MD Andreas Tzschach
email: tzschach@molgen.mpg.de

Hao Hu

Reinhard Ullmann

Masoud Garshasbi

Wei Chen

Hans Hilger Ropers

Andreas Walter Kuss

Kimia Kahrizi

Seyedeh Sedigheh

Hao Cougar

Hu

Seyedeh Sedigheh Abedini

Shirin Ghadami

Roxana Kariminejad

H.-Hilger Ropers

Hossein Najmabadi

Next generation sequencing in a family with autosomal recessive Kahrizi syndrome (OMIM 612713) reveals a homozygous frameshift mutation in SRD5A3

Keywords: SRD5A3, next-generation sequencing, congenital disorder of glycosylation, mental retardation, autosomal recessive, consanguinity, cataract, coloboma, kyphosis

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

Introduction

We have recently reported on a remotely consanguineous Iranian family of three affected siblings who suffered from a novel mental retardation syndrome characterised by severe mental retardation, cataract, coloboma and kyphosis (Kahrizi syndrome, OMIM 612713). 1 Linkage analysis in this family revealed a gene locus in the pericentromeric region of chromosome 4.

Here, we report on the results of mutation screening in the genes of this interval by next-generation sequencing, and on the identification of a frameshift mutation in the steroid 5α-reductase type 3 gene SRD5A3. In combination with other recent observations, this finding indicates that the clinical spectrum of Kahrizi syndrome is wide, and that mutations in the SRD5A3 gene lead to defective protein glycosylation, even though this feature may be missed upon routine testing.

Methods

Homozygosity mapping in this family had revealed a single linkage 10.4 Mb interval in the pericentromeric region of chromosome 4 flanked by markers rs728293 (chr4: 47052440, HG18) and rs1105434 (chr4: 57488508, HG18). 1

Library preparation, DNA enrichment and Illumina/Solexa Sequencing

For enrichment of the coding regions of all RefSeq genes and flanking intronic sequences of this interval, complementary oligonucleotide baits were designed for all 602 exons including 30 bp extensions at either end, using Agilent's eArray version 6.4. On the 244k sequence capture array, each of these oligonucleotides was represented four times. Repetitive sequences were not excluded. After fragmentation rvMS 408-10-EJHG 4 of the sample of genomic DNA of the index patient (II:4), 1 DNA fragments were repaired to generate blunt ends by T4 polymerase and Klenow DNA polymerase, and phosphorylated with T4 polynucleotide kinase. We measured the DNA concentration with a Nanodrop 7500 spectrophotometer, and a 1 μl aliquot was diluted to 10 nM.

After adding a single 'A' base to the 3′ end of the DNA fragments using Klenow exo (3′ to 5′ exo minus), we ligated Solexa adaptors (with a 'T' overhang) with the DNA fragments using DNA ligase. Ligated products (size range 150-200 bp) were gel purified on 2 % agarose, followed by 18 cycles of PCR-amplification.

The hybridization of 20 µg of library DNA and the subsequent sequence capture was performed according to the manufacturers' recommendations (Agilent, Santa Clara, CA). Adaptor-ligated DNA was hybridized to the surface of one lane of a flow cell, and DNA clusters were generated using the Illumina/Solexa cluster station, followed by 76 cycles of sequencing on the Illumina/Solexa 1G analyzer.

Data analysis

Data analysis was performed as described previously. 2

RT-Analysis

To check for SRD5A3 expression, total RNA was extracted from Epstein-Barr virus (EBV)-transformed lymphoblastoid cell lines (LCLs) of the index patient and two controls by using the TRIzol reagent (Invitrogen), and cDNA was generated by using the SuperScript III Reverse Transcriptase (Invitrogen) together with random hexamer primers. This cDNA was used to perform PCRs with a series of primer combinations rvMS 408-10-EJHG 5 for two adjacent exon sequences and together encompassing the entire gene (primer sequences are available upon request).

Results

Illumina/Solexa sequencing

In total, 25 million single-end 76 nucleotide (nt) reads were generated, which allowed sufficient coverage of approximately 94 % of the target sequence. 167 singlenucleotide variants (SNVs) matched variants from the references sequence, 13 of which were not annotated in the dbSNP database. These changes were either silent changes in the coding regions or changes in non-coding regions. A total of 31 indels were detected, 22 of which were novel, and all but one (in exon 1 of SRD5A3) were located in non-coding regions. The results of next-generation sequencing analysis of this interval are summarized in Table 1.

Mutation in SRD5A3

The only remaining variant in coding regions of this interval was the duplication of one cytosine in exon 1 of SRD5A3. According to NM_024592.3, the position of this change in the protein is c.203dupC (p.Phe69LeufsX2). The genomic position of this duplication is chr4:55907464dupC (HG18). 1a). The parents and two healthy siblings (II:1 and II:3) were heterozygous carriers of this duplication. We failed to detect this rvMS 408-10-EJHG 6 mutation in 366 control chromosomes from healthy Iranian and German control individuals.

RT-PCR

RT-PCR using RNA extracted from a lymphoblastoid cell line of the index patient showed missing or reduced expression of the five SRD5A3 exons (Figure 1b).

Discussion

In a consanguineous family of three affected siblings who were suffering from a complex congenital disorder, homozygosity mapping had revealed a linkage interval on chromosome 4, and mutation screening of the coding regions in this interval by exon enrichment and Illumina/Solexa sequencing revealed a frameshift mutation in SRD5A3.

Mutations in SRD5A3 have been identified independently of this study in other

patients and families with partially overlapping clinical features and congenital defects of glycosylation. 3-4 SRD5A3 encodes steroid 5α-reductase type 3, an enzyme which is required for the conversion of polyprenol to dolichol, the lipid anchor for Nglycosylation in the endoplasmatic reticulum. [START_REF] Cantagrel | The SRD5A3 gene is required for the conversion of polyprenol to dolichol, essential for N-linked protein glycosylation[END_REF] SRD5A3 is highly expressed in fetal brain. 3 Cantagrel et al (2010) 3 and Morava et al (personal communication) [START_REF] Cantagrel | The SRD5A3 gene is required for the conversion of polyprenol to dolichol, essential for N-linked protein glycosylation[END_REF] identified a total of 7 different SRD5A3 mutations in 9 families. Most of these cases were ascertained by abnormal transferrin isoelectric focussing patterns suggesting a type I congenital defect of glycosylation ("CDG type Ix", OMIM 212067). 5 In the family rvMS 408-10-EJHG 7 reported here, no clearly abnormal transferrin mobility had been detected in two independent routine tests for CDG screening. Interestingly, in the family reported by Al-Gazali et al ( 2008), [START_REF] Al-Gazali | A new autosomal recessive syndrome of ocular colobomas, ichthyosis, brain malformations and endocrine abnormalities in an inbred Emirati family[END_REF] now also known to carry an SRD5A3 mutation, 3 repeated CDG testing had failed to detect any abnormality, too. Thus, in patients with clinical features suggestive of Kahrizi syndrome, SRD5A3 mutations should be ruled out even if CDG testing is negative.

Apart from severe mental retardation which was observed in all patients with SRD5A3 mutations, the presence of additional clinical features seems to vary considerably, not only between different families, but also within families. Cerebellar ataxia was present in most patients, but malformation of the cerebellum or the cerebellar vermis were absent in the original family with Kahrizi syndrome and only detectable in some patients by MRI investigation. Ophthalmic problems (cataract, iris coloboma, optic nerve hypoplasia) were frequently observed. Cataracts were only present in two of the patients of the Cantagrel/Morava cohort. 3 In the family reported here, all three siblings developed cataracts at the age of about 17 years. Since the oldest patient in the Cantagrel/Morava cohort was only 12 years old, it may be expected that other patients will also develop cataracts as they grow older.

The syndrome reported here has some phenotypic overlap with Peter's plus syndrome (OMIM 261540), an autosomal recessive disorder which is caused by mutations in the gene encoding B3GALTL, a putative glycosyltransferase. [START_REF] Oberstein | Peters plus syndrome is caused by mutations in B3GALTL, a putative glycosyltransferase (vol 79, pg 562[END_REF] Also in patients with Peter's plus syndrome, routine CDG testing by isoelectric focussing of transferrin (IFT) failed to reveal any abnormalities. This example, and the family reported here, may serve as a reminder that a normal IFT result does not always

  This mutation was subsequently confirmed by conventional Sanger sequencing in the index patient and his two affected siblings (II:5 and II:6 according to Fig 2a in Kahrizi et al, 2009) 1 (Figure

Figure 1

 1 Figure 1 a) Graphical representation of the linkage interval in the pericentromeric region of chromosome 4 (red box) the position of SRD5A3 the position of the mutation and partial chromosome 4 (red box), the position of SRD5A3, the position of the mutation and partial chromatogram of exon 1 of the index patient. The asterisk denotes the duplication of one cytosine (c.203dupC;p.Phe69LeufsX2). b) Results of the RT-PCR using RNA derived from a lymphoblastoid cell line of the index patient showing absence (ex 1-4) or reduced (ex 4-5) expression of SRD5A3 transcripts. HUWE was used as an internal control.

Table 1

 1 Summary of the results of next-generation sequencing after exon enrichment of the interval on chromosome 4 * not annotated in dbSNP (version 130) Note: All variants mentioned in the list are located in the linkage interval (chr4: 47,052,440-57,488,508)

	Parameter

Acknowledgments

We are grateful to the patients and the parents of the family for their cooperation. We thank Vera Kalscheuer and Stefan Haas for bioinformatic support, and Ines Müller, Corinna Menzel and Melanie Bienek for technical assistance. This work was supported by the Iranian National Science Foundation (to H.N.), the Max Planck Innovation Funds and the German Federal Ministry of Education and Research through the NGFNplus -MRNET (to H.H.R.).

Conflict of interest

The authors declare no conflict of interest.

Legends to table and figure


Humera S Khan
email: a.h.khan@bham.ac.uk.

Maurice P Zeegers

Leo J Schouten

Boukje

C Van Dijk

Alexandra Goldbohm

Jack Schalken

Shahin Shajahan

Alexandra Pearlman

Carole Oddoux

Piet A Van Den Brandt

Boukje A C Van Dijk

Alexander Pearlman

Harry Ostrer

Genetic marker polymorphisms on chromosome 8q24 and prostate cancer in the Dutch population: DG8S737 may not be the causative variant

Keywords: Epidemiology, microsatellite repeats/genetics, SNP, prostatic neoplasm/genetics, cancer Surveillance, Epidemiology and End Results program SEER Logarithm

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

Both the rs1447295-A allele and DG8S737-10 allele were significantly associated with high grade tumours (OR, 1.4; 1.1-1.8 and OR, 1.9; 1.2-2.8 respectively) [START_REF] Suuriniemi | Confirmation of a positive association between prostate cancer risk and a locus at chromosome 8q24[END_REF] . Two recently reported genome wide association studies confirmed the association of the rs1447295-A allele and prostate cancer risk [START_REF] Yeager | Genome-wide association study of prostate cancer identifies a second risk locus at 8q24[END_REF][START_REF] Gudmundsson | Genome-wide association study identifies a second prostate cancer susceptibility variant at 8q24[END_REF] , but did not stratify by tumour stage. The variability in haplotype association results may be related to tumour stage heterogeneity or genetic heterogeneity within and between populations.

We have previously investigated founder mutations among the Dutch and found mutations that were specific for this population including those predisposing for hereditary breast-ovarian cancer and malignant melanoma [START_REF] Zeegers | Founder mutations among the Dutch[END_REF] . We also identified short chromosomal regions that have remained identical by descent resulting in relatively limited genetic heterogeneity within this population 6 thus increasing the power in detecting the associations among the Dutch. Genome wide association studies (GWAS) often experience type 1 errors, therefore confirmation of results are required. Here, we tested whether the association between rs1447295 and DG8S737 and prostate cancer can be confirmed among a population based Dutch sample and whether this association is different for localized versus advanced tumours.

METHODS

Study Population

Incident prostate cancer cases and controls were identified in the population of the Netherlands Cohort Study (NLCS), further details can be found elsewhere [START_REF] Van Den Brandt | A large-scale prospective cohort study on diet and cancer in The Netherlands[END_REF] . In brief, the NLCS includes 58,279 men who were between the ages 55 and 69 years at baseline. This paper reports from the dataset after 8.3 years of follow up. A case cohort approach was used. Cases were identified after follow up using computerized record linkage with all nine cancer registries in the Netherlands. Controls were selected from a random sub cohort sample of 2,411 men and biennially followed up for information on vital status.

Biological Samples

The NLCS cohort was linked to the Dutch pathology database to collect paraffin blocks of tumour and normal tissue samples of prostate cancer cases. After exclusion of prevalent cases and those with insufficient non tumorous tissue, 300 cases were available for analysis. We obtained buccal swab samples from 300 controls from the NLCS subcohort. The DG8S737 microsatellite marker (169bp, 128.433 loc) was amplified using

Statistical Analysis

Deviation from Hardy Weinberg equilibrium for the genotypes of each marker and linkage disequilibrium between marker alleles was tested by χ 2 tests. We calculated odds ratios (OR) and corresponding 95% confidence intervals (95%CI) using logistic regression for allelic and genotypic analysis of the SNP and microsatellite. For allelic analyses, robust standard errors have been calculated to model potential clustering of alleles within individuals. In microsatellite analyses, alleles -8 and -10 were compared to all other alleles. The microsatellite was further tested at different breakpoints to test association between groups of alleles. We also tested the marker using allele -14 (most common allele) as the reference group. Both crude and multivariable (age, alcohol intake from wine, body mass index (BMI), energy intake, family history of prostate cancer and level of education) adjusted analyses were performed. We evaluated differences in associations with the localised tumour stage (T0-2, M0) or advanced (T3-4, M0 and T0-4, M1). Stage was reported by the cancer registries and coded according to the International Union Against Cancer tumor-node-metastasis (UICC TNM) [START_REF] Sobin | Union Internationale Contre le Cancer and the American Joint Committee on Cancer[END_REF] . All statistical analyses were performed using Stata 9.0 (StataCorp, 2005).

RESULTS

After excluding subjects with missing data, we were left with 277 cases and 282 controls.

These did not significantly differ from their respective case and control source populations regarding age (P cases =0.50, P controls =0.50) and family history of prostate cancer (P cases =0.95, P controls =0.38). The mean age at baseline of cases in the study population was 63 years, which was significantly higher than the mean age of the sub cohort (60 years). A small proportion of the combined sample had positive family history of prostate cancer (4.13%). The frequency of alleles and genotypes for the microsatellite marker DG8S737 and the SNP rs1447295 did not deviate from Hardy Weinberg equilibrium among the controls (P=0.14). There was strong evidence for linkage disequilibrium between allele -10 of DG8S737 and the A allele of the SNP (χ 2 =61.2, P<0.001). Table 1 shows the results of the microsatellite and SNP analyses. DG8S737 marker allele -8 (22 repeats) was unexpectedly associated with a statistically significant decreased risk for prostate cancer (OR, 0.62; 95%CI, 0.40 -0.96; P = 0.03). The increased frequency of the -10 allele among cases was suggestive of association with increased risk of prostate cancer, however it did not achieve statistical significance (OR, 1.50; 95%CI, 0.88 -2.55). The results of all alleles can be found in the online appendix table. The SNP analysis suggested an increase in the crude OR with the presence of allele A, (OR, 1.38; 95%CI, 0.94 -2.20), although not statistically significant (P = 0.10). This was also true for carriers of one and two copies of allele A (OR, 1.40; P = 0.14 and OR, 1.54; P = 0.48 respectively). After multivariable adjustment, the results did not differ substantially, suggesting that an assumption of Mendelian randomisation can be made in this context [START_REF] Ebrahim | Mendelian randomization: can genetic epidemiology help redress the failures of observational epidemiology?[END_REF] . No influence was observed for TNM stage (data not shown).

DISCUSSION

A novel result of our study was a statistically significant decreased risk associated with allele -8 of the microsatellite marker (OR, 0.62; 95%CI, 0.40 -0.96, P = 0.03). This is unlikely to be a result of population structure, given the matching of cases and controls, the absence of apparent outliers or mismatching of ancestry observed by Structure analysis of the Codis set of microsatellite markers and the relative genetic homogeneity of the Dutch population [START_REF] Sarkar | Genetic diversity at two pentanucleotide STR and thirteen tetranucleotide STR loci by multiplex PCR in four predominant population groups of central India[END_REF][START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF] . The apparent protective effect of the DG8S737 -8 allele observed in this study contrasts with the Amundadottir study which detected an increased risk associated with this allele in Icelandic and Swedish men 2 . Their observation of an association of the -8 allele in conjunction with the A allele of rs1447295 in all of the Caucasian populations studied, but not in the more genetically diverse African American population, led them to conclude that the variant responsible for conferring the increased prostate cancer risk must be the DG8S737 -8 allele itself or be extremely close to it. The results of this study and those of the Suuriniemi study, which detected no association with prostate cancer risk for this allele in Caucasian men from Washington, but instead found an association with the -10 allele after stratifying by stage of disease (OR, 1.93; 95%CI, 1.27 -2.93), suggest that this allele itself is not directly responsible for conferring increased prostate cancer risk [START_REF] Suuriniemi | Confirmation of a positive association between prostate cancer risk and a locus at chromosome 8q24[END_REF] . It is more likely that DG8S737 and rs1447295 are tightly linked markers flanking the actual causative variant and that there may be potentially more than one high risk haplotype present in the Caucasian population. This hypothesis might also explain the observations of the Mayo clinic study that demonstrated that the 8/A haplotype showed the strongest association with familial prostate cancer, whereas the 10/A haplotype was most strongly associated with aggressive prostate cancer [START_REF] Wang | Two common chromosome 8q24 variants are associated with increased risk for prostate cancer[END_REF] .

Comparison of detailed haplotypes in this locus among populations may serve as useful means of further narrowing this interval and assisting with identification of the causative variant.

  as a reverse primer. Polymerase chain reactions (PCR) were set up using a HYDRA workstation (Matrix Technologies Corporation, NH) and run on MJR Thermocyclers (MJR Research, Inc). The PCR products of cases and sub cohort controls were sized on the Applied Biosystems 3730 Sequencer in comparison with CEPH1347-02 reference specimen. Genotyping was performed using Genemapper software version 4.0. The Taqman SNP Genotyping Assay (Applied Biosystems, CA) was used for allele typing of the rs1447295 SNP marker with an ABI PRISM 7900HT® (Applied Biosystems).

  Prostate cancer is the most commonly diagnosed cancer in men in Europe and Northern America. Genome wide association studies (GWAS) have detected an association with markers on chromosome 8q24. Allele -8 of microsatellite DG8S737 with 22 repeats and allele A of the single nucleotide polymorphism (SNP) rs1447295 have been found to be significantly associated with prostate cancer. As GWAS are subject to type 1 error, confirmation studies are required to validate the results. Here, we analyzed the same markers in 277 cases and 282 controls from the Netherlands using a nested case control

	Genome Wide Association Studies ABSTRACT approximately 192,280 new cases would arise in 2009, representing 25% of all new cases GWAS
	Netherlands Cohort Study of cancer among men 1 . In 2006, a genome wide linkage analysis of 877 Icelandic men NLCS
	Polymerase Chain Reaction with prostate cancer demonstrated a positive signal on chromosome 8q24 (LOD score PCR
	Body Mass Index 2.11). The variant allele -8 (22 repeats) of the microsatellite DG8S737 had the strongest BMI
	International Union against Cancer tumor-node-metastasis signal in a follow-up association study (OR, 1.79; P = 3.0 x 10 -6 ). This was replicated in UICC TNM
	Icelandic men (OR, 1.72; P = 1.8 x 10 -3 ) and among Swedish and European American
	men. In addition, allele A of the rs1447295 single nucleotide polymorphism (SNP)
	contained within the same haplotype block was also found to have a significant
	association with prostate cancer (OR, 1.72; P = 1.7 x 10 -9 ). Analysis of 598 African
	American men confirmed the results for DG8S737 but not for rs1447295, consistent with
	diagnosis in men in Europe and the United States of America. It was estimated that

study. Incident prostate cancer cases and controls selected were identified in the population of the Netherlands Cohort Study (NLCS). We also investigated clinical features of the disease by stratifying by tumour stage. We did not replicate the association with the SNP rs1447295-A allele (P=0.10) although the effect estimate was in the same direction as previous studies (OR, 1.38). Interestingly a statistically significant decreased risk was observed for DG8S737 allele -8 (OR, 0.62; P=0.03). The apparent protective effect of the DG8S737-8 allele observed in this study contrasts with the Amundadottir study. This suggests that DG8S737 and rs1447295 might be tightly linked markers flanking the actual causative variant and that there may be potentially more than one high risk haplotype present in the Caucasian population. This short report highlights the importance of validation although further confirmation is still needed.

INTRODUCTION

Research by the Surveillance, Epidemiology and End Results (SEER) program of the National Cancer Institute estimated prostate cancer to be the most common cancer the greater genetic diversity of this population 2 . Another recent replication study confirmed the association of rs1447295-A allele with prostate cancer in European men aged 40-64 years from Washington, but not the association with allele -8 of DG8S737 3 .

Grant Support

This study was established with financial support from the Dutch Cancer Society and the US Department of Defense.


Paolo Di Stefano

Luca Di

Di I Stefano

Paolo ; Universita&apos

D I Angelo
email: diangelo@ing.univaq.it

PARAMETRIC COST ANALYSIS FOR WEB BASED E-COMMERCE OF LAYER MANUFACTURED OBJECTS

Keywords: RAPID PROTOTYPING, COST rapid prototyping, cost estimating, e-commerce

and research institutions in France or

As a result of the diffusion of internet, e-business systems are the latest progress on information technology and business process improvement. In fact, many web-based applications have been developed to reduce transaction cycle time (Huang et al., 2003;Luol et al., 2004) in rapid prototyping services. The high level of competition characterizing the rapid prototyping service market requires competitive prices, fast quotation times and high quality products. One of the objectives of a company selling on-line is to increase its share of the market until it reaches production saturation capacity. The market reference for a company, which sells on-line, may reach international levels without a major increase in costs. Rapid prototyping service is an activity that works well on the web. The product specification may be formulated using a geometric model defined by a file that can easily surf the net even at great distances. The distribution network of shipping is characterized by an international dimension, capillary coverage of territory, fast delivery and relatively low costs. The combination of these elements has led the major companies, which operate in the Rapid Prototyping (R.P.) sector, to get equipped with suitable instruments for quoting and selling their services on-line.

Both the products sold and the distinctiveness of the customers requiring these services make this form of on-line selling different from other previous types of thriving e-commerce. It is important to bear in mind that the purchaser requiring these services is usually developing a new product for his company and discretion regarding such a product is essential and in some cases even strategic; therefore, the company supplying the service must guarantee the utmost confidentiality. For a company operating in the rapid prototyping sector, the necessity to expand its market share has an essential prerequisite: the possibility to supply quotations while at the same time satisfying the privacy that the customer demands. The discretion required in outsourcing rapid prototyping means that on-line quotations need to be made without transferring the geometric model. It is possible to solve this problem by dedicated software, available to purchasers, which is capable of remotely analyzing the geometric model, without the need to transfer any files. From the geometric model the software deduces parameters influencing the manufacturing cost (cost driving factors), and transmits the data to the manufacturer in order to make a quotation for the prototype. The quotation process can also be performed automatically. This approach guarantees the confidentiality of the purchaser's product, while at the same time providing the manufacturing company with an instrument that automatically formulates a quotation, which is constantly updated on actual costs. This could lead to particularly competitive quotations which are also dictated by the need to saturate a machine load [A. S. [START_REF] Gogate | Intelligent layout planning for rapid prototyping[END_REF].

One of the current tendencies is for companies in the rapid prototyping sector to be equipped with numerous prototype technologies in order to satisfy the wide range of customers' needs. The various layer manufacturing technologies differ not only in the material used but also in the operating principle and the modalities with which the material is deposited on each single prototype slice. The cost of an object made with rapid prototyping depends on numerous factors, some of which are easy to determine, while some others are more closely linked to the type of technology used. One of the most important factors influencing costs is the time involved in manufacturing the object, which is very difficult to estimate. Build time depends not only on the object dimension but also on the object complexity and on the R.P. technology used, which affect necessary movements of the forming tool. For this reason build time could not be easily evaluated from a remote station by using general purpose software. In order to estimate build time it is common practice to assume that it is proportional to the total volume of the prototype. In practice this approach only provides one component of the total build time. In a particularly competitive market, the error margin in production cost forecasting, and consequently, in price, is greatly reduced; therefore, such approximation cannot be accepted. The real risk is the estimation of either a non-profitable price or an excessive price which could drive the purchaser away.

In order to perform a remote estimation of the build cost, a new parametric approach is proposed, which also takes into account build-time prevision. It is based on the evaluation of some driving factors, which give the possibility to estimate cost without transferring the geometric model. This approach can be adapted for the cost estimation of the most common layer manufactured technologies.

A procedure is defined to evaluate the coefficients of the parametric formula for build time estimation.

The complete method is verified in some test cases that have been used in other research works described in literature.

Layer manufacturing technology costs' structure

Rapid prototyping costs comprise different components. [START_REF] Alexander | Part orientation and build cost determination in layered manufacturing[END_REF] identify three main cost components: prebuild cost (C pre ), build cost (C build ) and postprocessing cost (C post ).

Prebuild cost refers to any preparation jobs performed before the part is manufactured and in turn, comprises:

-Verification of the integrity of the geometric model and eventual repair (if the geometric model is not free from faults it must be rejected by the remote software); -Definition of the layers' thickness (L) and build direction (d) (Build direction is defined by the purchaser that knows the geometric model; this is one limit of the e-commerce of R.P.).

In e-commerce of R.P., prebuild cost cannot be estimated and it must be taken as a fixed value assigned to each unit produced.

Postprocessing costs comprise the works necessary to: remove supports; finish the surface model to obtain the desired surface quality, including extra operations such as polishing; smooth down surface The driving factor of the above cost components is the ratio between the build time required to produce it (t f ) and the total productive time (T).

Prebuild, build and postprocessing costs can be directly assigned to a specific prototype and they are all grouped under the direct costs category. Indirect costs, on the contrary, include administration, secretarial work, cleaning, utilities, indirect materials and other costs that arise independently from production levels and cannot be assigned directly to the products. Indirect costs for a single prototype can be allocated in different ways, which are specific to each company. Very often, indirect costs are evaluated as the product of the ratio t f /T and a cost factor (U comp ) that characterizes company management.

The total cost of the prototype is the sum of four main components:

C TOT = C pre + C build + C post +C indirect (1)
Some variable costs components are function of the prototype orientation (d); some others are function of manufacturing time, while others only depend on geometric parameters (volume, external surface area).

C TOT = C pre +[C mat + C sup (d)+C cons (t f )+C fixed (t f /T)]+[C' sup (d)+C fin ]+ C indirect (t f /T) (2)
where:

C pre = prebuild cost; Build cost estimation requires that both the prototype orientation and build time are known. Whereas prototype orientation is an assigned factor, build time must be estimated, so that the accuracy of cost evaluation depends on the accuracy of build time estimation. For this reason, many studies [START_REF] Cheng | Multi-objective optimization of part building orientation in stereolithography[END_REF][START_REF] Frank | Expert system-based selection of the preferred direction of build for rapid prototyping processes[END_REF][START_REF] Alexander | Part orientation and build cost determination in layered manufacturing[END_REF][START_REF] Majhi | Multi-criteria geometric optimization problems in layered manufacturing[END_REF][START_REF] Hong-Seok | Determination of the optimal build direction for different rapid prototyping processes using multi-criterion decision making[END_REF] have been carried out regarding build time estimation problems.

The costs of material and surface finish are independent from prototyping direction and build time.

These cost components can be estimated as a linear combination of geometric parameters that are characteristic of the object. Material cost (C mat ) is a linear function of the prototype volume (V mod ), which is multiplied by the unitary cost of the material (U mat ):

C mat = V mod *U mat .
(3)

The cost to finish the surface of the prototype (C fin ) can be calculated as the product of the size of surface area (S mod ) and the unitary cost of working (U fin ):

C fin = S mod *U fin .
(4)

Cost components dependent on prototype orientation

In rapid prototyping technologies, the prototype orientation can be selected without any manufacturing constraint. Nevertheless, it is important to bear in mind that prototype orientation affects some important factors, such as surface finish, build time, support structure, shrinkage and curling, some of which concern prototype quality. Prototype orientation can be chosen to minimize build costs and maximize surface quality. The surface quality of a rapid prototype depends on the staircase effect on inclined and curved surfaces. Surfaces, whose triangular facets are parallel or orthogonal to the build direction, have the best finishing. Moreover, the orientation of a prototype affects the space occupied in the prototyping machine. Occupation must be estimated to evaluate the height, which fixes the number of slices, and the space in the horizontal plane which, in turn, affects the number and dimensions of , which is the minimal rectangular-base straight prism that contains the object. Besides, the amount of supports material, necessary to manufacture a rapid prototype, depends on the object orientation. Indicating the supports material volume with V sup (d) and relative unit cost with U ms , the cost of the supports material is:

C sup =V sup (d)*U ms (5)
Except for selective laser sintering, which does not require supports, support material cost affects all typical layer manufacturing technologies. The material of the supports is specific for each technology: e.g., whereas in stereolithography it is the same used to construct the model, in FDM the supports are done with a different material, which is soluble in water.

Once the prototype has been built , the supports must be removed. The cost for removing supports depends on the size of the surface area of the object (S sup (d)) required for the supports:

C' sup =S sup (d)*U rs (6)
where Urs is the unitary cost of working to remove supports from the model.

Although build direction largely affects costs, it is important to notice that in e-commerce of R.P., the build direction is typically chosen by the purchaser, who knows the object geometry and the surface quality targets.

Cost components dependent on build-time

Build time t f depends on the characteristics of the layer manufacturing process, as well as on the geometry, the dimensions and the orientation of the prototype [START_REF] Kechagias | Process build time estimator algorithm for lamined object manufacturing[END_REF]. It is difficult to accurately calculate build time without taking into account all process parameters which affect machine movements, including acceleration and deceleration of the manufacturing tool (nozzle or laser beam) [START_REF] Alexander | Part orientation and build cost determination in layered manufacturing[END_REF]. Build time can be determined as the sum of the time required to form each layer. Layer forming time depends on the tool movements required to form the layer contours and the tool path loops necessary to form the internal part of the layer. The time required to execute a single tool path depends both on the tool path length and on the repositioning number of the forming tool (figure 1). The time which is necessary to form a single layer also comprises: the time for cooling or for solidification of deposited material; the non-productive time for prototype vertical movement and other auxiliary unproductive activities such as nozzle cleaning.

Figure 1: Layer filling path

There exists no general function to estimate build time but specific formulas can be defined, each of them adapted for a specific machine that uses a specific technology. Some methods for build time estimation are presented in literature [START_REF] Jiangand | TeleRP-an Internetweb-based solution for remote rapid prototyping service and maintenance[END_REF][START_REF] Alexander | Part orientation and build cost determination in layered manufacturing[END_REF][START_REF] Giannatsis | A study of the build-time estimation problem for Stereolithography systems[END_REF][START_REF] Luo | The development of Web-based E-business System for Rapid Prototyping Manufacturing[END_REF][START_REF] Hong-Seok | Determination of the optimal build direction for different rapid prototyping processes using multi-criterion decision making[END_REF][START_REF] Zhao | Determination of Optimal Build Orientation Based on Satisfactory Degree Theory for RPT[END_REF]. These methods calculate the total build time by computing the geometry through a detailed analysis of the activities associated to the prototyping process. These methods can only be used if combined with the slicing software and the tool path generator, which are dedicated to a specific layer manufacturing technology. The difficulty of generalization from specific technologies makes this approach unsuitable for e-commerce, where the geometric model analysis is carried out remotely by general purpose software. In order to evaluate build time for e-commerce, it is more useful to use a parametric-based approach which estimates build time as a function of some parameters deduced from geometric model.

The proposed method for build time estimation

STL is the standard universally accepted to describe the geometric model in commercial systems for rapid prototyping. This standard defines the boundary of the geometric model by means of a discrete set of adjacent, planar triangular facets. The parametric model used to estimate build time requires that some significant parameters should be identified from the geometric model. These parameters are defined by taking into account the STL standard. Parameters must be independent from each other so that any build time components can be evaluated separately. E-commerce applications impose that these parameters should also be independent from the specific technology used to produce the prototype. The same method can be used to estimate costs for all the rapid prototyping technologies available in a company by modifying the values of the coefficients to be multiplied by the relative parameters. [START_REF] Cheng | Multi-objective optimization of part building orientation in stereolithography[END_REF][START_REF] Frank | Expert system-based selection of the preferred direction of build for rapid prototyping processes[END_REF]Fadel, 1995, aiming t w = delay time between subsequent layers' deposition;

V mat = volume of material to be formed.

Formula ( 8) is easy to implement but it does not take into account the complexity of the geometric model associated to the presence of holes and to the complexity of layers' contours; these factors affect unproductive times for movements and the repositioning of the manufacturing tool. For this reason, in this work formula (8) has been improved by adding two new components of build time, both defined in parametric form. The build time components considered are associated to the layers' contours' depositions and to the repositioning of the tool. In any typical commercial rapid prototyping technology the deposition time of layers' contours is proportional to the sum of contour length for each layer. For a geometric model described by triangular facets, the total length of layers' contour is:

L S d p T n j j j = • = 1 2 ) ) ( 1 ( n (9)
where:

n j = unit normal vector at triangular facet j-th;

n T = number of the triangular facets.

S j = area of j-th triangular facet;

d = building model direction.
The term

j j S d • ) ) ( 1 ( 2 n
is the maximal value of the area of the j-th triangle projected in a vertical plane (figure 2). Formula (9) can be easily implemented; p parameter is calculated once the geometric model is given, and both build direction (d) and layer thickness (L) assigned. Time for tool repositioning is a function of the number of repositioning necessary to hatch the internal part of layers. The number of tool repositioning depends on prototype orientation and on the hatching vector (K) in the x-y plane (figure 3). In order to estimate the number of tool repositioning, the following formula is introduced: (10) where: H = hatch distance between two subsequent segments of tool path (figure 3); n j = unit normal vector at j th triangular facet; n j,xy = unit normal vector at j th triangular facet projected on stratification plane; S j = area of j th triangular facet; 2 = hatching vector; Many commercial R.P. technologies layer material by alternating hatching vectors which are, in consecutive stratification layers, orthogonal. In these cases, the tool repositioning number can be evaluated as the average value of n repos calculated for two orthogonal hatching directions:

F o r P e e r R e v i e w O n l y ( ) = • • = T n j xy j j j repos S d L H n 1 , 2 ) ) ( 1 ( 1 n 2 n
( ) = • + • • = T n j xy j xy j j j repos S d L H n 1 , 90 , 0 2 ) ) ( 1 ( 2 1 n 2 n 2 n (11)
Both formulas ( 10) and ( 11) can be calculated once the geometric model and the technological parameters (L, and H) are known.

Under the hypothesis that new build time components are linear functions of the total contour length and of the number of tool repositionings, the build time is:

p n t L b t W p L V t repos w z s f + + + = (12)
where: s t = solidifying rate or material deposition rate in the build time; The approach used to estimate build time for material stratification can also be used to calculate supports' build time. Some prototypes could require supports that are non-connected regions; in these cases, a more appropriate value for the total height of supports, b z,sup must be deduced according to the rule in figure 4.

+ + + + + + + = (13)
where the subscript mat refers to prototype and subscript sup refers to supports.

Experimental tests

The proposed method has been verified in a set of specifically-designed experiments. For these experiments, an R.P. machine with FDM technology (Fused Deposition Modelling) has been employed; the related technical specifications are quoted in table 1. Real build times have been measured for each model analysed. Geometric parameters are computed by processing the geometric model with the original software developed by the authors which implements the proposed model. The first set of experiments has been conducted to examine the dependence of build time on tool repositioning number. For this purpose, the geometric models considered are characterized by equal values for the total layer contour length, volume and height. A set of geometric models satisfying the previously mentioned conditions has been defined by using a prismatic object which has been rotated, as regards the building direction, in some assigned positions (Figure 5a). As a consequence of the prismatic model rotation, a different tool repositioning number is required. In figure 5b the build time for each of the 15 prismatic objects, defined as formerly, is quoted as a function of the tool repositioning number evaluated by using formula (11). The results of the experimental tests validate the assumed hypothesis that build time is a linear function of the tool repositioning number: the coefficient of determination of the linear fitting regression is R 2 = 0.9933 and the straight line slope is 2 mat = 0.00318. In a second set of experiments, in order to investigate the dependence of build time on the total length of layers' contour, the volume and height have been fixed. For this purpose, 6 rectangular-based prismatic objects, with different ratios for the base sides, have been taken into consideration. Build times are quoted in figure 6 (trend A) as a function of the total contour length, which has been calculated using formula (9).

The tool repositioning number and the total length of the contour affect two independent build time components, although they are correlated. For an assigned hatching vector the tool repositioning number increases as the total length of the contour increases. Build time (figure 6 trend A) is affected by two components: the number of tool repositionings and the total length of layer contours. In order to identify the contribution of p to build time, the component that deals with tool repositioning has been subtracted from the measured build time. In figure 6 (trend B) the build time component which is relevant to contour forming is quoted as a function of the total contour length p. The hypothesis that build time is a linear function of the total contour length (calculated as in formula ( 9)) is substantially verified: the coefficient of determination of the fitted regression is R 2 =0.9946 and the straight line slope is 3 mat = 0.0009. The approach followed to estimate build time coefficients 3 mat and 2 mat has been used to evaluate the analogous coefficients for the support build time formula (3 sup and 2 sup ).

In order to estimate the remaining coefficients in formula ( 13 In order to validate the build-time model proposed, this has been applied to calculate the build time of six test cases taken from literature (figure 7) (Huang et al., 2003;[START_REF] Kechagias | Process build time estimator algorithm for lamined object manufacturing[END_REF][START_REF] Hong-Seok | Determination of the optimal build direction for different rapid prototyping processes using multi-criterion decision making[END_REF]. These cases present some critical features that contribute to the difficulty of predicting build time (small thickness and holes). The estimated build times are compared to the actual process: results and errors are quoted in table 3. Although literature data refer to manufacturing processes which are different from FDM, the comparison of performances is however possible because the time driving factors are substantially the same and they are common to the most diffused R.P. technologies. The average of the absolute value of error, in the test cases (table 3), is 5.65 %, and the maximum error is 15.13%. The results obtained show the good performance of the proposed method especially when compared to the results presented in literature (Huang et al., 2003;[START_REF] Kechagias | Process build time estimator algorithm for lamined object manufacturing[END_REF][START_REF] Hong-Seok | Determination of the optimal build direction for different rapid prototyping processes using multi-criterion decision making[END_REF]. Furthermore, it is important to notice that build time estimations reported in literature should be more accurate intrinsically because they are dedicated to specific R.P. technologies and are designed to perform a detailed analysis of the movements of the forming tool.

Conclusions

An accurate prediction of build time is essential in order to calculate the precise cost of a layer manufacturing object. The methods for build time prediction can be dedicated to specific technologies or based on a parametric approach. The first approach requires that a lot of information, dealing with the kinematics and dynamical performances of the machine, should be known; for this reason, this approach cannot be used to remotely compute the geometric model, that is to say, following a technology independent approach. Parametric models are of general purpose and relatively simple to implement. Thus, they are suitable for e-commerce of R.P. The parametric methods described in literature only provide a component of the total build time: they do not take into account the complexity of the geometric model, which affects unproductive times for movements and the repositioning of deposition apparatus of all R.P. technologies. In this paper, a new parametric model is proposed, which satisfies the requirement of simplicity (necessary for implementation in the WEB for e-commerce) and provides a quite accurate estimation of build time (even in critical cases and when supports are required). Despite the fact that some improvement have been introduced, the new parametric model cannot perform the detailed analysis of activities required to manufacture an object. For this reason, some build time components, such as the time necessary to repose the forming tool after each tool path, are neglected. Other build time components cannot be strictly evaluated but must be assumed as medium values: for example, the speed of the deposition tool is, implicitly, assumed as constant. The proposed method requires that some process parameters should be known (L, H, W and ). Therefore, the procedure for e-commerce requires that necessary manufacturing parameters should be sent to the remote software.

The new method has been applied to estimate the build time of some test cases which are characterised by some critical features that contribute to the difficulty in build time prediction (small thickness and holes). The results obtained show good performances of the proposed parametric model.

  , etc. Postprocessing costs' evaluation is performed (or made) by multiplying the time required for the related activities by their unitary cost. This time can be assumed as a function of geometric model parameters such as the size of the external surface area (S).Build costs' components can be assigned to the prototype either as a function of addition of object and support volume (V mod + V sup ), or as a function of the build time. The cost components which are functions of the object volume are: -Material's and support material's costs which also include expenses caused by scrap and spoilage; -auxiliary materials.The cost components which are function of the build time are:-the labor component; -machine depreciation; -power consumption; -nonproduction labor and maintenance.

  d)= support material's cost; C cons (t f )= power consumption and auxiliary materials; C fixed (t f /T) = other fixed costs; C' sup (d)= cost of removing support material; C fin = surface finishing cost; C indirect (t f /T)= indirect cost.

  can be built in the meantime . Practically speaking, the occupation of space in a prototyping machine is estimated as the dimensions of the bounding box of the geometric model (b x (d), b y (d), b z (d))

Figure 2 :

 2 Figure 2: Vertical projection of the j th triangle Figure 3: Hatch distance and tool repositioning number

wt

  = delay time between each layer's deposition of material; = proportionality coefficient for material tip repositionings number; = proportionality coefficient for material layers' perimeter; W = material line segments width (figure1).The first term of formula (8) has been redefined in (12) by taking into account the time required to

Figure 4 :

 4 Figure 4: Rule for the evaluation of supports' total height (b z,sup ).

Figure 5 :

 5 Figure 5: Build time as a function of estimated repositioning number

Figure 6 :

 6 Figure 6: Influence of the total contour length on build time of prismatic prototypes

Figure 7 :

 7 Figure 7: Test cases used to validate the proposed method

Figure 4 :

 4 Figure 1: Layer filling path

Figure 5 :

 5 Figure 5: Build time as a function of estimated repositioning number

Figure

  Figure 7: Test cases used to validate the proposed method

  to search for the minimal cost build direction, propose a simple parametric approach which assumes build time to be proportional to the slices' number (b z /L).[START_REF] Xu | Consideration of optimal orientation for different rapid prototyping[END_REF], proposed a more sophisticated parametric approach which considers build time as the sum of layers' deposition time and total delay time between subsequent

	t f = (V mat /L)•t s +(b z /L)•t w	(8)
	where:
	b z = prototype height;
	L = layer thickness;
	t s = solidifying rate or material's deposition rate in the build time;
	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	layers' deposition:

  The total build time can be estimated as follows:

	t	f	L mat V	p	mat	W mat	t	s	,	mat	b z	, L mat	t	w	,	mat	mat	n repos	mat	mat	p	mat
		sup V L	sup p	sup W	t	s	,	sup				b z	sup L ,	t	w	,	sup				sup	n repos	sup	sup	sup p

Table 1 : Principal technical specifications of the used layer manufacturing machine.

 1

  ). The unknown coefficients have been obtained by solving the overdetermined system defined by the equation (13) applied to the 20 experiments, by means of the square root method. The obtained values of the eight coefficients are quoted in table 2.

								) ( mat s t , , mat w t , , sup , s t	, and sup , w t	) another set
	of experiments have been conducted. Twenty different geometric models have been taken into
	consideration and, for each of them, the parameters in equation (13) have been evaluated ( mat V , mat z b , ,
	n	repos	mat	, mat p , sup V , sup , z b ,	n	repos	sup	, sup

p

Table 2 : Values of the eight coefficients of the mathematical model for build time estimation.

 2

Table 3 : Results obtained for the six test cases selected

 3

uk International Journal of Production Research

	Ref\erence Ratios of sides
	1	16
	2	9.76
	3	6.25
	4	4
	5 6	2.44 F o 1
			r
		Figure 6:	P
			e e r
			R e v i e w
			O n
			l y

manuscriptcentral.com/tprs Email: ijpr@lboro.ac.

Influence of the total contour length on build time of prismatic prototypes Coefficient

		s t ,	mat	w t ,	mat	mat	mat	t	s	,	sup	t	w	,	sup	sup	sup
	Value	0,000249	0,3116	0,001318	0,0009	0,000455	0,2441	0,0009	0,0004

Table 2 : Values of the eight coefficients of the mathematical model for build time estimation. Build time [min] * Error [%]

 2

	Name Test case n°1	Dimension SST 222	Proposed model 192,8	Proposed model -15,13	In literature 11,4 (Huang et al., 2003) **
	Test case n°2	315	308,07	-2,25
	Test case n°3	334	293,3	-13,88
	Test case n°4 Test case n°5 Test case n°6	548 98 410	557,4 108,25 413,96	1,69 9,47 0,96	9.41 (Kechagias et al., 2004) *** 13.33 (Kechagias et al., 2004) ** 2.56 (Kechagias et al., 2004) **

* FDM manufacturing process. ** Manufacturing process not specified. *** Laminated object manufacturing process.

Table 3 : Results obtained for the six test cases selected

 3

http://mc.manuscriptcentral.com/tprs Email: ijpr@lboro.ac.ukInternational Journal of Production Research