Laure Latapie

Julien Le Gal

Bassem Hamaoui

Joe ¨l Jaud

Marie Gressier

Eric Benoist
email: benoist@chimie.ups-tlse.fr

First examples of neutral rhenium(V) complexes with a novel semi-rigid ligand containing a P,N,N,S donor atom set: Synthesis, characterisation and crystal structure

Keywords: Tetradentate PN 2 S ligand, Rhenium complexes, Crystal structure, Phosphine

A new PN 2 S ligand, N-[2-(diphenylphosphino)phenyl]-2-[(S-trityl)acetylamino]ethanamide [Ph-P(Ph 2 )N 2 S(Trt)], was synthesised and reacted with Re V precursors. The reaction of both tritylated and detritylated ligands with ReOCl 3 (PPh 3 ) 2 gave the same expected neutral complex [ReO{Ph-P(Ph 2 )N 2 S}] (4) in good yield. An unexpected neutral and diamagnetic species, [ReN{Ph-P(Ph 2 )N 2 S(Trt)}] (5), has been isolated during the complexation of the tritylated ligand with ReNCl 2 (PPh 3 ) 2 . The complexes, characterized by classical spectroscopic methods and X-ray analysis for 4, are the first examples of neutral semi-rigid-PN 2 S rhenium(V) complexes.

Introduction

Rhenium(V) complexes are of interest because of the potential use of 186/188 Re in nuclear medicine and the chemical similarity of Re/Tc, largely used for the design of 99m Tc radiopharmaceuticals [1]. Consequently, inorganic chemistry studies with the long-lived b-emitting isotope 99g Tc (weak b À -emitter, E max = 0.294 MeV, t 1/2 = 2.12 • 10 5 years) or with the naturally occurring non-radioactive rhenium isotopes ( 185 Re: 37.07%, 187 Re: 62.93% abundance) are still very attractive in order to clearly establish the molecular structure of 99m Tc-and 186/188 Re-based radiopharmaceuticals. One of the most important prerequisites in the design of new classes of technetium/rhenium ligands is the development of highly stable complexes with these metals and the elucidation of their structures [2]. In a previous work, we have developed a new family of tetradentate semi-rigid ligands, Ph-XN 2 S(Trt) [3]. We have shown that the incorporation of an aromatic ring fused into the chelate backbone imparted rigidity to a portion of the ligand, enhancing the formation and stability of the resulting complex by an entropy effect. Moreover, we have demonstrated that the nature of the donor atom set and more particularly the nature of the X aromatic function influenced the stability of the corresponding metallic complexes. Thus, coordination of Ph-XN 2 S-type ligands acting as a tetraanionic ligand X À N À N À S À (X = O, S, NH, NMe) towards the usual rhenium precursor ReOCl 3 (PPh 3 ) 2 in the presence of sodium acetate gave straightforwardly highly stable anionic complexes of the general formula [Na][ReO(Ph-XN 2 S)] under mild conditions [4]. In return, we never have been able to isolate doi:10.1016/j.poly.2007.07.032 the stable analogous neutral ReO complexes starting with Ph-XN 2 S-type ligands acting as a trianionic ligand XN À N À S À (X = OMe, SMe, NMe 2 ).

Due to their tendency to delocalize the electron density on the metal -a result of their r-donor and p-acceptor character -phosphines often lead to the stabilization of the complexes in which they are contained [START_REF] Cotton | Basic Inorganic Chemistry[END_REF]. This led us to anticipate that the incorporation of one phosphine group in the chelate ring should enhance the reactivity of the ligand towards the MO 3+ core (M = Tc or Re) and consequently increase the stability of the resulting neutral metallic complexes. This expectation has been realized in the isolation of two neutral semi-rigid PN 2 S rhenium(V) complexes and the structural characterization of one of them, [ReO{Ph-P(Ph 2 )N 2 S}] (4). To our knowledge, these compounds are the first Re V N and Re V O species including a semi-rigid PN 2 S framework, the only previous examples in ReO chemistry being the PN 2 S-tetradentate monooxorhenium complexes obtained with the non-semi-rigid ligands 3-diphenylphosphinoglycyl-L-(S-protected)cysteine and its methyl ester [6]. It is noteworthy that a Re V O species including a semi-rigid Ph-P 2 N 2 framework has been reported by Tisato et al. [7].

Results and discussion

The ligands of this study have been prepared under a strictly inert atmosphere according to the method outlined in Scheme 1. Thus, reaction of 2-iodoaniline with diphenylphosphine in the presence of NEt 3 and Pd(PPh 3 ) 4 as a catalyst in warm acetonitrile afforded the 2-diph-enylphosphinoaniline (1), in quite good yield [8]. A conventional carbodiimide amide coupling of N-[(Strityl)acetyl]glycine [3b] with 1 in THF, followed by the cleavage of the trityl group under acidic conditions (TFA, Et 3 SiH) [9] gave the ligands [Ph-P(Ph 2 )N 2 S(Trt)] ( 2) and [Ph-P(Ph 2 )N 2 SH] (3), respectively. The ligands showed good solubility in methanol, ethanol, dichloromethane, chloroform and acetonitrile. They were characterized by elemental analysis, 1 H and 31 P NMR spectroscopy, all consistent with the formula shown in Scheme 1. In particular, the 31 P spectra of 2 and 3 revealed only one peak at %À21.5 ppm corresponding to P III species. The IR spectrum of 3 exhibited an absorption band at 2482 cm À1 , which corresponds to the S-H stretching vibration.

Ligand-exchange reactions in warm methanol of labile ReOCl 3 (PPh 3 ) 2 with a slight excess of the relevant tritylated or detritylated ligand (1:1.2 metal:ligand ratio) in the presence of a methanolic sodium acetate solution as a deprotonating agent led to the same neutral complex 4 in satisfactory yield (Scheme 1). The cleavage of the trityl group of 2, accomplished during the coordination of the ligand to the ReO 3+ core, is explained by the acidic contribution of the metal (Lewis acid) in the mechanism of sulfur detritylation. Complex 4 crystallised from CH 2 Cl 2 /hexane solution by slow evaporation and afforded purple crystals suitable for X-ray analysis.

The spectroscopic characteristics of the oxo-rhenium complex 4 of the general formula [ReO{Ph-P(Ph 2 )N 2 S}], as evident from the elemental analysis, were similar to the analogous anionic complexes described previously [3b,10], i.e. (i) the characteristic rhenium(V) oxo isotopic pattern consistent with the presence of a neutral mononuclear complex ([M+H + ] = 607/609), (ii) an intense band in the IR spectrum attributable to the Re@O stretching vibration at 966 cm À1 , (iii) a non-equivalence of the two hydrogens of each methylene group (AX pattern) of the tetradentate ligand framework in the proton NMR spectrum, the downfield signal of both AX patterns being assigned to the endo protons (syn to the Re@O group) and the upfield signals to the exo ones (anti to the Re@O group) [6b,11]. The 31 P NMR spectrum showed a singlet peak in agreement with phosphine coordination, [12] the pertinent peak moving downfield to the +38.7 ppm positive region from the À21.6 and À21.2 ppm values exhibited by the uncoordinated detritylated and tritylated ligands, respectively. Thus only one single isomer was produced. The formation of a single isomer is important as isomerism can markedly influence the pharmacokinetics of a radiopharmaceutical [13].

As shown in Fig. 1, the crystal structure of 4 consists of a discrete monomeric and neutral monooxo complex packed with no intermolecular contacts shorter than the van der Waals radii sum. Selected interatomic distances and bond angles are listed in Table 2. The coordination geometry about the metal is distorted square pyramidal with the phosphorous of the linked phosphine, the two amide nitrogen and the sulfur atom occupying the equatorial plane and the oxo group directed in the apical position. The description in terms of a square pyramid is supported by the nearly equal N(2)-Re(1)-S(1) and N(1)-Re(1)-P(1) angles, leading to a very low trigonality index s of 0.05 (N(2)-Re(1)-S(1) = 135.91 (15)°and N(1)-Re(1)-P(1) = 138.88(14)°) [14]. This value is similar to those found for our analogous anionic complexes (0.00 < s < 0.07) [4,10] and the semi-rigid neutral complex [ReO{Ph-N 3 O}] recently developed by Papachristou et al. [15] (s = 0.01). The Re atom lies 0.78 A ˚above the basal plane, which is reflected by the O@Re-N and O@Re-S/P angles ranging from 106.73 (15)°to 114.1(2)°. This value is in agreement with the displacement normally observed for square-pyramidal rhenium complexes [4,16]. The tetradentate coordination mode of the triply deprotonated ligand leads to a three [START_REF] Cotton | Basic Inorganic Chemistry[END_REF][START_REF] Cotton | Basic Inorganic Chemistry[END_REF][START_REF] Cotton | Basic Inorganic Chemistry[END_REF]-membered chelate ring system around the rhenium atom. The two phenyl rings of the phosphine are roughly perpendicular to the Ph-PN 2 S plane; the mean planes passing through them make angles of 87.9°and 125.0°with the pyramidal basal plane. The same planes define an angle to each other of 64.2°.

The valence bond distances are unexceptional and are within the range observed for Re-oxo (1.675(4) A ˚), Re-N amide (ca. 1.99 A ˚) and Re-S thiolate (2.2614(17) A ˚) bonds in ReO five-coordinate square-pyramidal complexes. The dominating feature of this structure is the Re-P distance. The latter is 2.4052( 14) A ˚, and it is far shorter than that reported for the non-semi-rigid [ReO{P(Ph 2 )N 2 S}] compound developed by Mazzi et al. [6b] 2.4446(2) A ˚. The rigidity imposed by the aromatic ring conjugated with the strained five-membered chelate ring Re(1)-P(1)-C(6)-C(5)-N( 2) instead of a six-membered chelate ring for the Mazzi complex explains this difference. Consequently, the P(1)-Re(1)-N( 2) angle is shorter in our complex than in Mazzi's one (78.84( 14)°versus 90.5(2)°). It is noteworthy that the length of the X-Re bond in our [ReO(Ph-XN 2 S)] complexes (X = O, S, NH, PPh 2 ) is greatly influenced by the nature of the X atom. As expected, the bulkier is the X atom, the longer is the X-Re bond, with the following order: d N-Re 1.968(2)A ˚< d O-Re 2.000(4) A ˚( d S-Re 2.2969(18) A ˚< d P-Re 2.4052( 14) A ˚. In return, there are no significative differences for the other Re-N or Re-S bonds.

By using the above coordination conditions, treatment of 2 with the ReNCl 2 (PPh 3 ) 2 precursor afforded an intractable mixture, from which the isolation of pure and defined species was not possible. Surprisingly, use of solid sodium acetate as a deprotonating agent and toluene instead of methanol as the solvent allowed us to isolate an unprecedented non-detritylated neutral nitridorhenium(V) complex in 25% yield, as sketched in Scheme 1.

[ReN{Ph-P(Ph 2 )N 2 S(Trt)}] (5) was characterized by spectroscopical methods, even though crystals suitable for X-ray work could not be obtained. In particular, both 31 P and 1 H NMR spectra demonstrated that 5 is diamagnetic, suggesting a low-spin d 2 configuration, typical of distorted octahedral or distorted square-pyramidal species bearing a multiple oxo-or nitrido-core [17]. The presence of the trityl group is revealed by the integration ratio of total aromatic/aliphatic protons (29/4), consistent with three more phenyl rings in the complex. As expected, the methylene protons of the tetradentate ligand framework were found to be diastereotopic (AX pattern) with coupling constants in the range 17.5-19.5 Hz (Fig. 2). The DCI-MS spectrum of complex 5 showed the production of molecular cations at m/z 848/850 ([M+H + ]) and m/z 865/867 ([M+NH 4 + ]), with a detectable fragment ion at m/z 243 ([Trt + ]), revealing the loss of the trityl group. The IR spectrum of 5 exhibited an absorption band at 1098 cm À1 assigned to the characteristic ReN stretching vibration. No multiple strong bands were detected in the ranges 1500-1560 and 3200-3400 cm À1 of complex 5, confirming the deprotonation of the amide functions. The complex is non-conducting in acetonitrile solutions, as expected [18]. So, chelation of the ReN core proceeds by coordination with the PN 2 S 2À donor atom set formed from one neutral phosphine, two deprotonated amide groups and one neutral thioether. This is the first example where metal catalysed removal of the trityl group does not occur during a Re V complexation.

The isolation of these two complexes conjugated with the fact that we never succeeded in isolating a neutral Re V complex with [Ph-X(Me)N 2 S(Trt)] ligands (X = O or S) suggested that the phosphorus atom of the chelate (i) enhances the reactivity of the ligand towards the ReO 3+ core, (ii) binds first to the metal and this bond acts as the driving force for coordination. The latter hypothesis is consistent with the mechanism proposed by Visentin et al. for their similar ReO complexes with a P,N,N,S donor atom set [6b]. Our complexes are extremely stable in the solid state as well as in organic solvents for long periods of time, as shown by NMR spectroscopy. Their stability is not affected by the presence of air. The mixing of a p-donor S atom with a p-acceptor P atom ensures an appropriate electronic balance around the ReO or ReN core and this event contributes to the overall robustness of the system.

Conclusion

In conclusion, the new semi-rigid PN 2 S ligand studied here exhibits high chelating affinity for the rhenium(V) core. A neutral stable monooxorhenium(V) complex was produced as a single isomer by reacting the tritylated or detritylated ligand with a ReO precursor, in good yield. The high affinity of the PN 2 S set toward Re V O can be expected also for 99m TcO, making this ligand potentially useful as a 99m TcO-based brain perfusion or brain receptor imaging agent. A radio-labelling study with 99m Tc will start soon. Investigations on the unexpected neutral complex [ReN-{Ph-P(Ph 2 )N 2 S(Trt)}], isolated during the complexation of the tritylated ligand with ReNCl 2 (PPh 3 ) 2 , are still going on to better understand the formation of this complex.

Experimental

General methods

All preparations and manipulations were carried out under a nitrogen atmosphere using standard Schlenk techniques. All chemicals were of the highest purity commercially available. Rhenium(VII) oxide was purchased from Aldrich Chem. Co. It was converted to ReOCl 3 (PPh 3 ) 2 and ReNCl 2 (PPh 3 ) 2 according to published protocols [19]. Solvents were dried and distilled by standard methods before use and stored over 0.3 nm molecular sieves. 2-(diphenylphosphino)aniline (1) [8] and N-[(S-trityl)acetyl]glycine [3b] were prepared as described previously. Silica gel (0.060-0.200 nm) was purchased from Acros. TLC was performed using precoated Kieselgel 60 plates F 254 (TLC plates, Merck) and was visualised by UV or iodine. Column chromatography was carried out using ''gravity '' silica (Merck). Infrared spectra (4000-400 cm À1 ) were recorded as KBr pellets on a Vector 22 Bruker spectrophotometer. NMR spectra were recorded on a Bruker AC 200 (81.015 MHz for 31 P) and AC 250 N-[(S-trityl)acetyl]glycine (1.957 g, 5 mmol) and 1 (1.385 g, 5 mmol) were dissolved in anhydrous degassed THF (25 mL). Dicyclohexylcarbodiimide (1.135 g, 5.5 mmol) was added and the mixture was heated at reflux for 24 h. After cooling to room temperature, the insoluble dicyclohexylurea was removed by filtration and the filtrate evaporated under reduced pressure. The obtained brown oil was dissolved in AcOEt (20 mL) and cooled at 0 °C. A white solid was collected by filtration and washed with cold AcOEt. The solid was purified by column chromatography on silica gel (eluent: CH 2 Cl 2 /AcOEt, 96/4) to give 2 as a white powder (1.002 g, 30%).

Anal. Calc. for C 41 H 35 N 2 O 2 PS: C, 75.67; H, 5.42; N,4.30;S,4.93. Found: C,75.37;H,5.22;N,4.

N-[2-(diphenylphosphino)phenyl]-2-[mercaptomethylcarbonylamino]ethanamide (3)

To a chilled solution of 2 (0.250 g, 0.38 mmol) in degassed CH 2 Cl 2 (30 mL) were added TFA (13 mL) and triethylsilane (121 lL, 0.76 mmol). The solution became colourless and it was stirred for 2 h. After removal of the solvents under vacuum, the resulting residue was crystallised as a white powder upon addition of hexane (77 mg, 50% Method 1: To a suspension of 2 (200 mg, 0.308 mmol) and ReOCl 3 (PPh 3 ) 2 (307 mg, 0.370 mmol) in degassed MeOH (30 mL) was added a 1 M solution of sodium acetate in degassed MeOH (3 mL, 3 mmol). After refluxing for 3 h, the solution turned violet and clear. After cooling, the solution was filtered off and evaporated to dryness. The obtained brown violet solid was recrystallised from CH 2 Cl 2 /hexane (2/1) to afford 4 as a violet powder (123 mg, 66%).

Method 2: The same procedure as method 1 starting with 3 (50 mg, 0.122 mmol), ReOCl 3 (PPh 3 ) 2 (122 mg, 0.147 mmol) and sodium acetate in MeOH (1 mL, 1 mmol). After recrystallisation, 4 was obtained as a violet powder (44 mg, 60%

.2.4. [N-(2-diphenylphosphinophenyl)-2-{(triphenylmeth- ylmercapto) methylcarbonylamino}ethanamido(4-)-j 4 P,N, N 0 ,S]nitridorhenate(V) or [ReN{Ph-P(Ph 2 )N 2 S(Trt)}] (5)
To a suspension of 2 (200 mg, 0.308 mmol) and ReNCl 2 (PPh 3 ) 2 (294 mg, 0.370 mmol) in degassed toluene (30 mL) was added sodium acetate (304 mg, 3.7 mmol). After refluxing for 18 h the solution turned brown and clear. After cooling, the solution was filtered off and evaporated to dryness. Addition of ether (10 mL) gave a precipitate which was filtered off. The precipitate was dissolved in CH 2 Cl 2 . Addition of hexane gave a precipitate which was filtered off. The filtrate was concentrated to give 5 as a reddish-brown powder (65 mg, 25%).

Anal. Calc. for C 41 H 33 N 3 O 2 PReS: C, 58.00; H, 3.92; N,4.95;S,3.78. Found: C,58.08;H,4.20;N,4. 4.3. X-ray crystal structure determination of complex 4

[ReO{Ph-P(Ph 2 )N 2 S}] (4) was crystallised by slow evaporation of a CH 2 Cl 2 /hexane solution. A purple crystal of 4 thus produced was mounted on a Nonius Kappa CCD diffractometer equipped with a CDD detector, and was used for data collection. X-ray intensity data were collected with graphite-monochromated Mo Ka radiation (k = 0.71073 A ˚) at a temperature of 298 K. The most significant details of the crystallographic study are reported in Table 1. A collection of selected bond distances and angles are shown in Table 2. The structure was solved by direct methods. All the non-hydrogen atoms were refined anisotropically using the full-matrix, least-squares procedure based on F 2 . Structure determination and refinement were performed using the MAXUS [START_REF] Mackay | MAXUS, Computer Program for the Solution and Refinement of Crystal Structures[END_REF] and SHELX-97 [START_REF] Sheldrick | Program for the Refinement of Crystal Structures[END_REF] programs. 3621 independent reflections with I P 2r(I) were used for refinement of the unit cell (h 6 25°). Hydrogens for the mater molecule were not located.

  Scheme 1. Synthesis of compounds 4 and 5.

Fig. 1 .

 1 Fig. 1. ORTEP diagram of 4 with 50% probability thermal ellipsoids showing the atomic labelling scheme.

  10; S, 5.22%; IR (KBr): m (cm À1 ) 3328, 3269 (NH); 3052 (CH Ar ), 1702, 1652 (CO); 1026 (P-C); MS (DCI/NH 3 ) m/z 243 [Trt + ], 651 [M+H + ]; 667, [M+NH 4 + ]; 31 P{ 1 H} NMR (CDCl 3 ): d (ppm): À21.2 (s); 1 H NMR (CDCl 3 ) d (ppm): 3.15 (s, 2H, SCH 2 ); 3.49 (d, 2H, J = 5.5 Hz, CH 2 N); 6.42 (broad s, 1H, NH); 6.85-7.56 (m, 28H, CH Ar ); 8.09 (broad s, 1H, NH); 8.22 (m, 1H, CH Ar ).

4. 2

 2 .3. [N-(2-diphenylphosphinophenyl)-2-(mercaptomethylcarbonylamino)ethanamido(4-)j 4 P,N,N 0 ,S]oxorhenate(V) or [ReO{Ph-P(Ph 2 )N 2 S}] (4)

4

 4

  60; S, 3.56%; IR (KBr): m(cm À1 ) 3050 (CH Ar ); 1661, 1637 (CO); 1098 (ReN); MS (DCI/NH 3 ): m/z (%) 243 (14) [Trt + ], 848 (60), 850 (100) [M+H + ], 865 (3), 867 (6) [M+NH 4 + ]; 31 P{ 1 H} NMR (CDCl 3 ): d (ppm): 39.0 (s); 1 H NMR (CDCl 3 ) d (ppm): 3.31 (d, 1H, J = 17.6 Hz, SCH 2 ); 4.04 (d, 1H, J = 17.6 Hz, SCH 2 ); 4.26 (d, 1H, J = 19.5 Hz, CH 2 N); 4.76 (d, 1H, J = 19.5 Hz, CH 2 N); 6.70-6.82 (m, 6H, CH Ar ); 7.05-7.60 (m, 22H, CH Ar ); 9.05 (dd, 1H, J HH = 8.5 Hz, J HP = 4.7 Hz, CH Ar ). K M (CH 3 CN): 21.10 X À1 cm 2 mol À1 (neutral).

  (250.133 MHz for 1 H). Chemical shifts are indicated in d values (ppm) downfield from internal TMS. For the 31 P{ 1 H} spectra the external standard was H 3 PO 4 (82% D 2 O, d = 0.0 ppm). DCI-Mass spectra were obtained on a NERMAG R10-10 mass spectrometer. Microanalysis was performed by the Microanalytical Department of the Ecole Nationale Supe ´rieure de Chimie de Toulouse.

	9.0831	9.0642	9.0493	9.0302	7.2614	6.8198	6.8197	6.7902	4.8453	4.7671	4.3451	4.2670	4.1114	4.0407	3.3879	3.3173
	0.92 4.2.1. N-[2-(diphenylphosphino)phenyl]-2-[(triphenylmeth-11.48 7.39 3.93 6.21 CDCl3 Fig. 2. 4.2. Synthetic work ylmercapto)methylcarbonylamino] ethanamide (2)	1.00	1.00	0.97		0.95

1 H NMR spectrum of [ReN{Ph-P(Ph 2 )N 2 S(Trt)}] (5) (CDCl 3 ; 250 MHz; 25 °C).

apparatus

  ).

	Anal. Calc. for C 22 H 21 N 2 O 2 PS: C, 64.69; H, 5.18; N, 6.86;
	S, 7.85. Found: C, 64.80; H, 5.01; N, 6.50; S, 7.64%; IR (KBr)
	m (cm À1 ) 3338, 3241 (NH); 2482 (SH); 1696, 1640 (CO); MS
	(DCI/NH 3 ): m/z 409 [M+H + ]; 31 P{ 1 H} NMR (CDCl 3 ): d (ppm): À21.6 (s) ; 1 H NMR (CDCl 3 ) d (ppm): 1.33 (t, 1H,
	J = 8.8 Hz, SH); 3.22 (d, 2H, J = 8.8 Hz, SCH 2 ); 3.93 (d,
	2H, J = 5.5 Hz, CH 2 N); 6.90 (m, 1H, NH); 6.92 (m, 1H,
	CH Ar ); 7.06-7.41 (m, 11H, CH Ar ); 7.55 (m, 1H, CH Ar );
	8.10 (broad s, 1H, NH); 8.35 (m, 1H, CH Ar ).

  ). J = 17.4 Hz, SCH 2 ); 4.78 (d, 1H, J = 19.0 Hz, CH 2 N); 5.22 (d, 1H, J = 19.0 Hz, CH 2 N); 7.20 (t, 1H, J = 7.3 Hz, CH Ar ); 7.28-7.91 (m, 12H, CH Ar ); 9.10 (dd, 1H, J HH = 8.5 Hz, J HP = 4.6 Hz, CH Ar ).

	Anal. Calc. for C 22 H 18 N 2 O 3 PReS: C, 43.49; H, 2.99; N,
	4.61; S, 5.28. Found: C, 43.60; H, 3.12; N, 4.58; S, 5.12%;
	IR (KBr): m(cm À1 ) 1665, 1647 (CO); 966 (ReO); MS (DCI/
	NH 3 ): m/z (%) 607 (11), 609 (20) [M+H + ], 623 (1), 625 (2) [M+NH 4 + ]; 31 P{ 1 H} NMR (CDCl 3 ): d (ppm): 38.7 (s); 1 H
	NMR (CDCl 3 ) d (ppm): 3.88 (d, 1H, J = 17.4 Hz, SCH 2 );
	4.04 (d, 1H,

Appendix A. Supplementary material CCDC 651266 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html, or from the Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: (+44) 1223-336-033; or e-mail: deposit@ccdc.cam.ac.uk. Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.poly.2007. 07.032.


F Chirot

S Zamith

P Labastie

J-M L'hermite

"A new device to study unimolecular cluster nucleation"

Keywords: 36, 40, Jn Reactivity of clusters; 33, 15, Ta Mass spectra 39, 10, +j Atomic and molecular beam sources and techniques 36, 40, Qv Stability and fragmentation of clusters

We have developed an apparatus which allows measuring the sticking cross section of a neutral atom onto a mass selected charged cluster of known temperature. The main point is to reduce the kinetic energy dispersion in the mass selected cluster beam in order to work with ions of very low (near thermal) kinetic energy. A novel device is presented which focuses in energy with only a small loss in the beam intensity. An application is shown to the sticking of sodium atoms onto sodium clusters at an energy of a few tenths of an eV in the centre-of-mass frame.

Introduction

The unimolecular dissociation of clusters has been widely investigated during the last two decades [1,2,3,4,5]. The basic idea of all experiments is rather simple: one measures the number of atoms (or molecules) evaporated per unit time from an atomic (or molecular) cluster (for more simplicity, we restrict the following discussion to atomic clusters, but it can be applied without fundamental modification to molecular ones). The clusters are generally mass selected, and the variations of the evaporation rate with size and internal energy are measured. Evaporation can be either spontaneous [1], when the cluster is initially hot enough, or induced by an increase of its internal energy by photon absorption [2] or collision [3]. Such evaporation rates measurements give an insight into the thermodynamics of finite systems [4] in the frame of statistical models; they also give information on structural properties of clusters. Furthermore, the kinetic energy release distribution of neutral atoms emitted from photoexcited clusters can be analyzed [5].

Surprisingly, the opposite process, i.e. the sticking of a single atom onto a mass selected cluster, has never been investigated. Measurement of sticking cross sections is however of considerable interest. At a fundamental level, dissociation is closely linked to sticking according to the microreversibility principle [6]. From a more concrete point of view, nucleation processes are present everywhere in nature: for example, the nucleation of water molecules is responsible for cloud formation. Classical nucleation theory (CNT) is the most commonly used way to describe such nucleation processes. However, the discrepancy between this theory and experiment is often by orders of magnitude [7,8]. One crucial problem lies in a paradox of CNT. On the one hand, this theory is based upon macroscopic parameters, such as surface tension or latent heat. But on the other hand, one of its major postulates, the so-called "nucleation theorem" [9] states that there is a "critical size" n* which is a key parameter to describe the nucleation rate. The paradox is that n* is very small, ranging generally from ten to a hundred atoms, a range for which the macroscopic parameters used cannot be expected to give accurate results. For this reason, it is important to study the nucleation of clusters that are typically in this size range. Furthermore, Schmidt et al [10] have shown a strong size dependence of the melting temperature of small sodium clusters. The initial phase (liquid or solid) of the clusters should influence the nucleation process. Thus it is important to study the influence of the cluster's initial temperature on the sticking cross sections.

One possible reason for the lack of experimental data on the nucleation of clusters is that it is necessary to let cluster and atom collide at very low kinetic energy. If it is not the case, the cluster-atom collision leads to an effect exactly opposite to the expected one, i.e. the evaporation of an atom. The maximum allowed collision energy to observe sticking must be of the order of a few eV (depending on the size of the cluster). The practical problem is that the mass selection of clusters with classical methods (Time-Of-Flight (TOF) or quadrupole mass spectrometry) leads to much larger energy dispersions than a few eV.

Nevertheless, low energy collisions of mass selected clusters with atoms or molecules have already been carried out: ref. [11] deals with the fragmentation of M(H 2 0) 2 + (M=Fe, Co, Au), in [12] the collision Ar + n=2-23 + 36 Ar is studied, in [13] the reaction of H + (H 2 O) n=2-6 with acetone is investigated and in [14] the authors measure the cross section for incorporation of ND 3 in H + (NH 3 ) n=3-9 . In these experiments quite small clusters are produced in abundance in a supersonic expansion. In reference [11] mass selection is made by a TOF and the energy spread is reduced by setting particular temporal shapes to the extracting acceleration voltages.

However, it is not enough to get kinetic energies of a few eV in the laboratory frame. To get a smaller energy spread, the authors take advantage of the incoming ion beam being perpendicular to the acceleration plates: the thinner the beam, the lower the energy spread of the ions. Unfortunately, this is at the cost of a severe decrease in the intensity of mass-selected clusters. In references [11,12,13] the authors use the so-called guided ion beam (GIB) method. The mass selection of both reactant and products is done by quadrupole mass filters.

Without any additional device, the kinetic energy spread is about 10 eV [11]. In order to reduce it to a few eV, Kawai [12] and Orii [13] use a Bessel box energy analyzer. This last device does not reduce the energy spread, but selects the fraction of the clusters that have the desired energy to a given accuracy. Once again, it reduces the number of mass-selected clusters. This may be a crucial drawback when the amount of clusters is very low for an individual mass.

For experiments such as described above, the beam intensity is not an issue since they are performed with a supersonic expansion. In our case however, since we want to control the clusters temperature from 150 K to 500 K, we cannot use a supersonic expansion.

Furthermore, we want to explore clusters made of several hundreds atoms. For these sizes the cluster yield is drastically lower than for small clusters produced in a supersonic expansion.

Thus, these two reasons force us to work with relatively low beam intensities, so that it is crucial not to introduce too many losses when slowing down the clusters to the desired kinetic energy.

In this paper, we present a simple electrostatic device for generating thermalized mass selected clusters with kinetic energies of only a few eV in the laboratory frame (a few hundredth eV for a 100-atom cluster in the centre-of-mass frame). The key point is that no energy selection is made so that a very good transmission trough the apparatus is obtained.

The device performs an "energy focusing" that gives the same energy, to a good precision, to a large part of the clusters. We have applied successfully this technique to the sticking of individual sodium atoms onto sodium clusters and we measured absolute sticking cross section.

In section I, we give an overview of the experimental setup. We develop the principle of our method in section II, and section III is devoted to a detailed description of the device.

Finally we present the first experiments applied to the sticking of sodium atoms onto sodium clusters in section IV. Section V is devoted to a discussion of the relative advantages of our setup.

I. General overview of the experimental setup

A sketch of the experimental setup is shown in Figure 1. Sodium clusters are produced and ionized in a gas aggregation source. This source has been extensively used in previous cluster physics experiments [START_REF]Clusters of Atoms and Molecules, Theory, Experiment[END_REF] and will not be described in detail. Briefly, sodium is heated up to 580 K in a crucible in contact with helium gas cooled down to 170 K. The helium pressure is 1 mbar whereas the sodium vapor pressure is of the order of 10 -2 mbar. Cluster formation occurs due to the condensation of the hot sodium vapor in the cold buffer gas. A 150 V potential is applied to the crucible, creating a hollow cathode discharge that ionizes the clusters.

Next they enter a copper thermalization chamber (length 150 mm, diameter 20mm) through a 10 mm hole. Clusters are thermalized by collisions with helium atoms being themselves at the chamber temperature. The helium pressure in this chamber is of the order of 1 mbar. This leads to an average number of collisions between the clusters and the helium atoms on the order of 10 4 , thus insuring a good thermalization. The temperature of the chamber can be varied from 150 to 500 K. The output hole of the chamber is an iris diaphragm whose diameter can be adjusted in order to maximize the cluster yield. The working diameter is of the order of 5 mm. It must not be too small in order to avoid supersonic expansion that would cool the internal degrees of freedom of clusters, and then change their temperature. This feature limits the intensity of the beam. We estimate that for a given mass we produce 10 5 ions per second.

Charged clusters then enter the first mass selection stage through a 1 mm skimmer (Beam Dynamics). The clusters are accelerated in a three-plate Wiley-McLaren type device (WML) (see figure 2). The distances between plates are 10.9 mm and 13.5 mm. In order to define very precisely the potentials we use 90% transmission nickel mesh (Labelcomat, 70 lines/inch).

The next two stages labeled "energy focusing" and "braking" on Figure 1 reduce the kinetic energy spread of a mass selected cluster and allow adjusting its kinetic energy to low values. This is the crucial point of the experiment that will be described in detail in section II.

After these two stages, we have mass selected thermalized clusters of known kinetic energy.

Slow clusters then enter the collision cell (50 mm long, 5mm input diameter, 30 mm diameter). This cell contains a sodium vapor whose density is controlled by setting its temperature.

Under the right conditions, sticking of one or several atom(s) onto the clusters occurs.

The collision products are analyzed in a second Time-Of-Flight mass spectrometer. A reflectron improves its resolution up to about 4000. Its large angular acceptance (the entrance diameter is 60 mm) reduces losses due to transverse motion. The geometry of the three-plates acceleration zone has been optimized in order to collect efficiently the ions. Simulation shows that the spatial dispersion after the cell is about 20 mm. Thus the distance between the first two accelerating plates is 20 mm in order to avoid losses. The distance between the last two plates is 30 mm. These distances are larger than those of the first WML. Although we use nickel mesh on the first two plates, these rather large distances cause spatial dispersion that is compensated using an Einzel lens just after the end plate. The detector is a tandem microchannel plates device.

If the collision energy is low enough, the new clusters do not evaporate before they are detected. The sticking cross section can then readily be deduced from the size distribution.

II. Principle of the energy focusing

Let us first recall some key points of the operation of a WML [16]. We refer the reader to Figure 2a for notations. We consider clusters of a given mass m and charge q. At a time T=0, the voltages V s and V d are applied to the acceleration plates. The clusters then acquire a potential energy U which depends on the initial abscissa s of the cluster between the plates at

V s and V d . Specifically, if E s =(V s -V d )/
( ) ( ) ( ) ( ) d d d s d qE E qd U U qE U qE E qd U U m T U D 2 / 1 0 2 / 1 2 / 1 0 2 / 1 2 / 1 2 / 1 2 2 2 2 2 - + - - - = (1)
for a cluster of mass m and charge q. The relation between the position of a cluster and its kinetic energy is displayed in Figure 2b, for different times T. In order to characterize the effects of the dispersion in energy, we develop D(U) in a Taylor expansion around U=U 0 , the energy of a cluster starting from the middle between the first two plates, s=s 0 /2.

( ) ( ) ( ) ( ) ( ) 3 0 2 0 0 0 0 U U U U U U U D U D - + - + - + = β α
Because of the form of equation ( 1), coefficients α and β depend linearly on time. Hence they become zero at different times T. For the usual operation of WML mass spectrometers, the detector is placed at a distance such that α is zero. This is the time focus point. Here we want a focus in energy. By applying a pulsed electric field E foc = -1/(αq) at some distance when the selected clusters arrive, it is easy to compensate for the linear dispersion given by α. If we choose to apply the field at the time T foc where β is zero, the energy dispersion is compensated up to third order. In other words, the condition

0 2 2 = ∂ ∂ U D (2)
determines a time T foc and a distance D foc where a voltage V foc corresponding to E foc (see Figure 2a) is applied. T foc, D foc, and E foc are given by the following expressions:

( ) ( ) ( ) 2 / 1 2 2 / 3 0 2 1 2 s d s d s foc qE E E s E E d m T - = ( ) ( ) ( ) [ ]       + - + - + = 2 / 1 0 2 / 1 2 / 3 0 2 2 / 1 0 1 1 2 s d d s d s d s s d foc E E d s E E s E E E E s d E E d s D ( ) ( ) (
)

1 2 / 3 0 0 2 / 1 0 2 3 2 -         + - - - = d d d s d s d foc E qdE U qdE U E E U E E E
D foc depends only of the ratio E d /E s . Moreover, it should be noted that D foc and V foc do not depend on the mass. This is important: to change the mass under study, we only need to change T foc . A single mass corresponds to a given T foc . Thus, only this mass has an energy dispersion low enough to be slowed down without being spread out in time: The energy focusing also acts as a mass selection.

III. The energy focusing device

Description of the device

The device displayed on Figure 3 performs both energy focusing and braking of the ions. It is made of 14 stainless steel plates of 12 cm diameter held by four steel rods housed with a glass tube to ensure electric insulation. A 12 mm hole is drilled at the center of each plate (except the plate n°11 whose hole is 18 mm diameter). The distance between plates 1 and 2 is 25 mm. Plates 2 to 10 are separated by 10 mm. The distance between plates 10 and 11, 12 and 13, 13 and 14 is 5 mm and between 11 and 12 is 10 mm.

The focusing voltage is applied between the first two plates (n°2 is grounded) and a 90% transmission nickel mesh (Labelcomat, 70 lines/inch) is used to define a more homogeneous electric field.

Plates n°2 to 10 of the apparatus are used to slow down the ions. An exponential decelerating potential is applied (V i =V 0 (1-e -i/Γ ) for the plate i) in order to minimize spatial defocusing [11]. The exponential shape of the potential is obtained by connecting the plates with appropriate resistors. The end plates n°10, 12, 13 and 14 are set to the same potential in order to define a zero-field zone (we will see later why such a zone is necessary). A 20mm long cylindrical extension is added on plate n°14 in order to increase the length of this zone.

An additional plate (n°11) can be set to a potential V fs different from the plates n°10, 12 and 13: it acts as an Einzel lens by reducing losses due to transverse motion.

Although it would theoretically improve the performance, mesh cannot be used on the plates n°3 to 14 for two reasons: first, the total transmission would be too low; second, ions kinetic energy is reduced and the field distortion would produce a drastic spatial defocusing [17,18].

Operation

Time synchronization is very important since all voltages must be pulsed. The repetition rate is 100 Hz. High voltages are provided by low noise power supplies (Bertan model 205B) and pulses are generated by TTL driven fast high voltages switches (Behlke HTS 51) whose rise time is lower than 10ns. The value of pulsed voltages is defined to about ± 0.2 V and the pulse-to-pulse temporal jitter of the switches is less than 1 ns. The synchronized TTL signals are provided by a timer card (National Instrument) clocked to 80 MHz.

Figure 4 displays the main sequences of the operation. At T=0 the voltage pulses are applied on the two accelerating plates (Figure 4a). For a given mass, the voltage V foc must be applied at time T foc . At this time, a voltage V b is already established on the exponential barrier (Figure 4b). The value of this voltage is chosen as a function of the desired kinetic energy. It is straightforward to calculate the appropriate value: if the mean kinetic energy after focusing is E k0 and if E k is the desired kinetic energy, V b has to be set to (E k0 -E k )/q. However if this were all we did, the clusters would be accelerated again after the end of the braking device since the collision cell is grounded. Thus it is necessary to shut down V b at time T 1 , when the clusters are in the zero-field zone (Figure 4c). This has to be done very rapidly so that the voltage is zero to a good accuracy when the clusters go out of the device.

That's why a careful study of the time response of the system has to be done. Since the resistor chain used to provide the exponential barrier contains high resistances, the parasite capacitances due to the plates have to be considered. It's easy to show that the best performance is obtained for equal RCs at each stage. Adjustable capacitances have been added to achieve this.

Once the potential barrier is shut down, the clusters enter the collision cell and reach the last mass selection stage where they are accelerated again at time T 2 (Figure 4d).

IV. Experimental results

Energy focusing

The velocity distribution of slow clusters can be measured directly in our setup. When V b has been shut down at time T 1 , the clusters mean position is x 1 . When the 2 nd acceleration voltages are switched on at time T 2 , the mean position of the ions is x 2 (x 2 -x 1 = d in Figure 4).

The clusters mean velocity is then v = (x 2 -x 1 )/(T 2 -T 1 ). By recording the ion signal as a function of T 2 , one can determine the velocity distribution. The main difference from case I) to II) is that they are obtained under two different spatial focusing operating modes. Spatial focusing is necessary: when clusters are slowed down, one can no longer neglect their transverse motion. The entrance diameter of the cell being 5 mm, the beam has to be refocused so that all clusters go through the cell. The refocusing is achieved by setting plate n° 11 to a potential different from the neighboring ones. Doing so, it acts as an Einzel lens. The time at which the potential barrier has to be shut down is affected by this potential: the clusters take more (less) time to reach the zero-field zone for a higher (lower) potential. We estimate that the transmission is increased by about a factor 4 in case II) when spatial focusing is achieved.

Let us now detail the difference between mode I) and mode II). In I), the voltage V fs is set to a value larger than the potential barrier V b by a few tens volts whereas in II) V fs is smaller than V b by hundreds volts. The first mode results in an excellent focusing provided that the cluster kinetic energy is very close to the mean value E k0 . In the second mode, this point is less stringent. SIMION [19] simulations show that the margin of tolerance δE around E k0 is about ±0.7 eV in the first case and 7 eV in the second case. In case I) the energy dispersion is smaller because clusters whose energy is different from E k0 by more than 0.7 eV are spatially discarded. The signal is obviously reduced but remains comfortable enough to work. In case II), the width of 4 eV is the true total dispersion of the apparatus. The energy spread could theoretically be as low as 0.1 eV, but is larger than this for several reasons. First, the applied voltages and delays are subject to the noise mentioned in the previous section.

However, this gives a small dispersion, of the order of ±0.25 eV. The most important source of energy spread is the initial velocity distribution of clusters in the beam. As mentioned in section II, the energy focusing relies on a linear relation between the position and the kinetic energy at time T foc . Any initial velocity distribution will induce a deviation from it. Indeed, clusters starting from the same initial position s but having different initial velocities will end up at slightly different positions between the focusing plates at time T foc . In figure 5 II), Na 100 + clusters are thermalized at 143 K. In our experiment, clusters are seeded in helium; simulation shows that, although their mean velocity is shifted to the mean velocity of helium, their translational temperature remains the same: the FWHM of their velocity distribution is of the order of (2kT/m) 1/2 = 40 m.s -1 . This is exactly the value deduced from the fit in Figure 5 IIa).

One can actually choose between mode I) and mode II): if the ion yield is large enough, it is possible to select the mode I), for which the energy resolution is better; on the other hand mode II) provides a better ion yield.

It should be noted that, for a given T 2 , another feature limits the energy spread of the detected ions: only clusters that are present at T 2 between the first two plates of the second TOF are detected. Let v be the velocity of the cluster across the cell, E k the corresponding kinetic energy, d the distance from the zero-field zone to the middle of the accelerating region, and δd the width of this region (see figure 4). The restriction above mentioned is approximately defined by δE k /E k =2δv/v<δd/d. δd/d is about 20%, so δE k /E k <40%. It corresponds to δE k ≈4 eV for the example given in figure 5 II).

In cases where a supersonic expansion can be used to generate clusters, our apparatus is likely to provide better performances since we have demonstrated that the main limitation to the energy focusing is the initial velocity dispersion.

We estimate the overall transmission through the device to be more than 20% for Na 82 + slowed down to about 10 eV (using spatial focusing mode II)). This corresponds to about 3 clusters detected per pulse. This allows us to observe sticking under very good conditions.

Sticking of sodium atoms onto sodium clusters

Figure 6 displays the first experimental sticking results. We select Na 81 + thermalized at 158 K and with a kinetic energy E k of 20 eV in the laboratory frame (corresponding to a collision energy of about 0.3 eV). The experimental values are:

V s = 725 V, V d = 520 V, V foc =
222 V, T foc = 36.9 µs, V b = 719 V, V fs = 205 V, T 1 = 72 µs, T 2 = 162 µs.

Then we increase gradually the temperature from 293 K to 533 K, and thus the density of atoms, in the collision cell.

Without vapor in the collision cell (Figure 6a), there is no sticking and only Na 81 + is detected. For a density ρ = 7.10 18 atoms/cm 3 (Figure 6b), Na 82 + and a small amount of Na 83 + are produced. If one increases the density, up to 6 sticking events can be observed (Figure 6c).

Under these conditions the parent clusters are all converted to higher mass species, the maximum size being Na 87 + .

This "saturation" of nucleation is actually easy to explain if we focus on the lifetimes of the nucleation products. At each sticking event A n +A⇒A n+1 , the internal energy of the incoming cluster A n is increased by D n+1 +E c CM , where D n+1 is the dissociation energy of A n+1

and E c CM is the collision energy in the center of mass frame. In our case, D n+1 >>E c CM . The dissociation energies do not vary much from one size to another for clusters of a hundred atoms, so let's note it D. Thus, starting from a cluster of size p and internal energy E* p , the internal energy E* q of a cluster of size q obtained by sticking is approximately E* q =E* p + (qp)D. From previous experiments, the relation between internal energy and mean evaporation time is well known for sodium clusters [20]. As we know the initial temperature of Na 81 + , it is easy to calculate E* 81 and E* 81+n . In our experiment, clusters are detected at the right time of flight only if they do not evaporate before they enter the reflectron. The propagation time τ from the cell to the reflectron, which depends on the selected kinetic energy, the voltages and the mass, is easy to calculate. The first undetected mass m has an internal energy E* m leading to a lifetime smaller than τ. Using the parameters of [20], this simple theory gives an estimate that perfectly agrees with experimental observation. Moreover, the value of m depends on the initial temperature. The agreement between theory and experiment indicates that the cluster has been thermalized to the expected value. Note that this time τ is particularly small in our experiment (it is about 150 µs for the considered conditions). This feature reduces the awkward problem of spontaneous dissociation.

The measurement of the sticking probability for a cluster of size n leads to the absolute nucleation cross sections σ(n). Let I be the amount of clusters that have not undergone sticking, and I 0 the total amount of incoming clusters. For example, I 0 is the sum of the areas of all the peaks of Figure 6, whereas I is the area of the first one. Let E k denote the kinetic energy of the incoming clusters in the laboratory frame, d the length of the cell and ρ the density of atoms in the cell as deduced from the vapor pressure of sodium at the temperature of the cell T. A simple calculation gives σ(n):

( ) ( )

2 / 1 0 1 1 Ln -         + × - = k b E T nk d I I n ρ σ
For the nucleation reaction Na 81 + +Na ⇒ Na 82 + we determined a cross section of 200 Å 2 . For this preliminary result, the error bar is quite difficult to estimate. In particular, the density of sodium vapor in the collision cell needs to be known with a better accuracy. The measurement of nucleation cross sections for sodium clusters as a function of the size is the next step of the experiment, but it is out of the scope of this paper and will be the subject of a forthcoming publication.

V. Comparison with alternative devices

We have already briefly described in the introduction other methods to get low energy collisions.

One alternative device also uses a TOF [11] but our setup provides a better energy resolution [21]. GIB devices use quadrupoles and octopoles [12,13,14]. Without any "slicing" (i.e. without Bessel Box), they provide an energy dispersion of the order of 10 eV. Our setup is better on this point. Another advantage of our method is that the time between collision and detection, and thus post collisional evaporation, is reduced compared to GIB devices. On the other hand, their energy resolution is better than our when using a Bessel box. Concerning the overall transmission, we could not find quantitative data concerning the GIB method.

Anyway, when using a Bessel box the transmission is certainly much smaller than our.

To conclude, our apparatus is a competitive alternative to GIB. It seems to provide performances at least as good as GIB when no slicing is made. On the other hand, a GIB apparatus with a Bessel Box provides an excellent energy resolution that we are not able to reach with our effusive source. Nevertheless, a better energy resolution could be obtained with our setup using a supersonic expansion.

Finally, let us point out that our device is simpler and cheaper than a GIB apparatus (that uses two octopoles, two quadrupoles and a Bessel box).

Conclusion

We have developed a new device to produce mass selected thermalized clusters with very low kinetic energy. Energies as low as 10±2 eV in the laboratory frame are routinely obtained with a comfortable ion yield. We used successfully this device for measuring the absolute sticking cross section of sodium atoms onto sodium clusters. It opens the way to new investigations in the physics of nucleation processes.

Figure 5

 5 Figure 5 displays two examples of ion yield as a function of T 2 together with their corresponding kinetic energy distributions. Figure 5 I) concerns Na 82 + . The experimental parameters are set to the following values: V s = 745 V, V d = 520 V, V foc = 198 V, T foc = 37.9 µs, the potential barrier is set to V b = 702.2 V and the spatial focusing voltage to V fs = 729.6 V, they are shut down at T 1 = 90 µs. The measured kinetic energy is 12±0.6 eV. Figure 5 II) shows Na 100 + signal obtained with V s = 725 V, V d = 519 V, V foc = 219 V, T foc = 40.8 µs, the potential barrier is set to V b = 728.5 V and the spatial focusing voltage to V fs = 541.7 V, they are shut down at T 1 = 90 µs. The fitted curves are obtained from a numerical simulation of the signal detected in our second TOF as a function of T 2 . The simulation takes into account the distributions of initial positions s in the first acceleration stage and the initial velocity distribution of the clusters. Furthermore we introduce noise on times and voltages.

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Experimental setup.

Figure 4 :Figure 5 :Figure 6 :

 456 Figure 4: Illustration showing the different delays involved in the operation: (a) T=0: voltages are applied on the first acceleration stage. (b) T foc : the energy focusing voltage is switched on. (c) T 1 : the potential barrier voltage is switched off. (d) T 2 : voltages are applied on the second acceleration stage.

  s 0 and E d =V d /d 0 are the two accelerating electric fields,

	U=qsE s +qd 0 E

d , with s the abscissa of the cluster defined leftwards from the plate at V d . The particular design of the acceleration region with two fields allows a small relative dispersion of energy. This dispersion is however much too high for our purposes. Now, the distance D from the last accelerating plate reached after a time T is:

Acknowledgements

We thank M. Gianesin, Ph. Paquier, L. Polizzi, G. Trénec and W. Volondat for technical support. The authors are grateful to B. Whitaker for a critical reading of the manuscript.


Guillaume Sacco
email: sacco.g@chu-nice.fr

Véronique Joumier

Darmon Nelly

Deschamps Arnaud

Alexandre Derreumaux

Piano Ji-Hyun Lee

Nathalie Bordone

Alexandra Konig

Bernard Teboul

Nelly Darmon

Arnaud Dechamps

Julie Piano

Renaud David

Olivier Guerin

François Bremond

Philippe Robert

Detection of activities of daily living impairment in Alzheimer's disease and mild cognitive impairment using information and communication technology

Keywords: functional impairment, ICT, IADL, MCI Dovepress

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

Introduction

One of the key clinical features of Alzheimer's disease (AD) is impairment in daily functioning. Activities of daily living (ADLs) consist of bathing, dressing, going to the toilet, transferring, continence, and feeding. [START_REF] Katz | Studies of illness in the aged. The Index of ADL: a standardized measure of biological and psychosocial function[END_REF] Instrumental ADLs (IADLs) are the activities often performed by a person who is living independently in a community setting during the course of a normal day, such as using the telephone, shopping, food preparation, housekeeping, laundry, mode of transportation, responsibility for own medication, and ability to handle finances. [START_REF] Lawton | Assessment of older people: self-maintaining and instrumental activities of daily living[END_REF] The inability to perform ADLs and IADLs leads to loss of independence, affects quality of life of patients with dementia, and increases the burden of caregivers by shifting to them many daily responsibilities. [START_REF] Andersen | Ability to perform activities of daily living is the main factor affecting quality of life in patients with dementia[END_REF] Mild cognitive impairment (MCI) is often a precursor to AD and other forms of dementia, as 12% of individuals with MCI convert to AD within 1 year, [START_REF] Petersen | Mild cognitive impairment: clinical characterization and outcome[END_REF] and as many as 60% of individuals with MCI develop AD over a 5-year period. [START_REF] Morris | Mild cognitive impairment (MCI) represents early-stage Alzheimer's disease[END_REF] It has been shown that more complex IADL may already be impaired in the early stages of cognitive decline before a diagnosis of dementia is warranted. [START_REF] Tuokko | Clinical Interventions in Aging is an international, peer-reviewed journal focusing on evidence-based reports on the value or lack thereof of treatments intended to prevent or delay the onset of maladaptive correlates of aging in human beings[END_REF][START_REF] Artero | Revised criteria for mild cognitive impairment: validation within a longitudinal population study[END_REF][START_REF] Farias | MCI is associated with deficits in everyday functioning[END_REF][START_REF] Jefferson | Decisional capacity for research participation in individuals with mild cognitive impairment[END_REF] As indicated in the recommendations from the National Institute on Aging-Alzheimer's Association (NIA-AA), [START_REF] Albert | The diagnosis of mild cognitive impairment due to Alzheimer's disease: recommendations from the National Institute on Aging-Alzheimer's Association workgroups on diagnostic guidelines for Alzheimer's disease[END_REF] persons with MCI commonly have mild problems performing complex tasks. Nevertheless, they generally maintain their independence with minimal assistance. It is recognized that the application of this criterion is challenging but also necessary for the determination of whether a person has dementia. Methods to assess IADL comprise self-reported questionnaires, performance-based assessment, and informant-based questionnaires. These measurements have some limitations [START_REF] Sikkes | Do instrumental activities of daily living predict dementia at 1-and 2-year follow-up? Findings from the Development of Screening guidelines and diagnostic Criteria for Predementia Alzheimer's disease study[END_REF] because they do not offer accurate, reproducible, objective, and ecological perspectives. Moreover, these assessment batteries and standardized tools rely on quantitative scales, which are often lacking sensitivity.

For this reason, information and communication technology (ICT), particularly techniques involving imaging and video processing, is of interest [START_REF] Romdhane | Automatic video monitoring system for assessment of Alzheimer's disease symptoms[END_REF] and may overcome the limitations in reducing the inter/intra-rater variability due to human interpretation. Such techniques enable the patients' performances and actions in real time and real life situations to be captured and accurately evaluated.

In France, a third Alzheimer plan was launched in 2008 (French National Plan for "Alzheimer and Related Disorders" 2008-2012) [START_REF]Alzheimer Plan[END_REF] to strengthen research on Alzheimer's disease and related disorders, promote earlier diagnosis, and improve both patient management and support for carers. In this context, the French National Research Agency (ANR) launched a call to promote research projects in health and autonomy through innovative concepts and technological breakthrough. This call was proposed to engineers and companies involved in innovative computer sciences but also to clinical practitioners. This explains why clinical centers belonging to the nationwide network comprising 27 "memory resource and research centers" (CMRRs: centres mémoire de ressources et de recherche) also participated.

The overall aim of the SWEET Home (ANR TecSan 2009) project was to demonstrate that it is possible using a video monitoring system (VMS), to obtain a quantifiable assessment of IADLs in AD and in MCI.

Study participants and methods

This study was promoted by the Nice University Hospital (study 11-pp-03) and funded by the National Research Agency in France (ANR-09-TECS-016-01). Ethical approval was received from the Protection of Persons Committee "Sud Méditerranée V" (CPP N°11029 from May 24, 2011) and the "Agence Française de Sécurité Sanitaire des Aliments et des Produits de Santé" (AFSSAPS N°B110465-30 from April 14, 2011). Informed consent was obtained before the first assessment.

Participants and clinical assessment

Sixty-four individuals aged 65 or older were recruited at the Nice Research Memory Center within two consecutive protocols: P1 for AD and normal controls (NC), P2 for MCI (NIA-AA criteria) and NC.

For the AD group, the diagnosis was determined using the NINCDS-ADRDA criteria. [START_REF] Mckhann | Clinical diagnosis of Alzheimer's disease: report of the NINCDS-ADRDA Work Group under the auspices of Department of Health and Human Services Task Force on Alzheimer's Disease[END_REF] For the MCI group, patients with a mini-mental state examination (MMSE) score higher than 24 were included using the Petersen clinical criteria. [START_REF] Petersen | Mild cognitive impairment: clinical characterization and outcome[END_REF] Subjects were not included if they had a history of head trauma with loss of consciousness, psychotic or major depressive disorder according to the Diagnostic and Statistical Manual of Mental Disorders, 4th edition criterion, or aberrant motor activity (tremor, rigidity, Parkinsonism) as defined by the Movement Disorder Society Unified Parkinson Disease Rating Scale. [START_REF] Goetz | Movement Disorder Societysponsored revision of the Unified Parkinson's Disease Rating Scale (MDS-UPDRS): scale presentation and clinimetric testing results[END_REF] Participants were administered a cognitive and behavioral examination prior to completing the video monitoring session. Global cognitive functioning was assessed using the MMSE. [START_REF] Folstein | Mini-mental state". A practical method for grading the cognitive state of patients for the clinician[END_REF] Other cognitive functions were assessed with the frontal assessment battery, [START_REF] Dubois | The FAB: a Frontal Assessment Battery at bedside[END_REF] 5 Words, [START_REF] Dubois | The 5 words": a simple and sensitive test for the diagnosis of Alzheimer's disease[END_REF] clock drawing test, [START_REF] Sunderland | Clock drawing in Alzheimer's disease. A novel measure of dementia severity[END_REF] and verbal fluencies. [START_REF] Alberca | Verbal fluency and Alzheimer's disease[END_REF] Depressive symptoms were assessed using MADRS [START_REF] Montgomery | A new depression scale designed to be sensitive to change[END_REF] and GDS. [START_REF] Yesavage | Development and validation of a geriatric depression screening scale: a preliminary report[END_REF] Finally, functions were assessed using the IADL scale (IADL-E) [START_REF] Mathuranath | Instrumental activities of daily living scale for dementia screening in elderly people[END_REF] during a clinical interview with the caregivers.

Ecological assessment of autonomy based on a VMS

The ecological assessment of IADLs was conducted in an observation room located in the Nice Research Memory Center. This room was equipped with everyday objects for use in ADLs and IADLs, eg, an armchair, a table, a tea corner, a television, a personal computer, and a library. Two fixed monocular video cameras (eight frames per second) were installed to capture the activity of the participants during the experiment. The aim of this ecological assessment of autonomy was to determine the extent to which the participant could undertake a list of daily activities with the respect of constraint after having been given a set of instructions. To achieve this aim, two functional scenarios which could realistically be undertaken within the confines of the room were proposed to participants: one for the AD and NC participants (P1), and the other for the MCI and NC participants (P2). All assessments were performed at the same time of day, between 2 pm and 3 pm. The rating of the videos was made by engineers specialized in video signal analysis working at the Institut National de Recherche en Informatique et en Automatique.

Daily activity scenario (DAS) .,n associated with protocol P1

For the protocol P1 scenario, participants were assessed in their ability to carry out a list of seven activities (eg, reading the newspaper, turning on the television) in a specific order within a timeframe of 20 minutes (see Table 1).

DAS associated with protocol P2

For the functional scenario associated with P2, participants were assessed in their ability to carry out a list of ten activities in a logical order respecting temporal execution constraints within a timeframe of 15 minutes (see Table 1). Prior to leaving the room, the examiner described each of the activities and the location and use of various objects needed to undertake the tasks. The examiner left the room only after it was clear that the participant understood the tasks. The participant kept the list of instructions and referred to them at any point during the assessment. He/she could leave the room when he/she felt that he/she had completed the required tasks. The participant was also told that the examiner would be available for questions on the other side of the door and that he/she could leave the room at any point should he/she choose to do so. During the clinical scenario, an examiner located outside of the room monitored the safety of the participants.

The DAS score [DAS ., .()] for assessing the scenario

The first step (Step 1) was to manually select and collect the clinical relevant data to be extracted from videos. Secondly (Step 2), the mathematical algorithm for assessing the scenario (DAS score) was constructed, and then parameters k i,n included in the expression of the DAS score were determined using a fitting procedure (Step 3). The final step (Step 4; to validate the procedure and the values of parameters k i,n ) was done using the leave-one-out crossvalidation (LOOCV) methodology. All these steps are described below.

Step 1: DAS ., .

() development -annotated data

Researchers blinded to a participant's clinical status viewed and annotated the video to extract relevant parameters. To avoid inter-and intra-rater variability due to subjective interpretation of performed activities, the beginning and the end of each activity were defined using specific criteria (Table 2). A ratio related to the percentage of time participants carried out goal-oriented behaviors was computed as follows:

RE ff = (total time [in seconds] spent by the participant in performing the listed activities/total time spent in the room),

RE ff Є R [0,1] .
For the DAS associated with P1, the following parameters were extracted: a 1,P1 number of activities omitted, a 1,P1 Є [1,7]; a 2,P1 total number of repetitions, a 2,P1 Є N; a 3,P1 order error, a 3,P1 Є {0,1} with a 3,1 = 1 if order error was done; and a 4,P1 total number of attempts before completing a given activity, a 4,P1 Є N.

For the DAS associated with P2, the following parameters were extracted: a 1,P2 number of activities omitted, a 1,P2 Є [0,10]; a 2,P2 total number of repetitions excluding the leisure activities ("watching television," and "reading"), a 2,P2 Є N; a 3,P2 the number of activities performed but not achieved, a 3,P2 Є [0,10]; and a 4,P2 parameter related to the respect of temporal execution constraints a 4,P2 Є {0,1} with a 4,P2 = 1 if more than two or three temporal constraints were not respected.

Step 2: DAS ., .

() development -mathematical expression of DAS score

The score DAS j,n , n Є {P1, P2}, for a participant j was expressed by: DAS

j,n (k 1,n ,k 2,n ,k 3,n ,k 4,n ) (j) = [RE ff (j)] × Π 4 i a j k i n i n =1 , , ( ) with
k 1,P1 , k 2,P1 , k 3,P1 , and k 4,P1 verifying the following relationship 0 , k 1,P1 , k 2,P1 , k 3,P1 , k 4,P1 , 1, and no constraints were established for k i,P2 parameters i Є [1,4]. score was calibrated by using the combination of the mean of the parameters which were selected as the model parameter set during the second step of fitting procedure.

Step 4: Cross-validation methodology

Predictive performance of the DAS .,n score, n Є {P1, P2} was done by a LOOCV given the small sample sizes. Criteria used for validating the model with other current neuropsychological rating scales were the Spearman correlation between the DAS .,n score with both MMSE and IADL-E. Criteria used for performing the predictive performance of the model were accuracy rate, positive predictive value, negative predictive value, false-positive rate, and false-negative rate computed from test data according to the LOOCV methodology. [START_REF] Efron | A leisurely look at the bootstrap, the jackknife, and cross-validation[END_REF]

Statistical analysis

All analyses were performed following the per-protocol analyses, including all patients who correctly finished the protocol. Results are presented as means and their 95% confidence intervals (CIs) or standard deviations (SDs) (mean, 95% CI; or mean ± SD) for continuous variables, and as the value and its associated proportion (n, %) for categorical variables. Intergroup comparisons for continuous variables were performed using a nonparametric Mann-Whitney test. Analyses of association between two categorical variables (two modalities) were studied using the Fisher's exact test. Analyses of associations were measured using Spearman rank correlation. The significance level was set at an alpha risk of 5% (P , 0.05). The receiver operating curves (ROCs) and its area under the ROC was also provided to assess the predictive performance of the DAS .,n scores computed from all data. All calculations were performed using SPSS Statistics (IBM Corporation, Somers, NY) software, version 19.0, and R software, version 2.13.2.

Results

Protocol 1 Population

Sixteen AD patients (age = 76.7 ± 7.6) and 10 NC (age = 73.9 ± 6.2) were included in protocol 1. Table 3 shows the clinical and demographic data of the participants. Significant intergroup differences in demographic factors (gender and age) were not seen. The mean MMSE for the AD group was 20.7 (±2.0) and 28.1 (±1.3) for the NC group (P , 0.001), and the mean IADL-E scores also differed between groups, with the AD group having significantly different mean IADL-E scores (14.3 ± 5.9) compared with the NC group (10.5 ± 1.1) (P , 0.05). LOOCV results for DAS .,P1

Table 5 shows predictive performances results of the assessment methodology to classify the new test data as AD observation (refers to a positive case) or NC observation (refers to a negative case) using its DAS .,P1 () score fitted using the value of parameter set (k 1,P1 , k 2,P1 , k 3,P1 , k 4,P1 ) defined from the training dataset.

Assessment based on DAS .,P1

Figure 1 shows evolution of the indexes fitted from all data (n = 26). The differentiation between the AD and NC groups increased progressively when the cumulative impact of parameters k 1,P1 , k 2,P1 , k 3,P1 , and k 4,P1 were taken into account. The DAS .,P1 () scores fitted from all data (n = 26) differed signif icantly (Mann-Whitney, P , 0.001) between AD (DAS AD,P1 = 0.47, 95% CI 0.38-0.56) and NC (DAS NC,P1 = 0.71, 95% CI 0.68-0.74). The Spearman correlation coefficients were ρ (DAS .,P1 , MMSE) = 0.81, ρ (DAS .,P1 , IADL-E) = -0.65, and ρ (DAS .,P1 , diagnosis) = -0.76 (diagnosis = 0 refers to NC group, and diagnosis = 1 refers to AD group) (see Table 6). Based on the measurement of DAS .,P1 scores fitted from all data (n = 26), the test performance provided an area under the ROC of 0.98, 95% CI 0.92-1.00, and for a cutoff point of 0.65 (±0.01), the sensitivity and specificity were 100% and 94% (see Figure 2).

Protocol 2 Population

Nineteen MCI patients (age = 75.2 ± 4.25) and 19 NC (age = 71.7 ± 5.4) were included in protocol 2. Table 4 shows the clinical and demographic data of the participants. Significant intergroup differences in demographic factors (gender and age) were not seen. The mean MMSE for the MCI group was 25.8 (±2.2) and 28.8 (±1.0) for the NC group (P , 0.001), and the mean IADL-E scores did not differ between groups, with the MCI group having a mean IADL-E score of 9.9 (±1.7) and 9.6 (±1.1) for the NC group.

LOOCV results for DAS .,P2

Table 5 shows predictive performance results of the assessment methodology to classify the new test data MCI observation (refers to a positive case) or NC observation (refers to a negative case) using its DAS .,P2 () scores fitted using the value of parameter set (k 1,P2 , k 2,P2 , k 3,P2 , k 4,P2 ) defined from the training dataset. Predictive performance results are better with the DAS .,P1 than the DAS .,P2 (eg, higher accuracy rate, higher positive and negative predictive values), which is coherent with the increasing difficulty to differentiate NC participants from patients at earlier stages of AD disease.

Assessment based on DAS .,P2

(j)= [R Eff (j)]× k P F j 1 2 1 2 , , ( ) α
(impact of omission mistakes on the R Eff ). (C) Index 2,P2 (j

) = [R Eff (j)]× i=1 2 1, a , ( ) 2 1 2
∏ k P F j (cumulative impact of omission and repetition (excluding repetition of leisure activities) mistakes on the R Eff ). (D) Index 3,P2 (j) = [R Eff (j)]× Notes: a The leave-one-out cross-validation was used to provide an un-biased estimation of the prevision errors of our models (the DAS scores), and therefore to assess how the results of our models will generalize to an independent data (data not used during the fitting procedure). In our context, this methodology consists to estimate the parameter set (k 1,n , k 2,n , k 3,n , k 4,n ), n Є {P1, P2} with the training dataset (n training ) and to define the threshold of cut-off point from the DAS scores computed from the training dataset, and then to validate this assessment methodology to classify the test data. For the LOOCV, this procedure was repeated K times: each observation in the initial sample is used once as the test data; b predictive performance was computed according to the LOOCV methodology; c the threshold was defined for each training dataset as the cut-off that minimizes the absolute value between the specificity and the sensitivity to optimize both. group, and diagnosis = 1 refers to MCI group) (see Table 6).

Based on the measurement of DAS .,P2 scores fitted from all data (n = 38), the test performance provided an area under the ROC of 0.87, 95% CI 0.76-0.99, and for a cutoff point of 0.24 (±0.01), the sensitivity and specificity were 74% and 89% respectively (see Figure 4).

Discussion

In the present study, the use of VMS was sought to assess participants during complex daily living activity scenarios. Using VMS, it was possible to determine that in comparison to NC participants, those with AD performed worse on several outcome parameters including the time to achieve the set activities and the number of repetitions of the same activity. These results highlight the importance of executive function in the performance of basic daily activities and are consistent with previous findings. [START_REF] Marshall | Executive function and instrumental activities of daily living in mild cognitive impairment and Alzheimer's disease[END_REF][START_REF] Razani | Relationship between executive functioning and activities of daily living in patients with relatively mild dementia[END_REF] Esposito et al 27 explored executive function and multitasking in daily life using the modified six elements task. In that study, AD patients had significantly more multitasking deficits than NC participants. The VMS method made it possible to define an objective and continuous measure of functional impairment disturbances. It was interesting to note that as the complexity of the DAS score increased, so did the magnitude of the difference between the AD and the NC participants. The complex DAS score included several clinically quantifiable as well as qualitative parameters representative of daily functioning. The complex DAS score was significantly correlated with the MMSE as a marker of global cognitive level. This correlation was strong (0.81) even though the DAS score included specific executive characteristics that were not included in the MMSE, such as repetition, omission, and incorrect order. In addition, the ROC analysis of the DAS score showed 94% sensitivity and 100% specificity for discriminating AD from NC subjects. Taking these initial results into account, the authors of this present paper designed another scenario aiming to stress more subtle differences between MCI and NC participants. The ROC analysis of the DAS score showed 89% sensitivity and 73% specificity for discriminating MCI from NC participants. More specifically, this second protocol showed that MCI patients had impaired performances on DAS scores and had difficulty correctly reorganizing activities and successfully carrying out the activities. As for the AD patients, the observed impaired performances in the MCI patients highlight the importance of executive and planning parameters in IADLs [START_REF] Dechamps | Effects of different learning methods for instrumental activities of daily living in patients with Alzheimer's dementia: a pilot study[END_REF] (see Table 7). In fact, there is an increasing call for a stronger consideration of impairment in IADLs in the diagnostic criteria of MCI to improve the prediction of dementia. [START_REF] Marshall | Executive function and instrumental activities of daily living in mild cognitive impairment and Alzheimer's disease[END_REF] The aim of a recent longitudinal cohort study [START_REF] Luck | Prediction of incident dementia: impact of impairment in instrumental activities of daily living and mild cognitive impairment -results from the German Study on Ageing, Cognition, and Dementia in Primary Care Patients[END_REF] was to determine the predictive ability of MCI and IADL impairment for incident dementia. As part of the German Study on Ageing, Cognition, and Dementia in Primary Care Patients, a sample of 3327 patients from general practitioners, aged 75 years and older, was assessed with four assessments at 1.5-year intervals over a period of 4.5 years. Results indicate that MCI and IADL are significantly associated with higher conversion to, shorter time to, and better predictive power for future dementia. Regarding IADL, a significant impact was found for impairment in responsibility for one's own medication, shopping, and housekeeping, and in the ability to use public transport. These pilot studies have several limitations. From a logistical point of view, this assessment is not yet reproducible easily in others clinical facilities. In addition, even if the duration of the scenario is relatively short (20 minutes and 15 minutes respectively for the first and second study) the overall duration including preparation of the room and of the patient is too long. From a technical point of view, the main limitation of the computational model in this present study is that it relied on the fact that only the relative position of the participant in the room is automatically processed by computer vision algorithm. Automatic recognition of IADL remains in progress. Therefore, the annotation of timeframe when a participant performs an activity is made manually, which is time consuming for the clinicians. One possible option to have a more automated assessment would be to use other environmental sensors (such as contact sensors) in conjunction with the VMS system to give direct information concerning the correct realization of the activity and the time spent for performing the activity. Finally, a more accurate cognitive assessment for MCI patients to delineate amnesic from non-amnesic MCI patients needs to be proposed.

The next step of the research is to solve most of these technical limitations. These are the objectives of the ongoing European Commission project FP7 Dem@Care devoted to the development of an automatic system providing multiparametric monitoring of daily activity lifestyle behavior in combination with medical data.

In conclusion, this study outlines the interest of a novel tool coming from the ICT world for the assessment of autonomy in AD and MCI. The derived DAS scores provide a pragmatic, ecological, objective measurement which may improve the prediction of future dementia, be used as an outcome measurement in clinical trials, and lead to earlier therapeutic intervention.

Figure 1 F((F(

 1 Figure1DAS .,P1 scores for AD patients and NC participants for protocol 1 (P1). The first line (A) represents the ratio of efficacy for the two groups (Grey dots for NC and Black dots for AD). Then the next lines (B-E) show the evolution of the index from ratio of efficacy (index 0) to DAS .,P1 score (index 4) including omission (B), repetition (C), order error (D), and bad completion at the first attempt (E). Measurements represented for each participant j: (A) R Eff = Index 0,P1 (j) (Percentage of time spent in the room to behave directed to perform a listed activities). (B) Index 1,P1 (j) = [R Eff (j)]× i=1 4

Figure 3

 3 Figure3shows evolution of the indexes fitted from all data (n = 38). The first lines (a) represent the ration of efficacy for the two groups (one point represents one patient). The next lines (b, c, d, and e) show the evolution of the index from the ration of efficacy (index 0) to DAS .,P2 score (index 4) with the addition of omission (b), repetition (c), bad achievement (d), and planning mistakes (e). The differentiation between the MCI and NC groups is done progressively with the cumulative impact of parameters k 1,P2 , k 2,P2 , k 3,P2 , and k 4,P2 . The DAS .,P2 scores differed significantly (P , 0.001) between MCI (DAS MCI,P2 = 0.11, 95% CI 0.05-0.16) and NC (DAS NC,P2 = 0.36, 95% CI 0.26-0.45). The Spearman correlation coefficients were ρ (DAS .,P2 , MMSE) = 0.81, ρ (DAS .,P2 , IADL-E) = -0.06, and ρ (DAS .,P2 , diagnosis) = -0.66 (diagnosis = 0 refers to NC

Figure 3

 3 Figure3DAS .,P2 scores for MCI patients and NC participants for protocol 2 (P2). The first line (A) represents the ratio of efficacy for the two groups (Grey dots for NC and Black dots for MCI). Then the next lines (B-E) show the evolution of the index from ratio of efficacy (index 0) to DAS .,P2 score (index 4) including omission (B), repetition (C), bad achievement of activities (D), and planning errors (E). Measurements represented for each participant j: (A) R Eff = Index 0,P2 (j) (Percentage of time spent in the room to behave directed to perform a listed activities). (B) Index 1,P2 (j)= [R Eff (j)]× k P

(

  cumulative impact of omission, repetition (excluding repetition of leisure activities) mistakes and bad achievement of activities on the R Eff ). (E) Final DAS score S j,P2 (k 1,P2, k 2,P2, k 3,P2, k 4,P2 ) (j) = [REff(j)]cumulative impact of omission, repetition (excluding repetition of leisure activities) mistakes, bad achievements of activities, and planification mistakes on the R Eff ).

Figure 4

 4 Figure 4 Performance evaluation of the assessment methodology to classify observation data as MCI group or NC group. (A) Specificity and sensitivity in function of the cutoff point of DAS .,P2 () scores. (B) Receiver operating curve associated with the protocol 2. Abbreviations: DAS, daily activity scenario; MCI, mild cognitive impairment; NC, normal control.

Table 1

 1 Daily activity scenarios characteristics in protocols 1 (P1) and 2 (P2)

	Daily

activity scenario associated with the protocol 1 (P1) Daily activity scenario associated with the protocol 2 (P2)

	Activities	"Your task is to perform this list of activities in the order	"Your task is to perform this list of 10 activities
		given within a time frame of 20 minutes"	in a logical manner within 15 min. These 15 minutes
		• Walk to the reading table and read something	represent a typical morning period of everyday life"
		for 2 mn	• Read the newspaper
		• Walk to the coffee corner where the kettle is and	• Water the plant
		boil some water	• Answer the phone
		• Walk to the phone and compose this number:	• Call the taxi
		xxxxxx	• Prepare today's medication
		• Take the watering can and water the plant.	• Make the check for the Electricity Company
		• Walk to the television and turn it on with the	• Leave the room when you have finished all
		remote control	activities
		• Walk to the reading table, take the playing cards	• Watch the TV
		and classify them by color (reds with reds, blacks	• Prepare a hot tea
		with blacks)	• Write a shopping list for lunch
		• Take the green "ABCD" folder on the desk with the
		A, B, C, D sheets in it. Match the A, B, C, D sheets
		from the folder to the relevant folders dispersed all over
		the room; A with A, etc … Put the "ABCD" folder back
		on the desk
		• Leave the room
	Constraints	Participant has to perform the activities	1. watch the TV before the phone call
		in the given order	2. water the plant just before leaving the room
			3. call the taxi, which will arrive in 10 minutes and
			ask the driver to drive you to the market
	Duration	20 minutes	15 minutes
	Parameters extracted from video	-RE ff Є R [0,1]	-RE ff Є R [0,1]
	used to compute DAS .,n scores	-Number of activities omitted, a 1,P1 Є [1,7]	-Number of activities omitted, a 1,P2 Є [0,10]
		-Total number of repetitions, a 2,P1 Є N	-Total number of repetitions excluding the leisure
		-Order error, a 3,P1 Є {0,1} with a 3,1 = 1 if order error	activities ("watching TV", and "reading"), a 2,P2 Є N
		was done	-Number of activities performed but not achieved,
		-Total number of attempts before completing a given	a 3,P2 Є [0,10]
		activity, a 4,P1 Є N	-Respect of temporal execution constraints,
			a 4,P2 Є {0,1} with a 4,P2 = 1 if more than two
			or three temporal constraints were not
			respected

Table 2

 2 Observable criteria used to annotate video sequences of the protocol 2 (P2)To determine values of the model parameter set (k 1,n , k 2,n , k 3,n , k 4,n ), n Є {P1, P2}, the fitting procedure was divided into two steps. Firstly, 50,000 different combinations of parameter values, consistent with constraints of order (P1), and no specific constraints for (P2) were drawn up using a random number generator. Secondly, multiple model parameter sets (k 1,n , k 2,n , k 3,n , k 4,n ) to produce a "good fit" were selected if their associated score was both strongly and positively correlated with MMSE score, as well as being strongly and negatively correlated with IADL score using a nonparametric Spearman correlation coefficient as the criterion distance of good fit. For the analyses, the final functional DAS .,n (k 1,n , k 2,n , k 3,n , k 4,n )

	Activity	Activity period

Table 3

 3 Characteristics of the participants in protocol 1 (P1)

	Characteristics	NC n = 10	AD n = 16	P values
	Female, n (%)	5 (50%)	11 (68.8%)	0.425
	Age-yrs, mean [CI95%]	73.9 [69.4, 78.4]	76.7 [72.7, 80.7]	0.182
	Level of education, n (%)
	Unknown	0 (0%)	0 (0%)	-
	No formal education	0 (0%)	0 (0%)	-
	Elementary school	1 (10%)	7 (43.8%)	0.099
	Middle school	0 (0%)	4 (25.0%)	0.136
	High school	2 (20.0%)	2 (12.5%)	0.625
	Post-secondary education	7 (70.0%)	3 (18.8%)	0.015*
	MMSE a , mean [CI95%]	28.1 [26.8, 29.4]	20.7 [18.7, 22.7]	,0.001**
	IADL-E b , mean [CI95%]	10.5 [9.7, 11.3]	14.3 [11.2, 17.5]	0.031*
	MADRS c , mean [CI95%]	3.5 [0.3, 6.7]	4.3 [1.9, 6.6]	0.698
	GDS d , mean [CI95%]	7.2 [1.5, 12.9]	7.9 [5.4, 10.5] e	0.411

Notes: a Scores on the Mini Mental State Examination (MMSE) range from 0 to 30, with higher scores indicating better cognitive function; b score on the Instrumental Activities of Daily Living for Elderly (IADL-E) range from 0 to 36, with lower score indicating a better functional independency; c scores on the Montgomery Asberg Depression Rating Scale (MADRS) range from 0 to 60 (10 items range from 0 to 6), with higher scores indicating depressive state; d scores on the Geriatric Depression Scale (GDS) range from 0 to 30, with higher scores indicating depressive state; e 1 missing data. *P , 0.05; **P , 0.001. Abbreviations: NC, normal control; AD, Alzheimer disease.

Clinical Interventions in Aging 2012:7

Table 4

 4 Characteristics of the participants in protocol 2 (P2)

	Characteristics	NC n = 19	MCI n = 19	P-values
	Female, n (%)	15 (78.9%)	9 (47.4%)	0.091
	Age-yrs, mean [CI95%]/(±SD)	71.7 [69.2, 74.3]	75.2 [73.2, 77.3]	0.070
	Level of education, n (%)
	Unknown	2 (10.5%)	2 (10.5%)	1.00
	No formal education	0 (0%)	0 (0%)	-
	Elementary school	1 (5.3%)	5 (26.3%)	0.405
	Middle school	4 (21.0%)	7 (36.8%)	0.269
	High school	4 (21.0%)	3 (15.8%)	1.00
	Post-secondary education	8 (42.1%)	2 (10.5%)	0.062
	MMSE a , mean [CI95%]	28.8 [28.3, 29.3]	25.8 [24.8, 26.8]	,0.001**
	IADL-E b , mean [CI95%]	9.6 [9.0, 10.1]	9.9 [9.1, 10.7]	0.488
	MADRS c , mean [CI95%]	2.8 [1.1, 4.5]	4.6 [2.9, 6.4] e	0.075
	GDS d , mean [CI95%]	7.1 [3.7, 10.4] e	8.4 [5.5, 11.3]	0.525

Notes: a Scores on the Mini Mental State Examination (MMSE) range from 0 to 30, with higher scores indicating better cognitive function; b score on the Instrumental Activities of Daily Living for Elderly (IADL-E) range from 0 to 36, with lower score indicating a better functional independency; c scores on the Montgomery Asberg Depression Rating Scale (MADRS) range from 0 to 60 (10 items range from 0 to 6), with higher scores indicating depressive state; d scores on the Geriatric Depression Scale (GDS) range from 0 to 30, with higher scores indicating depressive state. e 1 missing data. **P , 0.001. Abbreviations: NC, normal control; MCI middle cognitive impairment.

  Performance evaluation of the assessment methodology to classify observation data as AD group or NC group. (A) Specificity and sensitivity in function of the cutoff point of DAS .,P1 () scores. (B) Receiver operating curve associated with protocol 1. Abbreviations: AD, Alzheimer's disease; DAS, daily activity scenario; NC, normal control.

	A			Sensitivity Specificity		B	1.0
		1.0
							0.8
		0.8
	Sensitivity, specificity	0.6 0.4				Sensitivity	0.6 0.4
							0.2
		0.2
							0.0
		0.0	0.2	0.4	0.6	0.8	0.0	0.2	0 .4	0.6	0 .8	1.0
				Cut-off point					1-specificity
	A B C D E 0.00 0.00 0.00 0.00 Figure 2 Clinical Interventions in Aging 2012:7 0.10 0.20 0.30 0.40 0.50 R EFF = Index 0 0.60 0.70 0.80 0.90 1.00 Index 1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Index 2 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Index 3 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 S., P2 ()= Index 4 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Table 5

 5 Evaluation of predictive performance of our assessment methodology based on the DAS scores: Leave-one-out crossvalidation (LOOCV) results a

	DAS .,P1 () score	DAS .,P2 () score

performance of the ecological assessment based on the DAS scores results b

	Threshold of cut-off point, mean (±SD) c	0.62 (±0.01)	0.21 (±0.01)
	Accuracy rate	88.5%	71.1%
	Predictive positive value	93.3%	68.2%
	Predictive negative value	81.8%	75%
	False positive rate	3.9%	18.4%
	False negative rate	7.7%	10.5%

Table 6

 6 Spearman's correlation coefficients between DAS .,n () scores with Diagnosis, MMSE and IADL-E

		Diagnosis		MMSE		IADL-E
		P1 a	P2 b	P1	P2	P1	P2
	RE ff	-0.50**	0.11	0.55**	-0.15	-0.53**	-0.01
	Index 1	-0.63**	-0.20	0.59**	0.32	-0.62**	-0.01
	Index 2	-0.69**	0.34*	0.70**	0.34*	-0.64**	0.07
	Index 3	-0.76**	0.77**	0.77**	0.77**	-0.65**	-0.08
	Index 4	-0.76**	0.81**	0.81**	0.81**	-0.64**	-0.06
	Notes: a For P1, Diagnosis = 0 refers to NC group, Diagnosis = 1 refers to AD
	group; b for P2, Diagnosis = 0 refers to NC group, Diagnosis = 1 refers to MCI group.
	*P , 0.05; **P , 0.001.

Table 7

 7 Ratio of efficacy and qualitative parameters in the two protocols for each diagnosis group Notes: *P , 0.05; **P , 0.001. Abbreviations: NC, normal control; AD, Alzheimer disease; MCI, middle cognitive impairment.

	Raw parameters

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Acknowledgments

This study was supported by a grant from the ANR-09-TECS-016-01 -TecSan -SWEET HOME, by the Innovation Alzheimer and ARMEP associations and by the platform patients of the Nice CHU member of the CIU-S.

Disclosure

The authors report no conflict of interests in this work for the past 5 years.