Tadesse Getnet

Mohamed Ayele

Pierrick Mabrouk

Björn Haurant

Bruno Laumert

Massimo Lacarrière

Santarelli

Getnet Tadesse Ayele
email: gtayele@kth.se

Mohamed Tahar Mabrouk

Pierrick Haurant

Björn Laumert

Bruno Lacarrière

Massimo Santarelli

Exergy analysis and thermo-economic optimization of a district heating network with solar-photovoltaic and heat pumps

Keywords: electrification of district heating network, energy hub, exergy, multi-carrier energy systems, particle swarm optimization, thermo-economic optimization

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Introduction

District heating network (DHN) transports heat using hot water as a media. The temperature levels and the mass flows determine the amount of heat injected into the network from the sources, the distribution loss and the amount of heat consumed at the consumers [START_REF] Frederiksen | District Heating and Cooling[END_REF]. For a given heat demand, a higher source temperature results in a higher temperature difference with the surrounding environment. It also means a lower mass flow rate and lower pumping energy requirement [START_REF] Bergman | Fundamentals of heat and mass transfer[END_REF]. However, the water will have higher residence time in the pipe. This causes a higher percentage of the heat flowing in the pipe to be dissipated. From exergy point of view, a higher temperature means a higher quality of heat [START_REF] Bejan | Thermal Design and Optimization[END_REF]. On the other hand, district heating networks are designed mainly to harness energy from cheap low-grade heat sources (characterized by lower temperature) and distribute it to the end users [START_REF] Frederiksen | District Heating and Cooling[END_REF]. Hence, operating these networks at lower temperature makes them more effective from the source temperature level point of view. As a lower supply temperature means a higher mass flow rate and, as a result, a lower residence time in the pipe, it decreases the heat that could be lost in the network. However, a higher mass flow rate means a higher pumping energy to circulate the water throughout the pipe network. The circulating pump uses electricity which is regarded as a very high quality, also referred as a pure exergy [START_REF] Bejan | Thermal Design and Optimization[END_REF][START_REF] Dincer | Exergy: Energy, Environment and Sustainable Development[END_REF]. The trade-off between temperature levels, distribution loss and the pumping energy, therefore, needs optimization.

The low-grade heat sources may not be enough to supply all the heat demand. In that case, heat pumps and gas fired combined heat and power (CHP) plants can also be used as a source of heat which are relatively more expensive. The optimal location of these plants, their size and operating temperatures should be included in the optimization in order to have a cost-effective operation of the DHN.

Exergy analysis, which considers both quantity and quality of energy, can be used to optimize thermal systems [START_REF] Dincer | Exergy: Energy, Environment and Sustainable Development[END_REF]. DHNs are one of such systems where exergy analysis can be applied to identify lossy branches and nodes in a meshed network topology. Many literatures focused on the exergy analysis of the heat source power plants rather than the heat distribution network. Yao et al. [START_REF] Yao | Thermo-economic optimization of a combined cooling, heating and power system based on small-scale compressed air energy storage[END_REF], for example, studied the thermo-economic optimization of combined heating, cooling and power plants. Wang et al. [6] followed a similar approach to study a combined cooling, heating and power plant assisted with solar system. Exergy analysis of heat pumps is discussed by Dincer and Rosen [START_REF] Dincer | Exergy: Energy, Environment and Sustainable Development[END_REF] and Bilgen and Takahashi [START_REF] Bilgen | Exergy analysis and experimental study of heat pump systems. Exergy[END_REF].

On the other hand, there are only limited exergy related researches conducted on the heat distribution networks. Vincio et al. [START_REF] Curti | An environomic approach for the modeling and optimization of a district heating network based on centralized and decentralized heat pumps, cogeneration and/or gas furnace. Part I: Methodology[END_REF] used exergy analysis to optimize emissions from a district heating system. Only emissions from power plants are considered in their study. Terehovics et al. [9] also applied exergy factor to identify the most influential component of a district heating network. Li and Svendsen [START_REF] Li | Energy and exergy analysis of low temperature district heating network[END_REF] used both energy and exergy analysis to study the performance of low temperature district heating networks in comparison to medium and high temperature district heating networks. They found that low temperature district heating networks have lower exergy and energy losses. Coss et al. [START_REF] Coss | Formulation of Exergy Cost Analysis to Graph-Based Thermal Network Models[END_REF] used exergy cost analysis to determine the unit exergy cost of each node in a radial heat distribution network. Transient analysis based on graph-based representation are considered in the determination of temperature and mass flows in the network. Only supply pipe networks are considered in their analysis. The exergy loss on the return network, the exergy requirement due to circulation pumps are not dealt in detail.

Once the critical and lossy components are identified using exergy/energy analysis, it is usually followed by optimization of operational parameters. Both mathematical and heuristic/metaheuristic approaches of optimizing energy systems are reported in literature. The management of future energy system, with respect to smart grids and distributed generations, is obvious to become more complex due to the interdependency between different energy carriers. Analysing and optimizing such systems mathematically will be cumbersome, if not impossible. Thanks to the computational power of computers, heuristic optimization techniques are getting wider acceptance as they are more suitable to handle highly nonlinear objective functions and constraints than the conventional deterministic approaches.

The level of optimization can be categorized into two: those at feasibility level and those at operational level. For example, HOMER [START_REF]HOMER -Hybrid Renewable and Distributed Generation System Design Software[END_REF] and RETScreen [13] can be used for size optimization of hybrid energy systems at feasibility level. The details of network topology and operational parameters are not considered in such tools. PowerWorld [14], on the other hand, considers operational network parameters to solve the economical dispatch and optimal power flow of electrical network. Some of the heuristic algorithms that are used in the energy field include: Genetic Algorithm (GA) [START_REF] Nemati | Optimization of unit commitment and economic dispatch in microgrids based on genetic algorithm and mixed integer linear programming[END_REF][START_REF] Subbaraj | Enhancement of combined heat and power economic dispatch using self adaptive real-coded genetic algorithm[END_REF],

Teaching Learning Based Algorithms (TLBA) [START_REF] Niknam | A new modified teaching-learning algorithm for reserve constrained dynamic economic dispatch[END_REF][START_REF] Shabanpour-Haghighi | A modified teaching-learning based optimization for multiobjective optimal power flow problem[END_REF], Honey Bee Mating Algorithms (HBMA) [START_REF] Niknam | Modified Honey Bee Mating Optimisation to solve dynamic optimal power flow considering generator constraints[END_REF], Mixed Integer Linear Programming (MILP) [START_REF] Nemati | Optimization of unit commitment and economic dispatch in microgrids based on genetic algorithm and mixed integer linear programming[END_REF][START_REF] Mazairac | Mixed-integer linear program for an optimal hybrid energy network topology[END_REF][START_REF] Wang | Mixed-integer linear programming-based optimal configuration planning for energy hub: Starting from scratch[END_REF], and Particle Swarm Optimizations(PSO) [START_REF] Aote | Improved Particle Swarm Optimization Based on Natural Flocking Behavior[END_REF][START_REF] Attous | Particle swarm optimization based optimal power flow for units with non-smooth fuel cost functions[END_REF][START_REF] Hazra | A multi-objective optimal power flow using particle swarm optimization[END_REF][START_REF] Juneja | Particle swarm optimization algorithm and its parameters: A review[END_REF].

Two main gaps are identified that are not well addressed in the literatures discussed above:

1. The temperature and pressure variations across the pipes of DHN, both on the supply and return sides, are not considered well in the exergy analysis.

2. The details of the electricity network parameters and the associated power losses are not taken in to account in thermos-economic optimization of DHN consisting of coupling devices such as HPs.

This paper tries to fill these gaps by combining a previously developed MCES model, called an extended energy hub modelling approach, with a heuristic optimization, such as particle swarm optimization (PSO) algorithm. Though the extended energy hub modelling approach is general and flexible enough to model varieties of coupling technologies with different energy carriers [START_REF] Ayele | An extended energy hub approach for load flow analysis of highly coupled district energy networks: Illustration with electricity and heating[END_REF], the scope of this paper is limited to only electricity and heating distribution networks consisting of solar PV and HPs. The model is used to formulate and solve the steady state load flow problems for both networks simultaneously. The details of network parameters that are determined by the load flow, such as temperature, mass flow rate and hydraulic heads on both supply and return pipe networks of the DHN, are explicitly included in the calculations of exergy efficiency for each branch and node in the DHN. Once lossy branches are isolated, thermoseconomic optimization is conducted on the reduced network topology using PSO technique. Temperature levels, cost of pumping energy, cost of electricity, cost of heat, capacity limits in both electricity and heating networks and sizes of HPs are considered in the optimization. More details about the methodology followed in this paper are discussed in Section 2.

Section 3 describes the parameters of a network topology which is taken as a case study. Section 4 presents the results and discussions while Section 5 concludes the main findings of the paper.

Methodology

System model

An extended energy hub approach, the details of which can be found in [START_REF] Ayele | An extended energy hub approach for load flow analysis of highly coupled district energy networks: Illustration with electricity and heating[END_REF], is used in this paper to model the interaction between different energy carriers including different energy conversion technologies. Figure 1 shows the three parts in the extended representation of a general MCES: the energy hub, the point of interconnection 4 and the energy network.

Local demands, local generations and coupling devices are altogether represented by the energy hub while the point of interconnection acts as an interface btween the energy hub and the remaining part of the the network. Coupled electricity and heating networks are considered in this paper. The main focus is, however, on the heating network part. The electrical distribution network is considered only for the purpose of delivering the electricity required by the DHN. No electrical load is considered at each hub. By doing so, the electricity lost in the network can be computed and taken into account in the optimization (see section 2.3).

For each hub k, the per unit active (Pel) and reactive (Qel) power injections, which are given by (1a) and (1b), defines the electrical sub-model [START_REF] Ayele | An extended energy hub approach for load flow analysis of highly coupled district energy networks: Illustration with electricity and heating[END_REF]. These equations are used to determine the electrical network parameters such as voltage magnitude, voltage angle, active and reactive power flows and losses in the network.

( ) = | | + (1a) ( ) = | | (1b) where
is the voltage angle difference between bus k and bus j; + = is an element of the network admittance matrix, N is number of buses and | | is voltage magnitude at bus k. Fig. 1. An extended energy hub representation in a general MCES [START_REF] Ayele | An extended energy hub approach for load flow analysis of highly coupled district energy networks: Illustration with electricity and heating[END_REF] 4 The point of interconnection refers to a bus in electricity network and a node in a heating network [START_REF] Ayele | An extended energy hub approach for load flow analysis of highly coupled district energy networks: Illustration with electricity and heating[END_REF].

On the other hand, the steady state thermo-hydraulic model of a district heating network is defined by ( 2) -( 6) [START_REF] Ayele | An extended energy hub approach for load flow analysis of highly coupled district energy networks: Illustration with electricity and heating[END_REF]. These equations are used to determine the heating network parameters, such as temperature, mass flow rate, heat power flows and hydraulic heads. The heat power injection (Ph) into the network from hub k is given by [START_REF] Bergman | Fundamentals of heat and mass transfer[END_REF].

( ) = ( ) (2)
where is the nodal mass flow rate flowing from hub k into the supply pipe network of the DHN; and are supply and return temperatures at hub k respectively and is specific heat capacity of water.

The nodal mass flows ( ) are subjected to the continuity of flow equations given by (3) which relates nodal flows with the pipe flows. The pipe flows are further related to the hydraulic heads using pressure drop equations, as defined in [START_REF] Dincer | Exergy: Energy, Environment and Sustainable Development[END_REF].

(all mass flows into the node) = (all mass flows out of the node)

= ( (3)
) 4
where and are hydraulic heads at nodes i and j; is pipe mass flow from node j to node i and is the corresponding pressure resistance coefficient.

Equation ( 5) describes the energy balance of mixing water at a given node while (6) represent the temperature drop across a pipe.

T m = T m (5) _ = _ (6a) = + + + ( 6 b )
where ( , ) terms are the incoming mass flow rates and water temperatures at a given node j while ( , ) terms are the outgoing mass flow rates and water temperature at the same node j respectively; _ and _ are outlet and inlet water temperatures, respectively. is the soil temperature at the surface of the pipe; U is the overall heat transfer coefficient; , , and are the inner radius of carrier pipe, outer radius of the carrier pipe, outer radius of an insulation layer and outer radius of an outer jacket, respectively; , , and represent the convective coefficient of water, thermal conductivity of carrier pipe, thermal conductivity of the insulating material and thermal conductivity of the outer jacket.

In addition to the above equations, which govern the network part of the energy system, there are additional equations which govern the conversion relationships between different energy carriers at each hub. These equations, as shown in [START_REF] Bilgen | Exergy analysis and experimental study of heat pump systems. Exergy[END_REF], relates the demands, generations, injections into the network and conversion between different energy carriers at a

given hub [START_REF] Ayele | An extended energy hub approach for load flow analysis of highly coupled district energy networks: Illustration with electricity and heating[END_REF][START_REF] Ayele | Pseudo-dynamic simulation on a district energy system made of coupling technologies[END_REF].

( ) ( ) ( ) = ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 7 )
where ( ) , ( ) and ( ) are the active electricity, reactive electricity and heat demands at hub k;

( ) represent a coupling coefficient at hub k relating generation type with load type ; ep, eq and h indicate active electric, reactive electric and heat carriers, respectively;

( ) , ( ) and ( ) are active electricity, reactive electricity and heat power locally generated at hub k.

Exergy analysis

Equations ( 1) -( 7) are solved using Newton-Raphson iterative methods to determine the operating conditions of the DHN and electric distribution network. The load flow solution is then used to calculate exergy flows in the DHN. The exergy streams involved in the DHN are the water flows at different temperature and pressure. These physical exergies are computed using (8) [START_REF] Bejan | Thermal Design and Optimization[END_REF][START_REF] Dincer | Exergy: Energy, Environment and Sustainable Development[END_REF].

= + ( 8 )
where is the physical exergy of a mass flow at temperature T and pressure P with respect to the restricted dead state reference of temperature, To and pressure, Po; is density of water; In this paper, a temperature of 283.15K, which is equal to the presumed soil temperature at the surface of the pipe, and a pressure of 10 5 Pa, which is equivalent to atmospheric pressure, are taken as restricted dead state references.

The electricity consumption by the circulation pump for each pipe is considered as a pure exergy. For a given branch, the same mass flows on both supply and return pipes which implies that the same amount of electricity is consumed by each of the circulation pumps on the return and supply pipes. Hence, the electricity consumed by the branch, We, to compensate the pressure drop on both supply and return sides can be computed using ( 9).

= 2 (9)
where is gravitational acceleration, is the pressure head difference between nodes i and j; is magnitude of the mass flow in the pipe and is efficiency of the circulation pump (it is assumed to be 80%).

Particle Swarm Optimization (PSO)

First developed by Kennedy and Eberhart [START_REF] Kennedy | Particle swarm optimization[END_REF] in 1995, PSO is an optimization algorithm which tries to find the global best value in analogy to the way a flock of birds scatter and regroup. The whole group is referred to as a swarm and its individual members are called particles. If there are M variables of optimization, then each particle in the swarm defines a point in M-dimensional space, usually referred to as position of the particle. In each iteration, all the particles try to adjust their position by taking their own past experience and the social knowledge into account. Randomness is also included in the algorithm to minimize the possibility of being trapped by a local optima. The position of particle i with M number of optimization variables is defined as shown in (10a).

= ( , , … , )

( 1 0 a )

The new direction and speed of the particle ( ) is updated using (10b). Using the new velocity of the particle, the new position of the particle ( ) is calculated as shown in (10c).

= + ( ) + ( ) (10b) = + (10c)
where is the inertia/damping factor; is the current velocity of particle i; is a self-accelerating (exploration) factor; is a global accelerating (exploiting) factor; is the current position of particle i; is the best position of the particle in the past; is the global best position achieved by the swarm in the past; and are random numbers between 0 and 1.

Though there is no strictly binding rule in selecting the values of , and , Aote et al. [START_REF] Aote | Improved Particle Swarm Optimization Based on Natural Flocking Behavior[END_REF] argues that better results are found using a step by step variation of parameters in the following order: decreasing from 2.5 to 0.5 and increasing from 0.5 to 2.5. The same strategy is employed in this paper and is made to vary from 0.9 to 0.4.

The objective function of the optimization, as given in [START_REF] Coss | Formulation of Exergy Cost Analysis to Graph-Based Thermal Network Models[END_REF], is minimization of the operating cost of the district heating network. There are both equality and inequality constraints that should not be violated while achieving the objective function. All the equations ( 1) -( 7) are taken as equality constraints while equations (12a) -(12e) are the main inequality constraints. Equation (12a) defines the bus voltage limits; equation (12b) defines the maximum transmission line ampacity either in the form of root mean square (rms) current or kW power [START_REF] Glover | Power System Analysis & Design, SI Version[END_REF]; equation (12c) defines the maximum allowed mass flow in each pipe [START_REF]isoplus: Flexible and rigid pipes and pipeline systems: isoplus -isoplus Fernwärmetechnik n[END_REF]; equation (12d) sets the limit on the supply temperature of heat source hubs and equation (12e) defines the allowed return temperature from heat consuming hubs. The temperature limits depend on the characteristics of heat sources, the temperature levels required at the secondary side of heat consumers and the regulations of the municipality, such as Legeionellosis issues [START_REF] Frederiksen | District Heating and Cooling[END_REF]. Additional constraints on the sizes of power plants and heat pumps are discussed in Section 3.

+ + + + (11)
where CPhg, CPelg, CPh-imported, and CPel-imported are costs of the generated heat, generated electricity, imported heat and imported electricity, respectively while CWe is the cost of electricity used for circulation pumps. The analysis is conducted in four different scenarios. The first two scenarios deal with topology reduction with fixed generation and temperature profiles while the last two scenarios deal with thermo-economic optimization on the reduced topology. The loading and HP sizes for each scenario are summarised in Table 1. In Scenario I, a 100kW heat demand is assumed at each of the Hubs 2, 4 and 6. Hubs 3 and 5 are selected as sources of heat so that there will be transport of heat throughout the network to meet the demands located at Hubs 2, 4 and 6. This will help to identify the lossiest branch from those which are part of the two loops. Accordingly, a HP of 40kWe electrical rating running at full load with a coefficient of performance (COP) of 4 is assumed to be connected at each of Hub 3 and Hub 5. All sources' temperatures of are assumed to be at 85 o C while all the return temperatures from the consumers are set at 35 o C. The steady state load flow is then performed to determine the operational state of the network. Scenario II is the same as Scenario I except that the lossy branches are isolated in the former case. Scenario III deals with cost and temperature optimization after the lossy branches are isolated. PSO is used with 150 a population size of and 200 maximum iteration. In addition to the constraints listed in [START_REF]HOMER -Hybrid Renewable and Distributed Generation System Design Software[END_REF], a continuous range of 0 -25kWe HPs at COP of 4.0 are considered as variables of optimization. A price of 0.20€/kWh of electricity and 0.10 €/kWh of heat are assumed at Hub 1. The operating cost of the solar PV is assumed to be zero. Scenario IV is the same as Scenario III except that the heat demand at Hub 4 is reduced by 40kW while the demand at Hub 6 is increased by 40kW.

Results and discussions

Identifying lossy branches (Scenarios I & II)

The hub level load flow results of Scenario I are presented in Table 2 while the branch parameters of the DHN are summarised in Table 3. The total amount of heat demand is 300kW. To meet this demand, 320kW of heat is generated from the two HPs using 80kW of electricity. Although the generated heat from the two HPs was 20kW more than the total heat demand, it was not enough to compensate the losses in the network. Hence, additional 99.75kW of heat is imported from the neighbourhood. The total heat loss in this network is about 119.75kW giving a DHN energy efficiency of 71.47%. The electricity lost in the distribution network is 0.0231kW which accounts 0.029% of the total electricity demand of HPs. Table 3 also shows the amount of heat transported by each branch and their corresponding efficiencies.

It is clear that branch 2-4 is dissipating all the incoming heat from the two nodes and shall be isolated. This is due to the lowest mass flow rate in the pipe which resulted into a temperature drop from 77.17 to 13.02 on the supply side and from 35 to 11.12 on the return side of the DHN (see Table 3). The next lossy branches, according to their energy efficiency, are branches 2-3 and 3-4. Though branch 2-3 has slightly lower energy efficiency than branch 3-4, the latter is selected to be isolated as the former is critical branch in order for keeping all the network parts interconnected. The preferred network topology after removing branches 2-4 and 3-4 looks like as shown in Fig 3.

On the other hand, based on the values of heating network parameters found from the load flow analysis, the exergy loss across each branch are calculated as shown in Table 4. The exergy loss calculation for each pipe considers the exergy destruction due to heat loss and pressure drop. The exergy loss associated with the pressure drop across each pipe is equivalent to the exergy input by the corresponding circulation pump (i.e. We/2, see equation ( 9)). The effect of friction on increasing the water temperature is neglected in this study. As it can be seen from Table 4, the branch 2-4 has the lowest exergy efficiency followed by branches 3-4 and 2-3. Isolating branches 2-4 and 3-4 results in a similar topology as in Fig 3. Fig. 3 The reduced network topology after isolating the lossy branches The exergy destruction at each node due to the irreversibility of mixing of water at different temperature is calculated by taking all the input and output exergy flows both on supply and return nodes. A complete mixing of water is assumed at all nodes. Each node represented by the grey circle in After running the load flow simulation with the reduced topology (i.e. Scenario II), the heat loss is reduced to 92.62kW giving a DHN energy efficiency of 75.64%. The detailed results of the load flow are summarised in Tables 5 and6. The loss in the electricity distribution network is about 0.028kW (0.036% of the demand) which is slightly higher than the loss in Scenario I. The exergy destruction at branch and node levels for Scenario II are summarised in Tables 8 and9, respectively. The lowest branch exergy efficiency in Scenario II is about 57.97% which is much higher when compared to that of Scenario I (which is 2.49%). There is no significant difference in the nodal efficiencies, except a slight improvement at node 2 due to the decrease in the number of mixing flows from 3 in Scenario I to 2 in Scenario II.

The total exergy input and output of the DHN for Scenario II are 73.62kW and 56.89kW, respectively, with an exergy efficiency of 77.29%. This shows that Scenario II has slightly higher efficiency for the same amount of loading and HP sizes. Considering the prices of 0.20€/kWh of electricity from the grid and 0.10 €/kWh of heat from neighbourhood, it is found that the total operating cost of the DHN before isolating lossy branches (Scenario I) is calculated to be 17.99€/h.

After the lossy branches are isolated (Scenario II), the operating cost is reduced to 15.68€/h.

Thermo-economic optimization (Scenarios III & IV)

Scenario III is the application of PSO on the reduced topology (Fig. 2) with the consideration of all the constraints discussed in Section 2.3 and Section 3. The load flow results of the DHN after running the PSO on Scenario III are shown in Tables 10 and11. As it can be seen from Table 10, the PSO selected HPs at Hubs 2, 4 and 6 to operate at 25kWe, each of them producing 100kW. The produced heat is equal to the heat demand at the corresponding hub. The HPs at Hubs 3 and 5 are set at zero. Although there is free electricity at Hub5, the corresponding HP is not selected by the PSO. It means that the electricity is transported to and used by HPs at the other hubs. In other words, the PSO found that the cost of transporting heat from Hub 5 is higher than the cost of transporting electricity from the same hub. As all the heat demands are met locally at each hub, the nodal and pipe mass flows are zero. Thus, there is no thermal exergy flow and no heat loss in the DHN (see Table 11). The DHN is at 100% of energy efficiency. The loss in the electric distribution network is 0.029kW which is about 0.038% of the electricity demand by the HPs (i.e. 75kW). The operating cost of the DHN is 7.005€/h which shows a 55% reduction compared to Scenario I.

The optimization is repeated on Scenario IV (unbalanced loading of hubs made by shifting 40kW of load from Hub 4 to Hub 6 while keeping the total demand at the same value of 300kW). The results are shown in Tables 12131415. The total cost has increased slightly to 8.35€/h compared to Scenario III. The HP at Hubs 2 is selected in Scenario IV to run at its full capacity producing 100kW of heat which is equal to the heat demand at the same hub. The HP at Hub 6 is also selected to produce 100kW of heat at full capacity. However, the demand at this hub is 40kW more than what is produced. The offset has to be met by heat generated at the other hubs. The HP at Hub 4, on the other hand, could have been set to generate only 60kW of heat. But, the PSO compared cost of production, loss in the transportation and capacity limits and selected HP at Hub 4 to run at its maximum capacity producing extra 40kW of heat than its demand. This heat is transported to Hub 6. As there is loss associated with the transport, additional heat power generation is required to compensate it. There are three options for this: running HP at Hub 3, running HP at Hub 5 and importing heat from Hub 1. HP at Hub 5 is selected by the PSO as there is a local generation of electricity at this hub. This will avoid the additional loss in the electric network that could have been incurred if the HP at Hub 3 was selected. It should also be noted that the size of the HP at Hub 5 is not at its maximum capacity. The reason could be associated to the cost of the possible heat loss in the heating network while transporting the heat produced. Generally speaking, supplying demands from locally available sources helps to decrease the loss in the network. HPs are demands from the electric network and sources from the heating network point of views. Their optimization is, therefore, affected by the possible losses in both networks.

The total heat lost in the network in Scenario IV is 26.8kW which implies a DHN energy efficiency of 91.8%. The power lost in the electric network is about 0.031kW which is about 0.038% of the demand by the HPs (i.e. 81.701kW). The total Figure 4 shows the exergy losses of the seven branches for Scenarios I, II and IV. Scenario III is not included as all the network flows and, hence, the corresponding heat losses are zero. From Fig. 4, it can be observed that the loss in branch 3-4 is higher in Scenario II than I, but the total heat loss is lower in Scenario II. From the four scenarios, the third scenario has the lowest (zero) heat loss in the network which is followed by Scenarios IV, II and I.

Figures 5 and6 show the electric power losses and branch mass flows with respect to their limits, respectively. It can be observed that the branch flows in both of the electric and heating networks are within their limits. Figure 7 shows the nodal voltage profiles in per unit. All of the voltage magnitudes are nearly equal to 1pu. It that the voltage drop on the branches is almost zero. This is because of the assumption of a unity power factor for each HP which implies a The supply temperatures at different hubs for different scenarios are shown in Fig 8 . The supply temperature at different hubs for Scenarios I and II are within the limits. For Scenario III, nodal mass flows from all hubs are nearly zero (see Table 10). Thus, equation (12d) is not binding. In the case of Scenario IV, the supply temperatures at Hubs 2, 3, 4 and 5 are found to be equal to 65 . As sat in (12d). 12) and, hence, the constraint (12e) is not binding for them. Thus, the return temperature inequality constraint of (12e) is satisfied at all hubs for all scenarios.

Conclusion

The network topology optimization based on branch efficiency showed that both of the energy and exergy analyses could result in the same reduced network topology. If exergy analysis is applied on DHN with the full consideration of temperature, mass flows and hydraulic heads, it could give a better clarity in identifying the lossy branches and nodes of thermal networks. Significant amount of exergy destruction takes place across the branches, rather than at the nodes. It has also been found that the contribution of the return pipe network in the exergy loss is indispensable, though it is much lower than the supply side pipe networks. On the other hand, exergy analysis is based on the load flow results which are computed on energy basis. Furthermore, energy analysis can be further combined with thermo-economic optimization using heuristic algorithms, such as Particle Swarm Optimization, in order to decrease operational costs of the reduced topology of the DHN. The optimization results show that distributed heat pumps are more economical than the neighbourhood DHN for the given load profile and price signals. However, the optimality of each HP highly depends on the system heat demand profiles and the relative location of each HP from the nearby heat load and from the nearby electricity generation plant. It also depends on the cost of electricity and heat in the neighbourhood and the coupling technology used. In general, avoiding the heating network, if possible, or running it at a lower possible temperature profile is found to have the lowest operational cost. In other words, HPs near to the thermal load are usually the first priority to run. If two similar HPs are far from the heat load, as is the case for HPs at Hubs 3 and 5 of scenario IV, then the HP which is located to cheaper electricity generation plant gets a priority. Thus, consideration of the electricity network model is very important in order to arrive at an optimal operation strategy of a district energy system consisting of coupling technologies such as HPs.

The methodology developed in this paper can be applied on different combinations of energy carriers, distributed generations, coupling technologies and thermal storage. The exergy analysis covered in this study is limited to only at DHN level. It can be complemented by considering the exergy interaction between different energy carriers inside the energy hubs. The COP of each HP is also assumed to be equal for partial and full load running. This could be improved by incorporating a model for partial loading COP of a HP. Electricity demands with both active and reactive loads together with CHPs and HPs with lagging power factors can also be considered to study the capacity of the electricity distribution network. The sensitivity of the optimal solutions can also be further investigated by considering a range of prices for different energy carriers, such as gas, fuel, electricity and heat. Optimization algorithms other than PSO can also be applied for comparative study.

Nomenclatures

  study A hypothetical district heating network with six nodes and two loops, shown in Fig 2, is considered as a case study. The solid lines with arrow represent the supply pipe network while the dotted lines with arrow represent the return pipe network of the DHN. The black solid lines without arrow represent the electric distribution network. Each of the grey circles represents node/bus at which the corresponding hub interacts with the network. Each hexagon represents an energy hub consisting of energy conversion devices, demands and local production of heat and electricity. The details of the pipe and insulation parameters together with the resistance and reactance of the electrical transmission lines are described

Fig. 2 A

 2 Fig. 2 A small hypothetical heating network

  Fig 1 has two physically separated thermal nodes: one on the supply side and the other on the return side of the DHN. Any heat flow from/to external environment is also treated as two separate flows, i.e. one on the supply side and the other on the return side with opposite direction of flow. The nodal exergy efficiencies, considering both supply and return nodes, are shown in Table5. Node 2 has the lowest nodal efficiency due to the mixing of three flows at different temperatures on the supply side. On the other hand, nodes 1 and 5 are at 100% efficiency because of having a single mass flow going into the node. It can be concluded that the nodal exergy destructions are negligible compared to the branch exergy destructions. The total exergy input and output of the DHN are calculated to be 77.04kW and 56.62kW, respectively. In other words, about 20.36kW of exergy is destroyed in the DHN giving a DHN exergy efficiency of 73.49%.

Fig. 4 Fig. 5 Fig. 6

 456 Fig. 4 Comparison of exergy losses on the branch different operating scenarios

  demand. Hence, only active power flow is required in the network. Active power flows are highly dependent on voltage angles and are less dependent on voltage magnitude unlike to reactive power flows. As a result, the voltage magnitude variations are negligible as shown inFig 7.

Fig. 7 Fig. 8 Figure 9 ,

 789 Fig. 7 Voltage magnitude in per unit at different nodes for different scenarios

  demand (var) Mass flow rate from a hub (kg/s) Mass flow rate from node i to j (kg/sparticle i current velocity of particle i We electricity used for circulation pumps (W) X current position of particle i new position of particle i Best position of particle i Global best position Z Depth of pipe from the boundary surface to the centre of pipe (m

Table A -

 A

1, Appendix A.

Hub1 is considered as a slack hub from which the deficit in heat and electric power balance is compensated from the neighbourhood networks. It also acts as a point of export to the neighbourhood should the district network have excess production than what is required. Hub 2, 4 and 6 are connected with heat consumers. Hub5 is assumed to have a solar PV generation of 40kW. HPs are considered as a means of coupling between the electricity and heating networks.

Table 1 :

 1 Description of scenarios

	Hub	Scenario I	Scenario II	Scenario III	Scenario IV
	1	Slack hub	Slack hub	Slack hub	Slack hub
	2	100kW of heat load	100kW of heat load	Heat load, HP (0 -25kWe)	Heat load, HP(0 -25kWe)
	3	40kWe HP running at full load	40kWe HP running at full load	HP (0 -25kWe)	HP (0 -25kWe)
	4	100kW of heat load	100kW of heat load	100kW of heat load	60kW of heat load, HP (0 -25kWe)
	5	40kWe HP running at full load	40kWe HP running at full load	HP (0 -25kWe)	HP (0 -25kWe)
	6	100kW of heat load	100kW of heat load,	100kW of heat load, HP (0 -	140kW of heat load, HP (0 -
				25kWe)	25kWe)

Table 2 :

 2 Load flow results at node level -Scenario I

	Hub Pepg (kW) Phg (kW) HP_e (kW) Lh (kW) m(kg/s)	Ts	Tr	Hs (m) Hr(m)
	1	40.0231	99.746	0	0	0.453	85.000 32.361 10.000	6.000
	2	0	0	0	100	-0.638	72.455 35.000	8.948	7.052
	3	0	160	40	0	0.693	85.000 29.846	9.130	6.870
	4	0	0	0	100	-0.567	77.166 35.000	8.952	7.048
	5	40	160	40	0	0.717	85.000 31.672 11.384	4.616
	6	0	0	0	100	-0.658	71.301 35.000	8.445	7.555

Table 3 :

 3 Load flow results of the DHN at branch level -Scenario I

	Nodes	Flow	Supply Pipe Network of DHN	Return Pipe Network of DHN		Branch i to j
												We
						Tsi	Tsj	Hi	Hj	Tri	Trj	(kW)	Net heat	Loss	Efficie
	i	j	(kg/s)	Hi (m)	Hj (m)	( o C)	( o C)	(m)	(m)	( o C)	( o C)		flow (kW)	(kW)	ncy %
	1	2	0.453	10.00	8.948	85.000	77.082	6.00	7.052 32.361	35.00	0.0117	79.74	20.0	79.94
	2	4	-0.016	8.948	8.952	13.017	77.166	7.05	7.048 35.000	11.12	0.0000	0.00	5.87	0.00
	2	3	-0.169	8.948	9.130	65.668	85.000	7.05	6.870 35.000	28.56	0.0008	-21.72	18.3	54.33
	3	4	0.167	9.130	8.952	85.000	65.461	6.87	7.048 27.197	33.26	0.0007	22.53	17.9	55.72
	3	6	0.357	9.130	8.445	85.000	75.099	6.87	7.555 31.700	35.00	0.0060	59.87	19.7	75.23
	4	5	-0.717	8.952	11.38	79.895	85.000	7.05	4.616 33.255	31.67	0.0427	-139.9	20.1	87.46
	4	6	0.301	8.952	8.445	77.166	66.807	7.05	7.555 31.144	35.00	0.0037	40.13	17.9	69.11

Table 4 :

 4

			At	At		Exergy	At	At		Exergy	Net exergy	Exergy	Exergy
	i	j	node i	node j	loss	efficiency	node i	node j	loss	efficiency	flow (kW)	lost (kW)	efficiency
	1	2	16.447	13.391	3.06	81.39%	1.812	2.245	0.433	80.51%	13.391	3.489	79.27%
	2	4	0.013	0.472	0.46	2.85%	0.079	0.010	0.069	12.14%	0.013	0.528	2.49%
	2	3	3.566	6.134	2.57	58.13%	0.839	0.510	0.329	60.77%	3.566	2.897	55.17%
	3	4	6.058	3.498	2.56	57.74%	0.447	0.733	0.285	61.02%	3.498	2.846	55.14%
	3	6	12.928	9.973	2.96	77.12%	1.387	1.786	0.399	77.51%	9.973	3.355	7 4 . 7 9 %
	4	5	22.847	26.139	3.29	87.33%	3.143	2.622	0.521	82.87%	22.847	3.813	85.56%
	4	6	8.937	6.575	2.36	73.55%	1.128	1.509	0.382	74.63%	6.575	2.744	70.53%

Exergy of water at the inlet and outlet of branch pipes and associated losses -Scenario I

Nodes

Exergy of pipe on the supply side (kW) Exergy of pipe on the return side (kW) Branch i to j

Table 5 :

 5 Exergy flow to/from the environment and exergy efficiency at each node -Scenario I

	Exergy

on supply side nodes (kW) Exergy on return side nodes (kW) Nodal exergy efficiency

	Node	External input	Total input	Total output	External input	Total input	Total output
	1	16.447	16.447	16.447	-1.812	1.812	1.812	100.00%
	2	-16.567	16.970	16.567	3.163	3.163	3.163	98.00%
	3	25.120	25.120	25.120	-2.327	2.344	2.327	99.94%
	4	-16.798	26.345	26.206	2.809	3.947	3.876	99.31%
	5	26.139	26.139	26.139	-2.622	2.622	2.622	100.00%
	6	-16.491	16.547	16.491	3.296	3.296	3.296	99.72%

Table 6 :

 6 Load flow results at node level -Scenario II

	Hub Pelg(kW) Phg (kW) HP_e (kW) Lh (kW) m(kg/s)	Ts	Tr	Hs (m) Hr(m)
	1	40.028	76.622	0	0	0.343	85.000 31.574 10.000	6.000
	2	0	0	0	100	-0.618	73.694 35.000	9.363	6.637
	3	0	160	40	0	0.718	85.000 31.730	9.792	6.208
	4	0	0	0	100	-0.532	79.914 35.000	9.000	7.000
	5	40	160	40	0	0.720	85.000 31.872 11.449	4.551
	6	0	0	0	100	-0.630	72.900 35.000	8.781	7.219

Table 7 :

 7 Load flow results of the DHN at branch level -Scenario II

	Nodes	Flow	Supply Pipe Network of DHN	Return Pipe Network of DHN		Branch i to j
				Hi		Tsi	Tsj	Hi	Hj	Tri	Trj	We	Net heat	Loss	Efficie
	i	j	(kg/s)	(m)	Hj (m)	( o C)	( o C)	(m)	(m)	( o C)	( o C)	(kW)	flow (kW)	(kW)	ncy %
	1	2	0.343	10.0	9.36	85.00	74.723	6.00	6.64	31.574	35.00	0.005	56.97	19.65	74.35
	2	3	-0.275	9.36	9.79	72.41	85.000	6.64	6.21	35.000	30.80	0.003	-43.03	19.30	69.03
	3	6	0.443	9.79	8.78	85.00	76.915	6.21	7.22	32.305	35.00	0.011	77.69	19.98	79.54
	4	5	-0.720	9.00	11.45	79.91	85.000	7.00	4.55	33.463	31.87	0.043	-139.89	20.11	87.43
	4	6	0.188	9.00	8.78	79.91	63.424	7.00	7.22	29.103	35.00	0.001	22.31	17.58	55.94

Table 8 :

 8 Exergy of water at the inlet and outlet of branch pipes and associated losses -Scenario II

Node Exergy of pipe on the supply side (kW) Exergy of pipe on the return side (kW) Branch i to j

			At	at node		Exergy	At	At		Exergy	Net exergy	Exergy lost	Exergy
	i	j	node i	j	loss	efficiency	node i	node j	loss	efficiency	flow (kW)	(kW)	efficiency
	1 2	12.45	9.510	2.94	76.38%	1.290	1.685	0.398	76.44%	9.510	3.344	73.99%
	2 3	7.14	9.977	2.84	71.54%	1.351	0.979	0.373	72.34%	7.139	3.217	68.94%
	3 6	16.08	13.031	3.05	81.02%	1.774	2.203	0.435	80.32%	13.031	3.498	78.84%
	4 5	22.95	26.242	3.3	87.37%	3.199	2.670	0.550	82.92%	22.947	3.910	8 5 . 4 4 %
	4 6	5.98	3.664	2.32	61.25%	0.595	0.933	0.339	63.69%	3.664	2.658	57.95%

Table 9 :

 9 Exergy flow to/from the environment and exergy efficiency at each node-Scenario II

		Exergy on supply side nodes (kW)	Exergy on return side nodes (kW)	Nodal exergy
	Node	External input	Total input	Total output	External input	Total input	Total output	efficiency
	1	12.448	12.448	12.448	-1.290	1.290	1.290	100.00%
	2	-16.645	16.649	16.645	3.036	3.036	3.036	99.98%
	3	26.055	26.055	26.055	-2.750	2.752	2.750	99.99%
	4	-16.965	22.947	22.947	2.635	3.229	3.199	99.88%
	5	26.242	26.242	26.242	-2.670	2.670	2.670	100.00%
	6	-16.575	16.695	16.575	3.136	3.136	3.136	99.40%

Table A -

 A 1: Pipe parameters in the heating network and transmission line parameters in the electricity network

	Hubs			Carrier Pipe Parameters		Insulation	Outer Jacket		Transmission lines
			L	D1 + t1	t1	k2	e	k3	D3	t3	k4	L	R	X	B
	from to	(m)	(mm)	(mm)	(W/mK)	(mm)	(W/mK)	(mm)	(mm)	(W/mK)	(mi)	( /mi)	( /mi)	(μS/mi)
	1	2 1000	60.3	3.2	40	0.05	0.027	140	3.0	0.40	0.5	0.307	0.458	9.46
	2	4 1000	60.3	3.2	40	0.05	0.027	140	3.0	0.40	0.5	0.307	0.458	9.46
	3	2 1000	60.3	3.2	40	0.05	0.027	140	3.0	0.40	0.5	0.307	0.458	9.46
	3	4 1000	60.3	3.2	40	0.05	0.027	140	3.0	0.40	0.5	0.307	0.458	9.46
	4	5 1000	60.3	3.2	40	0.05	0.027	140	3.0	0.40	0.5	0.307	0.458	9.46
	3	6 1000	60.3	3.2	40	0.05	0.027	140	3.0	0.40	0.5	0.307	0.458	9.46
	4	6 1000	60.3	3.2	40	0.05	0.027	140	3.0	0.40	0.5	0.307	0.458	9.46

Acknowledgments

The research presented is performed within the framework of the Erasmus Mundus Joint Doctorate SELECT+ program 'Environomical Pathways for Sustainable Energy Services' and funded with support from the Education, Audiovisual, and Culture Executive Agency (EACEA) (FPA-2012-0034) of the European Commission. This publication reflects the views only of the author(s), and the Commission cannot be held responsible for any use, which may be made of the information contained therein.

exergy input and output of the DHN are 15.16kW and 6.43kW, respectively, with an exergy efficiency of 42.42%. This shows that although the DHN is running at a lower exergy efficiency, the overall system is running at a lower cost due to the fact that very low amount of exergy is flowing through the network in comparison to Scenarios I and II.


MD Hester Colboc
email: hester.colboc@aphp.fr

MD Philippe Moguelet

MD Dominique Bazin

MD Priscille Carvalho

MD Anne-Sophie Dillies

MD Guillaume Chaby

MD Hervé Maillard

MD Diane Kottler

MD Elisa Goujon

MD Christine Jurus

MD Marine Panaye

MD Vincent Frochot

MD Emmanuel Letavernier

PhD Michel Daudon

MD Ivan Lucas

MD Raphaël Weil

MD Philippe Courville

MD; Jean-Benoit Monfort

MD François Chasset

MD Patricia Senet

Localization, Morphology and Chemical Composition of Calciphylaxis-Related Skin Deposits Running head: Characterization of calciphylaxis-related skin deposits

Question What are the precise localization, morphology and chemical composition of calciphylaxis-related skin deposits? Findings CUA calcifications are composed of pure calcium-phosphate apatite, always located circumferentially, mostly in the intima of otherwise normal-looking vessels, and often associated with interstitial deposits, unlike calcifications observed in cutaneous arteriolosclerotic vessels, which are associated with medial hypertrophy containing the calcifications and no interstitial deposits.

Meaning

The differences observed between CUA and cutaneous arteriolosclerosis regarding calcification location and vessel morphology suggest different pathogenetic mechanisms and provide new insights into CUA pathogenesis that could explain the poor efficacy of vasodilators and the therapeutic effect of calcium-solubilizing drugs.

SETTING Seven French hospitals participated in the study. PARTICIPANTS This study included consecutive adults diagnosed with CUA, confirmed according to Hayashi's clinical and histologic criteria. Patients with normal renal function were excluded. For comparison, 5 skin samples from patients with arteriolosclerosis and 5 others from the negative margins of skin-carcinoma resections were also analyzed.

MAIN OUTCOME(S) AND MEASURE(S)

Localization and morphology of the CUArelated cutaneous calcium deposits were assessed with optical microscopy and fieldemission-scanning electron microscopy (FE-SEM), and the chemical compositions of those deposits were evaluated with µFourier transform infra-red (FT-IR) spectroscopy, Raman spectroscopy and energy dispersive X-ray (EDX).

RESULTS

Thirty-six patients (median age: 64 years) were included, and 29 cutaneous biopsies were analyzed. CUA and arteriolosclerosis skin calcifications were composed of pure calcium-phosphate apatite. CUA vascular calcifications were always circumferential, found in small-to-medium-sized vessels, with interstitial deposits in 76% of the samples. A thrombosis, most often in noncalcified capillary lumens in the superficial dermis, was seen in 5 CUA patients' samples. Except for calcium deposits, CUA patients' vessel structure appeared normal, unlike thickened arteriolosclerotic vessel walls. Twelve (33%) patients died of CUA.

CONCLUSIONS AND RELEVANCE CUA-related skin calcifications were exclusively composed of pure calcium-phosphate apatite, localized circumferentially in small-tomedium-sized vessels and often associated with interstitial deposits, suggesting its pathogenesis differs from that of arteriolosclerosis. Although the chemical compositions of CUA and arteriolosclerosis calcifications were similar, the vessels' appearances and deposit localizations differed, suggesting different pathogenetic mechanisms.

Introduction

Uremic calciphylaxis, also called calcific uremic arteriolopathy (CUA), is a rare and severely morbid condition that predominantly affects dialyzed, end-stage renal disease (ESRD) patients. Its frequency among ESRD patients reaches 4% and its incidence increases for those on hemodialysis. [START_REF] Weenig | Calciphylaxis: natural history, risk factor analysis, and outcome[END_REF] CUA's significant morbidity and mortality result from extensive skin necrosis and septic complications, with the latter being the leading cause of death. For ESRD patients, an increased risk of subsequent CUA development has been associated with female sex, diabetes mellitus, higher body mass index, elevated serum calcium, phosphorus and parathyroid hormone levels, nutritional status cinacalcet or vitamin K-antagonist treatments. [START_REF] Nigwekar | A nationally representative study of calcific uremic arteriolopathy risk factors[END_REF] Although noninvasive imaging tools (eg, plain X-rays) have been reported to help diagnose CUA, [START_REF] Shmidt | Net-like pattern of calcification on plain softtissue radiographs in patients with calciphylaxis[END_REF] none of those tools have been systematically evaluated. [START_REF] Halasz | Calciphylaxis: comparison of radiologic imaging and histopathology[END_REF] Definitive CUA diagnosis requires a skin biopsy. However, because biopsying the skin is associated with the risk of new ulceration, bleeding and infection, actually obtaining one is often discussed sometimes debated. [START_REF] Nigwekar | Calciphylaxis: risk factors, diagnosis, and treatment[END_REF] When obtained, deep cutaneous biopsies of CUA lesions show smallsized calcifications, <500 µm, in hypodermal vessels and/or interstitial tissue, highly suggestive of CUA with good specificity. [START_REF] Cassius | Calciphylaxis in haemodialysed patients: diagnostic value of calcifications in cutaneous biopsy[END_REF] Despite well-characterized clinical and histologic descriptions of CUA, its precise pathogenetic mechanism remains unclear. [START_REF] Jean | Calciphylaxis in dialysis patients: to recognize and treat it as soon as possible[END_REF] Arteriolar calcification is probably the first event, followed by thrombosis and skin ischemia. Chemical composition determination and description of the skin calcifications through physicochemical techniques could contribute to understanding CUA pathogenesis, leading to more appropriate and specific treatments. [START_REF] Bazin | Characterization and some physicochemical aspects of pathological microcalcifications[END_REF] Indeed, nanotechnologies are receiving increased attention to improve understanding of the effects of pathologic deposits on living tissues. [START_REF] Colboc | Physicochemical characterization of inorganic deposits associated with granulomas in cutaneous sarcoidosis[END_REF][START_REF] Bazin | Pathological calcifications and selected examples at the medicinesolid-state physics interface[END_REF] The aims of this study were to determine precisely the localization, morphology and chemical composition of calcifications in the skin of CUA patients, and then examine whether any association could be established between their microscopy findings and clinical characteristics.

Methods

This study was conducted in compliance with Good Clinical Practices and the Declaration of Helsinki, and in accordance with French law. Formal Ethics Committee approval of the study protocol was obtained (no. EudraCT 2017-000906-39).

Case Selection and Histopathologic Analyses

This retrospective case-control study included consecutive adults diagnosed with CUA, confirmed according to Hayashi's clinical and histologic criteria, and seen in 7 French hospitals between January 2006 and January 2017. [START_REF] Hayashi | Calciphylaxis: diagnosis and clinical features[END_REF] Patients with normal renal function were excluded. Patients' medical histories, treatments and laboratory findings were extracted from their medical charts. They were classified into 2 clinical subgroups, distal or proximal CUA, according to the skin-lesion localizations described by Brandenburg et al. [START_REF] Brandenburg | Calciphylaxis: a still unmet challenge[END_REF] Five skin samples from patients with arteriolosclerosis and 5 others from the negative margins of skin carcinoma resections on the leg were included and served as controls. All 10 controls had normal renal function; only the 5 with arteriolosclerosis from among a cohort of patients with necrotic angiodermatitis had leg-skin biopsies.

Skin-biopsy samples were sent to and centralized in Tenon Hospital, Department of Pathology. For each subject, 1.5-µm-thick sections of paraffin-embedded skin biopsies were deposited on glass slides, for hematoxylin-eosin-saffron (HES) and von Kossa staining, and low-e microscope slides (MirrIR, Kevley Technologies, Tienta Sciences, Indianapolis, IN, USA) for field-emission-scanning electron microscopy (FE-SEM), µFourier transform infrared (FT-IR) spectroscopy and Raman spectroscopy. [START_REF] Dessombz | Shedding light on the chemical diversity of ectopic calcifications in kidney tissues: diagnostic and research aspects[END_REF] Vascular and interstitial calcifications, the calibers of calcified vessels and the topography of deposits in skin sections were analyzed and compared between CUA patients and controls.

FE-SEM

FE-SEM (Zeiss SUPRA55-VP, Oberkochen, Germany) was used to describe the ultrastructural characteristics of tissue sections. As previously described, high-resolution images were obtained with in-lens and Everhart-Thornley secondary electron detectors. [START_REF] Brisset | Microscopie Électronique à Balayage et Microanalyses[END_REF] Measurements were taken at low voltage (1-2 kV), without the usual carbon-coating of the sample surface. For some samples, energy-dispersive X-ray (EDX) was also used to identify calcium in the abnormal deposits.

FT-IR and Raman Spectroscopies

Using the same sample as that for FE-SEM analyses, FT-IR and Raman spectroscopies identified the chemical compositions of the CUA calcifications. All the FT-IR hyperspectral images were recorded with a Spectrum Spotlight 400 FT-IR imaging system (Perkin-Elmer Life Sciences, Courtaboeuf, France), with 6.25-mm spatial resolution and 8-cm -1 spectral resolution. [START_REF] Awonusi | Carbonate assignment and calibration in the Raman spectrum of apatite[END_REF] Raman spectra were collected with a micro-Raman system (LabRam HR-800 Evolution, Horiba, Japan) using 785-nm laser excitation wavelength, 100× objective (Olympus, numerical aperture 0.9) and 300 grooves per mm grating. Spectra were corrected at baseline to suppress the strong luminescence background. [START_REF] Carden | Application of vibrational spectroscopy to the study of mineralized tissues (review)[END_REF]

Statistical Analyses

Data are expressed as median [range] or number (%). χ 2 or Fisher's exact tests were used to compare qualitative variables; Wilcoxon or Mann-Whitney tests were used to compare paired or nonpaired nonnormally distributed variables, respectively. Parameters with P < .2 in univariate analysis were entered into a multivariate logistic-regression model, with Y as the dependent variable.

Results

Clinical and Histopathologic Findings

Among the 36 CUA patients included, 29 skin biopsies could be analyzed by optical microscopy, FE-SEM and spectroscopies. Clinical and histopathologic data are summarized in Table 1.

Optical microscopy analysis of HES-and von Kossa-stained CUA biopsies always found calcifications in small-and/or-medium-sized vessels (diameter: 10-300 m), mostly in hypodermal arterioles and capillaries (Figure 1). These deposits were massive, occupying in the entire circumference of the vessel, and located in the intima and sometimes the media.

They could be associated with intimal fibrous or myxoid changes.

Those CUA vascular calcifications were associated with interstitial deposits, mainly localized to the hypodermis, in 76% of the samples. Calcification size ranged from 1 to 500 m, sometimes becoming confluent, with clusters reaching several millimeters in diameter.

They were either isolated small clusters between adipocytes (Figure 2A andB) or aligned in a pearl collar along the cytoplasmic membranes of adipocytes (Figure 2D andE). Calcified elastic fibers and/or collagen fibers were also seen in hypodermic septa or deep dermis.

Thromboses were seen in 5 samples, most often in noncalcified capillaries in the superficial dermis.

The 5 arteriolosclerosis-control biopsies showed classical intimal fibrous endarteritis and Monckeberg medial calcinosis associated with calcium deposits that were localized within the media along the internal elastic lamina. Those calcifications were never circumferential and no interstitial localization was observed. Negative margins of resected carcinomas contained no vascular or interstitial calcium deposits. Twelve (33%) patients died of CUA. Poorer CUA prognosis was only associated with male sex or nodular lesions (eTable 1 in the supplement).

FE-SEM and EDX Analyses

Subcellular calcification localization and morphology were assessed with FE-SEM. CUA vascular deposits were circumferential (Figures 1F and2C); at least 1 thrombosis in 5/29 samples was located in the vessel lumen or intima, while the media usually appeared normal with rare calcifications. Interstitial deposits surrounded adipocytes, along the cell membranes.

Morphologically, these calcifications appeared to be composed of aggregated micrometric plates (Figure 2F).

FE-SEM analyses of control skin biopsies showing arteriolosclerosis contained vascular

calcifications in the media (Figure 1C), associated with medial hypertrophy and intimal fibrosis; no interstitial deposits were seen. FE-SEM analyses of negative resected carcinoma margins confirmed the absence of vascular and interstitial deposits.

EDX analyses of CUA samples verified the calcium and phosphate composition of vascular and interstitial deposits, with similar calcium/phosphate ratios in both sites. EDX analyses showed the composition of vascular deposits in control arteriolosclerosis biopsies to be similar to that found in CUA.

Spectroscopy Analyses

FT-IR analyses of CUA and arteriolosclerosis skin calcifications showed that all were composed of calcium-phosphate apatite (Figure 3). Careful examination of 3 CUA samples identified the presence of amorphous carbonated calcium-phosphate associated with calciumphosphate apatite that was not seen in any arteriolosclerosis patients' samples.

Raman spectroscopy confirmed the similar calcium-phosphate-apatite compositions of vascular and interstitial calcifications (Figure 4). [START_REF] Awonusi | Carbonate assignment and calibration in the Raman spectrum of apatite[END_REF]

Discussion

These FE-SEM, EDX and spectroscopy analyses were able to finally specify the localization and the complete chemical composition of CUA patients' skin calcifications. Our spectroscopic analyses demonstrated that those circumferential calcifications, located in the intima and media of CUA patients' skin vessels, were composed exclusively of calciumphosphate apatite. In 76% of the CUA patients' samples, calcium-phosphate apatite was also found in interstitial tissue of the deep dermis and hypodermis, along the cytoplasmic membranes of adipocytes, and elastic and collagen fibers.

The chemical composition and localization of cutaneous CUA calcifications have been investigated in only a few small series. Using EDX and FE-SEM, Kramann et al found calcium/phosphate accumulations, with a molar ratio matching that of hydroxyapatite, in the hypodermis of 7 CUA patients. [START_REF] Kramann | Novel insights into osteogenesis and matrix remodelling associated with calcific uraemic arteriolopathy[END_REF] Two other studies used mass spectrometry and Raman spectroscopy to detect and characterize CUA skin calcifications. Using mass spectrometry, Amuluru et al showed that tissue samples from 12 CUA patients had high iron and aluminum contents, suggesting a role of metal deposition in CUA pathogenesis. [START_REF] Amuluru | Metal deposition in calcific uremic arteriolopathy[END_REF] Using microcomputed-tomography and Raman spectroscopy, Lloyd et al confirmed the presence carbonated apatite in debrided CUA tissues from 6 patients. [START_REF] Lloyd | Raman spectroscopy for label-free identification of calciphylaxis[END_REF] However, those studies included only small numbers of samples and performed only chemical analyses. To the best of our knowledge, the precise localization and exact morphology of these abnormal deposits

have not yet been reported.

Patients with proximal lesions, high body mass index, ulcerated lesions and female were reported to have poorer prognoses. [START_REF] Nigwekar | Calciphylaxis[END_REF] Our univariate and multivariate analyses did not identify those factors as having a relationship with shorter survival, and retained only male sex and nodular lesions as being significantly associated with mortality. However, the relatively small number of patients included make those findings less relevant than risk factors identified in larger studies.

Skin deposits in CUA and arteriolosclerosis patients were always composed of calciumphosphate apatite, but their different localizations in the vessel walls could indicate different pathogenetic mechanisms. Indeed, arteriolosclerotic vessel walls are thickened, with media hypertrophy, suggestive of slowly progressive thickening and degeneration of the arteriolar wall with secondary calcium-phosphate apatite accumulation. Circumferential CUA vascular deposits were located mostly in the intima of otherwise normal-looking vessels, suggesting a faster and global process, with primary calcium deposition.

Ellis et al recently showed that pathognomonic cutaneous calcifications associated with CUA could also occur in viable tissue from ESRD patients without CUA, with ESDR amputated because of peripheral arterial disease. [START_REF] Ellis | Questionable specificity of histologic findings in calcific uremic arteriolopathy[END_REF][START_REF] Nigwekar | Cutaneous calcification in patients with kidney disease is not always calciphylaxis[END_REF] However, Ellis et al did not consider that some of their controls might have had undiagnosed acral calciphylaxis and undergone amputations for distal ischemia. Those possibilities might explain some of their histopathologic observations of calciphylaxis in their controls. However, Our histologic findings (circumferential calcifications of small-to-medium-sized vessels often associated with interstitial calcifications) and high-technology tools, such as FE-SEM, enabled us to demonstrate several differences between the vascular calcifications seen in CUA and arteriolosclerosis, thereby confirming our previous results and those of Chen et al.

6,23

Patients with calciphylaxis probably develop skin calcifications subsequent to a dysequilibrium between calcification promoters and inhibitors. Calcium-inhibitor deficiency, like matrix Gla protein, impaired inhibition of calcium-phosphate precipitation, thereby leading to skin calcifications. [START_REF] Nigwekar | Calciphylaxis[END_REF] Chronic inflammatory states, including ESRD, are associated with increased levels of reactive oxygen species that impair endothelial function. [START_REF] Sowers | Calcific uremic arteriolopathy: pathophysiology, reactive oxygen species and therapeutic approaches[END_REF] ESRD-related endothelial dysfunction engenders vessel-wall abnormalities, including the presence of bone morphogenetic protein in medial and intimal layers. [START_REF] Nigwekar | Increased bone morphogenetic protein signaling in the cutaneous vasculature of patients with calciphylaxis[END_REF] Such vascular protein modification, associated with increased calcium × phosphate products, might explain the intimal and medial calcifications observed in CUA.

Interstitial calcifications were also seen in 76% of CUA samples. Voluminous calcifications of the subcutaneous tissue or dystrophic and metastatic calcinosis cutis are known to occur in a variety of disorders, including dermatomyositis, lupus or trauma. The ectopic calcified masses, composed of hydroxyapatite and amorphous calcium-phosphate apatite, were disseminated throughout the dermis and hypodermis that appeared petrified, involving interstitial tissue and vessels. [START_REF] Reiter | Calcinosis cutis: part I. Diagnostic pathway[END_REF] The pathophysiology is still unclear but it has been hypothesized that hypodermal inflammation might release the phosphate bound to denatured proteins and serve as a niche for ectopic calcifications. [START_REF] Reiter | Calcinosis cutis: part I. Diagnostic pathway[END_REF] However, despite clinical and pathologic differences, the physiology of these calcifying disorders might be similar, and calcium deposits obstructing some hypodermis vessels in CUA might lead to detrimental adipocyte, collagen and elastic fiber alterations, and the release of the phosphate bound to denatured proteins and ectopic interstitial calcifications. According to that hypothesis, interstitial calcifications might be a secondary phenomenon, thereby explaining the inconstant interstitial localization. The constant presence of vascular deposits could suggest a primary vascular trigger of CUA.

Our finding that CUA vascular calcifications were always circumferential, suggests that therapeutic strategies with vasodilators might be less relevant than those using calciumsolubilizing drugs. Therefore, drugs directly impacting calcium-phosphate precipitation, like sodium thiosulfate, bisphosphonates and vitamin K supplementation would seem to be more appropriate and a rational approach for future therapeutic studies on CUA. [START_REF] Zitt | Use of sodium thiosulphate in a multi-interventional setting for the treatment of calciphylaxis in dialysis patients[END_REF][START_REF] Nigwekar | Vitamin K-dependent carboxylation of matrix Gla protein influences the risk of calciphylaxis[END_REF] Along the same line, Dedinszki et al, who studied other calcifying disorders, including pseudoxanthoma elasticum and generalized arterial calcifications of infancy, reported that oral pyrophosphate inhibited tissue calcifications. [START_REF] Dedinszki | Oral administration of pyrophosphate inhibits connective tissue calcification[END_REF] Because our study was retrospective, some information, including vital status was missing for some patients. Our failure to identify factors associated with higher mortality in larger studies might be explained by the relatively small size of our series. It is worth highlighting that calcification morphology can be modified by the sectioning of paraffinembedded skin biopsies and that the appearance of these deposits may differ between glass and low-e slides, making it more difficult to discern the relationship between optical microscopy and electronic microscopy.

Conclusions

In conclusion, our histologic, FE-SEM, EDX and spectroscopy results provide a better understanding of the morphologic, ultrastructural and chemical characteristics of CUA patients' skin calcium-phosphate-apatite deposits. Those deposits appear to be initially vascular and develop rapidly in normal vessel walls. Circumferential vascular and interstitial deposits, albeit inconstant, were specific to CUA. Although the chemical compositions of the calcifications were similar in CUA and arteriolosclerosis, the vessels' appearances and deposit localizations differed, suggesting different pathogenetic mechanisms.

Fig 1 .

 1 Fig 1. Skin biopsy sections. Arteriolosclerosis with asymmetrical fibrous intimal thickening

Fig 2 .

 2 Fig 2. Skin biopsy sections. CUA hypodermic capillaries with voluminous and

Fig 3 .

 3 Fig 3. µFourier transform infra-red (FT-IR) spectroscopy of the interstitial CUA deposits: A,

Fig 4 .

 4 Fig 4. Micro-Raman signatures and optical micrographs (magnification 10× and 100×) of A,

Acknowledgments

Access to Data and Data Analysis Hester Colboc had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.

The authors declared no conflicts of interest involving this work, no relevant financial activities outside the submitted work (during the 3 years prior to submission) and no other relationships or activities that readers could perceive to have influenced, or that give the appearance of potentially influencing, what is written in the submitted work (based on all relationships that were present during the 3 years prior to submission).

Funding/Support: no funding.

Role of Funder/Sponsor Statement

No funding organization or sponsor we involved in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

The authors thank LabEx MICHEM (ANR-11-IDEX-0004-02) for allowing us to use their nano/micro-Raman facilities in UPMC. We thank Quentin Rezard from CNRS, LPC, Ba340, Université Paris XI, and Chantal Jouanneau from INSERM, Hôpital Tenon, for their help and support in this study