Bita Manzouri
email: bita.manzouri@moorfields.nhs.uk

Masaharui Ohbayashi

Andrea Leonardi

Dilniya Fattah

Frank Larkin

Santa J Ono

D Frank

P Larkin

Characterization of the phenotype and function of monocyte-derived dendritic cells in allergic conjunctivae

Keywords: dendritic cells, allergic conjunctivitis, flow cytometry, mixed leukocyte reaction assay

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

INTRODUCTION

Approximately 20% of the Western world suffers from allergic diseases, such as allergic rhinoconjunctivitis, allergic asthma and the atopic asthma / dermatitis syndrome. [START_REF] Von | Dendritic cells and atopic eczema/dermatitis syndrome[END_REF] DCs are the sentinel cells that ensure that an immune response is appropriate in specificity, intensity, and type to the nature of the threat posed by the antigen bearing entity. DCs are divided into 2 major subtypes in human: the myeloid DCs (including Langerhan's cells (LCs)) and plasmacytoid DCs.

DCs are located in most tissues where they capture and process antigens, and where they exist in an 'immature' state: they lack the signals required for T cell stimulation but they are highly specialized to capture antigens. Following encounter with and uptake of an antigen, DCs process this antigen into smaller fragments, couple it to the major histocompatibility complex (MHC) class II molecule and present it on their surface to T cells. Additionally, a second costimulatory signal is also required to initiate T cell proliferation. [START_REF] Kleijmeer | MHC class II compartments and the kinetics of antigen presentation in activated mouse spleen dendritic cells[END_REF] DCs that display the MHC class II molecule and the co-stimulatory molecules (CD83, CD86) on their surface are considered to be mature.

KleinJan et al. [START_REF] Kleinjan | An essential role for dendritic cells in human and experimental allergic rhinitis[END_REF] studied nasal mucosal biopsy specimens taken from patients with perennial allergic rhinitis (AR) and found that the number of DCs in the nasal mucosa was higher and displayed a more mature phenotype in symptomatic patients than in healthy controls. This increase in LCs of the nasal mucosa was also observed during the pollen season in work done by Till et al. [START_REF] Till | Recruitment of CD1a+ Langerhans cells to the nasal mucosa in seasonal allergic rhinitis and effects of topical corticosteroid therapy[END_REF]. Allam et al. [START_REF] Allam | Comparative analysis of nasal and oral mucosa dendritic cells[END_REF] performed detailed phenotypical comparison of nasal and oral myeloid DC (mDC) from atopic and non-atopic donors. In atopic donors, these mDCs showed elevated expression of the high affinity receptor for IgE (FcεRI) with receptor occupation by IgE but FcεRI was present only in low amounts in these cells in non-atopic donors. Semper et al. [START_REF] Semper | Expression of the high affinity receptor for immunoglobulin E (IgE) by dendritic cells in normals and asthmatics[END_REF] studied the phenotype of DCs on bronchial biopsy specimens from normal and asthmatic airways and demonstrated the presence of FcεRI-bearing CD1a + LCs in both types of specimens. Total expression of FcεRI on all cells was slightly higher in the airways of asthmatics compared to normal controls, but this failed to reach statistical significance. They did find-in keeping with other studies [START_REF] Bellini | Intraepithelial dendritic cells and selective activation of Th2-like lymphocytes in patients with atopic asthma[END_REF][START_REF] Fokkens | The Langerhans cell: an underestimated cell in atopic disease[END_REF]-that the numbers of CD1a + DCs was higher in asthmatics when compared to normal controls.

We have previously demonstrated that the number of DCs expressing FcεRI in the substantia propria of the conjunctiva in the atopic disorder vernal keratoconjunctivitis (VKC) patients is increased, indicating an increased ability of DCs to capture and process specific antigens for presentation to CD4 + T cells, thereby initiating the immune response. [START_REF] Manzouri | Characterization of dendritic cell phenotype in allergic conjunctiva: increased expression of FcvarepsilonRI, the highaffinity receptor for immunoglobulin E. Eye[END_REF] In this study, we sought to further define the phenotypic and functional characteristics of DCs associated with VKC. We examined DCs derived from the peripheral blood of VKC patients and normal patients, testing the hypothesis that DCs in VKC are more mature,and have increased capacity for T cell proliferation.

METHODS

Selection of donors

Donors had a clinical history and signs of VKC, and were selected from patients attending clinic follow-up appointments. The control group donors did not have any history of atopy and did not display any signs of ocular allergy (table 1). A difference did exist between the mean age of the donors in the VKC group compared to the control group but this was unavoidable and was consequent to the difficulties in obtaining blood from children for the control group and in adequate volume quantities to perform the experiments. Local ethics committee approval was obtained for the research and each patient gave written informed consent. All research procedures adhered to the guidelines established in the Declaration of Helsinki. monocytes from the resultant buffy coat layer was performed using anti-CD14 mAb conjugated to magnetic MicroBeads and the autoMACS system as described in the manufacturer's instructions (Miltenyi Biotech, Bergisch Gladbach, Germany). The derived pellet of purified monocytes was cultured into dendritic cells as per the method described by Sallusto and

Lanzavecchia. [START_REF] Sallusto | Efficient presentation of soluble antigen by cultured human dendritic cells is maintained by granulocyte/macrophage colony-stimulating factor plus interleukin 4 and downregulated by tumor necrosis factor alpha[END_REF] To generate monocyte-derived DCs (MoDCs), IL-4 (4 μg/ml, R & D systems, Abingdon, United Kingdom) and GM-CSF (6 μg/ml, GlaxoSmithKline Research Institute, Stevenage, United Kingdom) were added to each well of purified monocytes.

Flow cytometry

On day 6 or 7 the MoDC cultures from each well were combined for fluorescent staining. The αCD28/αCD3 (GlaxoSmithKline, Stevenage, United Kingdom) was used as a positive control.

Events were acquired using the Beckman Coulter flow cytometry machine and analyzed with Expo32 (Beckman Coulter Ltd, High Wycombe, United Kingdom). Cells were acquired and manually gated on the physical properties of the cell by FSC versus SSC. The measurements taken were the mean fluorescence intensity (MFI) and the percentage of positive cells as defined by the proportion expressing higher levels of fluorescence than those of the isotype controls.

T cell isolation and culture

T cells were isolated and purified from the buffy coat following layering of blood over Lymphoprep (Sigma-Aldrich) and centrifugation. The T cells were isolated from the resultant PBMC cell pellet using the pan T cell isolation kit II from Miltenyi Biotech (negative selection)

according to the manufacturer's instructions. T cell purity was always greater than 99%.

Mixed leukocyte reaction (MLR) assays

MoDCs

Statistical analysis

The Mann Whitney U test was used to determine if there was significant up/down regulation of the measured cell surface markers when comparing VKC MoDC to those derived from control subjects and to determine if the proliferation of T cells observed between VKC and control subjects at the different ratios tested was significant. A value of p ≤ 0.05 was considered to be significant.

RESULTS

Flow cytometric analysis of circulating DC phenotype

MoDCs were isolated from the peripheral blood of 12 VKC patients and 13 normal controls. For each of the control group donors, a yield of 3 -16.2 x 10 6 MoDCs was obtained after culture as compared with the VKC donors where a yield of 0.5 -13.2 x 10 6 MoDCs was obtained. No morphological differences were readily identifiable between the two groups. DCs were identified as staining brightly for CD11c, the widely-used marker for human myeloid DCs.

The cells were gated on their FSC and SSC properties with the MoDCs within the gate being > 95% CD11c + (figure 1,(a)).

MoDCs of the control

Functional analysis of circulating DCs in VKC patients

Having determined that VKC patient-derived MoDCs had altered cell surface marker profiles compared to the controls, we then examined these cells for altered function by testing T cell stimulatory capacity. The responder T cells used were from a subject without any history of allergy or medication, and an IgE level of 61 kU/l (table 1).

For each of the control group donors, a yield of 2.4 -7.5 x 10 6 MoDCs was obtained after culture as compared with a yield of 8 -11 x 10 5 MoDCs for the VKC donors. No morphological differences were observed between the MoDCs from the VKC and the control donors. The MoDCs were labelled with anti-CD11c-PE and the T cells with anti-CD3-FITC. The yield of CD11c + cells from both normal and VKC cultured MoDC populations was >90% (figure 2 (a)), whereas the yield of T cells from the T cell donor was consistently >99% pure (figure 2 (b)).

As expected, MoDCs from both the control group and VKC patients stimulated T cell proliferation. The mitogenic effect was statistically significantly greater with MoDCs from control group individuals than with MoDCs from VKC patients (figure 2 (c)) and was observed for all ratios of MoDC to T cells that were tested. Since all T cells used were from the same donor, the observed differences are likely to be explained by differing stimulatory capacity of MoDCs in the two groups. In a trial MLR using MoDCs derived from a non-atopic donor outside of our group of experimental subjects and T cells from the same donor as for the experiments described in this study, adequate proliferative responses were observed (data not shown). This effect on stimulation is therefore not limited to the patients in our control group.

DISCUSSION

Phenotypic alterations in MoDCs derived from VKC patients

The MoDC derived from VKC patients are a more mature phenotype than those from control subjects as indicated in the statistically significant upregulation of MHC class II and the co-stimulatory molecules CD86 and CD83. This finding is comparable to those of McCarthy et al. [START_REF] Mccarthy | Inhaled allergen-driven CD1c up-regulation and enhanced antigen uptake by activated human respiratory-tract dendritic cells in atopic asthma[END_REF] who found that DCs in atopic asthma patients expressed higher levels of CD80 and CD86. The upregulation of MHC class II and co-stimulatory molecules is likely to increase the antigen presenting capacity of DCs in VKC patients. CD83 expression on the cell surface is a marker of DC maturation. [START_REF] Zhou | CD14+ blood monocytes can differentiate into functionally mature CD83+ dendritic cells[END_REF] Zhou and Tedder have demonstrated that most CD83 + cells express high levels of CD86; [START_REF] Zhou | Human blood dendritic cells selectively express CD83, a member of the immunoglobulin superfamily[END_REF] the VKC MoDCs in this study displayed upregulation of both molecules. As CD86 is upregulated in respiratory tract DCs and in circulating blood B cells in allergic asthma [START_REF] Mccarthy | Inhaled allergen-driven CD1c up-regulation and enhanced antigen uptake by activated human respiratory-tract dendritic cells in atopic asthma[END_REF][START_REF] Hofer | Upregulation of B7.2, but not B7.1, on B cells from patients with allergic asthma[END_REF] and on LC's in the conjunctiva of patients with VKC, [START_REF] Abu-El-Asrar | Langerhans' cells in vernal keratoconjunctivitis express the costimulatory molecule B7-2 (CD86), but not B7-1 (CD80)[END_REF] it is clear that this co-stimulatory molecule may contribute to the T-cell driven pathology of VKC.

Adhesion proteins upregulated on VKC MoDCs included CD58, CD11c and CD11b.

These molecules facilitate the interaction of DCs with T cells and influence the ability of DCs to migrate to regional lymph nodes upon maturation.

Expression of FcεRI on MoDCs

DCs can express the high-affinity IgE receptor FcεRI, which, in the presence of specific IgE, facilitates the uptake of allergen, leading to increased activation of allergen-specific T cells.

We found that MoDCs from VKC patients and normal subjects displayed similar levels of FcεRI expression. These results are consistent with those of Holloway et al., [START_REF] Holloway | Expression of the high-affinity IgE receptor on peripheral blood dendritic cells: differential binding of IgE in atopic asthma[END_REF] who found that the total expression of FcεRI on the surface of DCs isolated from the peripheral blood of healthy and asthmatic subjects were not significantly different. Other studies have associated elevated levels of DC FcεRI with atopic conditions. [START_REF] Novak | Immunoglobulin E-bearing antigen-presenting cells in atopic dermatitis[END_REF][START_REF] Semper | Surface expression of Fc epsilon RI on Langerhans' cells of clinically uninvolved skin is associated with disease activity in atopic dermatitis, allergic asthma, and rhinitis[END_REF] There are at least three possible explanations for the results in our study. First, the mature state of the VKC MoDCs may have led to downregulation of the FcεRI receptor: upon in vitro maturation, LCs completely and irreversibly downregulate their transcripts for FcεRI subunits, leading to a rapid loss of intracellular and surface receptor expression. [START_REF] Bieber | Fc epsilon RI on antigen-presenting cells[END_REF] Second, although a direct correlation between serum IgE levels and expression of FcεRI on human basophils from allergic subjects has been shown, [START_REF] Macglashan | In vitro regulation of FcepsilonRIalpha expression on human basophils by IgE antibody[END_REF] this control of FcεRI expression may not apply to DCs, since FcεRI on these cells exists as a trimeric complex lacking the β subunit, in contrast to the tetrameric form expressed by mast cells and basophils . Finally, DCs in different tissues may have different phenotypes which may be influenced by the microenvironment. Indeed we have found increased FcεRI expression in conjunctiva in allergic conjunctivitis. [START_REF] Manzouri | Characterization of dendritic cell phenotype in allergic conjunctiva: increased expression of FcvarepsilonRI, the highaffinity receptor for immunoglobulin E. Eye[END_REF] Mechanisms underlying reduced T cell proliferation in response to VKC MoDCs

Mature DCs are better able to prime T cells than immature DCs, an important early step in cell-mediated immunopathology. We found the expected potent T cell proliferation in response to MoDCs derived from control subjects, but it was surprising to find that our mature VKC MoDCs were less effective at stimulating T cell proliferation. This, however, is not the first The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an exclusive licence (or non-exclusive for government employees) on a worldwide basis to the BMJ Publishing Group Ltd, and its Licensees to permit this article (if

Figure & Table Legends

The cells were blocked for 10

 10 minutes with human Fcγ fragments (Miltenyi Biotech) and then incubated on ice with the appropriate fluoroscein isothiocyanate (FITC)-or phycoerythrin (PE)conjugated antibody or with the respective isotype-matched control immunoglobulins. Monoclonal antibodies directed against CD83 (FITC, clone HB15e), CD11c (PE, clone B-ly6), CD86 (FITC, clone 2331), HLA-DR (FITC, clone Tü39), CD23 (PE, clone M-L233), CD58 (PE, clone 1C3) and CD11c (PE, clone D12) were purchased from Becton Dickinson (Cowley, United Kingdom). The antibody against FcεRI-α (PE, clone AER-37) was purchased from eBioscience (Insight Biotechnology Ltd, Wembley, United Kingdom). FITC-and PE-conjugated isotype control mouse immunoglobulins (Igs; IgG 1 , IgG 2a , IgG 2b ,) were obtained from Becton Dickinson and eBioscience. Additional FACS staining of T cells was performed using CD3 (FITC, clone HIT3a) (BD Pharmingen) and CD209 (DC-SIGN, PE, clone eB-h209, eBioscience).

  were harvested on day 6 and purity of population assessed with flow cytometry for CD11c +/-CD209. The MoDCs were washed and resuspended in T cell medium at a concentration of 1 x 10 4 DCs/100 μl T cell medium. In all allogenic MLR assays, T cells from the same donor were used, thereby maintaining consistency between the MLR results obtained from the normal control MoDCs and the VKC-derived MoDCs. Each of the MLRs for each patient was performed in triplicate at five different concentrations of MoDC to T cells (1:10, 1:20, 1:40, 1:80 and 1:160). Graded doses of MoDC were added to T cells in 96-well U-bottom tissue culture plates (200 μl/well)-the T cell number remained constant whilst serial dilution of MoDCs was performed to obtain the appropriate DC:T cell ratios for the MLR assays. The control wells, consisted of two sets of negative controls (1 x 10 4 MoDC only in T cell medium and 1 x 10 5 T cells in T cell medium) and one positive control (1 x 10 5 T cells only in T cell medium in wells lined with αCD28/αCD3). The plates were incubated for 5 days at 37°C in 5% CO 2 . T cell proliferation was quantified by incubating the cells with 1 μCi of methyl-titrated thymidine deoxyriboside (10 μl; Amersham Life Sciences, Buckinghamshire, United Kingdom) during the last 16 hours of the 5-day culture. Cells were harvested on a filter and radioactivity measured in a beta-plate liquid scintillation counter.

  report of a reduction in T cell function in atopic disease-the literature in support of this finding is well summarized in the review article by Strannegård and Strannegård.[START_REF] Strannegard | T lymphocyte numbers and function in human IgEmediated allergy[END_REF] In the setting of allergic disorders, this reduced capacity to cause T cell proliferation might be one reason why those with allergic disease are so prone to viral and fungal infections, in particular herpes simplex virus infection. Upon presentation of viral antigen from virus-infected cells it may be that the ineffective ability of DCs to stimulate T cell proliferation leads to impaired clearance of viral infection in atopic patients. This is the first study to show a functional difference between the MoDCs derived from VKC patients and normal control subjects who had no known history of allergy. There are several possible explanations for reduced T cell-stimulating activity. The proliferative signal presented by the MoDCs to the T cells might be defective or insufficient. Indeed, the 'strength of stimulation' model of T cell activation and differentiation is based on the fact that naïve T cells interacting with DCs receive stimulatory signals of differing strengths, depending on the degree of DC maturation, the level of peptide-MHC and co-stimulatory molecule interaction, and the duration of T cell-DC interaction.[START_REF] Singh | The strength of persistent antigenic stimulation modulates adaptive tolerance in peripheral CD4+ T cells[END_REF] According to this model, T cells receiving a signal of excessive strength undergo activation-induced cell death. The MoDCs from VKC patients, being in a more mature state of differentiation, may deliver a signal of excessive strength to the T cells, thereby causing cell death and a reduced proliferative respons. Alternatively, inhibitory signals (DC-derived immunoglobulin receptor 2 (DigR2), cytotoxic T lymphocyte-associated receptor 4 (CTLA-4), programmed death-1 (PD-1), and DC-associated heparan sulfate proteoglycan-dependent integrin (DC-HIL)) presented or secreted by the VKC MoDCs hinder an adequate proliferative response from T cells. Finally, the difference in MoDC stimulatory capacity might be due to the differences in age and blood volumes between the donor groups, unavoidable limitations of this study. The normal control patients were older, on average, than the VKC patients, and the blood volumes withdrawn from the normal patients were higher than for the VKC patients.In conclusion, we have shown that MoDCs derived from circulating monocytes in VKC individuals display a more mature phenotype than their normal counterparts, as evidenced by enhanced expression of MHC II, CD86, CD83, CD58, CD11c and CD11b. Despite this phenotypic maturity, the VKC MoDCs are less-potent T cell stimulators -and potentially lesseffective APCs -than their normal counterparts. The impaired T cell proliferation may contribute to the abnormal inflammatory response, not least to viral or fungal infection, seen in patients with VKC and other allergic disorders. ACKNOWLEDGEMENT This work was supported by a grant from the Medical Research Council (grant number G78/7987) and supported in part by the NIHR Biomedical Research Centre in Ophthalmology at Moorfields Eye Hospital and the UCL Institute of Ophthalmology.

Figure 1 :Figure 2 :

 12 Figure 1: Flow cytometric analysis of (a) MoDCs cultured for analysis of CD11c surface marker.

Table 1 : Background patient information. 99 Patients for flow cytometry study Control subjects VKC patients Patient number Age (yr) Sex IgE level (kU/l) Patient number

 1

	Age (yr)	Sex	IgE level (kU/l)

Patients for MLR assays Control subjects VKC patients Patient number Age (yr) Sex IgE level (kU/l) Patient number

		MoDC isolation and culture
		Peripheral blood mononuclear cells were isolated from EDTA-treated blood using
		Lymphoprep (Sigma-Aldrich, Poole, United Kingdom) centrifugation. Isolation of CD14 +
						Age (yr)	Sex	IgE level (kU/l)
		41	M	11	1	10	M	80
		21	F	31	2	29	M	16
		50	M	13	3	13	M	69
		42	F	18	4	9	M	216
		49	F	37	5	31	M	10
		38	F	9	6	14	F	42
		21	F	212	7	11	F	48
		25	F	55
	100
	101	Measurement of IgE concentration
		Serum (6 ml) was collected for measurement of IgE levels by a normal sandwich
								6

Table 2 : The mean fluorescent intensity (MFI) recorded for each marker measured during flow cytometric analysis. * Denotes a statistically significant result.

 2 group individuals displayed constitutive cell surface expression of MHC class II, low expression of CD86, and no expression of CD83, a typical profile for DCs in the immature state. In MoDCs from VKC patients in comparison, there was a statisticallyThe cell surface adhesion proteins CD58, CD11b, and CD11c were constitutively expressed in the control MoDCs (figure1(c) and table 2). Of the two IgE receptors, only CD23was constitutively expressed on control MoDCs, and little or no expression of FcεRI was detected on these cells. There was statistically insignificant upregulation of surface FcεRI on VKC-derived MoDCs, but significant upregulation of CD11b, CD11c and CD58. CD23 was down-regulated in VKC-derived MoDCs (p = 0.02).

		Control subject MFI	VKC patient MFI	Fold	p
		Mean	SD	Range	Mean	SD	Range	change	value
	MHC class II	40.97 14.01 20.8-66.9	71.41	29.70	14.4-122	1.74	<0.01 *
	CD86	2.42	1.85	0.45-5.68	5.98	3.40	1.71-11.7	2.47	<0.01 *
	CD83	0.34	0.09	0.2-0.48	0.68	0.15	0.46-0.98	2.00	<0.001 *
	CD58	4.18	2.59	1.97-12	9.28	3.17	4.77-15.6	2.22	<0.001 *
	CD11c	7.86	4.29	3.63-18	12.09	6.77	5.07-30.7	1.54	0.05 *
	CD11b	76.92 33.56	38.7-152	111.05 48.28	40.4-192	1.44	0.05 *
	CD23	6.26	3.78	3.03-15.4	5.55	11.37	0.94-41.5	-1.13	0.02 *
	FcεRI	0.52	0.24	0.27-0.92	0.54	0.18	0.23-0.91	1.04	0.77

significant upregulation of MHC class II, CD83 and CD86 (figure 1 (b) and table 2), an expression profile consistent with a more-mature state of development.

Table 1 :

 1 Background patient information.

Table 2 :

 2 The mean fluorescent intensity (MFI) recorded for each marker measured during flow cytometric analysis. * Denotes a statistically significant result.

enzyme-linked immunosorbent assay (ELISA; ImmunoCAP 100, Phadia, Uppsala, Sweden).

Competing interests: None.


Leonardo Mastropasqua

Luca Agnifili
email: l.agnifili@unich.it

Marco Ciancaglini

Mario Nubile

Paolo Carpineto

Vincenzo Fasanella

Michele Figus

Stefano Lazzeri

Marco Nardi

In vivo analysis of conjunctiva in gold micro shunt implantation for glaucoma

Keywords: conjunctiva, trans-scleral outflow, suprachoroidal space, gold micro shunt, in vivo confocal microscopy, primary open angle glaucoma

Aims: To describe the conjunctival epithelial features seen with in vivo confocal microscopy (IVCM) after gold micro shunt (GMS) implantation in the suprachoroidal space, in patients with uncontrolled glaucoma.

Methods:

This was an observational case series study. Fourteen eyes of 14 consecutive glaucomatous patients with a history of multiple failed incisional surgeries followed by GMS implantation, were evaluated with digital confocal Laser-Scanning Microscope (HRT II Rostock Cornea Module).

Patients were divided into two groups: successful implantations (Group 1: eight patients, eight eyes), defined as a one-third reduction in preoperative intraocular pressure (IOP) with or without antiglaucoma medications and failed implantations (Group 2: six patients, six eyes) as a less than onethird reduction in preoperative IOP with maximal tolerated medical therapy. The examination was performed from three to 20 months (mean 15.4±5.4) postoperatively. Conjunctival mean microcyst density (MMD: cysts/mm 2 ) and mean microcyst area (MMA: µm 2 ) were the main outcome measurements.

Results:

The mean post-operative IOP was statistically different between the 2 groups (P<0.05), with the values of 14.3±2.77 and 32.3±8.01 mmHg in Group 1 and 2, respectively.

When comparing successful with failed implantation, the IVCM analysis showed a greater MMD (P<0.01) and MMA (P<0.01). Clinical evidence of filtering bleb was not found in any of the patients.

Conclusions: Successful GMS implantation significantly increased conjunctival microcysts density and surface at the site of the device insertion. These findings suggest that the enhancement of the aqueous filtration across the sclera may be one of the possible outflow pathway exploited by the shunt.

Introduction

To date, filtration surgery and drainage device implantation are the most reliable procedures for lowering the intraocular pressure (IOP) in patients with medically uncontrolled glaucoma. [START_REF] Jones | Recent advances in trabeculectomy technique[END_REF][START_REF] Hodkin | Early clinical experience with the Baerveldt implant in complicated glaucomas[END_REF][START_REF] Mermoud | Molteno tube implantation for neovascular glaucoma. Long-term results and factors influencing the outcome[END_REF][START_REF] Coleman | Initial clinical experience with the Ahmed Glaucoma Valve implant[END_REF] The basic mechanism of these procedures is the creation of a new drainage route which allows aqueous humour to drain from the anterior chamber, thereby circumventing the pathological outflow obstruction. The aqueous then flows directly or indirectly into sub-conjunctival spaces leading to an elevation of the conjunctiva at the surgical site, which is commonly referred to as a filtering bleb. [START_REF] Benedikt | The effects of filtering operations[END_REF][START_REF] Teng | Histology and mechanism of filtering operations[END_REF] In a variable percentage of patients, either filtration procedures or drainage device implantation can lead to significant post-operative complications such as bleb leaks, hypotony, blebitis, endophthalmitis and bleb encapsulation, the latter being widely recognized as the main cause of surgical failure. [START_REF] Kee | Prevention of early postoperative hypotony by partial ligation of silicone tube in Ahmed glaucoma valve implantation[END_REF][START_REF] Feldman | Needle revision of filtering blebs[END_REF] Intense clinical and instrumental analysis of the bleb with frequent post-operative management still represents the main challenge in the maintenance of long term surgical success of all available filtration surgical procedures.

In the last years, bleb-less surgical approaches which exploit and enhance alternative aqueous outflow pathways have been evaluated in order to avoid these complications.

One such procedure involves the use of gold micro shunt (GMS) devices which are 24-karat gold, biocompatible flat plates containing micro-tubular channels that create a bridge between the anterior chamber (AC) and suprachoroidal space. Thus forcing aqueous flow through the two compartments, taking advantage of the natural gradient of hydrostatic pressure (from 1 to 5 mmHg) between the AC and suprachoroidal space, respectively. [START_REF] Emi | Hydrostatic pressure of the suprachoroidal space[END_REF] Hence, aqueous humour is removed via the choroidal vascular system or by gradually flowing through the scleral layers and then the conjunctiva, without the creation of a bleb. Recently, Melamed et al 10 evaluated the efficacy and safety of GMS implantation in the supraciliay space in failed incisional glaucoma surgery, reporting a 79% surgical success, without relevant post-operative complications and without the formation of filtering bleb in any of the patients. However, to best of our knowledge, no reports have specifically focused on the possible aqueous outflow pathways exploited by the GMS device.

The aim of the present study was to describe the bulbar conjunctival features in glaucomatous patients who underwent GMS implantation by using in vivo confocal microscopy (IVCM), in order to elucidate modifications induced by this device.

Material and Methods

This was an observational case series study. The study adhered to the tenets of the Declaration of Helsinki and informed consent was obtained from all patients prior to their enrollment. Our local Ethics Boards were notified which determined that their approval was not necessary. We examined 14 eyes (8 right and 6 left eyes) of 14 consecutive Caucasian patients affected with primary open angle glaucoma (POAG) who had been referred to the Ophthalmic Clinics of the Universities of Chieti-Pescara and Pisa, Italy (8 males and 6 females, with an age range from 43 to 77 years, mean 64.6±11.8). All patients had a history of multiple failed incisional procedures, followed by GMS implantation (SOLX, Boston, MA) from 10 to14 months after the last failed surgery.

The number of failed procedures prior to GMS implantation ranged from 1 to 2 (mean 1.4±0.5) and corresponded to MM-C augmented trabeculectomy (14 procedures) or deep sclerectomy with T-Flux ® implant (6 procedures).

The GMS was inserted in the superior-temporal (9 eyes) or superior-nasal (5 eyes) region, as indicated on a patient-to-patient basis in order to avoid inadvertent intra-operative manipulations of the sites used in previous procedures. To comply with this intention, the conjunctiva overlying the site of the previous failed filtration procedure close to the planned site for GMS insertion, was pre-operatively marked (methylene blue) 2-3 mm outwardly to the limits of the presumed scleral flap. Therefore, the conjunctival flap and the scleral dissection for the GMS implantation were created at least 2 mm from delimited area.

A detailed description of the shunt and surgical technique have been previously reported. [START_REF] Melamed | Efficacy and safety of gold micro shunt implantation to supraciliary space in patients with glaucoma: a pilot study[END_REF] The time range of post-operative examinations was 3 to 20 months (mean: 15.4±5.4 mo) after GMS implantation.

Each patient, after a complete ophthalmologic assessment including visual acuity, applanation tonometry, anterior segment slit-lamp evaluation with particular attention at the conjunctiva overlying the site of implantation (a set of reference photographs was obtained in all cases) and fundoscopy, was carefully examined with a digital confocal Laser-Scanning Microscope (LSM) (HRT II Rostock Cornea Module, Heidelberg Engineering GmbH, Germany). Additionally, in order to verify the correct position of the proximal and distal end of the GMS implant, each patient underwent gonioscopy and anterior segment optical coherence tomography (AS-OCT) (Carl Zeiss Meditec, Inc, Dublin, CA).

According to the achievement of satisfactory post-operative IOP control and on evidence of surgery success, [START_REF] Picht | Development of the filtering bleb after trabeculectomy. Classification, histopathology, wound healing process[END_REF] GMS implantations were classified in 2 groups: successful implantations (qualified and complete success) (Group 1; defined as a third reduction in preoperative IOP with or without antiglaucoma treatment [START_REF] Edmunds | Factors associated with success in first-time trabeculectomy for patients at low risk of failure with chronic open-angle glaucoma[END_REF] ) and failed implantations (Group 2; as a reduction lower than a third in preoperative IOP in maximal tolerated medical therapy).

All the patients had been on preserved topical antiglaucoma medications; the mean duration of topical therapy and the drug regimen before GMS implantation in each group, were reported in Table 1.

During the three months before IVCM examination, none of the patients received systemic or topical therapy (steroids) which could modify ocular hydrodynamics .

In vivo confocal microscopy

The technical characteristics of the instrument and the details of conjunctival examination were previously described. [START_REF] Mastropasqua | Corneal and conjunctival manifestations in Fabry Disease: in vivo Confocal Microscopy study[END_REF] In this case series we investigated the microscopic epithelial features of the bulbar conjunctiva overlying the location of the GMS implantation.

In order to avoid in the field of analysis the site of the previous surgery close to the device location, we marked (methylene blue) the margins of the conjunctiva overlying the site of the GMS implantation (delineating a 4x5 mm area (20 mm 2 ), at least 2-3 mm from site of the previous surgery) and performed the IVCM at the centre of the selected area (2x3 mm (6 mm 2 )).

IVCM analysis of each eye was performed by a single operator (VF) who selected six images (from about 40 images) which were evaluated and the results averaged by a second IVCM operator (LA).

Both operators were masked for patient surgical history and status.

The patient was seated in front of the microscope, head steadied by a headrest and with the eye properly aligned using a dedicated target mobile bright red light provided with the instrument that the patient had to fix with the fellow eye, in order to obtain a tangential optical section of the superior bulbar conjunctiva. A digital camera was used to obtain am image of the lateral view of the eye and objective lens in order to check the position of the latter on the surface of the eye for each scan. LSM objective was gently positioned in contact with the ocular surface separated by a PMMA (polymethyl methacrylate) contact cap and a drop of 0.2% polyacrylic gel (Viscotirs® Gel, CIBA Vision® Ophthalmics, Marcon, Venezia, Italy) served as coupling medium. Sequential images 300X300 μm in size derived from automatic scans and manual frames were acquired at the intermediate layer of the bulbar conjunctival epithelium (10 to 20 µm), 2 mm from the limbus at the centre of the corresponding site of the GMS implantation, with the eye in opposite gaze with respect to site of the implant.

For the IVCM assessment, we evaluated the microcysts in the bulbar conjunctival epithelium, as first reported in the conjunctival wall of functioning filtering blebs. [START_REF] Labbé | In vivo confocal microscopy study of blebs after filtering surgery[END_REF][START_REF] Messmer | In vivo confocal microscopy of filtering blebs after trabeculectomy[END_REF][START_REF] Guthoff | In Vivo Confocal Microscopy of Failing and Functioning Filtering Blebs: Results and Clinical Correlations[END_REF][START_REF] Ciancaglini | Filtering Bleb Functionality: a Clinical, Anterior Segment Optical Coherence Tomography and In Vivo Confocal Microscopy Study[END_REF] The main parameters considered were the mean microcyst density (MMD) (cysts/mm 2 ) and the mean microcyst area (MMA) (µm 2 ).

The total surface area of epithelial microcysts was calculated in each of the 6 selected confocal images by means of ImageJ, an open source software (http://rsb.info.nih.gov/ij), using previous described methods. [START_REF] Messmer | In vivo confocal microscopy of filtering blebs after trabeculectomy[END_REF]

Statistical analysis

Statistical analysis was performed using SPSS ® Advanced Statistical TM 13.0 Software (2005, Chicago, IL, USA). Differences in age and gender in successful and failed groups at baseline were evaluated using Student's t test and chi-squared, respectively. Unpaired t test was used to analyze pre-and postoperative IOP, pre-and post-operative number of medications, duration of preoperative therapy and time of IVCM assessment after surgery between the two groups.

Paired t test was used to analyze the changes of post-operative of IOP or the number of medications in each group. U Mann-Whitney test was used to assess differences on conjunctival microcysts density and surface between the two groups.

For the given effect size the power of the study was 0.81 and 0.82 for microcysts density and area, respectively (Sample Power. SPSS ® Advanced Statistical TM

Results

The demographic and clinical data of each group are shown in Table 1. No significant differences were found in age, sex, preoperative IOP, follow-up period and the time range of post-operative examinations (months) between the 2 groups. All reported data corresponded to the last follow-up visit (15.4±5.4 months), which matched with the IVCM examination.

The mean overall (Group 1 and 2) post-operative IOP percentage reduction was 22.6%, from 28.8±3.9 mmHg to 22.1±10.6 mmHg (p<0.05).

Mean post-operative IOP was statistically different between the two groups (p=0.002), with values of 14.3±2.8 and 32.3±8.0 mmHg in Groups 1 and 2, respectively.

In Group 1, mean IOP decreased from 28.1±5.0 to 14.3±2.8 mmHg (percentage reduction of 50.6%) (p<0.001), while we did not observe statistically significant modifications in Group 2.

The drug dose regimen and the duration of preoperative therapy was not statistically different between groups. The mean number of antiglaucoma medications at baseline and at the last follow-up was not statistically different between groups; these values were not significantly modified in the post-operative period in either group: from 2.7±0.9 to 2.2±1.0 in Group 1 and 3.0±0.6 to 2.8±0.4 in Group 2.

In both groups the clinical assessment (according to MBGS criteria), [START_REF] Wells | Comparison of Two Clinical Bleb Grading Systems[END_REF] the evaluation of the set of the reference photographs and the AS-OCT images did not show evidence of filtering bleb at the current surgical site in any case (Figures 1 and2, A andB). In all eyes, as confirmed by gonioscopy and AS-OCT examination, the device was correctly positioned in both the AC and the suprachoroidal space with an appearance of spongy or tight overlying sclera (Figures 1 and2, B). Additionally, AS-OCT showed an hypoechoic space posteriorly to the shunt in several successful implantations (Fig. 1,B) When analyzing the considered IVCM parameters, we found a statistically significant difference between the 2 groups, either for the microcysts density (cysts/mm 2 ) or area (µm 2 ) (Table 2) (p<0.01).

Particularly, we did find values of 103.1±22.6 and 29489.3±12954.9 and 22.4±11.9 and 4696.0±3608.1 for MMD and MMA in functioning and failed implantations, respectively (Figures 1 and2, C).

Discussion

The scarring of conjunctival filtering bleb is the main challenge and limiting factor for long-term IOP control in glaucoma surgery. The bulk of the scientific evidences, strongly support that all anti-glaucoma procedures which create a fistula and route aqueous humour from AC to sub-conjunctival spaces, are exposed to a significant risk of bleb scarring and failure over time. [START_REF] Feldman | Needle revision of filtering blebs[END_REF][START_REF] Azuara-Blanco | Disfunctional filtering blebs[END_REF] The pathophysiological basis of the bleb scarring appear to be related to the action of a variety of factors present in the aqueous humour of glaucomatous eyes, which are capable of stimulating a fibrotic response after contact with the vascular Tenon's tissue. [START_REF] Epstein | Fibrosis response to aqueous. Its relationship to glaucoma[END_REF] Additionally, fibrosis may be mechanically activated by the immediate post-surgical aqueous filtration into the sub-conjunctival space, as demonstrated after the implantation of Ahmed devices. [START_REF] Tsai | The Ahmed shunt versus the Baerveldt shunt for refractory glaucoma -A single-surgeon comparison of outcome[END_REF] GMS (now commercially available only as Plus version) is one of the developing surgical procedures which works by shunting fluids from AC to suprachoroidal space, thus avoiding the direct and immediate post-operative aqueous outflow into sub-conjunctiva and the creation of a bleb. In the present study we analyzed the microscopic features of the bulbar conjunctiva at surgical site with particular attention to intra-epithelial microcysts, in patients who underwent uncomplicated GMS implantation after the failure of previous filtration surgeries.

Concerning the post-operative IOP, an average global IOP reduction of 22.6% from baseline was found at the last follow-up (15.4±5.42 months) and all successful patients were classified in qualified success.

These results are quite different with respect to those reported by Melamed et al. [START_REF] Melamed | Efficacy and safety of gold micro shunt implantation to supraciliary space in patients with glaucoma: a pilot study[END_REF] who found a postoperative IOP decrease and complete success of 32.6% and 13.2%, respectively. Such inconsistency could result from the surgical history of the patients: Melamed et al. included in their series either patients who had previous glaucoma surgery, a glaucoma drainage device (53%) or patients who did not, while in our series all patients underwent at least one previous filtration surgery and were to be considered refractory glaucoma.

Epithelial microcysts are empty optically clear spaces originally described in the conjunctival bleb wall of successful trabeculectomies, as hallmarks of humor aqueous filtration through the conjunctiva. [START_REF] Labbé | In vivo confocal microscopy study of blebs after filtering surgery[END_REF] Recently Amar and coll., [START_REF] Amar | Filtering Blebs and Aqueous Pathway. An Immunocytological and In Vivo Confocal Microscopy[END_REF] using both impression cytology and IVCM, modified and improved the definition of the bleb wall microcysts demonstrating that such structures correspond to goblet cells, mostly containing aqueous humor instead of highly hydrophilic gel-forming mucin. Based on these findings, the authors suggested that the trans-cellular pathway of the aqueous humor could occur at the level of goblet cells toward the ocular surface. More interestingly, in others studies [START_REF] Ciancaglini | Conjunctival Modifications in Ocular Hypertension and Primary Open Angle Glaucoma: An In Vivo Confocal Microscopy Study[END_REF][START_REF] Ciancaglini | Conjunctival characteristics in primary open-angle glaucoma and modifications induced by trabeculectomy with mitomycin C: an in vivo confocal microscopy study[END_REF] the presence of intra-epithelial microcysts was documented also in eyes affected with untreated ocular hypertension or medically treated POAG that had not undergone surgical procedures. These authors have speculated that these findings support the hypothesis of an activation and/or enhancement of alternative hydrodynamic pathways and, specifically, the trans-scleral outflow, in conditions of increased IOP.

In the present study, when comparing functioning with non functioning implantations we did find a statistically significant difference for both mean microcysts density and surface, with values approximately five fold and six fold higher.

At the biomicroscopic examination none of the implanted patients developed a post-operative filtering bleb, indicating the absence of a direct post-operative sub-conjunctival aqueous filtration just as the technique of implantation require. Therefore, the evidence of conjunctival microcysts at the site of successful GMS implantation might be interpreted as a sign of aqueous percolation through the scleral layers and then the conjunctiva.

Based on the results of a previous report [START_REF] Ciancaglini | Conjunctival Modifications in Ocular Hypertension and Primary Open Angle Glaucoma: An In Vivo Confocal Microscopy Study[END_REF] which ruled out an active role of topical anti-glaucoma medications in the conjunctival microcysts formation, the effects of topical drugs on IVCM considered parameters, was not investigated. Moreover, signs of inflammatory cells were not reported as significant features in the majority of cases, although this aspect was not methodically investigated.

To date, the main mechanisms involved in the IOP reduction after GMS implantation are yet to be determined. However, our results may validate the assumption of Melamed et al 10 who supposed that, once aqueous humor reaches the suprachoroidal space, it drains into the choroidal vascular system or permeates through the sclera. In support of this, the hypoechoic space sometimes observed posteriorly to the functioning implants, may indicate the suprachoroidal outflow pathway. Conversely, both the evidence of epithelial microcysts and the spongy appearance of the sclera at IVCM and AS-OCT examinations may be interpreted as the microscopic and macroscopic signs of the supposed activation of the trans-scleral aqueous outflow in functioning GMS shunts.

The patho-physiological basis of this mechanism is most likely an effect of the GMS introduction into the AC. This action technically require a scleral dissection and, therefore, the creation of a plane of 80-90% scleral thickness. The final result is a partial scleral thinning with a reduction of the trans-scleral fluid movement resistivity which permits aqueous humor to move easier and in larger amount from suprachoroidal space to sub-conjunctiva.

In support of this, the importance and the role of the scleral thinning in filtration surgery success, has been recently demonstrated also in eyes that underwent MM-C augmented trabeculectomy. [START_REF] Ciancaglini | Conjunctival characteristics in primary open-angle glaucoma and modifications induced by trabeculectomy with mitomycin C: an in vivo confocal microscopy study[END_REF] By considering such results, bleb-less surgical approaches which shunt aqueous humour to suprachoroidal space and/or thin the sclera thus increasing the trans-scleral outflow, could be useful to improve the success of antiglaucoma surgical procedures and avoid the intensive post-operative management.

However, as Melamed et al, we did not calculate the exact contribution of the suprachoroidal aqueous resorption and trans-scleral outflow to the mechanism of IOP reduction.

In non functioning cases, various mechanisms of failure may be hypothesized. The most relevant could be the formation of a fibrotic capsule around the device isolating the shunt from the choroidal vascular bed and the sclera. Alternatively, a connective invasion and/or an occlusion of the proximal end channels and the distal end holes or both mechanisms should be evoked. The effect is a proximal or a distal blockage of the aqueous outflow, therefore reaching and permeating the sclera would be unfeasible. These aspects could justify the very low density of epithelial microcysts at IVMC and the tight feature of the sclera at AS-OCT in failed implantations. Nevertheless, to verify our hypothesis, histological studies aimed at the analysis of the removed shunts in non functioning cases are mandatory.

The main limitation of our study is the lack of information regarding the status of conjunctival epithelium before GMS surgery, which may be useful to accurately calculate the trans-scleral aqueous flow enhancement achieved with the shunt, as recently verified for trabeculectomy. [START_REF] Ciancaglini | Conjunctival characteristics in primary open-angle glaucoma and modifications induced by trabeculectomy with mitomycin C: an in vivo confocal microscopy study[END_REF] Furthermore, to avoid reading biases due to the effect of the previous filtration procedures on the overall trans-scleral outflow, the effects of GMS should be evaluated in glaucomatous patients naïve for glaucoma surgery.

In conclusion, the in vivo analysis of conjunctiva in glaucomatous patients implanted with GMS provided valuable information which may contribute to clarify patho-physiological aspects of the aqueous outflow pathways exploited by the shunt.

Tables

  13.0 Software (2005, Chicago, IL, USA)).

Figure 1 .

 1 Figure 1. Functioning implantation. A. Biomicroscopic aspect of a functioning Gold Micro Shunt implant correctly positioned in the anterior chamber (proximal end) and in the suprachoroidal space (distal end). No signs of conjunctival filtering bleb are detectable. B. Anterior segment optical coherence tomography showing the Gold Micro Shunt in the anterior chamber (arrowhead) and in the suprachoroidal space (arrow), with a spongiform appearance of the overlying sclera and with the hypoechoic space posteriorly to the device (asterisk). C. In vivo features of conjunctival epithelium at the corresponding area of the device insertion, characterized by intra-epithelial microcysts (arrows) partially filled and surrounded by what appears to be inflammatory cells (arrowhead). Bar represents 100 µm.

Figure 2 .

 2 Figure 2. Non functioning implantation. A. Biomicroscopic aspect of a non functioning Gold Micro Shunt implant correctly positioned in the anterior chamber (proximal end) and in the suprachoroidal space (distal end). No signs of conjunctival filtering bleb are detectable. B. Anterior segment optical coherence tomography showing the Gold Micro Shunt in the anterior chamber (arrowhead) and in the suprachoroidal space (arrow), with a tight appearance of the sclera overlying the device. C. In vivo aspect of conjunctival epithelium at the corresponding area of the device insertion, showing a diffuse hyper-reflectivity of the layer with one intra-epithelial microcyst (arrow) containing what appears to be an inflammatory cell (arrowhead). Bar represents 100 µm.

Table 1 : Patient demographic and clinical characteristics Successful Implantations (Group 1)

 1

	Failed
	Implantations	p-value
	(Group 2)

CAI s 5 4 Duration of pre-operative therapy (mo) 86.8±14.2 89.1±13.3 ns* M=male; F=female; GMS=Gold Micro Shunt; IOP= intraocular pressure; mo= months; ns= not significant * T test for unpaired data ** Chi square test CAI s =carbonic anhydrase inhibitors IVCM: in vivo confocal microscopyTable 2 : In Vivo Confocal Microscopy (IVCM) parameters

 2

		Successful	Failed
	Parameters	(Group 1) Implantations	(Group 2) Implantations	p-value
	Mean microcysts density (MMD)	103.1±22.6	22.4±11.9	P<0.01*
	(cysts/mm 2 )
	Mean microcysts area (MMA) (cysts/µm 2 )	29489.3±12954.9	4696.0±3608.1	P<0.01*
	IVCM= in vivo confocal microscopy

*U Mann-Whitney test


Pierre-Yves Pechard

Christophe Tournier
email: tournier@lurpa.ens-cachan.fr

Claire Lartigue

Jean-Pierre Lugarini

Geometrical deviations versus smoothness in 5-axis high-speed flank milling

Keywords: Flank milling, minimum energy, High Speed Milling, Singular Value Decomposition, geometrical deviations

The paper deals with the Generation of Optimized 5-aXis Flank milling trajectories.

Within the context of 5-axis High-Speed Machining, oscillatory trajectories may penalize process efficiency. The control of the trajectory smoothness is as essential as the control of geometrical deviations. For this purpose the Geo5XF method based on the surface representation of the tool trajectory has been developed. In flank milling, this surface, also called the Machining Surface (MS), is the ruled surface locus of the tool axes defining the trajectory. Based on a first positioning, the method aims at globally minimizing geometrical deviations between the envelope surface of the tool movement and the designed surface by deforming the MS while preserving trajectory smoothness. The energy of deformation of the MS is used as an indicator of the smoothness. Hence, in most cases, results obtained using Geo5XF show that minimum energy tool paths lead to minimal machining time.

As geometrical deviations are not minimized for minimum energy tool paths, a compromise must be reached to find the best solution.

By promoting 5-axis HSM and the use of integrated CAD/CAM/CNC systems, a significant improvement in machining efficiency and accuracy has been achieved. Due to many advantages, such as a high removal material rate or a better surface roughness [START_REF] Tonshoff | Optimal tool positioning for five-axis flank milling of arbitrary shaped surfaces[END_REF], flank milling has become very popular compared with point milling. In particular, this process is now widely used for the machining of slender complex parts like impellers or turbine blades. However, process advantages now motivate industrials to apply high-speed flank milling to any types of surfaces, leading up to new challenges for tool path calculation. Over the last decade, several positioning strategies for flank milling have been developed with the objective of minimizing geometrical deviations [START_REF] Rehsteiner | Collision free five-axis milling of twisted ruled surfaces[END_REF]. Although the local control of geometrical deviations is still a major issue, the smoothness of the calculated tool trajectory is essential to ensure high performance machining. Indeed, oscillatory trajectories may penalize process efficiency.

Methods proposed in literature aim at developing positioning strategies so that geometrical deviations between the machined surface and the designed surface are minimized. Most flank milling methods rely on a first tool positioning on the surface at one or more points, followed by the tool positioning optimization to reduce geometrical errors [START_REF] Menzel | Triple tangent flank milling of ruled surfaces[END_REF]. Over the years, methods have evolved by increasing the number of contact points with the objective of minimizing the geometrical deviations to the detriment of trajectory smoothness and computation time.

Lui [START_REF] Liu | Five-axis nc cylindrical milling of sculptured surfaces[END_REF] developed two methods to machine non-developable ruled surfaces with These two offset points allow to define the tool axis orientation.

Redonnet et al., [START_REF] Redonnet | Side milling of ruled surfaces ; optimum positioning of the milling cutter and calculation of interference[END_REF] proposed a positioning strategy based on three contact points. The axis of a cylindrical tool is initially positioned collinear to the rule by an offset distance value equal to the tool radius. A rotation around the normal at the surface at the mid-curve is applied so that the tool becomes tangent to the two directrices while preserving a contact point with a rule. This leads to a system of seven transcendental equations that must be solved. An extension of the method to conical tools was developed in [START_REF] Monies | Improved positioning of a conical mill for machining ruled surfaces: application to turbine blades[END_REF]. More recently, the authors proposed an improvement of the method considering that the rotation axis is defined as one of the variables of the seven equations and the contact point is located at the mid-curve [START_REF] Senatore | Improved positioning for side milling of ruled surfaces: Analysis of the rotation axis's influence on machining error[END_REF].

The positioning method developed by Bedi et al, [START_REF] Bedi | Flank milling with flat end milling cutters[END_REF] consists in positioning the tool tangent to the two boundary curves of the ruled surface. As contact points are limited to the boundaries, the maximum error is located at the mid-curve. To reduce such errors, an optimization is developed in [START_REF] Menzel | Triple tangent flank milling of ruled surfaces[END_REF]. Contact points are moved along the rule until the deviation between the rule and the tool is minimized. A last step is thus carried out by moving contact points in the transverse direction until a third contact point is obtained, decreasing further geometrical errors.

A c c e p t e d m a n u s c r i p t

Chiou [START_REF] Chiou | Accurate tool position for five-axis ruled surface machining by swept envelope approach[END_REF] proposes a strategy in which errors between the envelope surface of the tool movement and the surface to be machined are all positive.

Gong developed the Three Point Offset method (TPO) for flank milling using a cylindrical tool [START_REF] Gong | Improved positioning of cylindrical cutter for flank milling ruled surfaces[END_REF]. Each tool axis is positioned thanks to three contact curves belonging to the offset surface of the surface to be machined. The initial position is defined by two points belonging to the boundary curves.

One of these points is moved until the deviation between the tool axis and the third curve is less than a threshold. A surface is built by interpolating the tool extremities with B-spline curves. The surface is thereafter deformed so that the geometrical deviations between the machining surface and the offset surface are minimized.

In previous works, a surface-based approach for tool positioning in flank milling has been proposed in [START_REF] Lartigue | Tool path deformation in 5-axis milling using envelope surface[END_REF]. The method relies on a first positioning of the tool according to a two contact point method. Extremity points of the tool axes are approximated by two curves. These two curves define the directrices of a ruled surface, defined as the Machining Surface (MS). To improve tool positioning, the Machining Surface is deformed so that the geometrical deviations between the envelope surface of the tool movement and the designed surface are minimized according to the least-square criterion. The deformation is performed thanks to the displacement of the curve control points using the small displacement torsor method [START_REF] Bourdet | The concept of small displacement torsor in metrology, Advanced Mathematical Tools in Metrology II[END_REF]. This leads to solve a large linear system. First results have shown the benefit of using the surface-based approach to improve tool positioning [START_REF] Lartigue | Tool path deformation in 5-axis milling using envelope surface[END_REF]. The control of the geometrical deviations is as essential as the smoothness of the calculated tool trajectory to ensure high performance machining. Indeed, works have shown that efficiency in 5-axis high-speed machining is better when trajectories are smooth [START_REF] Ho | Five-axis tool orientation smoothing using quaternion interpolation algorithm[END_REF], [START_REF] Lavernhe | Kinematical performance prediction in multi-axis machining for process planning optimization[END_REF]. The

A c c e p t e d m a n u s c r i p t

less solicited the axes are, the better the process performance. The smoothness of the trajectory can be apprehended through the energy; a curve which minimizes its energy then minimizes its curvature variations. As a result a minimum energy trajectory minimizes curvature variations and consequently acceleration and jerk variations are decreased during trajectory processing.

Taking advantage of the surface representation of the trajectory, the smoothness is evaluated by calculating the energy of the surface. Therefore, the issue of minimizing geometrical deviations between the envelope surface of the tool movement and the designed surface coupled to the trajectory smoothing in 5-axis flank milling is investigated in this paper. The method relies on the concept of the MS which has already shown its benefit not only for optimized tool positioning as regards geometrical deviations, but also for general 5-axis

milling optimization to answer kinematical criteria [START_REF] Affouard | Avoiding 5-axis singularities using tool path deformation[END_REF].

In the next section, the four steps of the method for optimized 5-axis flank milling trajectories are detailed. In particular, specific attention is paid to the calculation of the geometrical deviations between the envelope surface of the tool movement and the designed surface. The deformation of the initial tool positioning, which is expressed as a surface, leads to solve a large linear system. As the system is generally ill-conditioned, it is solved by means of the SVD giving thus approximate solutions. In section 3, the energy of deformation of the surface trajectory is introduced as an indicator of the trajectory smoothness. For each estimate of the solution, the cumulated energy during machining is calculated. A series of machining tests are carried out in section 4, highlighting that the minimum energy tool trajectory is in general the minimum machining time trajectory. Results demonstrate the efficiency of the surface-based approach for high performance process.

A c c e p t e d m a n u s c r i p t 2 Generation of Optimized Flank milling trajectories

The method for Generation of Optimized 5-aXis Flank milling trajectories (Geo5XF) is an extension of the method developed in [START_REF] Lartigue | Tool path deformation in 5-axis milling using envelope surface[END_REF] and consists of four main steps: Initial tool positioning; Approximation of the tool axis extremities by two curves defining the two directrices of the MS; Calculation of the deviations between the envelope surface and the designed surface; Positioning optimization by deforming the MS (Fig. 1).

Initial positioning

The initial tool positioning is carried out using the SPO positioning method developed by Liu [START_REF] Liu | Five-axis nc cylindrical milling of sculptured surfaces[END_REF] for its robustness and simplicity to implement. Indeed, whatever the nature of the surface to be machined, this method provides a result which is always exploitable in a minimal computation time. At this stage, a set of tool axes is created defining the initial tool positioning for which the values of undercuts and overcuts are generally too large.

Directrix definition

Cubic B-spline curves are then associated to the extremity points of the set of axes according to the least-square criterion. These two curves define the directrices of the ruled parametric surface MS(u, v) defining the Machining Surface (Fig. 1), the equation of which is:

MS(u, v) = (1 -v) • Cb(u) + v • Ct(u) ( 1 )

A c c e p t e d m a n u s c r i p t

where u and v are the parametric coordinates and Cb(u) and Ct(u) are the bottom curve and the top curve respectively. These curves are calculated as follows:

-→ Cb(u) = n 1 l=1 N l3 (u) -→ Cb l and -→ Ct(u) = n 2 m=1 N m3 (u) -→ Ct m (2)
where N l3 (u) and N m3 (u) are the basic spline functions as defined in [START_REF] Piegl | The Nurbs Book : Second Edition[END_REF].

Calculation of the geometrical deviations

In the literature, calculation methods of the geometrical deviations between the designed surface and the machined surface are most often based on the envelope surface of the tool movement. More generally, the calculation method is directly linked to the method used for tool path generation [START_REF] Bedi | Flank milling with flat end milling cutters[END_REF], [START_REF] Chiou | Accurate tool position for five-axis ruled surface machining by swept envelope approach[END_REF], [START_REF] Lartigue | Tool path deformation in 5-axis milling using envelope surface[END_REF], [START_REF] Abdel-Malek | Geometric representation of the swept volume using jacobian rank-deficiency conditions[END_REF], [START_REF] Yang | Approximate swept volumes of nurbs surfaces or solids[END_REF].

Concerning the envelope surface calculation, some methods use the implicit equations of the designed surface to determine the exact representation of the envelope surface [START_REF] Abdel-Malek | Geometric representation of the swept volume using jacobian rank-deficiency conditions[END_REF], [START_REF] Yang | Approximate swept volumes of nurbs surfaces or solids[END_REF]. Nevertheless, for simplicity reasons, kinematical methods leading to an approximation of the envelope surface are used in [START_REF] Bedi | Flank milling with flat end milling cutters[END_REF],

[9], [START_REF] Lartigue | Tool path deformation in 5-axis milling using envelope surface[END_REF]. In [START_REF] Li | Error measurements for flank milling[END_REF], the authors compared the main methods of geometrical error calculation proposed in literature and showed that kinematical methods relying on double projection provide good results regarding effective geometrical errors. Therefore, the kinematical approach as developed in [START_REF] Lartigue | Tool path deformation in 5-axis milling using envelope surface[END_REF] relying on a double projection method is adopted in this study.

The envelope surface is approximated by considering static instances of the tool axis movement. To each static instance, defined by a value u * of the u

ξ k (u * ) = ---------→ C k (u * )B k (u * ) • -→ n k (u * ) ( 3 )
where -→ n k (u * ) is the normal to the machining surface MS(u, v) at C k (u * ), and

h(u * ) is the height of the tool at u * and k p (u * ) is the distance ---------→ Cb(u * )B p k (u * ) .

Optimization through the MS deformation

The optimization is carried out by applying a deformation to the MS so that the envelope surface of the tool movement best fits the designed surface. The surface deformation is obtained by applying a small displacement -→ D C k (u * ) to each sampled point of the tool surface, giving the optimized deviation [START_REF] Bourdet | The concept of small displacement torsor in metrology, Advanced Mathematical Tools in Metrology II[END_REF] (Fig. 3):

e k (u * ) = ξ k (u * ) - -→ D C k (u * ) • -→ n k (u * ) ( 4 )
However, considering that displacements are small, the projection of the small displacement of C k (u * ) onto the normal to the tool surface -→ n k (u * ) is assumed to be equal to the projection of the small displacement of

B p k (u * ) onto -→ n k (u * ): -→ D C k (u * ) • -→ n k (u * ) = -→ D B p k (u * ) • -→ n k (u * ) ( 5 )

A c c e p t e d m a n u s c r i p t

Hence, by expressing -→ D B p k (u * ) in function of the displacement of the control points of each directrix, this yields to:

e k (u * ) = ξ k (u * ) -1 - k p (u * ) h(u * ) • n1 l=0 N l3 (u * ) • --→ δCb l • -→ n k (u * ) + k p (u * ) h(u * ) • n2 m=0 N m3 (u * ) • ---→ δCt m • -→ n k (u * ) (6)
As the objective is to find the optimized machining surface so that the envelope surface best fits the set of B k (u * ) points defining the designed surface, the least-square criterion is used, leading to the following optimization scheme:

Find --→ δCb l and ---→ δCt m , the displacements of the directrices control points so that

W = u * k e 2 k (u * ) is minimal.
This leads to solve a large linear system,

A • x = b with 3 • (n 1 + n 2 ) equations,
where n 1 and n 2 are the number of control points of the bottom and the top curve respectively.

First experiments have highlighted that the large linear system is most generally ill-conditioned; solutions are inconsistent [START_REF] Press | Numerical recipes in C : The art of scientific comuting[END_REF]. Hence, the Singular Value Decomposition (SVD) must be used to solve the system.

Resolution by means of the Singular Value Decomposition

In order to solve the linear system, the SVD is used leading thus to an estimate of the solution. Indeed, the SVD gives an estimate of a given matrix by a lower rank matrix of same dimensions. The method consists in the decomposition of a rectangular matrix into a product of three matrices, two orthogonal matrices

A c c e p t e d m a n u s c r i p t

and a diagonal matrix:

A = U • Σ • V T (7)
with :

• U ∈ M m×m (R) and V ∈ M n×n (R) are normalized.

• Σ (m×n) = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ Σ r 0 0 0 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ with Σ r = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ σ 1 . . . σ r ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
where σ i are the singular values of

A such as σ 1 > • • • > σ r ≥ 0. Singular values of a matrix A ∈ M m×n (R) are roots of the eigenvalues of A T • A: σ i = λ i (A T • A).
If A is a positive semi-definite matrix, the pseudo-inverse of A is obtained from the eigenvalues λ i of A as follows:

Â-1 = V • Σ-1 • U T with Σ-1 = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 1 λ 1 . . . 1 λ j 0 . . . 0 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (8)
Therefore, the estimate of the solution depends on the rank j of the pseudoinverse matrix (limit value of the eigenvalues). The rank determines the level of approximation. To each λ i corresponds a pseudo solution of the system giving

Minimum energy trajectories

As mentioned previously, the smoothness of the trajectories is a key criterion for high performance machining within the context of HSM. Machine tool solicitations are decreased for trajectories at least continuous in curvature [START_REF] Dugas | An enhanced machining simulator with error analysis[END_REF]. Within the framework of curve and surface fittings, many authors use the energy of deformation as a criterion to control element smoothness [START_REF] Faux | Computational geometry for design and manufacture, Mathematics and its applications[END_REF], [START_REF] Vassilev | Fair interpolation and approximation of b-spline by energy minimization and points insertion[END_REF].

The work reported in [START_REF] Wang | Energy and b-spline interproximation[END_REF] shows in particular that the energy is the most essential criterion when fitting curves and surfaces to clouds of points. As the tool trajectory is represented as a surface, the evaluation of the smoothness through the energy seems to be relevant. For this purpose, the calculation of the energy of deformation as proposed in [START_REF] Wang | Energy and b-spline interproximation[END_REF] is adopted in the present work.

The energy of deformation E of a parametric surface S(u, v) on a domain D, is given by the following formula:

E = D | ∂ 2 S ∂u 2 | 2 + 2 • | ∂ 2 S ∂u∂v | 2 + | ∂ 2 S ∂v 2 | 2 dudv ( 9
)
Since we are dealing with a ruled parametric surface, this leads to:

E = D | ∂ 2 S ∂u 2 | 2 + 2 • | ∂ 2 S ∂u∂v | 2 dudv ( 10
)

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To each estimate of the solution, the energy of the MS is calculated using Eq.

10. The objective is thus to find a pseudo solution that gives minimal geometrical deviations while preserving a correct smoothness of the trajectory. This point is investigated through various examples in the next section. Note that the energy along the tool path is numerically calculated using the trapezium rule. The value next denoted Energy corresponds to the cumulated energy for the whole tool path.

Applications

To show the efficiency of the Geo5XF method, two different kinds of experiments are conducted. First, literature surfaces are tested in order to compare results obtained with Geo5XF to those proposed in literature. The second experimentation concerns the application of the method to an industrial part composed of various patch surfaces. Indeed, literature surfaces are most generally composed of a unique patch surface which simplifies flank milling positioning.

Literature surfaces : "Senatore" and "Two flipped" surfaces

Various surfaces are proposed in literature to compare flank milling positioning algorithms. Among these surfaces, two test surfaces have been selected, both non developable ruled surfaces; the first one is called the "Two flipped" surface as defined in [START_REF] Menzel | Triple tangent flank milling of ruled surfaces[END_REF] (Fig. 4), and the second one is "Senatore" as it was introduced by Senatore in [START_REF] Senatore | Analysis of improved positionning in five-axis ruled surface milling using envelope surface[END_REF] (Fig. 4).

For each test surface, minimal and maximal deviations obtained with the

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different methods are given and compared to the optimal solution given by Geo5XF. In addition, in order to evaluate actual trajectory smoothness, the Energy is calculated and then correlated to the kinematical behaviour during machining. Particular attention is paid to the evolution of the tool axis during machining and to the effective relative tool/surface velocity. Both surfaces are machined using a cylindrical tool with a diameter equal to 20 mm for the "Two flipped" surface and 25 mm for the "Senatore" one.

Geometrical deviations

Geometrical deviations obtained using the various positioning algorithms are reported in Table 1. Concerning Geo5XF, reported values result from the double projection calculation obtained for the minimal deviations solution.

Whatever the surface, Geo5XF gives satisfactory results close to the optimal values obtained with methods issued from literature. Values given for the methods mentioned in Table 1 are taken from the authors' original papers.

Tool path Smoothness

To analyze the influence of the Energy, three estimates of the solution of the linear system defined by Eq.( 8) are tested. That means three pseudo solutions given for three different eigenvalues: the minimum energy solution (corresponding to min.E), the minimal deviations solution (corresponding to min.W ) and a compromise between energy and deviation, which locally minimizes the energy (corresponding to comp.). In Table 2, maximal and minimal deviations as well as the Energy and the sum of the squared deviations are reported for all three cases.

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For the "Two flipped" surface, results are different according to the considered pseudo solution. Therefore, the correlation between energy and kinematical behaviour is only investigated for this surface. In order to link the energy to the kinematical behaviour, the evolution of the tool axis orientation in the Part Coordinate System (PCS) is studied, through the evolution of the coordinates i, j and k of the tool axis. As shown in Fig. 5, the evolution of k is smoother for the minimum energy trajectory than for the other ones. Furthermore, when zooming, the correlation between the energy and the level of oscillation is clearly highlighted: the greater the energy, the more important the oscillations.

Energy thus seems a relevant parameter to characterize trajectory smoothness in the PCS.

In order to check the efficiency of the smoothness criterion in the Machine Coordinate System (MCS), actual machining is performed on a MIKRON UCP 710. The machine tool is a RRTTT structure, and the Inverse Kinematical Transformation (IKT) leads to solve equations below, which have zero, one, two or an infinite number of solutions:

A = ± arccos(k) and C = -arctan( i j ) [π] (11)
where A and C are the two rotational axes of the machine tool. The previous system of equations has two domains of solutions corresponding to A > 0 or A < 0 which vary in function of the coordinates i, j and k of the tool axis.

The IKT is carried out in real time by the NC unit SIEMENS 840D of the machine tool. Machining conditions are as follows: the tool is cylindrical, with a diameter equal to 20 mm; the programmed feedrate is set to 5 m/min and the spindle speed to 18000 rev/min. The evolution of machining time is reported in Table 2 for the three pseudo solutions confirming the correlation between

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energy and axis evolution smoothness: the less the energy, the shorter the machining time.

As a partial conclusion, the energy of the MS is a good parameter to evaluate the smoothness of the trajectory in the PCS. For the proposed example, as there is no swapping of solution space during the machining (A and C keep the same sign during machining), the smoothness is also effective in the MCS.

This result has to be confirmed through various examples.

Industrial surface: Impeller

Among papers dealing with flank milling, only a few one have undertaken the issue of industrial multi patch surfaces. In order to emphasize the efficiency of the Geo5XF method, the second illustration proposed concerns an impeller which is characteristic of the complex surfaces industrials attempt to flank mill (Fig. 4). The impeller is made of several blades each one defined by compound surfaces. The method is applied to one of the blades leading to a unique trajectory for the machining of both sides of the blade. Table 3 gathers results obtained considering, as in the previous example, three different pseudo-solutions: the minimum energy, the minimal deviations and a compromise. Due to the fact that the surface is representative of industrial complex surfaces, deviations are clearly greater than deviations obtained for literature surfaces. Moreover, as it is essential to obtain at the same time smoothness while minimizing geometrical deviations, the compromise makes sense.

The tool trajectory is calculated according to the following machining conditions: a cylindrical tool with a diameter equal to 6 mm; the programmed

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feedrate is set to 5 m/min and the spindle speed to 18000 rev/min (Fig. 6).

The evolution of the cumulated energy along the trajectory is reported in Fig. 7 for the three estimates of the solution. The figure brings out the adequacy of the energy value to the pseudo-solution; the minimum energy solution gives the minimal cumulated energy. Moreover, for the three trajectories, the gap of energy is clearly visible at the transition edge between the intrados and the extrados where the curvature is important. However, the magnitude of the gap varies according to the pseudo-solution. Hence, a gap in the evolution of the cumulated energy corresponding to the machining of the middle of both the extrados and the intrados only exists for the minimal deviations and the compromise solutions, accounting for trajectories less smooth than with the minimal energy solution.

The evolution of A and C (Fig. 8) and (Fig. 9) shows that oscillations are more important for the greatest energy pseudo-solution; the smoothest the tool path, the fastest (Table 3). Furthermore, levels are clearly visible in the evolution of C for times belonging to the intervals [2.4; 4.8] and [10; 12] which seems in adequacy with the energy gaps when machining the intrados and the extrados (Fig. 7).

A picture of each machined surface corresponding to each pseudo solution is presented in Fig. 10 showing the influence of the energy on the surface finish.

Marks at the middle of the extrados are consistent with the energy gaps observed in Fig. 7. The lack of marks confirms the smoothness effect of the energy parameter.

A c c e p t e d m a n u s c r i p t 4.3 Limits of the approach

As shown previously, when using the concept of the MS, it is possible to minimize geometrical deviations while preserving the trajectory smoothness through the energy of deformation of the MS. This statement is specifically valid when there is a single solution when passing from the PCS to the MCS. This is not always the case. Let us consider the surface proposed by Liu (Fig. 4)

which is machined according to the following conditions: a cylindrical tool with a diameter equal to 20 mm, a programmed feedrate of 5 m/min and a spindle speed of 18000 rev/min.

The smoothness analysis shows that the correlation between machining times and energy values has disappeared (Table 4). Machining time for the minimum deviation tool path is shorter than for the compromise whereas its energy is greater.

The evolution of the rotational axis C (Fig. 11), brings out that C is positive for the minimum deviations solution, whereas it is negative for the two other pseudo-solutions. Indeed, as the sign of i is not the same at the machining starting point, the rotational axis C moves to the programmed point along the shortest path, through the negative or positive values, according to the NC unit settings. During machining, IKT may involve solution space changes which are not predictable when considering only the energy of deformation in the PCS.

A c c e p t e d m a n u s c r i p t 5 Conclusion

In this paper, the Geo5XF method -a method designed to optimize tool positioning in 5-axis flank milling -has been detailed. Taking advantage of the surface representation of the tool trajectory, the method leads to globally minimize global gouging between the tool and the surface. Indeed, as far as geometrical deviations are concerned, results obtained with Geo5XF are similar to those obtained in literature. However, in 5-axis High-Speed Machining the control of the trajectory smoothness is essential for high performance trajectory. Hence, as the trajectory is defined as a surface, the smoothness is evaluated through the energy of the surface. Results show that, in general, minimum energy trajectories are the fastest. Energy is thus a relevant parameter to account for the trajectory smoothness. The limit of the method is linked to the IKT, as there is no univocity between the PCS in which the tool trajectory is calculated and the MCS system in which it is executed. Investigating smoothness in the MCS will be a future development of the method.

Acknowledgments

This work is funded by Missler Software and the French Ministry of Research.

A c c e p t e d m a n u s c r i p t •A c c e p t e d m a n u s c r i p t 1

 t1 MS(u, v) Machining Surface • Cb(u) Bottom curve • Ct(u) Top curve • Cb i Control point of the bottom curve • Ct i Control point of the top curve • N im (u) B-spline basis functions • n 1 number of control points of the bottom curve • n 2 number of control points of the top curve • S(u, v) Design Surface • A k (u) Sampled points on the tool axis • B k (u) Projected points on the Design Surface • B p k (u) Projection of B k (u) point on the tool axis • C k (u) Intersection points on the tool Surface • ξ k (u) Initial deviation • -→ n k (u) Normal vector to the Machining Surface • h(u) Distance between Cb(u) and Ct(u)• k p (u) Distance between Cb(u) and B p k (u)• -→ D C k (u) Displacement of point C k (u) • -→ D B p k (u) Displacement of point B p k (u)• e k (u) Optimized deviation• λ i Eigenvalues • W Sum of squared deviations• E Energy of deformation of the Machining Surface• i ,j , k cosine of the tool axis orientation• A, C Rotary axes of the machine tool Introduction

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  hemispherical tools. The first one, the Simple Point Offset (SPO), consists in positioning the tool collinear to the surface rule passing through a point offset at the mid curve. Geometric errors are thus divided into overcuts and undercuts. The second method is the Double Point Offset (DPO) method. Two contact points located at the parametric values 0.25 and 0.75 of the rule, are offset by a value equal to the tool radius along the normal to the surface.

A c c e p t e d m a n u

  s c r i p t parameter, corresponds a tool axis which is sampled into a set of A k (u * ) points (Fig.2). Each point A k (u * ) is normally projected onto the designed surface, giving the point B k (u * ) which is in turn projected onto the considered tool axis, giving the point B p k (u * ). This last projection intersects the tool surface at a point C k (u * ). Therefore, the geometrical deviation ξ k (u * ), between the envelope surface and the designed surface at the point B k (u * ) is given by:

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  optimal values of the control point displacements. The so calculated control points define the directrices of the optimized MS. The pseudo solution which gives the minimum of W = u * k e 2 k (u * ) is called the minimal deviations solution.

Fig. 1 .A c c e p t e d m a n u s c r i p tFig. 2 .A c c e p t e d m a n u s c r i p tFig. 3 .A c c e p t e d m a n u s c r i p tFig. 5 .A c c e p t e d m a n u s c r i p tFig. 7 .A c c e p t e d m a n u s c r i p tFig. 8 .A c c e p t e d m a n u s c r i p tFig. 9 .A c c e p t e d m a n u s c r i p tFig. 10 .A c c e p t e d m a n u s c r i p tFig. 11 .A c c e p t e d m a n u s c r i p t

 12357891011 Fig. 1. Geo5XF method: approximation of SPO tool postures (left) and optimisation of the Machining Surface (right)

Table 2

 2 Pseudo solution min.E comp. min.W Results of Geo5XF method in terms of geometrical deviations, energy of deformation and machining time (Two flipped surface) Pseudo-solution min.E comp. min.W

	Test surface	"Two flipped"
	Undercut (mm)	0.57	0.0086 0.0086
	Overcut (mm)	0.035	0.016	0.016
	e 2 i (mm 2 )	163	0.0470 0.0468
	Energy (mm -2 )	1.60	2.22	4.68
	Time (s)	4.8	5.0	5.1

Table 3

 3 Results of Geo5XF method in terms of geometrical deviations, energy of deformation and machining time (Impeller surface)