Roger Prud'homme

PERTINENCE OF MICRO-GRAVITY STUDIES FOR SOLID/LIQUID PHASE CHANGE

Some problems of solid/liquid phase changes are presented. Attention is focused on interface modeling for numerical analysis, and one-directional growing. Microgravity relevance of some situations is emphasized.

INTRODUCTION

Solid/liquid phase changes are sensitive to gravity. Natural convection occurs coupled to solidification front motion. The interfacial zone is often very complex to describe. Indeed, front curvature and solid phase structure depend on several factors and it will be interesting to eliminate some of them due to gravity for a best understanding of solidification process. Experiments in microgravity conditions are necessary, in drop towers, parabolic flight, sounding rockets and satellites. For instance, an experimental facility, named DECLIC (Dispositif d'Etude de la Croissance et des Liquides Critiques), will take place in the ISS (International Space Station). Experiments on transparent material solidification will be performed in DECLIC. At the same time it is very useful to perform calculations with and without gravity effects. Process control by vibration or magnetic field is sometimes required to stabilize solidification fronts. Several teams works on these topics in the French Research Group : "Transport Phenomena and phase transitions in Microgravity" (GDR -P2TPM -CNES/CNRS). The research topics of this teams are the following [

Natural convection.

Microgravity is relevant for fluid flows when density gradients are large and forced convection not too important. It is generally the case when Grashov number [START_REF] Landau | Mécanique des fluides[END_REF] is of order one or larger. Grashov number

2 3 L g Gr     (1)
permits to compare effects of buoyancy force to viscous drag force. It can be introduced writing momentum equation as follows:

U 2 µ g ' p dt U d              (2)
In these formula,   is the local density deviation

( one has       
where   corresponds to the liquid at rest at the same altitude),

   
is the kinematical viscosity, p' is the pressure deviation from the hydrostatic equilibrium, U  and dt U d  are local fluid velocity and acceleration. Fluid velocity resulting from buoyancy can be approximated

                g L U g L 2 U g x U U (3)
The resulting Reynolds number is then ISTP13,Victoria, Canada, 14-18 July 2002

PRUD'HOMME 2 Gr 2 3 L g L U Re         ( 4
)
Rayleigh number is more appropriate than Grashov number in the case of liquid phase, when coupling with energy equation [START_REF] Chandrasekhar | Hydrodynamic and hydro-magnetic stability[END_REF] happens and, sometimes, with mass balances of species. Two nondimensional numbers are then used according to the studied case

D L C g Sc Gr Ra , L T g Pr Gr Ra 3 C C C 3 T T T            (5)
where subscripts ( T ) and ( C ) refer to thermal and solutal origin of

  : T T      or C C      .
Rayleigh numbers take into account the experimental configuration. The classical Rayleigh-Bénard thermal instability occurs in a fluid layer heated from below. Solidification process is generally more complex; for instance, in directional solidification of alloys inside a cylindrical vertical crucible, the solidification layer is moving and the solidification front in not planar, upward temperature gradient is generally positive, there is a coupling between temperature and concentrations. Radial thermal gradients drive natural convection and modify concentration fields [START_REF] Benielli | Effect of the thermal convection on directional solidification of succinonitrile-acetone alloy: Comparison between experimental and numerical studies[END_REF]. Instability occurs when the appropriate Rayleigh numbers reach critical values corresponding to the considered processes.

Instabilities and coupling.

In solidification problems, many sources of motion are present. Natural convection occurs when the Rayleigh number becomes higher than a critical value which depends in particular on the geometrical configuration.

Increasing temperature (or concentration) gradient, higher order critical Rayleigh numbers appear, and resulting in very complicated situations. An other example of motion is produced by Marangoni effect and Marangoni instability [START_REF] Scriven | On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity[END_REF] that can occur in floating zone solidification (or in other solidification procedure, when the contact between the fluid phase and the wall of the crucible is not ensured, as it is often the case in microgravity), where there is a liquid-gas or liquid-liquid (monotectic alloys) interface. On the ground, this other effect is coupled with Rayleigh-Bénard instability [START_REF] Nield | Surface tension and buoyancy effects in cellular convection[END_REF]. Marangoni-Bénard instability can be coupled to Soret effect, possibly in microgravity [START_REF] Bergeon | Marangoni-Bénard instability in microgravity conditions with Soret effect[END_REF]. Magnetic field is used for measuring diffusion coefficients in liquids [START_REF] Lehmann | MHD convection control applied to chemical diffusivities measurements[END_REF], or for compensating for gravity, and numerical studies have been performed about coupling between buoyancy and magnetic effects [START_REF] Touhiri | Stabilisation par champ magnétique de la convection en cavité cylindrique chauffée par le bas[END_REF].

MORPHOLOGICAL INSTABILITIES IN DIRECTIONAL SOLIDIFICATION. "Convection

effects strongly influence the development of solidification microstructures. However, most microstructure models are based on purely diffusive transport mechanisms. For this reason, crucial benchmark data required to test fundamental theories of microstructural pattern formation have resulted from solidification experiments conducted in microgravity environment, where convection effects can be substantially reduced, and/or from ground based experiments with restricted samples sizes where convection effects can be eliminated" [START_REF] Karma | Microstructural patern formation during solidification, Introduction à la session 2[END_REF]. The conditions for instabilities to appear in directional solidification of dilute alloys were given by Mullins and Sekerka [START_REF] Mullins | [END_REF]. In the case of binary lamellar eutectics, relations between lamellar characteristic spacing, temperature gradient and front velocity has been found first by Hunt and Jackson, who also gave a first estimate of the stability bounds of the lamellar pattern [12]. These theories apply to highly idealized systems. They can not explain complex phenomena observed in real systems such as curvature of the front in relation to convective instabilities, or eutectic colony formation. These last phenomena have been observed in thin-sample directional solidification of the transparent eutectic alloy CBr 4 -C 2 Cl 6 . Fig. 1 shows existence of colonies when impurities are present. The transition between planar lamellar eutectic front and eutectic colonies goes through intermediate structures as traveling waves and twophase fingers which has been recently observed [START_REF] Akamatsu | Traveling waves, two-phase fingers, and eutectic colonies in thin-sample directional solidification of a ternary eutectic alloy[END_REF] and are now studied by linearized theory or by phase field method (see Section Phase field model for microstructures).

INTERFACIAL MODELING AND APPLICATIONS.

Transition-zone. Interfacial zone is often very complex to study. In some cases of directional solidification in alloys, the solidification front appears as a smooth (but generally non planar) surface with local thermochemical equilibrium between solid and liquid. In other cases, for sufficiently high values of pulling velocity, microstructures resulting from an instability process appear, but the interface remains relatively smooth. In the case of lamellar eutectic alloys it is important to determine the size and distribution of microstructures in relation to the external constraints.

The interfacial morphology becomes very complicated for dendrites and for dendritic layers. Local balance equations resulting from irreversible thermodynamics can be written in each case, both for the interface and for the bulk phases. A critical problem for numerical resolution is the presence of an interfacial discontinuity at the boundary between phases. To avoid this difficulty, some authors have replaced the discontinuity by a continuous description of the transition region. This is the concept of phase field. Two classes of phase field method, which differ by the scale of the description (macroscopic, and microscopic -or mesoscopic, but not molecular) are presented here. One of the macroscopic method is applied to dendritic-like porous structures. The main difference with the other cases is that a mushy zone between fully solid and liquid phases is considered [START_REF] Camel | Structural effects of convective flows in dendritic solidification -Numerical modelling[END_REF][START_REF] Goyeau | Numerical calculation of the permeability in a dendritic mushy zone[END_REF]. In this method of prescribing a Darcy source term the velocity value arising from the solution of the momentum equation are inhibited, reaching values close to zero on complete solid formation. The Darcy source term

  S 1 1 v v K µ      
appears on the right-hand side of momentum equation where K denotes the isotropic permeability and represents the direct link between microscopic morphology and the macroscopic equations of conservation. Here, K is a scalar for simplicity [START_REF] Camel | Structural effects of convective flows in dendritic solidification -Numerical modelling[END_REF]. It is expressed as a function of the volume fraction l f of the liquid. In more general case it becomes a second order tensor. Closure relations where given [START_REF] Goyeau | Numerical calculation of the permeability in a dendritic mushy zone[END_REF][START_REF] Favier | Analytical and experimental study of transport processes during directional solidification and crystal growth[END_REF] for the isotropic case, and more recently for the non isotropic one. There is not place to give more details on this method. In the following, basic equations of a macroscopic model, which is called enthalpy method, and some results of its application to particular cases, are given. Then the phase field model for microstructures is briefly presented. The two methods give continuous balance equations that are valid in the whole considered volume, containing solid and fluid phases.

Enthalpy method.

Benielli et al. [START_REF] Benielli | Effect of the thermal convection on directional solidification of succinonitrile-acetone alloy: Comparison between experimental and numerical studies[END_REF], El Ganaoui [START_REF] El Ganaoui | Modélisation numérique de la convection thermique instationnaire en presence d'un front de solidification deformable[END_REF] and Guérin et al. [START_REF] Guérin | Finite volume and spectral methods applied to Pb-30%Tl alloy solidification[END_REF] consider a single set of homogenous balance equations adapted to the problem of phase change in a 2D configuration:

0 ) v .(ρ t ρ       (6)          s l l l v v C C C D C v t C                        (7) ) s u (u l ρ ρ K l μ u) l ρ ρ l .(μ x p u) v .(ρ t ρu                  ( 8
)

) F T (T T β g 0 ρ ) s v (v l ρ ρ K l μ v) l ρ ρ l .(μ y p v) v .(ρ t ρv                  (9)   )) v v )( h h ( .( ) h h ( c k . ) h c k .( ) h v .( t h s l s                           ( 10
)
where ρ is an average density weighted by the liquid and solid mass fractions, v 

  S l l l C f 1 C f C    .
With this model, including appropriate closure relations and boundary and initial conditions, it is possible to obtain isotherms and streamlines which show, in particular, the position of a curved smooth interface. The numerical solution is obtained by the enthalpy model associated to a finite volume approximation. One obtains evolutions of the meltsolid interface, and of velocity and solutal fields. Fig. 2 is obtained in a case where the porous term is not relevant [START_REF] Benielli | Effect of the thermal convection on directional solidification of succinonitrile-acetone alloy: Comparison between experimental and numerical studies[END_REF]. Position of numerical isotherms is in good agreement with front recoil measurements performed on pure succinonitrile (SCN). This result gives information on the contribution of thermal convection to this recoil. However, the authors point out discrepancy between purely diffusive model and experimental data. Finally, it appears that comparative studies with and without convection are required to clarify and quantify convection influence, therefore underlining the great interest of microgravity (DECLIC spatial project) for solidification studies.

Phase field model for microstructures.

To explain microstructures in constrained growth, and recently in eutectic colony formation [START_REF] Akamatsu | Traveling waves, two-phase fingers, and eutectic colonies in thin-sample directional solidification of a ternary eutectic alloy[END_REF], Plapp and Karma have studied the problem first analytically [START_REF] Plapp | Eutectic colony formation: A stability analysis[END_REF], and then numerically, using a phase field model [START_REF] Plapp | Eutectic colony formation: A phase field model[END_REF]. They study a ternary alloy close to a binary eutectic which, for simplicity, they assume to have a symmetric phase diagram. They introduce a phase field   t , z , x  that distinguishes between solid and liquid, i.e., a scalar field, that has a fixed value in the bulk phases and vary continuously across the smooth, diffuse interface. They start from a dimensionless Helmholtz free energy functional, and they deduce, by minimization, three local equations between three variables, which are valid everywhere under appropriate assumptions:

    sol liq 3 2 f f ' h 2 2 W t                 (11)                              u W u u f M t u 2 2 u 2 liq 2     (12)                 C C f M t C ~2 liq 2   (13)
In these equations, u is a scaled concentration

      2 C C C t , z , x C t , z , x u E    
, where C E , C  and C  are the compositions of the liquid and the two solid phases in the pure binary eutectic at the eutectic temperature T E ,

  t , z , x C ~ is the concentration of impurities,                3 2 3 h 3 is an interpolation function,   T , C , u f
  C , u , M  and   C , u , M ~
are the mobility functions of the eutectic component and the ternary eutectic, respectively. Numerical simulations which have been performed with this phase field model, have enabled the authors to carry out large-scale simulations of colony formation starting from arrays of up to 40 lamella pairs. They found a good overall agreement with the theoretical predictions of linear analysis [START_REF] Plapp | Eutectic colony formation: A stability analysis[END_REF], which predicts a destabilization front by long-wavelength modes that may be stationary or oscillatory. But they find that the growth of the lamellae is not exactly normal to the large scale envelope of the composite interface, a rule used in the linear stability analysis [START_REF] Plapp | Eutectic colony formation: A stability analysis[END_REF]. The phase field model must be extended to 2D interfaces in 3D configuration [START_REF] Dejmeck | Etude numérique de la croissance dendritique et cellulaire[END_REF]. Akamatsu et al. [START_REF] Akamatsu | La dynamique de solidification des eutectiques lamellaires : des échantillons minces aux systèmes massifs[END_REF] compare results obtained in thin and massive sample experiments. In the first case, one has generally a flat solid-melt interface. In the last case, the 2D solidification front presents a curvature because the isotherms are curved for well-known technical reasons. This curvature is of course influenced by gravity but it exists also in microgravity. Thermosolutal convection will also lead to modifications in local dynamics of eutectic fronts and can also cause a macro-segregation. Other specific phenomena are pointed out for 2D fronts: varying orientations of lamellae between eutectic grains, global slow rotation of the microstructure around z axis, presence of "faults". The authors propose to compare benchmark space experiments to ground ones, and also to study the intermediate case of semi-massive samples.

Second gradient. Some fluid-fluid interfaces have been studied by second gradient methods [START_REF] Casal | La théorie du second gradient et la capillarité[END_REF][START_REF] Seppecher | Etude d'une modélisation des zones capillaires fluides : Interfaces et lignes de contact[END_REF]. In second gradient model, internal energy by unit mass depends not only on the entropy and the density but also on the magnitude of the density gradient [START_REF] Gatignol | Mechanical and thermodynamical modeling of fluid interfaces[END_REF] 

         2 , s, e e  (14)
The associated Gibbs relation is

                   d 1 d p ds T de (15)
where  is a coefficient called the "capillarity coefficient ". Using average quantities, and introducing the volumetric masses of the species and their gradients, this type of model can be certainly extended to solidification fronts in mixtures and can be considered as a phase field model [START_REF] Gatignol | Mechanical and thermodynamical modeling of fluid interfaces[END_REF][START_REF] Gouin | Energy of interaction between solid surfaces and liquids[END_REF].

OTHER RELEVANT PROBLEMS.

To complement previous sections and conclude this paper, some solidification problems relevant for microgravity experiments, and comparison with theoretical and numerical results are quoted. Melting and thermal stabilization stages preparatory to directional solidification greatly affect the initial state on which growth is started [START_REF] Benielli | Free growth and instability morphologies in directiona melting of alloys[END_REF], and then directional solidification [START_REF] Akamatsu | Traveling waves, two-phase fingers, and eutectic colonies in thin-sample directional solidification of a ternary eutectic alloy[END_REF]. It is pointed out that free melting is not the mere reversal of free crystal growth. Two phenomena have been observed in situ and in real time during directional melting of transparent succinonitrile-acetone alloys in a cylinder: nucleation and growth of liquid droplets in the bulk solid, and liquid dendrites, due to morphological instability of the phase boundary. Benielli et al. [START_REF] Benielli | Free growth and instability morphologies in directiona melting of alloys[END_REF] analyze the dynamics of melting morphology at the solid-liquid interface. The criterion for morphological instability in directional melting reads

      1 k C m G D D k V V 0 l s MI     (16)
with V MI the critical melting velocity, C 0 the initial solute concentration. The authors emphasize the interest of carrying out experiments in the limit of diffusive transport of solute in the liquid, that imposes to work in the absence of gravity. They participate to DECLIC project of CNES. Berne, Pasturel & Vinet [START_REF] Berne | Germination et sélection de phases dans les métaux et alliages réfractaires : approches expérimentales en tube à chute libre et théorique par calculs ab initio[END_REF] study crystalline nucleation and phase selection in refractory metals and alloys in the 50-meters high Grenoble drop-tube of CEA, they emphasize the interest of microgravity and ultra-vacuum to ensure absolute no-contact conditions and purification by evaporation of really spherical droplets. Camel & Dupouy [START_REF] Camel | Comparative study of the columnar-equiaxed transition in microgravity and on ground during directional solidification of a refined Al-3.5 wt% Ni alloy[END_REF] study the influence of natural convection on the formation of dendritic microstructures in the columnar/equiaxed transition range in the specific case of Al-3.5 wt% Ni alloy. Nguyen Thi et al. [START_REF] Nguyen Thi | Solidification dirigée d'alliages Al-3.5 %pds Ni : analyse des étapes préliminaires de fusion et de stabilisation[END_REF] stress the importance of microstructures for the resulting properties of materials. Spatial experiments LMS and STS-95 on directional solidification of Al-3.5 wt% Ni alloy unabled them to understand the role played by preparatory phases melting and stabilization, and the initial directional-solidification transient, so that the measured concentration variation in solidified samples in the AGHF (Advance Gradient Heating Facility) can be explained. The problem of solidification front curvature is very important and experiments will be performed on transparent material for a better knowledge of this phenomena in DECLIC instrument. Process control by vibration was studied for stabilizing solidification fronts and obtaining planar fronts. Reduced gravity experiments are to be performed in this field, for a better understanding of the effects of vibrating fields on fluids, interfaces and multiphase flows [START_REF] Lyubimov | Orienting effect of vibrations on interfaces[END_REF]. Finally it should be kept in mind that, even in microgravity conditions, solidification remains sensitive to the gravity level and orientation as shown by Simpson and Garimella, for instance [START_REF] Sympson | The influence of gravity levels on the horizontal Bridgman crystal growth of an alloy[END_REF].

ACKNOWLEDGMENTS

Fig. 1 .

 1 Fig. 1. Eutectic colonies in CBr 4 -C 2 Cl 6 -Naphtalene, V = 31 µm s -1 [13 ].

  weighted by the liquid and solid volume fractions. For instance one has:

Fig. 2 :.

 2 Fig. 2 : Isotherm and streamline plots obtained with SNC for pulling velocity 1

W

  are characteristic thicknesses of the solid-solid and of the solid-liquid interface, respectively, and

FT

  The author acknowledge B. Billia and G. Faivre for their help and M. Plapp, B. Zappoli, E. Arquis and D. Gobin for communicating him interesting papers.NOMENCLATUREGr Grashov number Pr Prandtl number Ra Rayleigh number Re Reynolds number Sc Schmidt number c specific heat of the material C solute concentration, average mass fraction C ~ concentration of impurities D mass diffusivity e internal energy per unit mass f l volume fraction of the liquid g gravitational acceleration G thermal gradient h enthalpy per unit mass, interpolation function k thermal conductivity, segregation coefficient K isotropic permeability L reference length m liquidus slope M mobility function of the eutectic M ~ mobility function of the impurities p pressure s entropy per unit mass t time T, mixture temperature, melting temperature, u x velocity component, scaled concentration U  local fluid velocity v z velocity components V, V t melting velocity, pulling velocity v  local velocity W characteristic thickness x horizontal coordinate y, z vertical coordinate T  thermal expansion coefficient of the liquid  jump  thermal diffusivity, capillarity coefficient µ,  dynamical viscosity, kinematical viscosity  density  phase field Subscripts E eutectic F melting l, s, sl liquid, solid, transition zone  , solid phases in a binary eutectic

"Transport Phenomena and Phase Transitions in Microgravity" (GDR-P2TPM) of Centre National d'Etudes Spatiales (CNES) /


Chuanxia Wang

Yuting He

Xiaoming Qi

Ziteng Zhao

Guanyu Yang

Xiaomei Zhu

Shaobo Zhang

Jean-Louis Dillenseger

Jean-Louis Coatrieux

BiSC-UNet: A fine segmentation framework for kidney and renal tumor

  L'archive ouverte pluridisciplinaire

Introduction

Renal cancer is one of ten most common cancers in human beings. The established treatments of renal cancer include surgery (radical or partial nephrectomy), chemotherapy, radiation therapy and radiofrequency ablation [START_REF] Grubb | Management of von hippel-lindau-associated kidney cancer[END_REF]. The most common treatment is surgery, such as: traditional radical nephrectomy (RN) and minimally invasive laparoscopic partial nephrectomy (LPN) [START_REF] Ljungberg | Eau guidelines on renal cell carcinoma: 2014 update[END_REF]. These treatments are image-based and use computed tomography (CT) or magnetic resonance imaging (MRI). Because of this, major information of kidney and renal tumor should be extracted from the images before surgery. Manual assessment of lesions characteristics in CT images is currently too tedious and time-consuming. Thus, an automatic or semi-automatic kidney and renal tumor segmentation method would be time-saving and useful in clinical practice.

This segmentation task concerns about two aspects: kidney segmentation and renal tumor segmentation. For kidney segmentation, several approaches have shown good performance in CT or MR images. By utilizing random forest algorithms, Cuingnet et al. [START_REF] Cuingnet | Automatic detection and segmentation of kidneys in 3d ct images using random forests[END_REF] proposed a two-step kidney segmentation method. Yang et al. [10] utilized multi-atlas image on a coarse-to-fine segmentation. Torres et al. [9] adapted the B-Spline Explicit Active Surfaces (BEAS) framework for semi-automatic kidney segmentation in CT images. These algorithms only addressed the segmentation of kidney. Some of them may be failed when the shape of kidney changes because of injuries and serious diseases.

For renal tumor segmentation, few research works were devoted to. Linguraru et al. [START_REF] Linguraru | Automated noninvasive classification of renal cancer on multiphase ct[END_REF] developed a level-set based method to extract the renal tumors. However, the seed point provided by the user inside the lesion is needed. Prevost et al. [8] detected the lesion through a multi-scale radial symmetry transform in 3D contrast-enhanced ultrasound data. In CT images, the kidney and tumors may be similar in intensity distributions and textures. More than this, different tumors between different patients usually show very diverse shape appearance and volumetric size according to the different growth stages. Because of these, a fine automatic segmentation of renal tumors is so challenging.

With the development of convolutional neural network (CNN), it has been applied into various aspects in computer vision, such as: image classification, object recognition, image segmentation, etc. Also, CNN has achieved outcome performance in medical image processing, especially in kidney tumor segmentation. [12,11] In [12], Yu et al. proposed the crossbar patches, which consists of two orthogonal non-squared patches and trained two sub-models for kidney tumor segmentation. Yang et al. [11] utilized a three-dimensional (3D) fully convolutional network (FCN) which combines a pyramid pooling module (PPM) for kidney and renal tumor segmentation. These two works focused on tumor shape information and contextual information separately. Yu et al. ignored the contextual information in CT images. The network that Yang et al. used is not focused on the shape information of tumor. To improve these shortcomings, we proposed a structural constraint 3D-UNet (SC-UNet) for kidney and renal tumor segmentation task. The proposed method considers not only contextual information but also shape information during training process.

The problem of category imbalance is a common problem in machine learning tasks, and it often has a serious impact on the segmentation results. Lin et al. proposed a focal loss [START_REF] Lin | Focal loss for dense object detection[END_REF] and keeps a category balance in the object detection task. The dice loss [START_REF] Milletari | V-net: Fully convolutional neural networks for volumetric medical image segmentation[END_REF] balances different categories in the segmentation task by calculating the dice coefficients on each channel. In the kidney and tumor segmentation task, kidney and tumors account for a very small region of the abdominal CT image, leading a serious category imbalance problem. We combines tow SC-UNets for excessive background region on CT images, and propose a BiSC-UNet framework. The proposed framework first take a rough network to get the kidney region of interest (ROI) for the balance between kidney regions and background and then take a fine network for fine segmentation on kidney ROI. We propose a balanced cross-entropy loss to ensure the balance between small tumors and big kidneys.

The rest of this paper is organized as follows. The details of proposed method are shown in Sec. 2. In Sec. 3, the experimental results are reported. Finally, the conclusion of this paper is drawn in Sec. 4.

Methodology

As is shown in Fig. 2, the BiSC-UNet (Sec. 2.2)consists of two cascade-connected network. In the first network, the rough segmentation of kidney and renal tumor will be achieved via a rough SC-UNet (Sec.

SC-UNet for shape and contextual information embedding

As is shown in Fig. 2, the SC-UNet consists of down-sampling part and upsampling part. The down-sampling part is same as 3D-Unet, which consists of three groups of convolutional layers and max-pool layer. The output of each group is represented by y i down i ∈ 1, 2, 3. In up-sampling part, the outputs of former two groups are represented by y 1 up and y 2 up . In Fig. 2, it can be found that the y 2 up is connected by three up-sampling groups. These three branches are corresponded with kidney and renal tumor label, edge of kidney label and edge of renal tumor label. The up-sampling groups are connected with the downsampling groups, like 3D-Unet. The edge labels are generated by taking use of Canny edge detection algorithm. The original CT image (X in × Y in × Z in ) is the input of the network and the segmentations of kidney, tumor, the edge of kidney, tumor are the output.

From the structure of SC-UNet, it can be found that the edge information of kidney and tumor are treated as important as the entire kidney and tumor. By the structure of three branches, the SC-UNet will focus on related shape information learning and combines the contextual information from 3D convolution, the SC-UNet can ensure both contextual and shape information be learned on training process.

BiSC-UNet for fine segmentation

As shown in

Balanced cross-entropy for category imbalance

The proposed balanced cross-entropy loss function utilize the L1 distance to measure the segmentation quality of each region, then the hard regions are selected to calculate the pixel-wise cross-entropy value. The pixel-wise loss value is averaged in each channel to get channel-wise loss value, so that each category will be divided by their size to weight dynamically. Finally, the channel-wise loss values are averaged in the channel direction for image-wise loss value:

L BCE = 1 C C c 1 N n y c,n N n (Sig(|y c,n -ŷc,n | > T )y c,n log ŷc,n ) ( 1
)
where C is the number or channels, N is number of pixels in each channel 3 Experiments and Results

Dataset

KiTS19 challenge data [START_REF] Heller | The kits19 challenge data: 300 kidney tumor cases with clinical context, ct semantic segmentations, and surgical outcomes[END_REF] is used to evaluate the performance of our proposed framework. This dataset contain 210 training cases and segmentation masks.

Each sample contains at least one kidney with a tumor and is resampled to the resolution of 0.781625, 0.781625 and 3 on the X, Y, and Z directions. In our experiment, 168 (4/5) cases are used for training and 42 (1/5) cases are used for testing. Random cropping and random mirroring in three directions are used to augment the data.

Training strategies and implementation

In the rough SC-UNet, the original image is downsampled to 128 × 128 in the X and Y directions, and then the patch cropped in the Z direction is input into the network. The rough output is upsampled to the original resolution and is performed the maximum connected component analysis for two kidney masks.

After that, the two largest regions are considered to be kidney masks and cropped as the kidney ROIs. The X and Y directions size are 160 or 192 (if bigger than 160), the Z direction size is bigger than the mask size on Z direction and a multiple of 16. In the fine SC-UNet, the kidney ROI in original resolution is input into the network for fine segmentation of kidney and tumor. Finally, the mask in kidney ROIs are restored to the original size for complete segmentation masks.

The optimizer of the rough SC-UNet and fine SC-UNet is Adam whose learning rate was 10 -4 . The training batch size was 8 and each network was trained 20 epochs who had 4000 iterations. Our framework has been implemented via Pytorch, and trained and tested on a workstation with the CPU of i7-5930K, the RAM of 128GB and one graphics card of TITAN X of 12GB memory.

Results and analysis

As shown in Fig. 3, our proposed BiSC-UNet achieves fine kidney and kidney tumor segmentation in two steps. The rough segmentation has low resolution and rough edges, and has the ability to used to identify the location of the two kidneys. The fine segmentation achieves a kidney and tumor mask with smooth edges from the kidney ROI. Cases 1, 2, and 3 show the patients with different sizes renal tumors, and each tumor is segmented accurately. In particular, the tumor that could not be detected by rough segmentation in case 3 is obtained in fine segmentation, demonstrating the validity of our cascade structure. As shown in Tab. 1, our balanced cross-entropy improves the performance of BiSC-UNet and increases the dice coefficient of kidneys and tumors by 0.012 and 0.005 compared with the standard cross entropy loss function.

Conclusion

In this paper, we propose a kidney and renal tumor segmentation framework consists of two cascade-connected SC-UNet. Our proposed SC-UNet combines shape information and contextual information and embeds these information into 3D-Unet. For contextual information, this network takes three-dimensional convolutional layers. For shape information, the edge maps of kidney and tumor are treated as important as the entire labeled map on training process. Then, for category imbalance problem, the framework takes two cascade-connected structures to solve the big background impact and the balanced cross-entropy loss to keep kidney and tumor balanced. The first SC-UNet is taken for kidney ROI, the second SC-UNet is trained for fine segmentation. The balanced crossentropy loss keeps the weight of each category balanced according to their size dynamically. By the experiments on KiTS19 challenge data, proposed method achieve outcome performance.

  2.1) to crop a kidney ROI to get background balance and reduce the data size. Then in the second network, the cropped kidney ROIs are input to a fine SC-UNet for fine segmentation. A balanced cross-entropy loss (Sec. 2.3) is proposed to keep category balanced during the training process dynamically to improve the generalization ability.

Fig. 1 .

 1 Fig. 1. The structure of our proposed BiSC-UNet framework.

Fig. 2 .

 2 Fig. 2. The structure of SC-UNet.

Fig 1 ,

 1 the proposed BiSC-UNet framework consists of a rough SC-UNet and a fine SC-UNet which share same structure as is shown in Fig 2 to obtain fine segmentation gradually. The rough SC-UNet takes low resolution images as input and gets rough kidney and tumor segmentation. A maximum connected component analysis is used to remove the noise region and get the kidney ROI in original resolution CT image completely. The fine SC-UNet takes the original resolution kidney ROI image to obtain the fine kidney and kidney tumor ROI segmentation. Finally, two kidney ROI segmentation masks for each image are restored to the original size and generated a complete segmentation mask.

  . The function Sig(|y c,n -ŷc,n | > T ) means if |y c,n -ŷc,n | > T , Sig() = 1, otherwise Sig() = 0. y c,n is the pixel label on the ground truth and ŷc,n is the predicted pixel label probability.

Fig. 3 .

 3 Fig. 3. The visual superiority of our proposed BiSC-UNet. The kidney ROI is cropped according to the rough segmentation and the fine segmentation is achieved from this ROI.

Table 1 .

 1 The dice coefficient of kidney and renal tumors.

	Network	Dice kidney(std)	Dice tumor(std)
	BiSC-UNet(BCE)	0.954(0.070)	0.741(0.262)
	BiSC-UNet(CE)	0.942(0.078)	0.736(0.241)

  8. Prevost, R., Cohen, L.D., Corréas, J.M., Ardon, R.: Automatic detection and segmentation of renal lesions in 3d contrast-enhanced ultrasound images. In: Medical Imaging 2012: Image Processing. vol. 8314, p. 83141D. International Society for Optics and Photonics (2012) 9. Torres, H.R., Oliveira, B., Queirós, S., Morais, P., Fonseca, J.C., D'hooge, J., Rodrigues, N.F., Vilaça, J.L.: Kidney segmentation in 3d ct images using b-spline explicit active surfaces. In: 2016 IEEE International Conference on Serious Games and Applications for Health (SeGAH). pp. 1-7. IEEE (2016) 10. Yang, G., Gu, J., Chen, Y., Liu, W., Tang, L., Shu, H., Toumoulin, C.: Automatic kidney segmentation in ct images based on multi-atlas image registration. In: 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. pp. 5538-5541. IEEE (2014) 11. Yang, G., Li, G., Pan, T., Kong, Y., Wu, J., Shu, H., Luo, L., Dillenseger, J.L., Coatrieux, J.L., Tang, L., et al.: Automatic segmentation of kidney and renal tumor in ct images based on 3d fully convolutional neural network with pyramid pooling module. In: 2018 24th International Conference on Pattern Recognition (ICPR). pp. 3790-3795. IEEE (2018) 12. Yu, Q., Shi, Y., Sun, J., Gao, Y., Zhu, J., Dai, Y.: Crossbar-net: A novel convolutional neural network for kidney tumor segmentation in ct images. IEEE Transactions on Image Processing (2019)

Acknowledgements. This research was supported by the National Key Research and Development Program of China (2017YFC0107903), National Natural Science Foundation under grants (31571001, 61828101), the Short-Term Recruitment Program of Foreign Experts (WQ20163200398), Key Research and Development Project of Jiangsu Province (BE2018749) and Southeast University-Nanjing Medical University Cooperative Research Project (2242019K3DN08).


Pavle Mocilac

John F Gallagher
email: john.gallagher@dcu.ie

Christian Jelsch

Aggregation in three benzamide or pyridylcarboxamide hydrates: formation of 1D chains comprising water molecules in a chloro(pyridyl)benzamide dihydrate

Keywords: Benzamide, Carboxamide, Contact Enrichment, Hydrate, Hydrogen bonding, Interactions, Structural systematics

Three benzamide hydrated derivatives as para-methyl- N-(3-pyridyl)benzamide monohydrate (I) or MpmH 2 O; N-(3-fluorophenyl)-4-pyridylcarboxamide monohydrate (II) or NpmFH 2 O and parachloro-N-(3-pyridyl)benzamide dihydrate (III) or Clpm2H 2 O are obtained from a series of crystallization experiments using a range of solvents to obtain polymorphs and solvates (hydrates).

Most of the crystallization experiment attempts did not provide hydrates and yielded the starting parent crystalline materials. However, from the experiments, two benzamides, Mpm as a monohydrate and Clpm as a dihydrate were isolated and together with a carboxamide monohydrate as NpmFH 2 O are reported herein. The water molecules play a key role in crystal structure formation using classical hydrogen bonding via amide N-H…OH 2 , O-H…N pyridine and O-H…O=C interactions. They compensate for the excess of strong hydrogen bonding acceptors over donors in the benzamide/pyridinecarboxamide molecules, by participating as O-H hydrogen bond donors twice and usually as an O acceptor once. In the Clpm dihydrate, both water molecules form hydrogen bonded chains along the a-axis direction. The lack of hydrate formation in the majority of related benzamides is presumably related to the relative hydrophobicity of these compounds.

INTRODUCTION

Many pharmaceutical drugs are non-polar organic based molecules with limited solubility in polar solvents and water. [1][2][3][4][5][6] This solubility problem can hamper bioavailability in aqueous solutions and requires considerable time and effort in the design of drug delivery systems that are effective in delivery and cost. Significant efforts have been devoted to overcoming this problem over the last few decades using a variety of strategies and has been commented on in several papers and comprehensive reviews. [1,2,6] In this paper we describe three aromatic amide hydrates (I)-(III). These benzamide/carboxamide hydrates are obtained from crystallization reactions using a range of solvents and conditions with the purpose of generating polymorphs and solvates (hydrates) from extensive series of benzamides [7,8] and pyridinecarboxamide derivatives. [9,10] Most crystallization attempts did not provide solvates (or hydrates) and yielded the same parent products as those isolated and reported previously. [7][8][9][10] However three benzamide and carboxamide hydrates were obtained and are reported herein as two benzamide hydrates MpmH 2 O, (I) and Clpm2H 2 O, (III) and a carboxamide monohydrate as NpmFH 2 O, (II), (Scheme 1).

Scheme 1.

Molecular structures of the (I)-(III) hydrates.

EXPERIMENTAL Synthesis and Crystallisation

The parent benzamide/carboxamides of compounds (I) and (II) are Mpm and NpmF and have been reported previously as part of extensive structural systematics studies. [7,10] Three derivatives of Mpm [7] and NpmF [10] (in addition to Clpm) yield hydrates, the former two as monohydrates and Clpm as a dihydrate, when recrystallised from solvents with water being incorporated adventitiously in the crystallization process or from aqueous mixtures. The Mpm hydrate was recrystallized from ethyl acetate, NpmF from diethyl ether and Clpm from acetonitrile/water solution to yield hydrates (I)-(III) as crystalline materials (Figures 1a-c).

Refinement

Crystal structure, data collection and structure refinement details are summarised in Table 1. The refinements of the three crystal structures were performed using similar strategies, as described previously. [7] Hydrogen atoms attached to C atoms were treated as riding using the SHELXL14 [11] defaults at 294(1) K with C-H = 0.93 Å and U iso (H) = 1.2U eq (C) (for aromatic) and the methyl C-H = 0.96 Å (aliphatic) and U iso (H) = 1.5U eq (C). All amino N-H and water H atoms were refined on x,y,z and with isotropic displacement parameters. The Clpm2H 2 O dataset was collected using Cu radiation and as a hemisphere of data to 100% completion to 120. All experiments were performed using a Xcalibur, Sapphire3, Gemini Ultra diffractometer with experiments undertaken at 294(1) K. [START_REF]Oxford Diffraction, CrysAlis CCD and CrysAlis RED[END_REF] Analytical absorption corrections were performed on colourless crystals using ABSFAC. [START_REF] Clark | [END_REF] Computer and graphics programs used include:

CrysAlisPRO, [START_REF]Oxford Diffraction, CrysAlis CCD and CrysAlis RED[END_REF] SHELXS14/6, SHELXL14, [11] PLATON [14] and Mercury. [15] RESULTS AND DISCUSSION

Structural Commentary

From the crystallization experiments two benzamide hydrates were obtained as 1a-c). The experimental details are in Table 1 with selected interactions in Table 2.

Table 2. Selected hydrogen-bond parameters in (I) to (III)

D-H•••A D-H (Å) H•••A (Å) D•••A (Å) D-H•••

A (°) MpmH 2 O N1-H1•••O1W 0.90(3) 1.98(3) 2.863(2) 166 (2)
O1W-H1W Symmetry code(s):

(i) x-½,y-½,z; (ii) x,-y+1,z+½; (iii) -x+1,-y+1,-z; (iv) x,y+1,z; (v) -x,-y,-z; (vi) -x+2,- y+1,-z+1; (vii) x+1,y,z; (viii) -x+2,y+½,-z+½.
The crystal structure of the unsolvated Mpm or para-methyl-N-(3-pyridyl)benzamide (FADZOB) [16] has been reported by us previously [7] and crystallises with Z'=4 (molecules A-D) in the triclinic space group P1. For the MpmH 2 O structure as isolated from ethyl acetate, the aromatic C 6 and C 5 N rings are essentially coplanar at 1.37(9), and at angles of 30.97( 14) and 31.30 (14) to the five atom (C)OCN(C) group incorporating the amide bridge. These geometric data are similar to the conformations of molecules C, D in Mpm [7] as noted with interplanar angles of 1.5(2), 1.9(2) (for C 6 /C 5 N); 24.47(16), 24.79( 16) (for C 6 /amide)and 24.16(16), 24.79( 16) (for C 5 N/amide), respectively. The introduction of the water into the crystal structure of (I) is accommodated by rotation of the central amide group by 6-7 closer to co-planarity with the aromatic rings as compared with the Mpm parent structure. [7] The Mpm hydrate shows the clear role that the water molecule plays in the molecular assembly of (I) and overall crystal structure stability (Figure 2). Water molecules link the Mpm benzamides into 1D chains using a C(7) graph set via N-H…OH 2 and O-H…N pyridine hydrogen bonds as a classical N1-H1…O1W-H1W…N23 i composite interaction (Table 2). This hydrogen bonded assembly is arranged parallel with the (-113) plane. The H 2 O molecule in the Mpm hydrate crystal structure is a hydrogen bond donor twice (H1W, H2W to the pyridine N23 i and amide O1 ii ; Table 2) and acceptor only once (O1W, from the amide N1-H1), which compensates for the presence of one strong donor N1-H1 versus two strong acceptors on the Mpm benzamide molecule (as O1, N23).

This gives a crystal structure with a balanced total of three strong hydrogen bonding donor and three acceptor groups with D:A = (3,3). A similar hydrogen bonding pattern involving the water molecule occurs in the NpmF hydrate crystal structure of (II) (see below). In the structure of (I), the O1W water molecules use their second O-H moiety to link benzamides via longer O-H…O=C interactions into cross linked C(6) chains while extending the interactions into a 3D structure. The two weak C-H…O=C contacts per molecule have little overall effect on the crystal structure.

In comparison with the crystal structure of MpmH 2 O (I), there are small differences between the two sets of similar though independent molecules (A, B and C, D) in the unsolvated Mpm. [7] Given the unusual crystal structure and unexpected number of molecules in the asymmetric unit (Z'=4) [17] it can be surmised that the parent Mpm structure could be the initial kinetic crystallisation product isolated from ethyl acetate.

Figure 2

An ORTEP view of the crystal structure packing in (I) along the b-axis direction. (3-fluorophenyl)-4-pyridylcarboxamide (AMUDIW) [10,16] and is easily accommodated in the crystal structure. This is not unexpected due to free rotation about the CN-CC torsion angle and interchange of the meta-F13 with H15 atoms to give a F13/F15 site occupation of 0.924(3):0.076(3). This disorder was noted previously in the isomorphous NpoF (AMUDOC) and NomF (AMUFIY) structures [10,16] (both in space group Cc), but not in the parent NpmF structure.

Fluorine atom site disorder in fluorinated benzamides is quite common where ortho-or metafluorine atoms adopt either of two sites with the distinct conformations related by rotation of the aromatic ring by 180. [18,19] The structure of (II) can be considered to assemble from N-H…OH 2 and O-H…N interactions about inversion centres as R 4 4 (18) rings comprising two NpmF benzamide [10] and two water molecules (Table 2; Figure 3). Within the grouping of 2  (NpmFH 2 O), tight parallel offset aromatic π…π stacking occurs with a short N24…C25 i contact distance of 3.2036(18) Å and C25…C25 i = 3.346(2) Å (symmetry code i: Table 2). The remaining water O-H donor per asymmetric unit forms an O-H…O=C interaction with the carbonyl O=C group to link dimers into a 1D tape (ca. [20] where two CmoX molecules (X = methyl (M), Br) are effectively linked by two bridging water molecules into cyclic hydrogen bonded (N-H…O-H…N) 2 rings of graph set size R 4 4 (14). The difference in hydrogen bonding cyclic ring sizes between (II) and CmoX [20] is due to the para-N pyridine and nature of the amide bridge in (II). 14) ring via N-H…O-H…N interactions (Figure 4a). This arrangement is similar in geometry to that observed in the isomorphous CmoX monohydrate pair (as noted), [20] though with differences in the O•••N hydrogen bonding distances of 0.15 Å (Table 2). In Clpm2H 2 O the second hydrogen bond donor from O1W forms a hydrogen bond to the second water molecule O2W (while O1W also accepts one hydrogen bond from a symmetry related O2W) generating an alternating 1D hydrogen bonded water arrangement. Therefore, hydrogen bonding is maximised in O1W with two donors and two acceptors. The remaining O2W-H4W donor forms O-H…O=C interactions (with the carbonyl O1 atom) to total two donors and one acceptor in O-H…O hydrogen bonding. The O1W, O2W water molecules assemble in an alternating fashion as (O1W…O2W…O1W…) along the a-axis direction as 1D hydrogen bonded chains. This is not unusual and comparable 1D chains of water molecules have been reported which stabilise the crystal structure e.g. HUWQAS (Figures 3,5). [21] In addition, two weak C-H…O contacts augment the O1W…O2W and N1…O1W interactions and the closest C14-Cl14…Cl14 ix halogen bonding contacts are 3.4353(9) Å and with C14-Cl14…Cl14 ix = 153.58( 7) (symmetry code ix = -x,1-y,-z).

Figure 5

A view of the water molecules in the asymmetric unit of HUWQAS [16,21] An alternative way of understanding the hydrogen bonding process is to consider it to arise from a 1D relay of (O-H…O-H…) interactions as (…O1W-H1W…O2W-H3W…O1W-H1W•••) n with both water molecules using their two remaining O-H donors to form O-H…N pyr and O-H…O=C interactions. The remaining classical interaction involves the amide N1-H1…O1W hydrogen bond.

Structural summary

The three hydrate structures (I) to (III) show features that enhance their supramolecular stability.

Hydrogen bonding is almost fully maximised in all three crystal structures with the observed hydrogen bonding donor:acceptor (D:A) ratio for the two moieties is 1:2 for benzamide, 2: with D-H…A angles of 170-175. Of interest is that two of the three structures contain a metaaminopyridine moiety which is oriented to easily form a hydrogen bonded assembly containing two benzamides and two water molecules. Of further note is the reluctance of the benzamides and pyridine carboxamides to form hydrate or even solvate derivatives despite crystallisation of these series of compounds from a wide range of solvents and conditions. [7][8][9][10]22] Hirshfeld surface analysis Hirshfeld surface analysis of the three benzamide hydrate crystals (I) to (III) was undertaken with the MoProViewer software [23] to further characterize on a statistical basis the intermolecular contacts. The Hirshfeld surface is representative of the region in space where contacts and interactions arise between molecules. Therefore, quantitative insights into the chemical nature of intermolecular interactions can assist in understanding crystal structure packing. Integral Hirshfeld surfaces were generated around the benzamide and water molecules by selecting moieties in the crystal which are not directly in contact with each other. The hydrogen atoms Hc bound to carbon were distinguished from the more polar Ho/n bound to oxygen or nitrogen atoms. For NmpF, the conformer of major occupancy was considered. The presentation and data analysis are similar to Table 3a.

The contact enrichment ratio is an indicator of the likelihood of chemical species to form intermolecular interactions with themselves and other species. [24] In all cases, the most enriched contacts are Hn/o…N (with an E ratio between 3.3 and 3.7), followed by Hn/o…O (with an E ratio 3b).

In a statistical study of several families of halogenated compounds, [25] it was found that the hydrogen Hc is a preferred partner for halogen atoms. This is the case in the two halogenated benzamides reported herein with E(F,Hc) = 2.5 in (II) and E(Cl,Hc) = 1.7 in (III). The Hc chemical type constitutes by far the major partner for the (F, Cl) halogen atoms. The chlorine…chlorine interaction is also quite over-represented in the Clpm structure with a E=2 value as the halogen atom happens to be in proximity of a symmetry related atom (Table 3c). The presentation and data analysis is similar to Table 3a.

The hydrophobic C…C contacts are enriched due to extensive parallel offset π…π stacking between aromatic rings in the three structures (I) to (III). [26] This type of interaction has been analysed and well-described by Martinez and Iverson in a recent review and with descriptors for the various types of stacking arrangements. [26] The Clpm2H 2 O structure is particularly rich in C…C contacts

Figure

  Figure 1a-c. ORTEP views of the asymmetric units of the structures of (I) to (III) with the atomic numbering scheme. Displacement ellipsoids are drawn at the 30% probability level. Only the major conformation of NpmFH 2 O is depicted.

  MpmH 2 O, (I) and the dihydrate Clpm2H 2 O, (III) as well as a pyridinecarboxamide monohydrate NpmFH 2 O, (II) (Figures

Figure 3

 3 Figure 3 Autostereogram of the classical hydrogen bonding in the NpmF hydrate (II) with atoms depicted as spheres of size 0.15 times the van der Waals radius.

20. 5 Å

 5 wide) parallel with the (104) plane; this is further linked by the formation of weaker C-H…O interactions into columns. The inclusion of the water molecule in (II) bears a resemblance to the isomorphous pair of CmoMH 2 O (VUXLIH) and CmoBrH 2 O (VUXLIL) carbamate structures

Figure 4 (

 4 Figure 4 (a) An ORTEP view of the benzamides linked into dimers by water molecules in (III) and (b) An extended view of (III) with the unit cell and with aromatic hydrogens removed for clarity.

  1 for water or a total D:A = 3:3 in MpmH 2 O, (I). Likewise in NpmFH 2 O, (II) the D:A = 3:3 with the water as a single hydrogen bond acceptor (from N1) and with two donor O-H groups from O1W providing a total of three medium strength hydrogen bonds (Table 2). In Clpm2H 2 O the crystal structure has an observed D:A ratio for each of the three moieties Clpm, H 2 O, H 2 O as (1:2, 2:2, 2:1) or a total D:A = 5:5 from a calculated D:A ratio of 6:5 if O2W had a maximum D:A = 2:2. A total of 5 classical hydrogen bonds are observed (Table 2). The hydrogen bonding interactions (as O-H…O, N-H…O, O-H…N) are such that the D•••A geometric distances are typically from 2.80-2.85 Å and

between 2 .

 2 8 and 3.1) illustrating that these hydrogen bonds are presumably the driving force in the crystal packing. The hydrogen bonds towards the N atom are systematically more enriched than those towards the O atom. The weaker Hc…O hydrogen bonds are slightly enriched except for the NpmF compound where E is unitary. The weaker Hc…N interactions are absent or underrepresented, presumably due to competition with the much stronger Hn/o…N hydrogen bonds (Table

(

  E=2.0) due to parallel offset π…π stacking between molecules related by a translation along the short axis a = 4.562 Å resulting in the structure to have an under-representation of Hc…C hydrophobic interactions. The NmpFH 2 O compound is the only structure with a weak C-H…π interaction, as C25-H25…(fluorophenyl). This is rendered possible by the very different orientation of the two aromatic rings at a 68.76(6) angle and is corroborated with a slight

Table 1 :

 1 Crystallographic

	Crystal structures	MpmH 2 O	NpmFH 2 O	Clpm2H 2 O
	Crystal data
	Chemical formula	C 13 H 12 N 2 OH 2 O	C 12 H 9 FN 2 OH 2 O	C 12 H 9 ClN 2 O2(H 2 O)
	M r	230.26	234.23	268.69
	Crystal system, space group Monoclinic, Cc	Monoclinic, P2 1 /c	Monoclinic, P2 1 /c
	a, b, c (Å)	15.2403(4),	8.5053(5),	4.5623(1),
		6.1683(1),	7.1083(4),	13.8473(3),
		13.5400(4)	18.9462(13)	20.5984(5)
	 ()	111.516(3)	93.768(5)	95.218(2)
	V (Å 3 )	1184.15(6)	1142.98(12)	1295.92(5)
	F(000), Z	488, 4	488, 4	560, 4
	 range () for cells	3.4-27.4	3.6-27.2	3.2-62.4
	 (mm -1 )	0.09	0.11	2.65
	Crystal shape, colour	Block, colourless	Block, colourless	Plate, colourless
	Crystal size (mm)	0.38 × 0.26 × 0.17	0.44 × 0.41 × 0.28	0.53 × 0.11 × 0.05
	Data collection

Experimental details for (I), (II) and (III)

MpmH 2 O, NpmFH 2 O and Clpm2H 2 O structures:

Table 3a :

 3a Chemical proportions on the Hirshfeld surface, % contact types and their enrichment ratios for MpmH 2 O (I). The major interaction types and the most enriched are in bold. The The two most prominent chemical types on the Hirshfeld surface are the hydrophobic hydrogen Hc and carbon atoms whose proportions together sum up to 55-75% in the three structures (I) to (III) (Table3a-c). As a result, the hydrophobic contacts Hc…C, C…C and Hc…Hc are the most abundant interactions, except in the dihydrate compound Clpm where O…Ho/n is the second major contact type (Table3c).

	hydrogen atoms (Ho/n and, Hc) bound to O/N and C are distinguished, as their electrostatic
	properties are different.
	Atom	Ho/n	C	N	O	Hc
	%	11.6	31.2	4.7	8.9	43.6
	Atom	Ho/n	C	N	O	Hc
	Hn/o	0.01
	C	3.29	14.54	% contacts		MpmH 2 O
	N	4.18	2.78	0.00
	O	6.86	0.67	0.00	0.00
	Hc	10.05	26.42	2.35	10.76	18.11
	Hn/o	0.01
	C	0.43	1.50		Enrichment
	N	3.68	0.96	0.00
	O	3.08	0.12	0.00	0.00
	Hc	0.96	0.99	0.59	1.37	0.98

Table 3b :

 3b Chemical proportions on the Hirshfeld surface, % contact types and their enrichment ratios for NmpFH 2 O (II).

	atom	Hn/o	C	N	O	F	Hc
	% surface 12.6	32.2	4.6	9.5	5.8	35.2
	H n / o	0 . 2 0
	C	7.1	11.9		% c o n t a c t s		NmpF
	N	4.6	3.4	0.0
	O	8.1	4.4	0.3	0.0
	F	0.0	0.9	0.7	0.0	0.0
	Hc	6.6	24.0	0.2	6.6	10.5	10.4
	H n / o	0 . 1 1
	C	0.83	1.17
	N	3.7	1.17	0.00		Enrichment
	O	3.1	0.72	0.33	0.00
	F	0.00	0.23	1.27	0.00	0.00
	Hc	0.72	1.10	0.05	0.99	2.5	0.88

Table 3c :

 3c Chemical proportions on the Hirshfeld surface, % contact types and their enrichment ratios for Clpm2H 2 O (III).

	Atom	Ho/n	C	N	O	Cl	Hc
	%	17.41	26.44	4.35	12.13	10.85	28.81
	Hn/o	1 . 8 7
	C	6.79	13.30		% contacts		Clpm2H 2 O
	N	5.32	1.77	0.01
	O	12.97	2.46	0.00	0.00
	Cl	0.00	6.54	0.00	0.17	2.54
	Hc	9.27	7.37	1.21	8.72	10.76	8.92
	Hn/o	0 . 5 2
	C	0.69	2.00		Enrichment
	N	3.3	0.83	0.07
	O	2.8	0.39	0.00	0.00
	Cl	0.00	1.12	0.00	0.06	2.0
	Hc	0.88	0.52	0.53	1.30	1.7	1.17

ACKNOWLEDGEMENTS

This research was funded by the Programme for Research in Third Level Institutions (PRTLI) Cycle 4 (Ireland) and co-funded through the European Regional Development Fund (ERDF), part of the European Union Structural Funds Programme (ESF) 20072013. JFG thanks the School of Chemical Sciences, Dublin City University for grants in aid of chemical and crystallographic research. PM thanks the T 3 (PRTLI-IV) program for a studentship. JFG and CJ thank the Université de Lorraine and Region Lorraine for a "Chercheur d'Avenir" grant.

enrichment of Hc…C contacts. The C…Hc and Hc…Hc hydrophobic contacts are generally mildly enriched or impoverished. In all three crystal structures of (I) to (III), electrostatically unfavourable self-contacts between charged atoms such as Hn/o…Hn/o, O…O or N…N are strongly avoided.

Summary comparisons

The two distinct approaches provide information that enhances the study of hydrates (I) to (III). Of note is the importance of the O-H…O/N and N-H…O interactions that are seen to dominate in hydrogen bonding interactions in the crystal structures and in the enrichment studies. In all three structures the Hn/o…N is more enriched by 18-19% than the Hn/o…O (Tables 3a-c). Of further note is that in NmpFH 2 O, there is parallel offset … stacking with a short N24•••C25 i contact distance of 3.2036(18) Å and C25•••C25 i = 3.346(2) Å) involving the pyridine rings, with the C…C contacts lower and the C…N contacts raised in (II) when compared to both (I) and (III). [26] This difference is also noted in the enrichment statistics as well. The effect of the global C…C contacts in (I) and (III) is more notable and this is something that may not be easily discerned in crystal structure analysis by programs such as SHELXL or PLATON. [11,14]

CONCLUSIONS AND FUTURE WORK

In our research on isomer series of benzamides and carboxamides to date we have observed the paucity of hydrates or even solvates. When a hydrate structure is structurally characterised it is noted that the hydrate is easily accommodated in the crystal structure and the hydrogen bonding is usually balanced in D:A ratios and maximised in the structure. Of note is that there are two recent examples of neutral benzamide or carboxamide active pharmaceutical ingredients as hydrates: niclosamide [27] and pranlukast. [28] Some experimental drugs are also known as either neutral benzamide/carboxamide hydrates [29] or hydrochloride hydrates. [30] However, there is a growing group of approved and experimental protein kinase blockers including so called targeted anticancer drugs that have become lifesaving therapies: these are mostly longer but simple organic molecules featuring benzamide linkers and moieties. [31][32][33] It may be expected that their hydrates could become important as APIs with different release rates and pharmacokinetics or be more stable in formulations in future pharmaceutical research. From a structural viewpoint, additional knowledge gained from series of pharmaceutical hydrates such as (I) to (III) will aid in pharmaceutical drug design and development. CIF data may be downloaded from the CCDC website https://summary.ccdc.cam.ac.uk/structuresummary-form or obtained free of charge from The Director, CCDC, 12 Union road, Cambridge, CB2 1EZ, U.K. (fax: +44-1223-336033; e-mail:deposit@ccdc.cam.ac.uk). The data are available as CIF files from the corresponding author Dr. John F. Gallagher.

SUPPLEMENTARY INFORMATION

Crystallographic