRK 3 N-ter) also induces phosphorylation of SRK.

Acknowledgements

We thank Jean-Loïc Giranton for production of baculovirus-insect cell microsomes and Anne-Marie Thierry for her technical assistance. J.M. Cock is a member of the Institut National de la Recherche Agronomique and T.Gaude of the Centre National de la Recherche Scientifique.


Yaël Kolasa
email: ykolasa@cybernano.eu

Thierry Bastogne

Jean-Philippe Georges

Simulation and sensitivity analysis of sensors network for cardiac monitoring

Keywords: Computer systems organization → Simulation, Sensors, • Networks → Network reliability, Security, • Statistics → Robustness Analysis, Internet of Things, Simulation, Sensitivity Analysis, Cardiac Monitoring

This study's aim was to model and simulate a wireless sensor network and to propose a two-step sensitivity analysis for a targeted application related to home cardiac monitoring. After an initial phase of research to design the appropriate network simulator implemented in Omnet++, 13 simulation parameters have been selected to test their criticality. The sensitivity analysis relies on two consecutive steps carried out in Matlab: a screening phase (Plackett-Burman design) and a global sensitivity analysis (Space-fiiling design). Two output variables are considered: the number of packets received by the sink and the reception cache hit percentage. Four critical simulation parameters have been identified: the message length, bit rate, the background noise power and the energy detection of the radio receiver. In perspective, this sensitivity analysis will be included as a component of a Quality-by-Design approach of network development. This contribution is the early stage result obtained by Y.

Introduction

This study comes from a double context, the high-throughput analysis in preclinical cardiotoxicity tests and the growing use of smart or connected objects to monitor patients' health. In both cases, the goal is to transmit cardiac signals for remote processing. These last years, the improvement of measuring systems in pharmaceutical laboratories allowed to gather more accurate and numerous data during preclinical analysis. This increase in data size has two direct consequences : problem of storage, and sharing over internet [START_REF] Aledhari | Design and Implementation of Network Transfer Protocol for Big Genomic Data[END_REF][START_REF] Marx | The Big Challenges of Big Data[END_REF][START_REF] Tierney | Efficient Data Transfer Protocols for Big Data[END_REF]. Furthermore, some of those can contain sensitive data for which confidentiality must be ensured. In parallel, more and more smart objects are available and allow to monitor daily cardiorespiratory activity over long period of time, longer than traditional ECG (10s) or Hölter ECG (24h). Those huge generated files beget transfer problems DH'2018, April 2018, Lyon, France Yaël Kolasa, Thierry Bastogne, and Jean-Philippe Georges to which are added network connectivity constraints. Both times, files' size can sire too long transfer times, files' potential corruption, and a poor users' experience quality. In order to ensure a faultless quality of service, we propose thereafter an innovative approach combining network simulation and sensibility analysis.

Network Modeling 2.1 A Study Case

The study case was to simulate a network of five sensors. One of them was moving, and was the only emitter of messages. Another one was the sink of the network, the only target, which was able to acknowledge received messages. The other three were retransmitters, used to forward the messages if they received them. The emitter moves straight through a modeled flat with different materials and ensuing different disturbances.

Omnet++ Implementation

This case was implemented in Omnet++ with the help of the library INET, which provides more realistic elements to build a simulation with. It integrates widely used TCP and UDP protocols, support for sensor networks, energy consumption and management, interferences, path loss, etc.

Model & Simulation Outputs and Parameters

Two output variables (quality attributes) were examined. The first one was the number of packets received by the sink at the end of each simulation. The second output is the reception cache hit percentage. 13 network parameters have to be tested: the message length, the send interval, radio types and associated parameters, battery power, mac type, the use (or not) of acknowledge receipt of a packet, carrier frequency, energy detection and associated parameters, bit rate, max queue size, header bit length, path loss type and antenna type. They were selected to have a wide range of action on the sensors' capacity to interact with their environment.

Sensitivity Analysis

The sensitivity analysis was split into two phases. The first one aims at screening the most active parameters through a minimal number of simulations while in a second step a global sensitivity analysis was carried out to rank the total effects of the parameters selected after the screening study.

Screening of Parameters

A Plackett-Burman design of experiments was used to implement the preliminary selection of active parameters [START_REF] Lewis | Pharmaceutical Experimental Design[END_REF].

HDMR-ANOVA

Once the most active simulation factors have been identified, a Sobol' sequence was implemented to generate the simulated data we need to estimate the sensitivity indices by an Analysis of Variance approach based on a High Dimensional Model Representation (HDMR-ANOVA) [START_REF] Saltelli | Global Sensitivity Analysis -The Primer[END_REF].

Matlab Implementation

Matlab was used to generate a Sobol' sequence of experiments and Omnet++ was launched via a batch file specifically created to run each simulation of the experimental design.

Results

For the number of packets received, two critical parameters were identified: the message length and the bit rate. For the reception cache hit percentage, the first two most critical factors are the background noise power and the energy detection of the radio receiver.

Conclusion

A prototype sensitivity analysis of a sensors network guided by simulations has been proposed. Preliminary results have demonstrated its practical feasibility by combining two simulation environments: Omnet++ and Matlab. The proposed technique allows to quickly identify the most critical parameters impacting the whole quality of service of the network. This PhD thesis will be carried out in the context of the Hôpital virtuel de Lorraine to better account for the constraints of the medical context. The main objective is to develop a holistic and safe engineering approach of medical sensors networks following the recents works on Quality-by-Design [START_REF] Bastogne | Quality-by-design of nanopharmaceuticals -A state of the art[END_REF] and by adapting it to remote cardiac monitoring.


ROBUST ESTIMATION OF FIELD POTENTIAL DURATION IN MULTI-ELECTRODE ARRAY SIGNALS

L. BATISTA 1 , T. BASTOGNE 1,2,3 1 CYBERnano, 2 CRAN UL-CNRS UMR 7039, 2 INRIA BIGS Background. Electrical signals measured by microelectrode arrays (MEAs) allow non-invasive long-term monitoring of cardiomyocyte cultures. However, variability of local responses between electrodes and noise makes difficult the accurate estimation of the field potential duration (FPD). False peaks are often detected and falsify the FDP estimated value, which finally requires for the user to perform some manual corrections for each well. This drawback not only slows down the analysis but also introduces arbitrary estimations and inter-individual errors.

The new estimation method relies on a Monte Carlo technique, i.e. a random sampling simulation process adapted to MEA signals. To test it, we used a MEA data set measured by an Axion Maestro platform with N=8 electrodes in each well. For the validation step, the new FPD estimates were compared to two sets of estimated values. The first set is provided by an expert who observed and manually estimate the FPD value for each sweep and each well. The second set of estimates is automatically computed by the platform software. Comparisons were repeated on 128 items (64 wells at two different time instants, before and after compound administration). Histograms and correlation coefficients of the estimation errors were compared for the three estimation techniques. Statistical analysis was carried out in the R computing environment.

Results

The correlation coefficient between the expert FPD values and the FPD estimates given by the two tested estimation techniques has been drastically improved with the new statistical method developed in this study (before: r=0.14 vs r=0.44 with the new method). By removing 5 outliers among the 128 estimates, we obtained a correlation coefficient: r=0.95, which is fully acceptable.

Conclusion

This study demonstrates the practical efficacy of a new estimation technique to automatically estimate the FPD parameter from MEA data.

Annual Meeting of Safety Pharmacology Society, Washington DC, Sep 30 -Oct 3 2018

Fig

  Fig.3: Results of the FPD estimations from MEA signals. Comparison of correlations between the two estimation methods and the expert values (left: r=0.14, right: r:0.44)

Fig. 4 :

 4 Fig.4: Comparison of correlations between the i-Cardio estimation method and the expert values after elimination of five estimation. Correlation coeff.: r=0.95


Levy Batista

Leo Doerr

Krisztina Juhasz

Sonja Stoelzle-Feix

Matthias Beckler

Thierry Bastogne

Mixed

Mixed-effects modeling for concentration effect profiling in cardiomyocyte contractility assays

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

MIXED-EFFECTS MODELING FOR CONCENTRATION EFFECT PROFILING IN CARDIOMYOCYTE CONTRACTILITY ASSAYS

L. BATISTA 1 , L. DOERR 2 , K. JUHASZ 2 , S. STOELZLE-FEIX 2 , M. BECKLER 2 , T. BASTOGNE 1,3,4 1 CYBERnano, 2 NANION, 3 CRAN UL-CNRS 7039, 4 INRIA BIGS Background. With the advent of new realtime technologies such as impedance assays, extracellular field potential measurement and optical sensing for in vitro cardiac safety screening studies, researchers have now to frequently deal with analyzing voluminous amounts of complex time responses. In this context, main issues are to speed up the data analysis process and to extract accurate information for cardiotoxicity profiling.

The proposed estimation method relies on the combination of a dynamic system identification method and a mixed-effect modeling technique. An output-error polynomial model structure is used for the system identification step and a stochastic approximation expectation maximization is implemented for the estimation of the hyperparameters. Input signals to be analyzed are the contractility amplitudes of cardiomyocytes submitted to compounds to be tested. Impedance signals and contractility amplitude were provided by a CardioExcyte96 system (Nanion Technologies). human iPSC-derived cardiomyocytes were provided by Cellartis Takara with 30,000 cells per well.

Results

Our data-driven profiling method extracted four parameters that completely fit the contractility time variations and fully characterize the effect of compound concentration on the contractility amplitude. The proposed method not only estimates the values of the model parameters but also their uncertainty distribution. The latter allows to compute p-values associated with each effect.

Conclusion

We show that the population-based estimation method developed in this study is suited to the fully characterize dynamic effects in cardiomyocyte contractility assays. Each parameter becomes a profiling characteristics of the concentration effect.

It can be applied to estimate concentration and compounds effects with an optimal accuracy and could be extended directly to multielectrode array and optical sensing responses

Fig. 2

 2 Fig.2 In bold lines: average responses of the analysis model for the two tested concentrations. We clearly observe a dynamic effect of the compound concentration on the contractility amplitude.