Roberta Russo
email: russor@ceinge.unina.it

Mario Capasso
email: capasso@ceinge.unina.it

Paolo Paolucci
email: paolo.paolucci@unimore.it

Achille Iolascon
email: iolascon@ceinge.unina.it

MD Iolascon Achille

Pediatric pharmacogenetic and pharmacogenomic studies: the current state and future perspectives Part of TEDDY Supplement

Keywords: pharmacogenetics, pharmacogenomics, GWAS, transcriptomics, metabonomics, proteomics

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Introduction

After more than 50 years of pharmacogenetics (PGt) and pharmacogenomics (PGx) research, we have learned that genetic differences between individuals can explain some of the variability observed in the pharmacokinetics, efficacy and toxicity of some drugs. Indeed, the magnitude of variation in the pharmacokinetics of a drug caused by genetic variants often far exceeds the range considered as acceptable when comparing the bioavailability of two different drug formulations [START_REF] Kirchheiner | Pharmacogenetics of antidepressants and antipsychotics: the contribution of allelic variations to the phenotype of drug response[END_REF]. Furthermore, there is evidence that consideration of PGt when prescribing drugs could significantly improve the safety and efficacy of therapy [START_REF] Stanulla | Thiopurine methyltransferase (TPMT) genotype and early treatment response to mercaptopurine in childhood acute lymphoblastic leukemia[END_REF][START_REF] Phillips | Potential role of pharmacogenomics in reducing adverse drug reactions: a systematic review[END_REF].

The term pharmacogenomics refers to the investigation of variations of DNA and RNA characteristics as related to drug response, while pharmacogenetics is a subset of PGx and defined as the influence of variations in DNA sequence on drug response [START_REF] Krekels | Pharmacogenetics and paediatric drug development: issues and consequences to labelling and dosing recommendations[END_REF]. An increasing number of examples describing differences in drug response as a result of genetic polymorphisms and gene expression have been published, but most of these reports include only adult individuals. Few studies deal with PGx of children and highlight the most important difference between children and adults. This review seeks to describe the main biological differences in drug metabolizing capabilities between children and adults, to give an overview on the rapidly evolving research fields of both PGt and PGx, and also to illustrate what impact these studies can have on the development of personalized medicine in pediatric patients.

Response to the drugs: what is the difference between children and adults?

Human development, from the prenatal period through to adolescence, is a dynamic process.

Newborns and infants rapidly undergo simultaneous stages of organ growth and demonstrate large variability in drug response and metabolizing capabilities [START_REF] Leeder | Developmental and pediatric pharmacogenomics[END_REF]. Drugs may have different actions on individuals, not only within the adult population but also in children, because of genetic polymorphisms. There are several demonstrations of acute adverse effects (ADR) of drugs, even fatal, due to the presence of genetic variations in drug metabolism that alters the levels of active drugs and metabolites. One frequently cited example is the morphine poisoning in a breastfed neonate of a codeine-prescribed mother which has been afterward classified as an ultra-rapid metaboliser for CYP2D6 polymorphism: since the frequency of CYP2D6 ultra-rapid metaboliser genotypes ranges from 1% in Finland and Denmark to 10% in Greece and Portugal, and 29% in Ethiopia, this polymorphism is clinically relevant [START_REF] Koren | Pharmacogenetics of morphine poisoning in a breastfed neonate of codeine-prescribed mother[END_REF]. CYP2D6 polymorphisms are clinically significant also for atomoxetine treatment, which has been approved in 2002 for the treatment of attention deficit hyperactivity disorder (ADHD) in children, adolescents and adults, in addition to methylphenidate (MPH), the most commonly prescribed psycho-stimulant in ADHD affected children, as described later in this review. CYP2D6 genotyping may be beneficial in preventing overdosing and subsequent ADRs or early cessation. Moreover, recently it has been demonstrated that recognizing intermediate metabolizers is clinically important, because these children receive tailored therapeutic advice based on their genotype [START_REF] Ter Laak | Recognition of impaired atomoxetine metabolism because of low CYP2D6 activity[END_REF].

While it is known the effect of genetic variations in drug metabolism, much less attention has been given to developmental pharmacogenomics. Some genes are expressed much more in early life than in adults. One of the best example of gene switching is represented by CYP3 gene family: CYP3A7 expression level is detectable as early as 50 to 60 days gestation in fetal liver, and its expression begins to decline after the first postnatal week, reaching non-detectable levels in most individuals by 1 year of age. Simultaneously, hepatic CYP3A4/ 3A5 expression begins to dramatically increase at about 1 week of age, reaching 30% of adult levels by 1 month. So, total CYP3A protein expression over the entire developmental period remains constant. However, because CYP3A7 and CYP3A4 exhibit differences in substrate specificity and catalytic efficacy, some differences in metabolic capacity during development are observed [START_REF] Hines | The ontogeny of human drug-metabolizing enzymes: phase I oxidative enzymes[END_REF]. If is true that many genes are expressed much more in early life than in adults, is also true that many drug metabolizing enzymes (DME) are less developed in children than in adults. An example is the UDP glucuronosyltransferase (UGT), which is a liver enzyme essential for body's elimination of xenobiotic substances as well as endogenous substances including endogenous toxins and bilirubin.

Only 1% of the normal adult level of hepatic bilirubin-UGT activity is present at birth [START_REF] Odell | Physiologic" hyperbilirubinemia in the neonatal period[END_REF]. Postnatal maturation of bilirubin-UGT is birth related, and increases rapidly to adult levels by 14 weeks, regardless of the gestational age at birth [START_REF] Kawade | The prenatal and postnatal development of UDPglucuronyltransferase activity towards bilirubin and the effect of premature birth on this activity in the human liver[END_REF], maybe in relation to the methylation or acetylation status of this locus.

The application of pharmacogenetic and pharmacogenomic approaches to the treatment of pediatric diseases requires an appreciation of these dynamic changes in gene expression. It is assumed that drug effects differ in children but in reality this perception often arises because the drugs have not been adequately studied in pediatric populations of different ages and with different diseases [START_REF] Stephenson | How children's response to drugs differ from adults[END_REF]. Moreover, part of the reason for the perception that pharmacodynamics are different in children is because the pharmacokinetics may be different at different ages. However, advances in this field have been hampered by several problems. Most reports on the developmental expression of DMEs have limited their studies to short time frames of development, many have depended on a small number of tissue samples, mostly confined to the hepatic expression during fetal development. Furtherome, there is also a paucity of information regarding changes during early childhood or at puberty [START_REF] Hines | The ontogeny of human drug-metabolizing enzymes: phase I oxidative enzymes[END_REF]. While the pharmacogenetics as the study or clinical testing of genetic variation that gives rise to differing response to drugs might be considered similar in adults and children, the 'pharmacogenomics' as the study of how interacting systems of genes determine drug response [START_REF] Klein | Integrating genotype and phenotype information: an overview of the PharmGKB project[END_REF] is particularly appealing in a pediatric and developmental context because this definition captures the essence of the developmental processes that characterize maturation from the time of birth through to adulthood [START_REF] Leeder | Developmental and pediatric pharmacogenomics[END_REF].

Methods for Pharmacogenetics and Pharmacogenomics Studies

In this section, we consider recent genetic and genomic strategies for identifying genetic and genomics variations that influence the response to particular treatments or therapies. We describe common methodological approaches that can be applied to pharmacogenetics and pharmacogenomics studies for both children and adults.

Case-Control Association Studies: From Candidate Genes to Genome-wide Screen

One of the most common study designs used to assess pharmacogenetic effects is that of the case-control association study. In the context of pharmacogenetics, the usual approach is to examine the active treatment arm of a clinical trial and divide subjects in the treatment arm into those with a positive response to the drug and those with a negative or no response. These two groups then constitute cases and controls who are genotyped for a particular candidate gene thought to be related to the treatment phenotype.

The problem with such studies is that, though they are easy to perform, they are fraught with a host of potential biases or difficulties in interpretation. Four design issues must be considered in any genetic case-control association study.

1. The major problem in case control studies is ensuring a good match between the genetic background of cases and controls, so that any genetic difference between them is related to the disease under study and not to biased sampling. Clearly, cases and controls should be from similar ethnic groups. More subtle genetic differences can be guarded against by collecting controls from the same geographical area as cases, or by collecting information such as the birth place of grandparents to check a similar distribution between cases and controls. Matching of cases and controls for ethnicity or use of multiple unlinked markers to assess for the presence of this confounding variable are useful techniques to detect or eliminate the potential bias of population stratification [START_REF] Pritchard | Use of unlinked genetic markers to detect population stratification in association studies[END_REF].

2. The key determinant of quality in an association study is sample size. With the remote chance of finding common genes with large effects, studies must be powered to detect variants that are common -but have low relative risk -or rarer -but with higher relative risk -which means samples sizes of thousands. Rare variants with low relative risks are largely beyond the reach of genetic epidemiology because of the massive sample size that would be needed [START_REF] Campbell | Estimating sample sizes for binary, ordered categorical, and continuous outcomes in two group comparisons[END_REF].

3. An additional criterion for evaluation of the quality of the case-control study is assessment of Hardy-Weinberg equilibrium in the markers studied within the control group. Hardy-Weinberg equilibrium implies that the genotype frequencies can be determined directly from the allele frequencies and provides a check to ensure that genotyping errors, mutation, or population stratification do not explain observed results.

4. The final key to these studies is replication, which can be performed with a second case-control association study or a family-based study. Replication performed with family-based designs can be used in conjunction with a case-control association study.

Careful attention to these four issues that we have highlighted would go a long way to improving the quality of existing studies and preventing false positive associations. However, we would like also to notice that other issues can be addressed in any case-control association study such as: selection of candidate gene polymorphism (bioinformatic tools), observation bias (phenotyping and genotyping methods), linkage disequilibrium, allele or genotyped analysis, multivariate analysis, gene-gene and gene-environment interaction, correction for multiple comparisons.

The availability of very high throughput DNA analysis technologies (like single nucleotide polymorphism (SNP) array) and the development of databases (HapMap project) harboring information about the genomic positions of DNA sequence variations have provided geneticists with efficient and powerful tools for identifying inherited DNA sequence variations that contribute to phenotypic expression and variability. In fact, it is now possible to test literally hundreds of thousands, if not a million or so, polymorphic markers for association with a particular phenotype in a single study. This kind of study focus on as many variations as possible in the absence of such a priori knowledge is named genome-wide association study (GWAS).

Each study can look at hundreds or thousands of SNPs at the same time. Researchers use data from this type of study to pinpoint genes that may contribute to a person's risk of developing a certain disease. Because GWASs examine SNPs across the genome, they represent a promising way to study complex, common diseases in which many genetic variations contribute to a person's risk. This approach has already identified SNPs related to several complex conditions including diabetes, heart abnormalities, Parkinson disease, and Crohn disease. A few of GWAS have been performed to discovery SNPs involved in drug therapy. Results of the 12 pharmacogenomics GWASs published so far are summarized in a recent review by Crowley et al. [START_REF] Crowley | Pharmacogenomic genome-wide association studies: lessons learned thus far[END_REF], as well as in the NHGRI GWAS catalog [16]. Six GWASs evaluated the association of genetic variation with drug efficacy, five evaluated adverse effects, and one examined a dose-response relationship (warfarin) [START_REF]HuGE Navigator[END_REF].

GWASs have been recognized as an important approach for uncovering polymorphisms accounting for individual differences in drug efficacy and drug safety [START_REF] Gurwitz | Genome-wide association studies: powerful tools for improving drug safety and efficacy[END_REF]. A vast reservoir of observational studies and randomized clinical trials (RCTs) -completed, ongoing or plannedprovides a largely untapped resource for pharmacogenomic studies of drug safety and efficacy. In particular, RCTs allow for precise measurement of drug exposure and consistent ascertainment of phenotype; randomization produces unbiased treatment assignments and helps balance unmeasured confounding factors [START_REF] Maitland | Interpreting P values in pharmacogenetic studies: a call for process and perspective[END_REF]. Performing GWASs within clinical trials, in which more potentially interacting variables can be identified, measured and controlled, improves efficiency. So far, only two GWASs have been conducted in drug clinical trials; each of these studies provides relevant insights for future research. Given their efficiency and potential for leading to useful clinical medicine and public health applications, it seems surprising that so few GWASs have been done in the field of pharmacogenomics, especially within clinical trials. The incentives for conducting such studies deserve closer evaluation, especially for the studies of childhood-disease treatment response.

Pharmacogenetics studies in childhood conditions

Genetic diversity is a consequence of differences in DNA sequences. There are multiple types of genetic variation including SNPs, copy-number variations (CNVs), variable number of tandem repeats (VNTR), microsatellite polymorphisms, and cytogenetic rearrangements. There are a lot of scientific evidences that show how genetic variation can determine impaired response to drugs (Table 1). Here we present an overview of pharmacogenetic studies of the most common childhood conditions, such as attention-deficit/hyperactivity disorder (ADHD), growth hormone deficiency (GHD), Acute lymphoblastic leukemia (ALL) and asthma.

Attention-deficit/hyperactivity disorder

Attention-deficit/hyperactivity disorder (ADHD) is a multifactorial disorder characterized by physical hyperactivity and behavioural disinhibition that typically emerges during childhood or adolescence and often persists into adulthood. It was estimated approximately 70% of response rate to methylphenidate (MPH), the most commonly prescribed psycho-stimulant, in ADHD affected children [START_REF] Elia | Methylphenidate and dextroamphetamine treatments of hyperactivity: are there true nonresponders?[END_REF][START_REF] Spencer | Pharmacotherapy of attention-deficit/hyperactivity disorder across the lifespan[END_REF]. Pharmacogenetic studies suggest that inter-individual differences in stimulantresponse may be related to genetic influences [START_REF] Gilbert | Dopamine transporter genotype influences the physiological response to medication in ADHD[END_REF][START_REF] Winsberg | Association of the dopamine transporter gene (DAT1) with poor methylphenidate response[END_REF][START_REF] Roman | Dopamine transporter gene and response to methylphenidate in attention-deficit/hyperactivity disorder[END_REF][START_REF] Purper-Ouakil | Pharmacogenetics of Methylphenidate Response in Attention Deficit/Hyperactivity Disorder: Association With the Dopamine Transporter Gene (SLC6A3)[END_REF][START_REF] Kereszturi | Catechol-O-Methyltransferase Val158Met Polymorphism Is Associated With Methylphenidate Response in ADHD Children[END_REF][START_REF] Tl Da Silva | Adrenergic a2A receptor gene and response to methylphenidate in attention-deficit/hyperactivity disorder-predominantly inattentive type[END_REF][START_REF] Kirley | Association of the 480bp DAT1 allele with methylphenidate response in a sample of irish children with ADHD[END_REF][START_REF] Langley | No support for association between the dopamine transporter (DAT 1) gene and ADHD[END_REF]. The search for candidate genes associated with ADHD has been largely driven by the understanding that medications for the disorder have drug targets in the catecholamine system. Genes associated with increased risk for ADHD are the dopamine transporter (DAT1) [START_REF] Purper-Ouakil | Pharmacogenetics of Methylphenidate Response in Attention Deficit/Hyperactivity Disorder: Association With the Dopamine Transporter Gene (SLC6A3)[END_REF], the dopamine receptors (DRD4 and DRD5) [START_REF] Van Tol | Multiple dopamine D4 receptor variants in the human population[END_REF], serotonin transporter (5-HTT), and synaptosomal-associated protein (SNAP-25) [START_REF] Husain | Clinical pharmacogenetics in pediatric patients[END_REF][START_REF] Faraone | Molecular genetics of attention-deficit/hyperactivity disorder[END_REF][START_REF] Mcgough | Pharmacogenetics of methylphenidate response in preschoolers with ADHD[END_REF]. Other genes of potential interest in pharmacogenetic studies of ADHD include catehol-O-methyltransferase (COMT) [START_REF] Kereszturi | Catechol-O-Methyltransferase Val158Met Polymorphism Is Associated With Methylphenidate Response in ADHD Children[END_REF], the adrenergic α2-receptor (ADRA2A and ADRA1A) [START_REF] Tl Da Silva | Adrenergic a2A receptor gene and response to methylphenidate in attention-deficit/hyperactivity disorder-predominantly inattentive type[END_REF][START_REF] Polanczyk | Association of the adrenergic alpha2A receptor gene with methylphenidate improvement of inattentive symptoms in children and adolescents with attention-deficit/hyperactivity disorder[END_REF][START_REF] Elia | Candidate gene analysis in an on-going genome-wide association study of attention-deficit hyperactivity disorder: suggestive association signals in ADRA1A[END_REF] (Table 1).

However, some pharmacogenetic studies show conflicting results. For example, in some of them individuals homozygous for the DAT1 10-repeat 480 bp-VNTR showed poorer outcome [START_REF] Winsberg | Association of the dopamine transporter gene (DAT1) with poor methylphenidate response[END_REF][START_REF] Roman | Dopamine transporter gene and response to methylphenidate in attention-deficit/hyperactivity disorder[END_REF], whereas others report improved clinical outcome [START_REF] Kirley | Association of the 480bp DAT1 allele with methylphenidate response in a sample of irish children with ADHD[END_REF] or no effect [START_REF] Langley | No support for association between the dopamine transporter (DAT 1) gene and ADHD[END_REF] on MPH response.

Growth hormone deficiency

GH replacement is standard therapy for children with short stature due to GH deficiency (GHD). The usual treatment is carried out with fixed doses of human recombinant GH (hGH) adjusted for body weight or surface [START_REF] Jorge | Growth Hormone (GH) Pharmacogenetics: Influence of GH Receptor Exon 3 Retention or Deletion on First-Year Growth Response and Final Height in Patients with Severe GH Deficiency[END_REF]. Two of the most common isoforms of GHR in humans are generated by retention (full-length GHR, GHRfl) or exclusion of exon 3 (exon 3-deleted GHR, GHRd3) [START_REF] Pantel | Speciesspecific alternative splice mimicry at the growth hormone receptor locus revealed by the lineage of retroelements during primate evolution[END_REF]. These isoforms present a widespread distribution in humans, with the frequency of each allele ranging from 68-75% for GHRfl and 25-32% for GHRd3 [START_REF] Pantel | Speciesspecific alternative splice mimicry at the growth hormone receptor locus revealed by the lineage of retroelements during primate evolution[END_REF][START_REF] Santos | A common polymorphism of the growth hormone receptor is associated with increased responsiveness to growth hormone[END_REF]. In 2004, in a study conducted on two cohorts of 76 and 96 children of European descent with idiopathic short stature or who were born small for gestational age, it has been demonstrated that, patients with at least one GHRd3 allele presented 1.7 to 2 times more growth acceleration induced by hGH therapy than patients homozygous for the full-length isoform [START_REF] Santos | A common polymorphism of the growth hormone receptor is associated with increased responsiveness to growth hormone[END_REF]. These observations have been confirmed in some but not all studies, so it remains unclear at this time as to whether the d3-GHR isoforms actually conveys increased GH responsiveness. It will require a large-scale, prospective, wellcontrolled study, with appropriate assessment of proteomic and genomic markers of GH action, as well as auxological data, to settle this issue. Nevertheless, this study served to open the door to the potential importance of genomic and proteomic biomarkers as indicators and predictors of GH responsiveness [START_REF] Rosenfeld | Pharmacogenomics and pharmacoproteomics in the evaluation and management of short stature[END_REF]. Another study, conducted by Jorge and colleagues, is a good example of a direct relation between genetic variability and adult height after long-term treatment with hGH, since there are only few data in literature about long-term effects of drugs. They demonstrated that patients carrying at least one GHRd3 allele had a significantly better growth velocity in the first year of hGH replacement and achieved a taller adult height when compared with patients homozygous for GHRfl alleles [START_REF] Jorge | Growth Hormone (GH) Pharmacogenetics: Influence of GH Receptor Exon 3 Retention or Deletion on First-Year Growth Response and Final Height in Patients with Severe GH Deficiency[END_REF].

Acute lymphoblastic leukemia

The therapeutic class that could benefit more from PGt and PGx is cancer chemotherapy.

Anticancer agents are often given at doses near those that produce toxicity, show wide inter-patient variability in disposition and effects, and should be given at optimal doses for the best chance of cure. Cancer is the leading cause of death by disease in children between 1 and 15 years of age in the USA, with leukemia continuing to cause the highest proportion (33%) of these deaths [START_REF] Cheok | Acute lymphoblastic leukaemia: a model for the pharmacogenomics of cancer therapy[END_REF]. ALL accounts for about 25% of all cancers in children. Despite the significant progress in treatment of ALL, long-term event-free survival rates are currently almost 80%, with 20% of patients who do not respond to standard therapy [START_REF] Husain | Clinical pharmacogenetics in pediatric patients[END_REF]. Treatment response can be altered by polymorphisms in genes encoding enzymes that metabolize chemotherapeutic agents. The thiopurine methyltransferase [START_REF] Cheok | Acute lymphoblastic leukaemia: a model for the pharmacogenomics of cancer therapy[END_REF][START_REF] Lennard | Genetic variation in response to 6-mercaptopurine for childhood acute lymphoblastic leukaemia[END_REF][START_REF] Yates | Molecular diagnosis of thiopurine S-methyltransferase deficiency: genetic basis for azathioprine and mercaptopurine intolerance[END_REF]. Patients who are heterozygous at the TPMT locus are at intermediate risk of dose-limiting toxicity and might require a modest dose reduction of approximately 35-50%, whereas TPMT-deficient patients require a dose reduction of >90% [START_REF] Cheok | Acute lymphoblastic leukaemia: a model for the pharmacogenomics of cancer therapy[END_REF]. Other important genes involved in ALL therapy are those codifying for the enzymes of the glutathione-S-transferase (GST) family. The polymorphisms of these genes have been associated with increased cancer incidence, therapy-related cancers and toxicity following chemotherapy [START_REF] Cheok | Acute lymphoblastic leukaemia: a model for the pharmacogenomics of cancer therapy[END_REF][START_REF] Hayes | Glutathione transferases[END_REF]. Polymorphisms of GSTM1, GSTP1, and GSTT1 exist in all populations. The GSTM1*0 (GSTM1 null) and GSTT1*0 (GSTT1 null) alleles represent deletions of GSTM1 and GSTT1 genes respectively and result in a loss of enzymatic activity [START_REF] Rebbeck | Molecular epidemiology of the human glutathione S-transferase genotypes GSTM1 and GSTT1 in cancer susceptibility[END_REF]. The 1578 A > G transition in GSTP1 gives rise to the Ile105Val polymorphism, which confers reduced enzyme activity [START_REF] Ye | Glutathione s-transferase polymorphisms (GSTM1, GSTP1 and GSTT1) and the risk of acute leukaemia: A systematic review and meta-analysis[END_REF]; it is associated with high etoposide clearance in African-Americans treated with steroids [START_REF] Kishi | Effects of prednisone and genetic polymorphisms on etoposide disposition in children with acute lymphoblastic leukemia[END_REF]. Methotrexate (MTX) is also an important chemotherapeutic drug in the treatment of ALL. Methylenetetrahydrofolate reductase (MTHFR) is an essential enzyme in the folate/methotrexate metabolism pathway. About 10% of Caucasians show a genotypic variant of MTHFR (677 C >T; Ala222Val), which encodes a protein with about 30% of the wild-type activity [START_REF] Frosst | A candidate genetic risk factor for vascular disease: a common mutation in methylene tetrahydrofolate reductase[END_REF]. This SNP has been linked to hepatotoxicity following methotrexate treatment [START_REF] Ulrich | Pharmacogenetics of methotrexate: toxicity among marrow transplantation patients varies with the methylenetetrahydrofolate reductase C677T polymorphism[END_REF]. Another low-function variant of MTHFR results from the 1298 A >C (Glu429Ala) substitution; it has been reported to be protective for adult acute lymphocytic leukemia [START_REF] Skibola | Polymorphisms in the methylenetetrahydrofolate reductase gene are associated with susceptibility to acute leukemia in adults[END_REF][START_REF] Wiemels | Methylenetetrahydrofolate reductase (MTHFR) polymorphisms and risk of molecularly defined subtypes of childhood acute leukemia[END_REF] but not to altered effects of MTX in leukaemia [START_REF] Krajinovic | Role of polymorphisms in MTHFR and MTHFD1 genes in the outcome of childhood acute lymphoblastic leukemia[END_REF] (Table 1).

Asthma

Asthma is the most common chronic disease among children. In 2002, >30 million US individuals reported having been diagnosed as having asthma, including 122 per 1000 children [START_REF] Mattke | Quality of care for childhood asthma: estimating impact and implications[END_REF].

Agonists of β2 adrenergic receptor (ADRB2) are the most widely used drug in the treatment of asthma: it has been demonstrated that a common polymorphism in the coding region of ADRB2 gene influences the response to shortacting albuterol therapy in children with asthma (Table 1).

Bleecker and colleagues have recently tested the drug response effect of ADRB2 coding polymorphism in two randomised studies, the first conducted on 2250 asthmatics, the second on 405. The results of this important study showed no pharmacogenetics affect of this genetic variant on therapeutic response when the patients were treated with inhaled corticosteroids plus longacting β2-agonists [START_REF] Bleecker | Effect of ADRB2 polymorphisms on response to longacting β2-agonist therapy: a pharmacogenetic analysis of two randomised studies[END_REF]. However this one of the few examples of PGt application in clinical trials in childhood (the participants aged 12 years or more) and mainly emphasizes the problem of small sample sizes in case control association studies that leads to false-positive or false-negative findings.

The other two modality of asthma treatment are corticosteroids and leukotriene modifiers, and polymorphisms of the genes (CRHR1, LTC4, ALOX5) involved in their modulation have been described (Table 1). However, also on this field contradictory results have been reported. For example, the LTC4S -444 A>C promoter polymorphism has been associated to a reduced risk for asthma exacerbations when compared with individuals homozygous for reference allele [START_REF] Sampson | Variant LTC(4) synthase allele modifies cysteinyl leukotriene synthesis in eosinophils and predicts clinical response to zafirlukast[END_REF][START_REF] Whelan | Effect of montelukast on time-course of exhaled nitric oxide in asthma: influence of LTC4 A(-444)[END_REF][START_REF] Husain | Clinical pharmacogenetics in pediatric patients[END_REF]; in other studies this observation was not consistent [START_REF] Currie | Leukotriene C4 synthase polymorphisms and responsiveness to leukotriene antagonistis in asthma[END_REF][START_REF] Kedda | Characterization of two polymorphisms in the leukotriene C4 synthase gene in an Australian population of subjects with mild, moderate, and severe asthma[END_REF] (Table 1).

The omics world: current state and future perspectives

Implication and importance of miR-polymorphisms in Pharmacogenomics

MicroRNAs (miRNA) are small, single-stranded, 21-23 nucleotide-long, independent functional units of noncoding RNA [START_REF] Lagos-Quintana | Identification of novel genes coding for small expressed RNAs[END_REF][START_REF] Lau | An abundant class of tiny RNAs with probable regulatory roles in Caenorhabditis elegans[END_REF][START_REF] Lee | An extensive class of small RNAs in Caenorhabditis elegans[END_REF]. Often referred to as the "micromanagers of gene expression", miRNAs are evolutionarily well-conserved and, by binding to the target transcript in the 3'-UTR, can inhibit the translation of proteins and destabilize their target mRNA [START_REF] Mishra | A miR-24 microRNA binding-site polymorphism in dihydrofolate reductase gene leads to methotrexate resistance[END_REF][START_REF] Selbach | Widespread changes in protein synthesis induced by microRNAs[END_REF].

Pharmacogenomics of miRNA is a novel and promising field of research that holds new possibilities for tailor-made medical therapy. MiRNA pharmacogenomics can be defined as the study of miRNAs and polymorphisms affecting miRNA function in order to predict drug behavior and to improve drug efficiency [START_REF] Mishra | MiRSNPs or MiR-polymorphisms, new players in microRNA mediated regulation of the cell: Introducing microRNA pharmacogenomics[END_REF][START_REF] Mishra | MicroRNA polymorphisms: the future of pharmacogenomics, molecular epidemiology and individualized medicine[END_REF]. MiRNA pharmacogenomics has strong clinical implications for several reasons: miRNAs are attractive drug targets, are differentially expressed in malignant versus normal cells and regulate expression of several important proteins in the cell [START_REF] Calin | Frequent deletions and down-regulation of micro-RNA genes miR15 and miR16 at 13q14 in chronic lymphocytic leukemia[END_REF][START_REF] Hon | The roles of binding site arrangement and combinatorial targeting in microRNA repression of gene expression[END_REF][START_REF] Iorio | MicroRNA gene expression deregulation in human breast cancer[END_REF]. MiR-polymorphisms can interfere with miRNA function resulting in loss of the miRNAmediated regulation of a drug-target gene conferring drug resistance [START_REF] Mishra | A miR-24 microRNA binding-site polymorphism in dihydrofolate reductase gene leads to methotrexate resistance[END_REF]. Therefore, these miRpolymorphisms have potential as predictors of drug response in the clinic and will result in development of more accurate methods of determining appropriate drug dosage based on a patient's genetic makeup, thus decreasing the likelihood of drug overdose [START_REF] Mishra | MicroRNA polymorphisms: the future of pharmacogenomics, molecular epidemiology and individualized medicine[END_REF].

Transcriptomics, Metabonomics and Proteomics: other research areas completing

Pharmacogenetics and Pharmacogenomics

Transcriptomics [START_REF] Kiechle | Genomics, transcriptomics, proteomics, and numbers[END_REF] refers to the study of gene transcripts, generally analyzed by cDNA expression microarrays. Such cDNA expression studies have led to a number of exciting breakthroughs in basic science. For example, microarray analysis of certain tumors has been successful in correlating a particular microchip pattern with a patient's prognosis [START_REF] Mcgregor | Gene expression in cancer: the application of microarrays[END_REF]. Recent works indicate that global gene-expression profiling using DNA microarrays can identify genes with levels of expression that are related to drug response. An advantage of this strategy is that it includes all genes of potential importance and, therefore, might identify new therapeutic and diagnostic targets. Its disadvantage is that, as a non-targeted genome-wide approach, it is influenced by 'noise' (that is, expression signals of irrelevant genes) and increases the number of false positives (that is, unimportant genes that are identified by chance). Identification of genes on the basis of mRNA expression relative to drug response is complementary to the identification of SNPs in genes that alter protein function and drug response. Moreover, this might lead to the identification of SNPs that are associated with altered mRNA expression of genes associated with drug response. Acute lymphoblastic leukemia (ALL) is an ideal model system in which to assess global gene expression in cancer, because it is a 'liquid' tumour and therefore relatively homogeneous within a patient, and because it is easy to isolate and characterize. Robust geneexpression profiling for diagnosis and classification of childhood ALL might ultimately represent a less labour-intensive and more automated alternative to the multiple methods that are currently used (for example, immunochemistry, cytogenetics and molecular diagnostics) [START_REF] Armstrong | MLL translocations specify a distinct gene expression profile that distinguishes a unique leukemia[END_REF][START_REF] Golub | Molecular classification of cancer: class discovery and class prediction by gene expression monitoring[END_REF][START_REF] Ramaswamy | DNA microarrays in clinical oncology[END_REF][START_REF] Moos | Identification of gene expression profiles that segregate patients with childhood leukemia[END_REF][START_REF] Ross | Gene expression profiling of pediatric acute myelogenous leukemia[END_REF]. Studies of leukaemia-cell gene-expression patterns might also reveal new prognostic features and therapeutic targets. For instance, gene profiles might ultimately be able to identify children for whom therapy is likely to fail (that is, those who will experience relapse) or those who are at high risk of therapyinduced second cancers [START_REF] Ross | Classification of pediatric acute lymphoblastic leukemia by gene expression profiling[END_REF][START_REF] Yeoh | Classification, subtype discovery, and prediction of outcome in pediatric acute lymphoblastic leukemia by gene expression profiling[END_REF][START_REF] Teuffel | Gene expression profiles and risk stratification in childhood acute lymphoblastic leukemia[END_REF][START_REF] Willenbrock | Prediction of immunophenotype, treatment response, and relapse in childhood acute lymphoblastic leukemia using DNA microarrays[END_REF].

The major limitation of microarray studies is the availability of the appropriate source of sampling-blood or excreta (urine, saliva, sweat, breast milk, ejaculate, menses, feces) or tissue in which relevant cDNAs or proteins exist (dissected tumor, tissue biopsies, placenta, foreskin). It would be unethical and unreasonable to attempt to predict individual drug response outcomes from biopsies of liver, lung, kidney or brain in healthy patients.

Metabonomics (also called "metabolomics") refers to the study of metabolite profiling [START_REF] Plumb | Metabonomics: the use of electrospray mass spectrometry coupled to reversed-phase liquid chromatography shows potential for the screening of rat urine in drug development[END_REF][START_REF] Reo | NMR-based metabolomics[END_REF]. Although this field is similarly limited by the same sampling problems as transcriptomics, there is an important difference. The metabonome represents an integrated (systems biology) response, in real time, to all endogenous plus all exogenous stimuli (drugs, chemical exposures, occupation, lifestyle, nutrition, age, gender). Metabonomics thus might provide an exquisitely sensitive means to follow an individual patient's phenotype, as a function of age, nutrition, course of disease, or therapy. Accordingly, in principle, this technique offers great promise in personalized drug therapy and medicine, but may also be subject to some of the pitfalls identified above for pharmacogenomics.

Metabonomics might therefore be considered analogous to a "liver profile" test in clinical pathology, except that metabonomics includes measurement of metabolites present at much lower concentrations and, accordingly, provides several orders of magnitude greater sensitivity (femtomolar to attomolar range). Even though metabolite profiling can be performed only on easily available samples -such as blood, urine or other excreta, dissected tumor, or biopsy tissues -this method still holds promise of clinical success, and might be regarded as an extension of the present practice of clinical pharmacology [START_REF] Nebert | Pharmacogenomics and bindividualized drug therapyQ: high expectations and disappointing achievements[END_REF]. It seems practicable that, in the more distant future, metabonomics will help genomics to revolutionize and individualize drug therapy.

Proteomics, the study of all proteins encoded by the genome [START_REF] Campbell | Molecular signatures for diagnosis of infection: application of microarray technology[END_REF], has also been successful in certain areas of basic research. Although a recent study [START_REF] Xing | The multi-assembly problem: reconstructing multiple transcript isoforms from EST fragment mixtures[END_REF] estimated an average of 3.0 human proteins per gene, others have estimated that the true number of proteins per gene might be considerably higher. Proteomics -like transcriptomics and metabolomics -suffers from the types of source that must be sampled, e.g., blood, excreta or biopsy or tumor tissue in which relevant proteins exist. It is conceivable however that in the future proteomics investigators might identify certain protein profiles, similar to ways in which metabonomics can identify certain metabolite profiles, which might be useful for predicting adverse drug reactions long before they become overt. We expect to see during the next several years a successful complementation of genetics and genomics by both metabonomics and proteomics. Particularly, when the population understudy is composed of children as their drug response capability may be different at different ages.

Conclusions

Pharmacogenetics and pharmacogenomics hold out the promise of helping to achieve the goal of individualized drug therapy. Their translation into the clinic has been relatively slow both for the adulthood diseases as well as for the childhood diseases. Often pharmacogenetics and pharmacogenomics studies show contradictory results, that reflect inconsistent research methods, small sample sizes, no replication study, no standardized outcome measures, or little consideration of potential covariates such as co-morbidity. Before pharmacogenomic testing can be effectively utilized clinically, more data are necessary from randomized controlled clinical trials to determine the efficacy and clinical utility. Nevertheless, there is no estimate of what and how much genetic variations in gene products involved in drug disposition are useful in clinical practice and there are only few data on long-term adverse effects of drugs. We expect that future approaches will use also large-scale public genetic databases such us the HapMap project to elucidate linkage of genetic markers and drug effects in different populations, towards the identification of new genes and the elucidation of polygenic determinants of drug responses.

We also would like to underline that children should not be considered as small adults when we approach to a pharmacogenetic or pharmacogenomic studies. Children present differences arising from the various stages of development. Many patterns of ontological development in the systems of the body illustrate how paediatric patients can differ from adults. Genotypes do not always correspond with expected phenotypes, making the job of deciding how to treat childhood disease and apply genomic research to paediatric medicine all the more complex. The scientific and lay communities should work diligently and creatively to design research appropriate for pediatric populations. For instance, we expect to see during the next years a complementation of genetics and genomics by both metabonomics and proteomics. The impacts of pharmacogenetic and pharmacogenomic research already stand to greatly enhance the safety of treating children diagnosed with ALL, as TPMT-deficient individuals can be easily identified. Pharmacogenetic and pharmacogenomic study should be continually applied to pediatric populations in an effort to provide for children the equity and hope for progress in treatment, discovery and understanding of disease already present in adult populations.

(

  TPMT) genetic polymorphisms and mercaptopurine toxicity are one of the best-studied examples in pharmacogenetics. Although 23 variant alleles have been identified to date [41], 3 variant alleles (TPMT*2 [Ala80Pro], TPMT*3A [Ala154Thr and Tyr240Cys] and TPMT*3C [Tyr240Cys]) account for >95% of low or intermediate TPMT enzyme activity: patients with TPMT deficiency are at very high risk of severe hematopoietic toxicity if treated with conventional doses of thiopurines

ACKNOWLEDGEMENTS

This work was supported by grants from Regione Campania (DGRC 2362/07) and from MIUR (PS 35-126/Ind). Mario Capasso was supported by Associazione Oncologia Pediatrica e Neuroblastoma (OPEN). This contribution is part of the Task-force in Europe for Drug Development for the Young (TEDDY) Network of Excellence supported by the European Commission's Sixth Framework Program (Contract n. 0005216 LSHBCT-2005-005126)


H Wirsing Von König

Hans Hallander
email: hans.hallander@smi.sereza.advani@smil.se

Abdolreza Advani

Frits R Mooi
email: frits.mooi@rivm.nlguy.berbers@rivm.nl

Guy Berbers

Dorothy Xing
email: dxing@nibsc.ac.uk

Camille Locht
email: camille.locht@pasteur-lille.fr

David Hot
email: david.hot@pasteur-lille.fr

What to do and what not to do in serological diagnosis

of pertussis: recommendations from EU reference laboratories

What to do and what not to do in serological diagnosis of pertussis: Recommendations from EU reference laboratories

Nicole Guiso 1 , Guy Berbers 2 , Norman K. Fry 3 , Qiushiu He 4 , Marion Riffelmann 5 , Carl Heinz Wirsing von König § 5

Indications for pertussis diagnostics

Diagnosis of pertussis should only be attempted in patients with symptoms compatible with pertussis, such as prolonged coughing with paroxysms and/or whooping or choking. In infants, older vaccinated children, adolescents and adults the clinical course may not be typical, and prolonged coughing may be the only symptom. In these cases, diagnosis of pertussis requires laboratory methods for confirmation.

Direct and indirect tests are available. Direct tests are real-time PCR and culture whereas indirect tests measure specific antibodies in oral fluid or sera. Here, we focus on the detection of antibodies against B. pertussis antigens.

Development of the recommendations

The EU Pertstrain group consists of representatives of the Bordetella reference laboratories in their respective EU countries. In a face-to-face meeting in the Istituto Superiore di Sanita (ISS) in Rome in 2009, the outline of a manuscript was discussed and agreed upon. After a search of relevant databases, a first draft was written (NG) and intensively reviewed by members of the group. In a second face-toface meeting in the Rijksinstituut voor Volksgezondheid en Milieu (RIVM) in June 2010, the draft recommendations were broadly discussed and agreed upon. A second version of the recommendations was drafted (NG, CHWvK). This version was then reviewed again by all authors.

Serological tests

Blood / Serum

Most serological assays are validated to test serum; some may also be validated to test heparinised plasma or EDTA-plasma. Capillary blood samples may be used if a sufficient volume can not be obtained otherwise. Serum or plasma must be separated as soon as possible after blood sampling (24h at room temperature). If acute and convalescent serum samples taken at least three weeks apart from one individual are available, they should be tested together in one run. All serum samples may be frozen (at -20°C) after the primary assay and reanalyzed later together with a possible second sample.

ELISA in serum samples:

In preparation for the acellular vaccine studies in the 1990s, the ELISA methodology, the type of antigens as well as the reference sera have been standardized, and they have been used in all acellular vaccine trials, in sero-epidemiological studies in many countries, and for diagnostic purposes in various laboratories [START_REF] Andre | Comparison of serological and real-time pcr assays to diagnose Bordetella pertussis infection in 2007[END_REF][START_REF] Guiso | Laboratory manual for the diagnosis of whooping cough caused by bordetella pertussis/bordetella parapertussis[END_REF][START_REF] Meade | Description and evaluation of serologic assays used in a multicenter trial of acellular pertussis vaccines [published erratum appears in pediatrics 1995 dec;96(6):Following 1199[END_REF][START_REF] Simondon | Evaluation of an immunoglobulin g enzyme-linked immunosorbent assay for pertussis toxin and filamentous hemagglutinin in diagnosis of pertussis in senegal[END_REF][START_REF] Tondella | International bordetella pertussis assay standardization and harmonization meeting report. Centers for disease control and prevention, atlanta, georgia, united states[END_REF].

Antigens: ELISA is normally done with highly purified antigens. The antigens most frequently used are PT, and FHA, and to a lesser extent Pertactin (PRN) and Fimbriae (FIM).

Sometimes Adenylate Cyclase-hemolysin Toxin (ACT) is also used. These antigens are used in their active, i.e. non-detoxified form. The storage conditions of the antigens as well as the duration of storage can vary significantly according to the manufacturers who provide the purified antigens. Anti-PT antibodies are specific for B. pertussis, whereas anti-FHA, anti-PRN, anti-FIM and anti-ACT are less specific due to cross-reactivity with other microbial antigens (eg. other Bordetella species, Haemophilus species, Mycoplasma pneumoniae, Escherichia coli). For this reason, in routine diagnosis, only measurement of anti-PT antibodies is recommended. However, measurement of other antibodies may be used for transmission, immunogenicity or vaccine non-inferiority studies. Some ELISAs, especially commercial kits, use a mixture of antigens or supernatants or sonicates of whole B. pertussis cells. The use of kits with mixed antigens is not recommended (Riffelmann et al. submitted).

Reference sera: WHO references are available from the NIBSC (Potters Bar, UK) ("WHO International Standard (06/140)" and "WHO Reference Reagent (06/142)") for the measurement of human antibodies to B. pertussis antigens, and thus quantitative results should be reported IU/ml [START_REF] Xing | Characterization of reference materials for human antiserum to pertussis antigens by an international collaborative study[END_REF].

Plates: For in-house ELISAs differences between plates were observed, and Thermo Scientific Nunc Maxisorp (Nunc AS, Copenhagen, Denmark) plates and Greiner Microlon High Binding (Greiner Bio-One, Frickenhausen, Germany) plates seemed to work better than others [START_REF] Dalby | Pertussis serology: Assessment of a quantitative igg-anti-pt elisa for replacement of the cho cell assay[END_REF].

Flow cytometry: Bead based multiplex assays that simultaneously measure antibodies to various antigens have also been applied to B. pertussis antigens. The assays use fluorescent microparticles to which purified antigens are covalently coupled and are based on a proprietary method patented in 1983 in Germany [START_REF] Reder | Measuring immunoglobulin g antibodies to tetanus toxin, diphtheria toxin, and pertussis toxin with single-antigen enzyme-linked immunosorbent assays and a bead-based multiplex assay[END_REF] or on xMAP technology from Luminex TM [START_REF] Van Gageldonk | Development and validation of a multiplex immunoassay for the simultaneous determination of serum antibodies to bordetella pertussis, diphtheria and tetanus[END_REF]. These assays seem to produce results comparable to conventional ELISA systems.

Immunoblots, line-and dot-blots:

Many commercial kits detect anti-B. pertussis and/or anti-PT, anti-FHA, anti-PRN and also ACT antibodies in serums using blotting techniques. Kits using whole cell suspensions as antigens are not specific for the detection/diagnosis of pertussis infections due to a lot of cross-reactivity with other bacteria (eg. other Bordetella species, Haemophilus species, Mycoplasma pneumoniae). Antigens used in these kits have to be validated concerning their purity, as contaminations with other antigens or antigen aggregates can also produce false positive results. A quantitative interpretation of blot results is not possible; a semi-quantitative reporting may be possible.

Although various CE marked commercial kits are available, a recent comparison showed significant differences between kits and an insufficient correlation to the values of the 1 st International Reference preparation (Riffelmann et al. submitted). Consequently, the use of immunoblots for pertussis serology is not recommended by the EU Pertstrain group.

Micro-Agglutination: Micro-agglutination has been widely used before ELISA systems became available [START_REF] Blumberg | The agglutinin response to whole cell and acellular pertussis vaccines is bordetella pertussis strain dependent[END_REF]. As with other bacterial agglutination assays, micro-agglutination with B. pertussis cells mainly measures IgM-antibodies to outer surface antigens such as FIM, PRN and lipooligosaccharide (LOS). Results are reported in titres starting at 1:20 or 1:40. No agglutinin titre has been attributed to the WHO reference preparation so far. Agglutinating antibodies can be used to measure the exposure of a population to B. pertussis antigens; on an individual level the micro-agglutination method is not useful for confirming the clinical diagnosis of pertussis.

CHO cell neutralization:

This test used the ability of PT to induce characteristic morphological changes in a culture of chinese hamster ovary (CHO) cells. These changes can be neutralized by the presence of anti-PT antibodies. The titres of CHO-cell neutralizing antibodies correlate well with the IgG-anti-PT ELISA values, and thus CHO cell assays are rarely used for diagnostic purposes [START_REF] Dalby | Pertussis serology: Assessment of a quantitative igg-anti-pt elisa for replacement of the cho cell assay[END_REF][START_REF] Granström | Evaluation of serologic assays for diagnosis of whooping cough[END_REF].

The interpretation of CHO assays cannot be standardized, and it is difficult to interpret the morphological changes and to score the results objectively.

Complement fixation: Complement fixation using whole cells of B. pertussis has been rarely used and suffers from lack of sensitivity and specificity.

Indirect immunfluorescence: Indirect immunofluorescence using whole cells of B. pertussis has the same disadvantages as complement-fixation

Oral fluid

Oral fluid can be sampled by standardized means, e.g.. Oracol swab (Malvern Medical Developments) or Orasure oral specimen collection devices (Orasure Technologies Inc.). The diagnostic sensitivity of measuring antibodies in oral fluid samples is lower (~80%) as compared to serum samples, but the samples can easily be obtained and offer an adjunct to diagnostic serology ELISA in oral fluid: An IgG-capture ELISA capable of detecting anti-PT IgG in oral fluid has been developed. The assay was evaluated by comparison to a serum ELISA. The results showed that the oral fluid assay detected seropositive subjects with a sensitivity of 79.7% [95% confidence interval (CI) 68.3-88.4] and a specificity of 96.6% (95% CI 91.5-99.1) relative to the ELISA [START_REF] Litt | Detection of antipertussis toxin igg in oral fluids for use in diagnosis and surveillance of bordetella pertussis infection in children and young adults[END_REF]. This assay has since been modified to include a monoclonal capture antibody however no commercial assays for measuring antibodies in oral fluid are available.

Reporting of serological results using ELISA or flow cytometry

Concentrations of antibodies to B. pertussis antigens should be quantitatively expressed in IU/ml as reference preparations are available [START_REF] Xing | Characterization of reference materials for human antiserum to pertussis antigens by an international collaborative study[END_REF]. The reference preparation defines values for antibodies of isotypes IgG and IgA to PT, FHA, PRN, and to FIM. Assigned values of the reference preparation are described in table 1. The numerical values of IU/ml are equivalent to the previously used ELISA units/ml (EU/ml) derived from the human reference preparations lot 3, lot 4, and lot 5 from CBER/FDA, Bethesda, MD, USA.

Interpretation of serological results

PT and FHA are contained in substantial amounts in all acellular vaccines licensed in Europe (except in Denmark), and PRN and FIM are also components of licensed acellular pertussis vaccines. Thus, the immune response against infection or vaccination cannot be distinguished and pertussis vaccination may interfere with the interpretation of serological results. Due to a continuous circulation of Bordetellae in the population, IgG-anti-PT and other antibodies to Bordetella antigens are detectable in the majority of all adolescent and adult populations tested so far [START_REF] Pebody | The seroepidemiology of bordetella pertussis infection in western europe[END_REF]. Thus, serological diagnosis of pertussis must be performed in immunological non-naïve populations with different kinetics of antibody production. Dual sample serology based on ≥100% increase in antibody concentration or on ≥100% decrease in antibody concentration is a sensitive and specific way for serological diagnosis [START_REF] Andre | Comparison of serological and real-time pcr assays to diagnose Bordetella pertussis infection in 2007[END_REF][START_REF] Simondon | Evaluation of an immunoglobulin g enzyme-linked immunosorbent assay for pertussis toxin and filamentous hemagglutinin in diagnosis of pertussis in senegal[END_REF]. However, even in paired sera no antibody increase may be seen after infection due to the secondary immune response, and the diagnosis may also be based on a decrease of antibodies, which may be too slow to reach 50% between the acute and convalescent sample.

In clinical practice, diagnosis is mostly based on single sample serology using a single or a more continuous cut-off. For single-sample serology various cutoff-values for IgG-anti-PT have been proposed (Table 2): In Massachusetts, 100 EU/ml was used, and later, in order to increase specificity >~200 EU/ml IgG-anti-PT (>20µg/ml) was employed. In the Netherlands, a cutoff >~125 EU/ml IgGanti-PT with higher specifity or 62 EU/ml with slightly lower specificity has been used [START_REF] Melker | Specificity and sensitivity of high levels of immunoglobulin g antibodies against pertussis toxin in a single serum sample for diagnosis of infection with bordetella pertussis[END_REF][START_REF] Versteegh | Agespecific long-term course of igg antibodies to pertussis toxin after symptomatic infection with bordetella pertussis[END_REF]. In Germany, a cut-off of ~50 EU/ml IgG-anti-PT was suggested, together with ~50 EU/ml IgA-anti-FHA. A seroepidemiological survey was recently performed in various countries in Western Europe using a cut-off of 125 EU/ml for recent infection, and it can be used as a population based reference [START_REF] Pebody | The seroepidemiology of bordetella pertussis infection in western europe[END_REF]. Another recently completed sero-surveillance in US sera found that three populations could be separated according to their levels of IgG-anti-PT: one cut-off was estimated at 94 EU/ml, and a lower cut-off was estimated at 48 EU/ml [START_REF] Baughman | Establishment of diagnostic cutoff points for levels of serum antibodies to pertussis toxin, filamentous hemagglutinin, and fimbriae in adolescents and adults in the united states[END_REF]. Using the lower 50 EU/ml cut-off may be especially useful in outbreak situations, and overall this cut-off of 50 EU/ml seems to be more adapt for diagnosis rather than a higher cut-off with lower sensitivity [START_REF] Horby | A boarding school outbreak of pertussis in adolescents: Value of laboratory diagnostic methods[END_REF].

Overall, it is astonishing that, irrespective of various vaccination strategies, cut-offs for single sample serology are comparable throughout the countries where they were evaluated.

A comparison of ROC curve analyses with data from Denmark, the Netherlands, and the UK showed for all three countries that the single cut-off with optimal sensitivity and specificity may be in the range between 60 IU/ml and 75 IU/ml.

It may be sensible to use dual a cut-off between 62-125IU/ml according to countries as a proof of a recent infection with B. pertussis provided that the patient was not vaccinated during the last twelve months (Table 2). If diagnosis cannot be established with certainty from a single serum, but is deemed to be necessary according to the clinical symptoms, antibodies should be measured in a second (convalescent) serum sample at two to four weeks interval. In case of non-availability of a second serum sample, measurement of IgA anti-PT antibodies can be an alternative, but no broadly accepted cut-off is available for this antibody subclass. Considering its relatively high specificity and low sensitivity, a cut-off near the minimal level of quantification, which may be between 10 IU/ml and 20 IU/ml may seem reasonable [START_REF] Ward | Bordetella pertussis infections in vaccinated and unvaccinated adolescents and adults, as assessed in a national prospective randomized acellular pertussis vaccine trial (apert)[END_REF].

Recommendations for serological testing with suspected pertussis

In neonates and young infants PCR and/or culture should be performed on nasopharyngeal samples, nasopharyngeal swabs (NPSs) or nasopharyngeal aspirate (NPAs), as soon as possible post-onset of symptoms. Measurement of IgG-anti-PT is only meaningful for older children/adults including parents and other household members. In vaccinated children, adolescents and adults with less than two weeks of coughing culture and PCR from nasopharyngeal samples should be done. For adolescents and adults with coughing less than three weeks PCR and measurement of IgG-anti-PT should be performed [START_REF] Andre | Comparison of serological and real-time pcr assays to diagnose Bordetella pertussis infection in 2007[END_REF]. If coughing lasted at least 2-3 weeks, measurement of IgG-anti-PT should be sufficient.

In outbreak situations, PCR and culture should be done from nasopharyngeal samples and IgG-anti-PT should be measured in serum samples.

Word count: 1998

  for the EU Pertstrain group* (*Members of the EU Pertstrain group are listed in the appendix) 1: Institut Pasteur, Paris, France 2: National Institute for Public Health and the Environment, Bilthoven, the Netherlands 3: Health Protection Agency Centre for Infections, London, UK 4: National Institute for Health and Welfare, Turku, Finland 5: HELIOS Klinikum Krefeld, Germany § Corresponding author: Prof. Dr. Carl Heinz Wirsing von König Institut für Hygiene und Labormedizin HELIOS Klinikum Krefeld Lutherplatz 40 D-47805 Krefeld, Germany Phone +49 2 151 32 24 67 Fax: +49 2 151 32 20 79 e-mail: carlheinz.wirsingvonkoenig@helios-kliniken.de

  Additionally, pertussis serology suffers from various other drawbacks: -Commercial ELISAs are of different antigen composition and quality, -Reference antigens with good purity are not easily available -Population-based cut-offs for single-sample serology may need verification after changes in the vaccination schedule, -Interpretation of anti-PT concentrations in recently vaccinated persons is difficult.

Table 1 : Reference preparations from WHO and CBER/FDA Values

 1 are given in IU/ml for the WHO preparations and in ELISA units (EU)/ml for the CBER/FDA preparations IU/ml and EU/ml are numerically identical [##]

	WHO international	335 IU/ml	65 IU/ml	130 IU/ml	65 IU/ml	65 IU/ml	42 IU/ml
	standard (06/140)
	WHO reference	106 IU/ml	18 IU/ml	122 IU/ml	86 IU/ml	39 IU/ml	38 IU/ml
	reagent (06/142)
	CBER/FDA#3	200 EU/ml	15 EU/ml	200 EU/ml	100 EU/ml	ND	ND
	CBER/FDA#5	ND*	140 EU/ml	ND	280 EU/ml	ND	90 EU/ml
	CBER/FDA#4	ND	ND	ND	ND	90 EU/ml	25 EU/ml
	ND: not declared

IgG-anti-PT IgA-anti-PT

IgG-anti-FHA IgA-anti-FHA IgG-anti-PRN IgA-anti-PRN

Table 2 Suggested cut-off values for IgG-anti-PT for adolescents and adults Adapted from WHO Immunological basis for vaccination series (http://whqlibdoc.who.int/publications/2010/9789241599337_eng.pdf)

 2

	Country	Type of study	Cut-off	Sensitivity	Specificity	Reference
	MA, USA	Population study	~ 100 IU/ml	78%	98%	[19]
	MA, USA	Population study	~200 IU/ml	67%	99.9%	[20]
	NL	Population study	125 IU/ml	70%	99%	[21]
			62 IU/ml	80%	95%
	D	Population study	50 IU/ml	80%	95%	[22]
	EU	Epid. survey	125 IU/ml	n.a.	n.a.	[13]
	USA	Epid. survey, model	94 IU/ml	n.a.	n.a.	[16]
			46 IU/ml	n.a.
	AUS	Clinical validation	50 IU/ml	better than 100 IU/ml		[17]
	MA, Massachusetts.
	n.a., not applicable.

List of participants of the EUpertstrain network


P J Andrianiaina
email: patrick.andrianiaina@airbus.com

A Seuret

D Simon

Robust control under weakened real-time constraints

Patrick Jocelyn Andrianiaina, Alexandre Seuret and Daniel Simon Abstract-A weakened implementation scheme for real-time feedback controllers is proposed to reduce the conservatism due to traditional worst-cases considerations, while preserving the stability and control performance. Based on recent results to assess stability of linear systems with delayed and sampleddata inputs, this paper takes into account both the effects of deadline misses of control tasks and uncertainties in the plant. The methodology is applied to the pitch control of an aircraft, showing that weakening the real-time constraints allows for saving computing power while preserving the system's stability.

Index Terms-Robustness, delay, real-time scheduling.

I. CONTEXT

The development process of critical avionics products are done under strict safety regulations. These regulations include determinism and predictability of the systems' timing. The overall approach is based on a separation of concerns between control design and implementation, [START_REF] Årzén | An introduction to control and scheduling co-design[END_REF], [START_REF] Xia | Control-scheduling codesign: A perspective on integrating control and computing[END_REF].

On one hand, traditional control design considers constant sampling rates with equidistant samples (e.g. no jitter) and negligible, or fixed and known delays. On the other hand real-time scheduling theory has mainly focused on how to dimension resources for meeting deadlines (or equivalently, on the schedulability analysis for a given resource) [START_REF] Sha | Realtime scheduling theory: A historical perspective[END_REF]. Therefore the computer science and real-time scheduling communities do their best to implement control tasks considering fixed periods and hard deadlines, and assuming that the Worst-Case Execution Time (WCET) is precisely known. This assumption has served the separation between control and scheduling designs, but leads to an under utilization of CPU resources, and such approach faces both technical, economical, and industrial challenges.

One of the toughest challenges in the current approach is the determination of the WCET, in order to correctly size the system. The tightness of the result is related to the predictability of the processing unit. The future generations of processors seems to go apart from the predictability and determinism objectives of the execution time. Processing speeds and performances grow up very fast thanks to accelerating but unpredictable mechanisms of new processors. However it becomes difficult to foresee their effects on the execution time considered in the worst case. Nowadays, even if many attempts are proposed to give an upper bound of the WCET (e.g. [START_REF] Rochange | 7th Intl. Workshop on Worst-Case Execution Time (WCET) Analysis[END_REF]), both the traditional and current approaches are difficult to be applied to modern processor generations and produce values which are pessimistic [START_REF] Puschner | On composable system timing, task timing, and WCET analysis[END_REF].

Then, to implement the control laws the hard and costly way consists in building a highly deterministic system so that the actual implementation parameters meet the ideal ones. By essence, implementations purely based on WCET and hard deadlines considerations are conservative and lead to a large under-utilization of the computing and networking resources and finally ending to an oversizing of both electrical supplies, cooling systems and aircraft weight.

Current real-time systems design methods and associated analysis tools do not provide a model flexible enough to fit well with control systems requirements, while classic control theory does not give advice on how to include resource and dependability constraints into the controller, both at the design and implementation stage. However, as far as closedloop control systems are considered, more flexible solutions can be expected by exploiting the basic features of feedback loops, robustness w.r.t. modeling uncertainties, disturbance rejection and adaptiveness to various operative conditions. Indeed robustness of feedback controllers also implies some fault-tolerance w.r.t. deviations from the ideal timing pattern, e.g. equidistant sampling. This feature can be efficiently used to guarantee the end-to-end control quality, i.e. stability and performance level, under weakened real-time constraints, therefore improving the computing power average utilization.

The remainder of the paper is organized as follows: Section II provides the motivation of the paper and the problem statement. This section also gives different points of view on design assumptions concerning critical system design. Section III formulates the problem of systems under uncertainties and input delays. Section IV provides new stability conditions, based on [START_REF] Seuret | Stability analysis of networked control systems with asynchronous sampling and input delay[END_REF], for systems subject to uncertainties, delays and varying sampling. Finally in section V the methodology is applied to the case study of the pitch control of an F-16 aircraft.

Notations: Throughout the article, the sets R + , R n×n and S n denote respectively the set of positive scalar, the set of n × n matrices and the set of symmetric matrices of R n×n . The superscript 'T ' stands for the matrix transposition. The notation P > 0 for P ∈ S n means that P is positive definite. For any matrix A ∈ R n×n , the notation 2He{A} > 0 refers to A + A T > 0.

II. PROBLEM STATEMENT AND PAPER CONTRIBUTION A. WCET based assumption

Currently many control systems, e.g. flight control, braking control systems, are considered to be hard real-time, i.e. it is most often assumed at design time that control tasks must be executed strictly periodically. Therefore control tasks executions are bounded to fixed time-slots, and deadline misses or jitter are forbidden. It is assumed that any deviation from the ideal timing pattern inevitably leads to a failure of the system. The implementation of such control tasks relies on a safe evaluation of the WCET of each task, which is used to dimension the size of the time slot allocated for the execution of the control tasks. The execution schedule of a control task is depicted on Figure 1.

T T t k x(s k ) x(s k+1 ) t k+1 U imp (t k ) = U (x(s k )) U imp (t k+1 ) = U (x(s k+1 ))
Fig. 1. WCET based control task execution pattern A given task execution is strictly periodic, i.e. a time slot T slot = W CET is allocated to the task execution. It is triggered at a period s k -s k-1 = T by the occurrence of measurements x(s k ) at time s k . The controller computation takes a time T ex which is always smaller than the W CET . To avoid jitter, the control signal U (x(s k )) is applied to the actuators at the end of the slot, i.e. at time s k + W CET :

∀t ∈ [s k + W CET, s k+1 + W CET [, U = U (x(s k )).
Therefore, it is a periodic control system, with constant period T , subject to a constant delay T slot = W CET . This implementation fits with the hard real-time assumption, and should be applied when the controller is really hard, e.g. if it is a Finite State Machine which may fail in an unpredicted state in case of deadline miss and interrupted transition.

However, as the time slots are allocated based on the WCET of the control tasks, the computations always finish before the end of the slot. Therefore, a fraction of the computing power is unused. The wasted computing power is all the more important as the WCET is far from the average value of the observed execution time T ex . Indeed, due to an increasing demand on services, new control systems are more and more based on networked architectures and shared off-the-shelf computing devices. However high computing power are often based on the usage of multiple levels of cache and pipe-lines, lowering the determinism of the processors and increasing the difficulty of searching for the program's WCET, which are, in fact, approached by increasingly conservative upper bounds [START_REF] Souyris | Computing the worst case execution time of an avionics program by abstract interpretation[END_REF]. Indeed the execution times distribution plot (as shown in Figure 2 for a dedicated embedded processor [START_REF] Hansen | Statistical-based WCET estimation and validation[END_REF]) is expected to spread out, so that approaching the worst case execution time is foreseen to become a rare event. Therefore the amount of wasted computing power is expected to increase, leading to costly over-sizing of embedded computers, power supplies and cooling systems. Hence it is worth to discuss and revisit the "hard realtime" assumption and examine how it can be weakened in the particular case of feedback control systems.

B. Robustness considerations

The design of critical systems must satisfy requirements, specifications and certification levels. Robustness is a general concern that grows with system complexity. For instance, it is known that small task core execution time modifications in systems with complex performance dependencies can have drastic non-intuitive effects on the overall system performance, and might lead to constraint violations. [START_REF] Hamann | A formal approach to robustness maximization of complex heterogeneous embedded systems[END_REF] claims that robustness evaluation using simulation is a tedious tasks and practically impossible for the reason that simulation models do not support many of the possible property changes (for instance, increased processor execution times or modified communication volumes). This same paper proposes an interesting formal approach to robustness of embedded realtime systems with definition of robustness metrics. However the present article uses recent developments and moreover is more dedicated to practical industrial problems.

Robustness in control usually deals with the plant's parameters uncertainties, but in the present case the insensitivity or adaptability w.r.t. timing deviations from the theoretical pattern, such as jitter or deadlines misses, is also investigated. For SISO linear systems robustness can be quantified using phase margins, delay margins and module margins. It appears that a phase margin implies a delay margin (i.e. the maximum unmodeled constant extra delay that can be suffered before instability) and certainly a jitter margin, which is more difficult to quantify ( [START_REF] Cervin | The jitter margin and its application in the design of real-time control systems[END_REF]) but which can be experimentally shown ( [START_REF] Cervin | Towards the integration of control and real-time scheduling design[END_REF]). A feedback control system can be even robust enough to tolerate missed samples, e.g. in [START_REF] Felicioni | Overload Management Through Selective Data Dropping[END_REF], where selective data dropping is applied to lighten the computing and networking burden while preserving closed-loop stability. The interesting point is that a feedback control system which is robust w.r.t. the plants parameters uncertainties is also robust, to some extent, w.r.t. timing deviations. Hence a feedback control system is not as hard as it is often considered in the literature, but should be better considered as weakly hard, i.e. able to tolerate specified timing deviations without leaving its requested performance [START_REF] Bernat | Weakly hard real-time systems[END_REF].

C. Weakened real-time and control objectives

To improve the average efficiency of embedded computers while preserving the control stability and performance, and relying on the robustness of feedback control laws, it is proposed to weaken the usual real-time constraints according to the following schedule and control objectives (Figure 3):

Tslot Tslot Tex s k s k+1 T T x(s k ) x(s k+1 ) t k

Sampling sensors

Computation slots dedicated to control

Effective computing times

Application of control to the actuators

Tslot < WCET t k +1 Tslot Tex Tex Deadline miss Abort computation s k+2 x(s k+2 ) U (x(s k )) U (x(s k+2 ))
Fig. 3. Proposed task execution pattern

The sensors data are still expected to occur at a fixed period T , and their occurrence trigger the control tasks. The time slot allocated to a given task T slot < W CET is now smaller than the worst case. As usual the control signal is sent to the actuators at the end of the slot, i.e. U (x(s k )) is sent at time s k + T slot , and the delay is equal to

T slot ∀t ∈ [s k + T slot , s k+1 + T slot [, U = U (x(s k )).
But now it may happen that occasionally a control task deadline is missed : in that case it is proposed to stop the current computation, hold the current value of the control signal for the next period and start a fresh computation with the next sensor value. In that case, the control signal U (x(s k )) is hold for one extra period, i.e. if the deadline miss occur at time s k + T slot :

∀t ∈ [s k + T slot , s k+2 + T slot [, U = U (x(s k )),
and for N consecutive deadline misses and data loss:

∀t ∈ [s k + T slot , s k+N + T slot [, U = U (x(s k )).
In other words a newly computed control signal is sent to the actuators at non-equidistants instants t k only if the control computation has been successfully carried out:

t k = s k + T slot if T ex ≤ T slot ,
where k is a positive integer representing the number of input values which have been implemented before s k = kT . Then, the control input can be asynchronous since the difference between two sampling instant t k +1 -t k is timevarying but bounded by T and N T . Hence t k +1 -t k = αT , where the integer α ∈ [1, ..., N ] and the asynchronous sampling is determined by the couple (T, N ).

As already observed and reported in aforementioned references, it is likely that a robust feedback control systems can keep stability despite occasional data loss, at the price of a decreased performance and robustness. Therefore, for a given LTI plant, a given control law, a known distribution of execution times and the weakened real-time constraint, problems to be solved can be informally stated as :

• find N , the maximum value of consecutive data loss before loosing the closed-loop stability; • find an adequate value of T slot to fulfill a given trade-off between the control and the computing performances.

• evaluate the weakly-hard closed-loop robustness w.r.t. the plant's parameters uncertainties.

III. PROBLEM FORMULATION

Consider the linearized system representing the pitch control of a plane with a sampled and delayed input:

ẋ(t) = (A + ∆ µ A(t))x(t) + (B + ∆ µ B(t))u(t), (1)
where x ∈ R n and u ∈ R m represent the state variable and the input vector. The matrices A and B are constant and of appropriate dimension. The matrices ∆ µ A and ∆ µ B represent the uncertainties of the model which can be constant or time varying. The (time-varying) uncertainties are given in a polytopic representation:

∆ µ A(t) = µ M i=1 λ i (t)A i , ∆ µ B(t) = µ M i=1 λ i (t)B i
, where M corresponds to the numbers of vertices. The matrices A i , B i and C i are constant and of appropriate dimension. The scalar µ ∈ R characterizes the size of the uncertainties. Note that when µ = 0, no parameter uncertainty is disturbing the system. However the greater the µ, the greater the disturbances. The functions λ i (.) are weighted scalar functions which follow a convexity property, i.e. for all i = 1, .., M and for all t ≥ 0, λ i (t) ≥ 0 and M i=1 λ i (t) = 1. In this paper it is assumed that the control scheduling induces a constant transmission delay T slot and a sampling of the transmitted signal. For a given gain K in R n×m , the control law is a piecewise-constant static state-feedback of the form u(t) = Kx(t k -T slot ), for all t ∈ [t k , t k +1 ]. These instants t k represent the instants where the control input is updated. The closed loop system is thus rewritten, for all t ∈ [t k , t k +1 ], as

ẋ(t) = Ā(t)x(t) + B(t)Kx(t k -T slot ), (2)
where Ā(t) = A+∆ µ A(t) and B(t) = B +∆ µ B(t). Several authors investigated in guaranteeing the stability of such systems. In [START_REF] Fridman | Robust sampled-data stabilization of linear systems: An input delay approach[END_REF], a continuous-time approach to model sampleddata systems was developed. It allows assimilating sampling effects as the ones of a particular delay. In [START_REF] Fridman | Robust sampled-data stabilization of linear systems: An input delay approach[END_REF], [START_REF] Millán | Improved delaydependent stability criterion for uncertain networked control systems with induced time-varying delays[END_REF] or [START_REF] Liu | Stability analysis of networked control systems: a discontiuous Lyapunov functional approach[END_REF], the authors propose an aggregated delay formulation. They develop stability criteria which take into account the delay δ. However they did not consider the different natures of the transmission and the sampling delay. More especially the additional characteristic of sampled delay which is δ = 1 has not been included and thus leads to conservative conditions. When µ is zero, the discrete-time modeling of such systems is easily obtained by integrating the differential equation ( 2) over the interval [t k , t k + τ ], for any τ in [0, T ],

x(t k + τ ) = Ã(τ )x(t k ) + B(τ )Kx(t k -T slot ), Ã(τ ) = e Aτ , B(τ ) = τ 0 e A(τ -θ) dθB.
(3) Thus, define, for all integer k , the function χ

T slot k : [0, N T ] × [-T slot , 0] → R n such that for all τ in [0, N T ] and all θ in [-T slot , 0], χ k (τ, θ) = x(t k + τ + θ). The set K T slot N T represents the set of functions defined by χ T slot k as the set of continuous functions from [0, N T ] × [-T slot , 0] to R n .
However, the same discretization method is not valid when the system is subject to time-varying uncertainties. Thus discrete-time analysis of (3) leads to unavoidable difficulties. Thus there is a need to introduce novel stability conditions to cope with this type of discrete-time systems.

In this paper, a novel method to assess stability of systems subject to varying sampling, constant delay and time-varying uncertainties is proposed. The main idea is to consider separately the two delays types. To do so, the stability conditions are based on the discrete-time Lyapunov Theorem but expressed with the continuous-time model of the system. It leads to less conservative necessary conditions.

IV. STABILITY ANALYSIS

A. System without uncertainties

In this section, a study on the asymptotic stability of the solutions of sampled-data systems presented in (1) with µ = 0 is provided. There exist several results in the literature to ensure asymptotic stability of linear systems with input delay and sampling. In the present article, the contribution is based on the asymptotic stability conditions developed in [START_REF] Seuret | Stability analysis of networked control systems with asynchronous sampling and input delay[END_REF].

Theorem 1: Consider an integer N and two non negative scalars T slot and T . Assume that there exist Q > 0, R 1 > 0 and R 2 > 0 ∈ S n , P > 0, U > 0 and S 1 ∈ S 2n and S 2 and X ∈ R 2n×2n , Y ∈ R 5n×2n that satisfy for j = 1, 2 :

Ψ 1 (A, B) = Π 1 (T slot ) + T j Π 2 + T j Π 3 < 0, Ψ 2 (A, B) Π 1 (T slot ) -T j Π 3 T j Y T j Y T -T j U < 0, (4)
where

T 1 = T , T 2 = N T and Π 1 (T slot ) = 2He{N T 1 P N 0 } + M T 1 QM 1 -M T 2 QM 2 +M T 0 (R 1 + T slot R 2 )M 0 -M T 12 R 2 /T slot M 12 -M T 5 R 1 M 5 -N T 12 S 1 N 12 -2He{Y N 12 } -2He{N T 2 S 2 N 12 }, Π 2 = N T 0 U N 0 + 2He{N T 0 (S 1 N 12 + S T 2 N 2 )}, Π 3 = N T 2 XN 2 ,
and

M 0 = [A 0 0 BK 0] , M 1 = [I 0 0 0 0] , M 2 = [0 I 0 0 0] , M 3 = [0 0 I 0 0] , M 4 = [0 0 0 I 0] , M 5 = [0 0 0 0 I] N 0 = [M T 0 M T 5 ] T , N 1 = [M T 1 M T 2 ] T , N 2 = [M T 3 M T 4 ] T , M 12 = M 1 -M 2 , N 12 = N 1 -N 2 .
System (2) is thus asymptotically stable for any asynchronous sampling defined by (T, N ) and the delay T slot .

Proof: Because of space limitations, the proof is omitted. However the details can be found in [START_REF] Seuret | Stability analysis of networked control systems with asynchronous sampling and input delay[END_REF].

Note that the conditions from Theorem 1 include the robust stability properties with respect to the input delay T slot . This means that (4) requires the system to be stable at least for the transmission delay T slot and T = T i .

B. System with uncertainties

In this section we will consider that µ = 0. Then we want to extend the previous theorem to the case of timevarying uncertainties. In the previous stability theorem, the conditions depends almost linearly on the matrices defining the continuous-time model. Then the following corollary presents an extension of the previous theorem to uncertain and time-varying model.

Corollary 1: Consider an integer N and there non negative scalars T slot , T and µ. Assume that there exist the same matrices Q, R 1 , R 2 , P , U , S 1 and S 2 as in Theorem 1 and

X i ∈ R 2n×2n , Y i ∈ R 5n×2n that satisfy, for i = 1, . . . , M and j = 1, 2 Ψ 1i (A i , B i ) = Π 1i (T slot ) + T j Π 2i + T j Π 3i < 0, (5)
Ψ 2i (A i , B i ) = Π 1i (T slot ) -T j Π 3i T j Y i T j Y T i -T j U < 0, (6)
where

Π 1i (T slot ) = 2He{N T 1 P N 0i } + M T 1 QM 1 -M T 2 QM 2 +M T 0i (R 1 + T slot R 2 )M 0i -M T 12 R 2 /T slot M 12 -M T 5 R 1 M 5 -N T 12 S 1 N 12 -2He{Y i N 12 } -2He{N T 2 S 2 N 12 }, Π 2i = N T 0i U N 0i + 2He{N T 0i (S 1 N 12 + S T 2 N 2 )}, Π 3i = N T 2 X i N 2
, and M 0i and N 0i are defined as M 0 and N 0 but with the polytopes A i = A + µA i and B i = B + µB i . The system (2) is thus asymptotically stable for for the periodic sampling defined by T and the delay T slot .

Proof: Consider the stability conditions from Theorem 1. By noting that

M 0 (t) = Ā(t) 0 0 B(t)K 0 = M i=1 λ i (t)M 0i , N 0 (t) = M T 0 (t)M T 5 = M i=1 λ i (t)N 0i
, and by introducing the matrices variables

Y (t) = M i=1 λ i (t)Y i , X(t) = M i=1 λ i (t)X i .
Then, using the Schur complement, we note that the two conditions are linear with respect to the matrices M 0i and N 0i so that, for j = 1, 2, Ψ j ( Ā(t), B(t)) = M i=1 λ i (t)Ψ ji (A i , B i ). This allows to conclude the proof.

V. CASE STUDY

The case study applies the previous robustness approach to a weakened scheduling scheme for the pitch controller of an aircraft. We consider only the so-called "short period approximation" linearized model of an aircraft around the pitch axis. The model is given by [START_REF] Stevens | Aircraft Control and Simulation[END_REF]:

E ẋ = F x + Gu, y = Hx. (7)
The state vector is x = α θ q where α is the angle of attack, θ is the pitch angle, q is the pitch rate, the input vector u = δ E is the elevator deflection and where

E = V T -Z α 0 0 0 1 0 -M α 0 1 , H = 0 0 0 180 π 0 180 π 0 0 , G = Z δe 0 M δe , F = Zα -g 0 sinγe V T + Zq 0 0 1 Mα 0 Mq . ( 8
)
where the E matrix is always non-singular in normal flight conditions. The model parameters are the dimensionless derivatives of the standard aircraft model ( [START_REF] Stevens | Aircraft Control and Simulation[END_REF]). In practice low-pass filtering is systematically added to the noisy α angle of attack. State-of-the-art pitch control design also takes into account the elevator's dynamics, and an integrator is added in the feed-forward channel to ensure a zero steady-state error. The full controlled plant has an augmented state vector given by α q δ E α F β where α F is the filtered measure of α and β is the output of the integrator. We can then obtain standard state space equation of the form:

ẋ = Ax + Bu, y = Cx, (9)
where A = E -1 F and B = E -1 G.

An output feedback controller u = Ky = -k α α F -k q qk i β is designed using standard pole placement giving K = [-0.04238; -0.4098; 0.8426]. The control period is chosen as T = 0.08 sec, and the nominal computing slot is chosen as W CET = 0.02 sec (considering that the CPU is shared by four control tasks). The matrices A i and B i , elements of the convex combination ∆ µ A(t) and ∆ µ B(t) are defined in a simple 2 vertices polytope as A i = (-1) i A and B i = (-1) i B for i = 1, 2. Starting from the initial 'hard real-time' pattern described in Figure 1, where a W CET time slot is allocated to the control task with a period T , two weakened scheduling schemes have been considered (Figure 4):

• Case 1: A time slot T slot < W CET is allocated to the control task, but the system's period T keeps its initial value. In that case, some extra time remains to compute other activities before the new control activation. Some control improvement can be expected from the reduction of the latency from W CET to T slot ; • Case 2: Again, a time slot T slot < W CET is allocated to the control task, but the system's period is now also reduced by the same value, while the time remaining for computing other activities remains T others as in the initial scheme. In that case control improvement is expected from both the latency and sampling period reduction. The stability conditions of Theorem 1 are used to find the relations between the computing slot value (given by the ratio = T slot W CET and the maximum number of consecutive deadlines misses before unstability N , for the two cases and for several values of µ. The analysis of Case 1 (top of Figure 5) shows that the tolerance of the controller w.r.t. deadlines misses, measured by N , increases when T slot is decreased (therefore also decreasing the systematic latency). It also shows that increasingly uncertain systems, with growing values of µ, are less tolerant w.r.t. deadlines misses. In Case 2, (bottom of Figure 5) the number N of sustainable consecutive deadline misses is even improved, as the reduction of T slot induces a decreasing in both the delay and the sampling interval. Nevertheless decreasing T slot obviously increases the risk of missing deadlines. For a given distribution of execution times, the probability of missing deadlines decreases from 1 to 0 as the scheduling factor decreases from 1 (T slot = W CET ) to a minimum value where T slot = BCET (Best Case Execution Time), as depicted by the black plot in Figure 6. Assuming that the execution times of the task instances are independent, the probability of reaching the maximum tolerable number of consecutive misses are given in the same figure for the two cases and for different values of µ. Hence, for a given scheduling scheme and uncertainty assumption, it is easily possible to compute the scheduling factor corresponding at a given failure probability. In this paper the hard real-time assumption has been revisited based on robustness considerations. The theoretic contribution provides new stability conditions for feedback linear systems submitted to delays, varying sampling and uncertainties. In the case of a control task miss its deadline, the computation should be aborted and the preceding control signal hold for an extra control period, leading to a varying sampled system. In this framework, the stability condition allows computing the maximum number of consecutive deadline misses which can be tolerated by an uncertain system while keeping stability. Future design and implementation rules may be investigated to find cost effective trade-offs between embedded computing power, control performance, control robustness and overall fault-tolerance.

Fig. 2 .

 2 Fig. 2. Typical execution time distribution

0

  .35c, θ = 0. Using the nominal condition and a flight at sea level, we obtain the following numerical values for the pitch model:

Fig. 4 .

 4 Fig. 4. Scheduling cases

Fig. 5 .

 5 Fig. 5. Maximum allowed consecutive deadline misses

Fig. 6 .

 6 Fig. 6. Probability of reaching the maximum tolerable consecutive deadline misses

  In our case study, we have considered the F16 aircraft with the flight conditions given in table I. The nominal condition is: h = 0f t, x cg =

	Variable	Nominal	xcg = 0.3c	xcg = 0.38c
	V T (ft/s)	502.0	502.0	502.0
	α(rad)	0.03691	0.03936	0.03544
	θ(rad)	0.03691	0.03936	0.03544
	Q (rad/s)	0	0	0
	Thtl (0-1)	0.1385	0.1485	0.1325
	El (deg)	-0.7588	-1.931	-0.05590
			TABLE I
	FLIGHT CONDITIONS FOR SIMULATIONS