Julia Muellner

Iman Gharrad

Marie-Odile Habert

Aurélie Kas

Jean-Baptiste Martini

Florence Cormier-Dequaire

Khadija Tahiri

Marie Vidailhet

Niklaus Meier

Alexis Brice

Michael Schuepbach

Alain Mallet

Andreas Hartmann

Jean-Christophe Corvol
email: jean-christophe.corvol@psl.aphp.fr

Dopaminergic denervation severity depends on COMT Val158Met polymorphism in Parkinson's disease

Keywords: COMT, Parkinson's disease, dopaminergic denervation, motor symptoms, compensatory mechanism

Background: Catecholamine-O-methyl-tranferase (COMT) initiates dopamine degradation.

Its activity is mainly determined by a single nucleotide polymorphism in the COMT gene (Val158Met, rs4680) separating high (Val/Val, COMT HH ), intermediate (Val/Met, COMT HL ) and low metabolizers (Met/Met, COMT LL ). We investigated dopaminergic denervation in the striatum in PD patients according to COMT rs4680 genotype.

Methods: Patients with idiopathic PD were assessed for motor severity (UPDRS-III rating scale in OFF-state), dopaminergic denervation using [123I]-FP-CIT SPECT imaging, and genotyped for the COMT rs4680 enzyme. [123I]-FP-CIT binding potential (BP) for each voxel was defined by the ratio of tracer-binding in the region of interest (striatum, caudate nucleus and putamen) to that in a region of non-specific activity. Genotyping was performed using TaqMan® SNP genotyping assay. We used a regression model to evaluate the effect of COMT genotype on the BP in the striatum and its sub-regions.

Results: Genotype distribution was: 11 (27.5%) COMT HH , 26 (65%) COMT HL and 3 (7.5%) COMT LL . There were no significant differences in disease severity, treatments, or motor scores between genotypes. When adjusted to clinical severity, gender and age, low and intermediate metabolizers showed significantly higher rates of striatal denervation (COMT HL+LL BP=1.32 +/-0.04) than high metabolizers (COMT HH , BP=1.6 +/-0.08; F(1.34)=9.0, p=0.005). Striatal sub-regions showed similar results. BP and UPDRS-III motor scores (r=0.44, p=0.04) (p<0.001) were highly correlated. There was a gender effect, but no gender-genotype interaction.

Conclusions: Striatal denervation differs according to COMT-Val158Met polymorphism.

COMT activity may play a role as a compensatory mechanism in PD motor symptoms.

INTRODUCTION

The underlying mechanism for the appearance of motor symptoms in Parkinson disease (PD) has long been identified as a progressive degeneration of dopaminergic neurons in the substantia nigra pars compacta (SNc). Motor symptoms appear when 40-60% dopaminergic neurons have died, and when striatal denervation reaches about 80% [START_REF] Bezard | Relationship between the appearance of symptoms and the level of nigrostriatal degeneration in a progressive 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine-lesioned macaque model of Parkinson's disease[END_REF][START_REF] Agid | Parkinson's disease: pathophysiology[END_REF]. Compensating mechanisms are thus needed to delay the onset of motor symptoms which start when they are no longer sufficient to counterbalance striatal dopamine deficiency. In particular, an increase of dopamine turnover has been observed in animal models as well as in PD patients [START_REF] Goldberg | Dopaminergic and behavioral correlates of progressive lesioning of the nigrostriatal pathway with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine[END_REF][START_REF] Pifl | Dopamine turnover is upregulated in the caudate/putamen of asymptomatic MPTP-treated rhesus monkeys[END_REF][START_REF] Nandhagopal | Longitudinal evolution of compensatory changes in striatal dopamine processing in Parkinson's disease[END_REF]. This increase can be partly explained by an increase in dopamine synthesis through an up-regulation of tyrosine hydroxylase (TH) and aromatic acid decarboxylase (AADC) in the non-affected neurons [START_REF] Bezard | Compensatory mechanisms in experimental and human parkinsonism: towards a dynamic approach[END_REF][START_REF] Zigmond | Compensations after lesions of central dopaminergic neurons: some clinical and basic implications[END_REF][START_REF] Zigmond | Neurochemical compensation after nigrostriatal bundle injury in an animal model of preclinical parkinsonism[END_REF][START_REF] Lee | In vivo positron emission tomographic evidence for compensatory changes in presynaptic dopaminergic nerve terminals in Parkinson's disease[END_REF], as well as a decrease of dopamine uptake by a down-regulation of dopamine transporter (DAT) expression [START_REF] Agid | Parkinson's disease: pathophysiology[END_REF][START_REF] Nandhagopal | Longitudinal evolution of compensatory changes in striatal dopamine processing in Parkinson's disease[END_REF].

The catechol-O-methyl-transferase (COMT) enzyme initiates the degradation of brain synaptic dopamine levels by introducing a methyl-group from S-adenosylmethionin (SAM).

Later, methylated dopamine is further degraded by monoamine oxidase (MAO). The human COMT gene (OMIM 116790) is located on chromosome 22q11.2. and contains two codominant alleles (Val158Met polymorphism, rs4680) which impact the enzyme activity [START_REF] Floderus | The inheritance of human erythrocyte catechol-Omethyltransferase activity[END_REF].

The substitution of valine (Val) by methionine (Met) at codon 158 (Val158Met) in the membrane-bound isoform results in a trimodal distribution of high (COMT HH ), low (COMT LL ) and intermediate (COMT HL ) enzymatic activity. COMT activity has been shown to be two-to four-fold higher in the liver and red blood cells of COMT HH subjects than in those with the COMT LL variant [START_REF] Lotta | Kinetics of human soluble and membrane-bound catechol O-methyltransferase: a revised mechanism and description of the thermolabile variant of the enzyme[END_REF][START_REF] Lachman | Human catechol-O-methyltransferase pharmacogenetics: description of a functional polymorphism and its potential application to neuropsychiatric disorders[END_REF]. In a previous study, we found an association between the age at onset of motor symptoms in PD and the COMT rs4680, patients carrying COMT HH and COMT HL genotypes showing an earlier age of onset than patients with COMT LL genotypes [START_REF] Klebe | The Val158Met COMT polymorphism is a modifier of the age at onset in Parkinson's disease with a sexual dimorphism[END_REF]. These results suggest that COMT activity may be involved in the We hypothesized that COMT-activity in the striatum in PD patients contributes to the compensatory mechanisms that impact on clinical severity of motor symptoms in PD. As the extent of this activity is defined by COMT-genotype, we investigated whether, if normalized to motor severity, patients with low COMT-activity would show a higher level of dopaminergic denervation in the striatum measured by [123I]-FP-CIT than patients with high COMTactivity.

METHODS

Subjects and study design

The data in this study was obtained from a clinical trial investigating the effect of subcutaneous injections of bee venom in PD patients (clinicaltrials.gov, NCT01341431).

Clinical and imaging data used in the study were obtained at the screening visit, before randomization and before any therapeutic intervention. Out of 50 patients who were seen for

Dopamine transporter imaging

SPECT studies were performed in all subjects using a triple-head camera equipped with low energy, high resolution parallel hole collimators (Irix, Philips), 3 hours after injection of 185 MBq (range 165-188 MBq) of [123I]-FP-CIT. Thyroid uptake was blocked before the scan by administration of potassium perchlorate (400 mg orally). One hundred and twenty projections were acquired during 30 minutes in a 128 x 128 matrix. Projections were reconstructed using an iterative algorithm, post-filtered (low pass filter: order = 4, cut-off frequency = 0.35 cm-1), then corrected for attenuation using the Chang method [START_REF] Chang | Investigating the use of nonattenuation corrected PET images for the attenuation correction of PET data[END_REF] (µ = 0.12 cm-1).

All reconstructed volumes were converted from DICOM to NIFTI format. Parametric images of binding potential (BP) were computed from the reconstructed [123I]-FP-CIT volumes using the Anatomist and Brainvisa software packages (http://brainvisa.info/). For each FP-CIT study, a volume of interest was drawn within the occipital cortex to obtain non-specific activity, and BP was calculated in each voxel using the following formula: [START_REF] Kas | Validation of a standardized normalization template for statistical parametric mapping analysis of 123I-FP-CIT images[END_REF]. Next, BP was estimated for each parametric image in a standard set of specific volumes of interest (VOI), i.e. right and left caudate nuclei and putamens. These VOI were manually delineated on the MNI single subject MRI by AK in a previous work [START_REF] Kas | Validation of a standardized normalization template for statistical parametric mapping analysis of 123I-FP-CIT images[END_REF].

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 7 using a custom [123I]-FP-CIT template

Genotyping

DNA was extracted from peripheral blood lymphocytes using a salting out procedure and stored at -80°C. The rs4680 was analyzed using an a llelic discrimination Taqman assay (ABI PRISM 7900 sequence detection system). The 5' nuclease activity of taq DNA polymerase was used to detect the fluorescent reporter signal generated after the polymerase chain reaction (PCR). As positive controls, two samples of DNA with the COMTHH, COMTHL, and COMTLL genotyped previously confirmed by sequencing were processed concomitantly for each assay. Patients signed a specific informed consent form for the genetic analysis.

Statistics and Analysis

Clinical characteristics were compared between genotypes using the non-parametric Mann-Whitney test and the Fisher Exact test. Gender differences were compared using the Mann-Whitney test. A general multiple regression model was used to analyze the effect of the COMT genotype (COMT HH , COMT HL+HL ) on nigrostriatal denervation, adjusted for UPDRS-III score, age and sex. Univariate correlation between BP, UPDRS III and age was performed using the Spearman Rank Correlation test. A non-corrected threshold of p<0.05 was defined for significance. All statistical analyses were performed using Statistica 9.1 software (Statsoft, Maison Alfort, France). 1. There were no significant differences between age, gender, age at onset, disease duration or motor severity (UPDRS III) between genotypes. The number of patients on levodopa and/or dopamine agonists was similar between the COMTHH and the COMTHL+LL groups (respectively 10/11 (91%) and 24/29 (83%) on levodopa, p=0.46; 7/11 (64%) and 22/29 (76%), p=0.35), as well as and the current total levodopa equivalent daily doses did not differ between groups (table 1).

RESULTS

Patient characteristics

Table 1

Total striatal dopaminergic denervation

The BP in the total striatum had an average of 1.38 (+/-0.34, standard deviation) with a range from 0.62 to 2.21. BP in the putamen (1.24 +/-0.32) was significantly lower than in the caudate nucleus (1.52 +/-0.39, p < 0.001). BP in the total striatum was significantly different between genotypes when adjusted to clinical severity (UPDRS III), gender and age (F(1,34)= 9.0, p=0.005, Table 2). Low and intermediate metabolizers (COMT HL+LL ) showed a higher rate of denervation than high metabolizers (COMT HH ) (Figure 1). By considering the different sub-regions of the striatum, we found similar results for the caudate nucleus (F(1,34)= 8.6, p=0.006, , Figure 1B and Table 2) and the putamen (F(1,34)= 7.0, p=0.01, Figure 1C and Table 2). Dopaminergic denervation was higher in low and intermediate metabolizers as compared to high metabolizers for both the caudate nucleus and the putamen. The LEDD had no significant effect when introduced as a cofactor in the model.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

Other factors associated with dopaminergic denervation

There was a significant independent correlation between BP in the total striatum and clinical motor symptoms (UPDRS III: p=0.04, r=-0.44) (Table 3, Figure 2). This correlation was significant for both the putamen and the caudate nucleus denervation (r=-0.43, p=0.04, and r=-0.44, p=0.04 respectively). In accordance with previous studies [START_REF] Haaxma | Gender differences in Parkinson's disease[END_REF], we also found an independent effect of gender (Table 3). In our study, BP in women was 1.59 +/-0.30 as compared to 1.19 +/-0.27 in men (p <0.001). However, there was no significant gendergenotype interaction in our model (p=0.33).

Table 3

DISCUSSION

We observed differences in dopaminergic denervation between Val158Met COMT genotypes in PD patients when adjusted for clinical motor symptom severity (UPDRS III score). Our results show that, for similar motor severity, patients with a COMT HL+LL genotype, associated with a lower COMT activity, have a greater extent of nigrostriatal denervation than those with a COMT genotype associated with a higher COMT activity (COMT HH ). This result suggests that patients with a lower COMT-activity are able to compensate the neuronal loss to a greater extent by increasing dopamine bioavailability in the striatum. The Val158Met COMT polymorphism has a functional impact on enzyme activity in the periphery in healthy subjects [START_REF] Lachman | Human catechol-O-methyltransferase pharmacogenetics: description of a functional polymorphism and its potential application to neuropsychiatric disorders[END_REF] as well as in PD patients [START_REF] Maltete | Erythrocytes catechol-o-methyl transferase activity is up-regulated after a 3-month treatment by entacapone in parkinsonian patients[END_REF][START_REF] Corvol | The COMT Val158Met polymorphism affects the response to entacapone in Parkinson's disease: a randomized crossover clinical trial[END_REF]. A PET study recently confirmed that the Val158Met polymorphism also modifies dopamine turnover in the prefrontal cortex in PD patients [START_REF] Hirvonen | COMT Val158Met genotype does not alter cortical or striatal dopamine D2 receptor availability in vivo[END_REF].. Indeed, this polymorphism has been associated with prefrontal cortex function, such as working memory, in several studies performed in healthy controls [START_REF] Mier | Neural substrates of pleiotropic action of genetic variation in COMT: a meta-analysis[END_REF] as well as in PD [START_REF] Ch | Catechol Omethyltransferase Val158Met genotype influences frontoparietal activity during planning in patients with Parkinson's disease[END_REF]. However, the role of the COMT Val158Met polymorphism Indeed, by contrast to the prefrontal cortex, uptake of dopamine by the DAT is the most effective mechanism in the striatum, where the contribution of the COMT remains secondary under normal conditions. Although COMT is expressed in the striatum, inhibition of its activity in rodents either via pharmacological intervention or via disruption of the COMT gene in rodents reveals minor change in their motor behaviour and brain dopamine levels [START_REF] Gogos | Catechol-Omethyltransferase-deficient mice exhibit sexually dimorphic changes in catecholamine levels and behavior[END_REF]. In accordance with this finding, a study analyzing D2-receptor binding (an indirect measure of endogenous striatal dopamine bio-availability) failed to demonstrate a significant difference between Val158Met genotypes in healthy subjects [START_REF] Mier | Neural substrates of pleiotropic action of genetic variation in COMT: a meta-analysis[END_REF]. However, although COMT deficiency does not alter dopamine concentrations in the striatum, its metabolism is changed as demonstrated by a dramatic increase of DOPAC levels in the dorsal striatum of mice lacking COMT activity [START_REF] Huotari | Effect of dopamine uptake inhibition on brain catecholamine levels and locomotion in catechol-Omethyltransferase-disrupted mice[END_REF][START_REF] Tammimäki | Effect of S-COMT deficiency on behavior and extracellular brain dopamine concentrations in mice[END_REF]. Higher levels of DOPAC in the striatum of patients with the COMTHL+LL genotype could partly explain the motor compensation observed in our study since intracerebral administration of DOPAC in the brain in rats has been shown to cause a modest increase of behavioural activity and stereotypy in rats [START_REF] Nakazato | Behavioral activity and stereotypy in rats induced by L-DOPA metabolites: a possible role in the adverse effects of chronic L-DOPA treatment of Parkinson's disease[END_REF]. A better explanation would be that, in the pathological condition of PD in which dopaminergic terminals degenerate and the DAT expression is dramatically decreased in the striatum, the COMT becomes the major pathway to control dopamine extracellular levels. The effect of the disruption of the COMT gene after dopaminergic denervation has not been studied yet in knockout mice. However, the pharmacological inhibition of DAT in mice lacking COMT resulted in higher dopamine levels in the striatum although this effect increase had little effects on behaviour [START_REF] Huotari | Effect of dopamine uptake inhibition on brain catecholamine levels and locomotion in catechol-Omethyltransferase-disrupted mice[END_REF][START_REF] Huotari | Damphetamine responses in catechol-O-methyltransferase (COMT) disrupted mice[END_REF].

The hypothesis that COMT activity participates in the dopamine bioavailability in the dorsal striatum, is also supported by previous findings showing that PD patients with the COMT HH genotype have an earlier age of disease onset as compared to COMT LL [START_REF] Klebe | The Val158Met COMT polymorphism is a modifier of the age at onset in Parkinson's disease with a sexual dimorphism[END_REF]. This result is consistent with our study suggesting that patients with a higher COMT activity (COMT HH ) have lower compensatory capacity than patients with a lower COMT activity (COMT HL+LL ).

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 11

Importantly, this effect is unlikely to be related to a role of the COMT on striatal dopaminergic denervation since no association has been found between the COMT Val158Met polymorphism and PD in the Caucasian population [START_REF] Lechun | The COMT Val158Met polymorphism as an associated risk factor for Parkinson's disease in Asian rather than Caucasian populations[END_REF]. A potential role of the COMT as a susceptibility factor for PD in patients with other ethnic background, particularly in the Asian population, is still controversial [START_REF] Lechun | The COMT Val158Met polymorphism as an associated risk factor for Parkinson's disease in Asian rather than Caucasian populations[END_REF][START_REF] Fj | COMT gene and risk for Parkinson's disease: a systematic review and meta-analysis[END_REF]. Another indirect evidence of a potential role of the COMT activity in the striatum is the association that has been found between the low-activity genotype of theVal158Met COMT polymorphism and an increased risk of levodopa-induced dyskinesia in PD [START_REF] De Lau | Catechol-O-methyltransferase Val158Met and the risk of dyskinesias in Parkinson's disease[END_REF].

Interestingly, a gender dimorphism has been found for the Val158Met-polymorphism effect in mice [START_REF] Chen | Functional analysis of genetic variation in catechol-O-methyltransferase (COMT): effects on mRNA, protein, and enzyme activity in postmortem human brain[END_REF] as well as on the age of onset in PD patients [START_REF] Klebe | The Val158Met COMT polymorphism is a modifier of the age at onset in Parkinson's disease with a sexual dimorphism[END_REF] which remains to be understood.

In this study, we did not find an interaction between Val158Met COMT polymorphisms and gender for nigrostriatal denervation adjusted on motor severity, but the sample size was too small to properly evaluate this effect.

Our study has some limitations. As PD patients included in this study were more advanced in the course of their disease, this explains the greater extent of dopaminergic denervation in comparison to previous studies in de novo PD patients [START_REF] Ichise | SPECT imaging of pre-and postsynaptic dopaminergic alterations in L-dopa-untreated PD[END_REF]. In addition, we cannot rule out a residual treatment effect although UPDRS III testing and [123I]-FP-CIT imaging were performed in the OFF-state after a period of washout taking into account the pharmacology of anti-parkinsonian drugs [START_REF] Storch | Effects of dopaminergic treatment on striatal dopamine turnover in de novo Parkinson disease[END_REF]. The robust correlation between motor state (UPDRS part III) and dopamine denervation suggests that the OFF state indeed reflects the motor status of the patients. Our study is also limited by the relative small sample size and will have to be replicated in a larger population of de novo, drug-naïve, PD patients.

CONCLUSION

We showed that genotypes associated with low COMT activity is correlated with a greater extent of nigrostriatal denervation when adjusted to UPDRSIII-score. How COMT activity influences compensatory mechanisms of motor symptoms during the course of PD and whether it influences disease progression remains to be determined. -We performed a UPDRSIII-score and [123I]-FP-CIT SPECT imaging on 40 PD patients -All patients were genotyped for the COMT-Val158Met polymorphism -Adjusted to UPDRSIII-score PD patients had different levels of striatal denervation -We showed that the COMT-genotype impacts on clinical severity of motor symptoms -We conclude that COMT enzyme activity may act as a compensatory mechanism in PD

  delay of motor symptoms in PD, a lower COMT activity acting as a compensatory mechanism of dopaminergic denervation. The level of dopaminergic neuronal degeneration in the substantia nigra pars compacta can be indirectly measured by [123I]-FP-CIT Single Photon Emission Computed Tomography (SPECT). [123I]-FP-CIT binds to the dopamine transporter, the level of its binding capacity reduction in the striatum reflecting the amount of dopaminergic terminals denervation.

  a pre-screening visit, 44 were included between April 2011 and October 2012 at the Pitié-Salpêtrière Hospital (Paris, France). Inclusion criteria were age > 40, and idiopathic PD according to United Kingdom Parkinson's disease society brain bank criteria (UKPDSBB) with a Hoehn and Yahr score between 1.5 and 3 in the OFF-state. Exclusion criteria were magnet resonance imaging (MRI) indicating atypical or vascular PD, normal [123I]FP-CIT single photon emission computerized tomography (SPECT), and allergy to bee venom. The study was submitted to the regulatory authority and the local ethics committee. Written informed consent was obtained by all subjects before being included in the study.

  Clinical characteristics were obtained for each patient including medical history, drug history and current medication, Mini-Mental State Examination (MMSE), Frontal Assessment Battery (FAB), Unified Parkinson disease Rating Scale (UPDRS) part I-IV, Hoehn and Yahr stage, onset of PD symptoms and time of PD diagnosis. The UPDRS motor scale (part III) was addressed at the screening visit to patients in the OFF state, i.e. in the morning, after withdrawal of dopaminergic drugs for at least 12 hours for L-DOPA, and 48 hours for dopamine agonists and rasagiline. A [123I]-FP-CIT SPECT scan was performed 1-25 days before or 3-17 days after the screening visit. The examining neurologist and the patient were blinded for COMT-genotype and SPECT evaluations.

  (mean voxel activity / mean occipital activity) minus 1. The resulting parametric volumes were then spatially normalized to the Montreal Neurological Institute (MNI) space with the Statistical Parametric Mapping software (SPM8, Welcome Department of Cognitive Neurology, University College, London)

  M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 8 Among the 44 patients screened, 4 were excluded from the analysis: 2 patients had vascular abnormalities on brain MRI, 1 patient had a normal [123I]-FP-CIT SPECT, and 1 patient refused to participate in the genetic study. The distribution of the Val158Met COMT polymorphism genotype for the remaining 40 patients, all of Caucasian origin, was in slight Hardy-Weinberg disequilibrium (p-value = 0.03): 11 (27.5%) COMT HH , 26 (65%) COMT HL and 3 (7.5%) COMT LL . Subjects with COMT HL and COMT LL were considered as a group for further analyses since there was only 3 patients with the COMT LL genotype. The clinical characteristics of these patients are summarized in Table

  and on the dopamine turnover in the striatum remains controversial.

FiguresFigure 1 Title:

 1 Figures

Figure 2 Title:

 2 Figure 2

Table 1 Title

 1

	: Patient characteristics
	Genotype	COMT HH (n=11)	COMT HL+LL (n=29)
	Age, years	63 (54-78)	63 (44-80)
	Age at onset, years	56 (49-74)	54 (36-75)
	Sex ratio, m/f	7/4	14/15
	UPDRS III	30 (10-42)	26 (6-59)
	Levodopa daily	300 (0-1132)	400 (0-1132)
	doses, mg/day
	Dopamine agonists	120 (0-371)	300 (0-600)
	daily dose, LEDD,
	mg/day
	Total LEDD	500 (154-1132)	657 (130-1640)

Legend: LEDD: levodopa equivalent daily dose; values are median (range).

Table 2

 2 Title: Striatal denervation in the striatum according to COMT genotypes Values are mean +/-standard errors. P-value: regression analysis of the COMTgenotype effect on binding potential (BP) in the total striatum, putamen, and caudate nucleus, adjusted to UPDRS part III, age and gender.

		Striatum	Putamen	Caudate nucleus
	COMT HH	1.5 +/-0.1	1.4 +/-0.1	1.6 +/-0.1
	COMT HL+LL	1.3 +/-0.06	1.2 +/-0.05	1.5 +/-0.06
	p-value	0.005	0.006	0.01
	Legend:

Table 3

 3 Title: Effects of Age, COMT genotype, UPDRS-III score and gender on striatal denervation Legend: Regression analysis parameters for age, UPDRS-III score, COMT-genotype, gender, and genotype*gender interaction on nigrostriatal denervation (BP) in the total striatum, the caudate nucleus, and the putamen.

		Striatum		Caudate nucleus	Putamen
		F	p	F	p	F	p
	Age	3.0	0.09	3.3	0.08	2.1	0.16
	UPDRS III	5.6	0.02	5.2	0.03	5.3	0.03
	Genotype	9.0	0.005	8.6	0.006	7.0	0.01
	Gender	23.2	0.0003	33.9	<0.001	10.1	0.003
	Genotype*gender
		1.0	0.33	2.6	0.12	0.02	0.90
	interaction

French government's program "Investissement d'Avenir" (ANR-


Julien Burgin

Satyabrata Si

Marie-Hélène Delville

Jean-Pierre Delville
email: jp.delville@loma.u-bordeaux1.fr

Enhancing optofluidic actuation of micro-objects by tagging with plasmonic nanoparticles

We report experimentally and theoretically on the significant exaltation of optical forces on microparticles when they are partially coated by metallic nanodots and shined with laser light within the surface plasmon resonance. Optical forces on both pure silica particles and silica-gold raspberries are characterized using an optical chromatography setup to measure the variations of the Stokes drag versus laser beam power. Results are compared to the Mie theory prediction for both pure dielectric particles and core-shell ones with a shell described as a continuous dielectric-metal composite of dielectric constant determined from the Maxwell-Garnett approach. The observed quantitative agreement demonstrates that radiation pressure forces are directly related to the metal concentration on the microparticle surface and that metallic nanodots increase the magnitude of optical forces compared to pure dielectric particles of the same overall size, even at very low metal concentration. Behaving as "micro-sized nanoparticles", the benefit of microparticles coated with metallic nanodots is thus twofold: it significantly enhances optofluidic manipulation and motion at the microscale, and brings nanometric optical, chemical or biological capabilities to the microscale.

Introduction

Since the pioneer works by Ashkin and associates on optical levitation and tweezing [START_REF] Ashkin | Optical trapping and manipulation of neutral particles using lasers[END_REF], investigation on optical forces has known a tremendous development and is now considered as the corner stone of contactless manipulation techniques of small objects in fluid environments. Classically, optical tweezing takes advantage of opposing scattering and gradient forces to trap and move single particles [START_REF] Grier | A revolution in optical manipulation[END_REF][START_REF] Jonás | Light at work: the use of optical forces for particle manipulation, sorting, and analysis[END_REF]. The radiation pressure from scattering forces has also shown its efficiency in countering and balancing the Stokes drag for optical sorting and optical chromatography in order to separate flowing particles of different polarisabilities within microfluidic devices [START_REF] Lall | On-the-fly cross flow laser guided separation of aerosol particles based on size, refractive index and density-theoretical analysis[END_REF][START_REF] Hart | Refractive-index-driven separation of colloidal polymer particles using optical chromatography[END_REF][START_REF] Hart | Particle separation and collection using an optical chromatographic filter[END_REF][START_REF] Kaneta | Theory of optical chromatography[END_REF]. Up to now, most of the efforts have been devoted to describe these light couplings with model particles and to optimize light patterns for dedicated optical functionalities such as positioning [START_REF] Bowman | Optical trapping and binding[END_REF], conveying [START_REF] Applegate | Microfluidic sorting system based on optical waveguide integration and diode laser bar trapping[END_REF], and sorting [START_REF] Macdonald | Microfluidic sorting in an optical lattice[END_REF][START_REF] Ploschner | Bidirectional optical sorting of gold nanoparticles[END_REF]. The manipulated particles were mainly pure dielectric or metallic [START_REF] Hart | Refractive-index-driven separation of colloidal polymer particles using optical chromatography[END_REF][START_REF] Ploschner | Bidirectional optical sorting of gold nanoparticles[END_REF][START_REF] Zelenina | Tunable optical sorting and manipulation of nanoparticles via plasmon excitation[END_REF][START_REF] Ashkin | Observation of a single-beam gradient force optical trap for dielectric particles[END_REF][START_REF] Svoboda | Optical trapping of metallic Rayleigh particles[END_REF][START_REF] Guffey | Plasmon-driven selective deposition of au bipyramidal nanoparticles[END_REF], with sizes around the micrometer for dielectric particles and down to a few tens of nanometers for metallic particles [START_REF] Moffitt | Recent advances in optical tweezers[END_REF][START_REF] Dienerowitz | Optical manipulation of nanoparticles: a review[END_REF]. The optical manipulation of cells [START_REF] Zhang | Optical tweezers for single cells[END_REF], bacteria [START_REF] Ashkin | Optical trapping and manipulation of viruses and bacteria[END_REF], pollens or spores [START_REF] Terray | Cascade optical chromatography for sample fractionation[END_REF], is also a very active field which has evidenced the importance of particle's internal complexity making difficult any attempt at quantitatively predicting the amplitude of the optical forces. This was our first motivation to investigate optical forces on microparticles with a controlled complexity [START_REF] Kim | Radiation pressure efficiency measurements of nanoparticle coated microspheres[END_REF]. The second motivation was to find a way to increase the amplitude of optical forces which is often too weak for applications. For instance the optical chromatography efficiency is limited in terms of particle downsizing due to the weakness of the scattering force amplitude compared to the Stokes drag; the actual limit being roughly the micrometer range for particle velocities of a few tens of µm/s under a 1W laser power [START_REF] Kaneta | Theory of optical chromatography[END_REF]. Conversely, metallic particles exhibit much larger scattering cross sections than pure dielectric particles due to the presence of optical resonance in the visible spectrum, the socalled surface plasmon resonance (SPR), related to the dielectric confinement and imputable to the collective oscillations of the free electrons cloud. Such plasmon resonances in silicametal raspberry and core-shell hybrid particles should increase the optical force amplitude and make their manipulation easier [START_REF] Ploschner | Bidirectional optical sorting of gold nanoparticles[END_REF][START_REF] Zelenina | Tunable optical sorting and manipulation of nanoparticles via plasmon excitation[END_REF][START_REF] Agayan | Optical manipulation of metalsilica hybrid nanoparticles[END_REF][START_REF] Rodriguez-Otazo | Nanometer gold-silica composite particles manipulated by optical tweezers[END_REF]. The third motivation to optically manipulate these hybrid dielectric-metal particles is related to the role they can play in several nanoscale promising applications: local sensing (hybrid particles allow enhanced sensitivity to their environment compared to single plasmonic particles) [START_REF] Choi | Core-satellites assembly of silver nanoparticles on a single gold nanoparticle via metal ion-mediated complex[END_REF], electromagnetic field enhancement (silica-metal particles are promising SERS active probes) [START_REF] Balint | Simple route for preparing optically trappable probes for surface-enhanced Raman scattering[END_REF][START_REF] Tamoto | Gold nanoparticle deposition on silica nanohelices: a new controllable 3d substrate in aqueous suspension for optical sensing[END_REF], and subwavelength optics (dielectric metal particles are used as elemental bricks for assembled metamaterials or as components in nano-devices) [START_REF] Mühlig | Optical properties of a fabricated self-assembled bottom-up bulk metamaterial[END_REF][START_REF] Engheta | Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials[END_REF]. Nevertheless a quantitative description of optical forces on hybrid metal-dielectric particles still remains elusive but challenging even from a fundamental point of view.

Wet chemistry now allows the synthesis of a large diversity of particles [START_REF] Jones | Templated techniques for the synthesis and assembly of plasmonic nanostructures[END_REF][START_REF] Tao | Shape control of colloidal metal nanocrystals[END_REF], and particularly silica-gold raspberry-like particles [START_REF] Pastoriza-Santos | Optical properties of metal nanoparticle coated silica spheres: a simple effective medium approach[END_REF][START_REF] Pham | Preparation and characterization of gold nanoshells coated with self-assembled monolayers[END_REF]. From the material engineering point of view, these complex particles are very attractive as "micron-sized nanoparticles" because they present both micrometric size and nanoscale optical properties such as SPR [START_REF] Pastoriza-Santos | Optical properties of metal nanoparticle coated silica spheres: a simple effective medium approach[END_REF][START_REF] Pham | Preparation and characterization of gold nanoshells coated with self-assembled monolayers[END_REF]. They are also very striking systems because they are able to show how nanoscale tags can impact the mobility of microscale objects. Finally, these raspberries offer the opportunity to investigate the role of increasing complexity in optical manipulation. The goal of the present work is to present quantitative results on the metallic contribution of the optical radiation pressure on silica-gold raspberries flowing in a microfluidic channel. We evidence a significant increase of the optical force magnitude compared to pure silica particles of the same overall size even at very low metal concentration (less than 1%). We also perform numerical simulation to quantitatively address the measured forces, and quantify the role of nanometric metallic tags. These results open up the way for the optofluidic actuation of hybrid plasmonic particles within microfluidic environments.

Experimental design

The experimental setup is based on the optical chromatography scheme illustrated in Fig. 1(a). We fabricate a microfluidic device using a 50 µm internal diameter cylindrical capillary (VitroCom). It is connected to a syringe pump or to a hydrostatic pressure control and then inserted in a water-filled quartz spectroscopy cell (Hellma) mounted on an Olympus IX71 inverted microscope allowing x and ŷ displacements; ẑ is the vertical axis. A continuous wave laser beam (wavelength in vacuum λ 0 = 532 nm from a Coherent Verdi Laser) with a single transverse mode and a Gaussian intensity profile is sent into the microchannel with a wave vector in the direction x opposed to the fluid flow. 1.).

The beam waist ω is set a few mm inside the microchannel exit at the center of the observation area of the microscope; it is controlled by a series of three fused silica lenses to be 15 µm large. Such a value ensures an overall coverage of the microchannel section by the transverse beam intensity distribution as it prevents diffraction effects by the microchannel edges. It also leads to a Rayleigh length of 1.4 mm, that allows to ignore the laser beam divergence over more than 2 mm centered around the beam waist by considering a mean beam waist ω = 17 ± 2 µm during the overall displacement of the particles. The two first lenses play the role of a telescope of magnification 6X and the third lens, of focal length 40 cm, loosely focuses the laser beam into the channel. Observation is performed with a 10X objective (Olympus UIS2 LMPLFLN) using both the white light Köhler source of the microscope and the green laser light scattered by the flowing particles; an orange band-pass filters allows to reduce the scattered intensity for naked eye observation and prevents camera saturation. Images, as that shown in Fig. 1(b), are grabbed at a frame rate of 5 fps with a USB camera mounted in place of one of the microscope eyepieces. The videos are analyzed with a homemade Matlab particle tracking program adapted from a free online code [START_REF] Blair | The matlab particle tracking code repository[END_REF].

The particles are produced using a three-step method. First, we synthesize the silica microparticles with a constant monomer supply technique [START_REF] Nozawa | Smart control of monodisperse Stöber silica particles: effect of reactant addition rate on growth process[END_REF][START_REF] Nozawa | Growth of monodisperse mesoscopic metal-oxide colloids under constant monomer supply[END_REF] to preserve monodispersity during particle growth; the final size of the particles is monitored by the flow rate amplitude of a diluted tetraethyl orthosilicate solution. The particles are then characterized by Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). We choose two suspensions of average particle diameters, D = 1.17 µm and D = 1.46 µm with a standard deviation smaller than 3%, above the micron to guaranty optical actuation of pure silica particles with beam powers below the Watt. Gold nanodots were synthesized according to literature methods [START_REF] Frens | Controlled Nucleation for the regulation of the particle size in monodisperse gold suspensions[END_REF][START_REF] Basu | Biomolecule induced nanoparticle aggregation: effect of particle size on interparticle coupling[END_REF][START_REF] Pramanik | Size-dependent interaction of gold nanoparticles with transport protein: a spectroscopic study[END_REF], yielding nanodots of diameter d = 15 ± 2 nm. Following the Pastoria-Santos method [START_REF] Pastoriza-Santos | Optical properties of metal nanoparticle coated silica spheres: a simple effective medium approach[END_REF], the silica-gold raspberries are eventually assembled by performing a coating of the silica core with (3-aminopropyl)triethoxysilane (APS) and then by adding a determined volume of citrate stabilized gold nanodots that adsorb on the APScoated silica surface. Assuming a perfect theoretical coverage of silica beads by 100% of the nanodots added in solution, concentrations are chosen so as to adsorb ~400 gold nanodots on a 1.17 µm-diameter particle (sample α, volume fraction for 100% yield φ 100% = 1.1%) and ~250 and ~500 gold nanodots on a 1.46 µm-diameter particle (corresponding respectively to samples β and γ with volume fractions for for 100% yield φ 100% of 0.45% and 0.9%); see Table 1. Figure 1(c) shows a TEM image of sample α, a raspberry with diameter D = 1.17 µm coated with d = 15 nm gold nanodots. The samples are diluted to get 1.5 10 8 particles per mL in aqueous solution and infused in the microchannel with a 1.5 mL Terumo syringe. The flow is actuated either by a KD Scientific syringe pump or a pressure gauge. The first method, called optical chromatography mode, consists in establishing a controlled flow rate in the microchannel and using the counter-propagating electromagnetic wave to apply optical forces on the flowing particles in the opposite direction; particle are eventually immobilized when Stokes drag and optical radiation pressure are balanced. The second method, preferentially used in the present investigation is called velocimetry mode. It consists in initially immobilizing the particles within the microchannel by adjusting the hydrostatic pressure and setting them in movement by turning on the laser.

Theoretical aspects

Optical forces are related to momentum exchanges and/or transfer between the exciting electromagnetic wave and the irradiated particle. This occurs whenever the momentum of photons is modified in amplitude and/or in direction. For instance particles may be set in motion when they scatter photons elastically, a mechanism used in optical chromatography, or when photons are partially or totally absorbed by the particle. As a consequence, the momentum conservation produces a density force which is proportional to the wave momentum, n I c x , and to the radiation pressure particle cross section C rp related to the scattering C scatt and the absorption C abs cross section; here I is the laser beam intensity, x the wave vector direction, n the index of refraction of the surrounding fluid and c the light celerity. The calculation of these cross sections is performed from the Generalized Lorentz Mie Theory [START_REF] Ren | Radiation pressure forces exerted on a particle arbitrarily located in a gaussian beam by using the generalized Lorenz-Mie theory, and associated resonance effects[END_REF][START_REF] Harada | Radiation forces on a dielectric sphere in the Rayleigh scattering regime[END_REF]. Meanwhile, when the radius R of the particles is far smaller than the waist ω of the laser beam, as in the present experiments, one can consider the incident field as a plane wave and use the formalism of Mie Theory as described by Bohren and Huffman [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF]. Mie theory calculation basically allows for the determination of C ext (the so-called extinction cross section) and C scatt , and then abs ext scatt C C C = -, from Mie wave amplitudes a n and b n involving Bessel functions and particle characteristics such as size and index of refraction (see [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF] for details). In order to estimate the radiation pressure forces, one also needs to take into consideration the angular dependence of scattering by introducing the asymmetry parameter cos g θ =

, which gives the averaged scattering angle (incident wave direction θ = 0, back scattering θ = π) [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF]. The force resulting from the interaction between the beam and the particle contains two contributions: one due to absorption, proportional to C abs , and another one due to scattering ( )

1 cos scatt C θ ⋅ -
to take angular dependence into account. The radiation pressure cross section is then the sum of these two terms:

( ) , where P is the laser beam power.

1
The resulting radiation pressure force is:

2 2 rp rp P n F C c πω =
. For convenience, we can also use the definition of the cross section efficiency

2 rp rp Q C R π =
to rewrite the force expression as:

2 2 2 2 2 2 . rp rp rp P n n R F R Q P Q c c π πω ω = = (1)
At a given optical wavelength, we can consider two limiting particle size regimes: the Rayleigh regime for small particles (condition:

0 2 R n π λ <<
) and the ray optics model for large particles (condition:

( ) 0 2 1 part R n n n π λ ->>
, where n part is the refractive index of the particle). The latter is widely used in optical chromatography since this technique is mainly devoted to microparticles separation. In this case, Q rp can be advantageously replaced by the ray optics efficiency Q* which only depends on the refractive indices n part and n [START_REF] Kaneta | Theory of optical chromatography[END_REF][START_REF] Ashkin | Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime[END_REF]. However when the size range of the used particles is close to the optical wavelength, a rigorous description of optical forces becomes mandatory and requires a Mie description of light scattering from Maxwell's equations. In this study, we performed calculations of F rp within the framework of Mie theory for two main reasons. Firstly, the particles belong to a regime in between the Rayleigh and the ray optics one. Secondly, the Rayleigh and the ray optics formalism are not well-adapted to hybrid particles. For pure silica particles, we nonetheless performed Mie and ray optics calculations in order to compare them with previous works and to figure out the validity range of the approximation. For metal-dielectric particles, we calculated F rp with a Matlab code implemented for spherical core-shell particles [START_REF] Mätzler | Matlab functions for mie scattering and absorption[END_REF]. To do so, we need the dielectric functions of the core ε core and the shell ε shell . As the metal nanodots adsorbed on the silica microparticle surface are very small compared to the optical wavelength and since they are isotropically distributed onto this surface with a volume fraction φ around the percent, we can confidently assume a description of the shell as a continuous composite medium and use the Maxwell-Garnett approach to determine its dielectric constant:

( ) ( ) ( ) ( ) 1 2 2 1 , 1 2 m shell m m ε φ ε φ ε ε ε φ ε φ + + - = -+ +   (2)
with ε the complex gold dielectric function derived from Johnson and Christy π η υ = for a solid sphere and η is the water viscosity. However, the optical absorption of gold nanoparticles present in the shell of the raspberries will heat the surrounding water [START_REF] Seol | Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating[END_REF]. As a result, the viscosity of water will decrease as well as Stokes drag Stokes F which varies linearly with η, and fitting the data without considering this issue may artificially increase the intrinsic enhancement of the optical force due to the gold layer. The temperature dependence of the viscosity of water can be estimated from the Vogel-Fulcher empiric law [START_REF] Ruijgrok | Brownian fluctuations and heating of an optically aligned gold nanorod[END_REF]. To calculate this overheating, we assume that neither silica nor water absorb light at the used wavelength. Using flux and temperature continuity conditions at both core/shell and shell/water interfaces, the absence of thermal gradient at the center of the particle and convergence to room temperature T ∞ at infinity, the stationary radial profile of temperature in water due to the thin composite shell is given by [START_REF] Seol | Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating[END_REF]:

( ) 1 , 4 abs C I T r R d T r π ∞ ≥ + = + ⋅ Λ ( 3
)
where Λ is the thermal conductivity of water ( -1 1 0.6 W.K .m - Λ =

). In our case the temperature increase ( )

T R d T ∞ + -
at the surface of the particles varies from 0 to 20 K, depending on the incident power and the volume fraction φ.

Results and discussion

To investigate the optical forces applied onto hybrid silica@gold raspberries in a microfluidic flow, we use the optical chromatography setup in the velocimetry mode illustrated in Figs. 1(a-b). The particles are initially immobilized within the microchannel by adjusting the hydrostatic pressure and then set in motion by turning on the laser. After a short time, the particles move at a constant speed, typically a few tens of µm/s depending on the laser beam power. We measure the particle velocity of both pure silica microparticles and silica@gold raspberries based on the same core particle. For pure silica microparticles, we deduce the optical force from a direct balance with the Stokes drag ( To measure the optical force enhancement induced by the metallic nanoparticles tags that partially cover the silica core (Fig. 1(c)), we proceed iteratively due to laser heating and the subsequent temperature dependence of the viscosity of water. Fixing the gold volume fraction φ, we first calculate the laser overheating and the water viscosity to get the Stokes drag and the enhancement factor on optical forces. Secondly, we use Mie theory to calculate the radiation pressure cross section C rp of silica@gold raspberries, deduce the optical force and calculate the enhancement factor relatively to core particles. Dichotomy in volume fraction φ is performed up to equality of the enhancement factors. The converging gold volume fraction φ is finally compared to estimates from TEM images of the raspberries.

A typical snapshot illustrating particles in the microchannel is presented in Fig. 1(b). Figure 2 shows the time varying positions of silica-gold raspberries (Table 1, sample α, silica D = 1.17 µm, gold d = 15 nm) shined by the laser at the beam power P = 0.75 W. We performed linear fitting of at least 75 trajectories to measure an average velocity at a given laser power. The inset of Fig. 2 shows the velocity distribution obtained from this run with an average of 24 µm/s and a standard deviation of 6 µm/s. The trajectories being linear, this suggests that the particles remain in the Rayleigh zone where the field can be considered as almost axially uniform. Moreover, we observed that most particles move right in the center of the microchannel. This effect is ascribed to two collaborating effects: (i) the weak shear associated to the Poiseuille flow velocity profile within the microchannel before stopping particles with pressure actuation and (ii) the presence of optical gradient forces due to the transverse Gaussian profile of the laser beam, as largely demonstrated in optical chromatography experiments [START_REF] Kaneta | Theory of optical chromatography[END_REF][START_REF] Harada | Radiation forces on a dielectric sphere in the Rayleigh scattering regime[END_REF]. Fig. 2. Trajectories of 75 silica-gold raspberry particles (sample α, silica core diameter D = 1.17 µm coated by 15 nm gold nanodots) measured in the velocity mode as a function of time lapse for a laser beam of power P = 0.75 W and beam waist ω = 17 µm. The Inset shows the statistic distribution in particle velocity extracted from linear fitting of the trajectory set.

The measured velocity is directly related to the optical radiation forces applied to the particles. In such a low Reynolds number flow, equilibrium is rapidly set up between the optical and the drag force due to viscosity. For silica core particle, laser heating at the used wavelength can be discarded and we can derive forces easily. A linear fit of the experiments performed with D = 1.46 µm silica particles yields to a force of 0.36 pN/W. For particles with the smallest diameter, D = 1.17 µm, we measure a weaker force: 0.23 pN/W. The ratio of these two slopes, 1.57, is in very good agreement with the square of particle diameter ratio, as expected from the optical force expression given by Eq. (1).

To investigate the contribution of the gold nanodots on optical forces, we performed particle velocity measurements on suspensions with different silica core diameters and gold concentrations at the surface. Figure 3 shows a significant increase of the velocity for the silica microparticles coated with gold compared to that obtained for pure silica particles of same core diameter for both D = 1.17 µm (Fig. 3(a)) and D = 1.46 µm silica core diameter (Fig. 3(b)). We observe an enhancement of the velocity by a factor 2.34 for sample α, 1.55 for sample β and 2.31 for sample γ. This behavior is interpreted as a metal-induced enhancement of the radiation pressure cross section C rp . Indeed, considering, on the one hand, the optical wavelength of the laser wave (λ 0 = 532 nm) and the SPR wavelength of 15 nm gold nanoparticles (λ SPR = 525 nm) on the other hand, the presence of metal increases the scattering and absorption of the incident wave, increasing de facto radiation pressure forces [START_REF] Rodriguez-Otazo | Nanometer gold-silica composite particles manipulated by optical tweezers[END_REF]. To estimate the amplitude of these enhancement factors, we performed numerical Mie calculations of the extinction, absorption, scattering cross section and the asymmetry parameter for our core-shell approach of silica@gold raspberry in order to obtain the gold volume fraction φ dependence of the radiation pressure cross section C rp . Results are shown in Fig. 4 for D = 1.46 µm and d = 15 nm. The four colored curves correspond to the radiation pressure cross-section of dielectric-metal particles for φ = 0.2, 0.45, 1 and 2%. As expected, the radiation pressure cross section C rp deeply increases when approaching the SPR, depending on φ, and then decreases to asymptotically collapse with the prediction for pure silica particles, in black. The comparison to pure silica particles at the used optical wavelength (indicated by the vertical dashed line) gives the theoretical variation of the expected enhancement factor versus the volume fraction φ of gold nanodots. The inset of Fig. 4 shows that the enhancement factor is linear in φ at low φ values. distance of 156 nm which is compatible with a rough estimation made from geometric calculation on TEM images, Fig. 1(c), where we found a mean inter gold nanoparticles distance of 120 nm. These volume fractions φ are finally used to estimate optical forces and compare them to absolute values calculated from Mie theory. In Fig. 6 we plot together the optical radiation pressure force predicted by Mie theory for the gold volume fraction φ obtained from the enhancement factor matching procedure and the set of optical forces measured for the various combinations of particles diameters and gold nanodot concentrations. Results on pure silica particles are also presented, including the force estimated in the ray optics approximation as it is used in most optical chromatography investigations [START_REF] Hart | Refractive-index-driven separation of colloidal polymer particles using optical chromatography[END_REF][START_REF] Kaneta | Theory of optical chromatography[END_REF][START_REF] Terray | Cascade optical chromatography for sample fractionation[END_REF]. The error bars associated to calculations (solely represented for pure silica) are estimated at ± 29% and originate from the beam waist 11%

δω ω = and standard deviation of the radius of silica particles 3% R R δ < . The error bars on experimental data points are estimated at ± 15% and originate from the standard deviation on R and the statistical error 12% δυ υ = extracted from velocity measurements (Fig. 2). The error on ω seems large but it takes into account the fact that strictly speaking, particles do not flow along a perfect cylinder of light but in a slightly converging/diverging beam so that optical forces slightly vary along the beam axis. Consequently, agreement between Mie calculations of optical radiation forces and experimental measurements is fairly good; the largest data shift between predicted and measured forces is smaller than 25%, a value which has never been reached to the best of our knowledge, except by further adaption of the laser beam parameters [START_REF] Kaneta | Theory of optical chromatography[END_REF]. Note nonetheless that experimental results are systematically over evaluated by Mie calculations; this is likely due to the internal porosity of Stöber like silica that randomly scatters light and thus reduces the force efficiency [START_REF] Garcia-Santamaria | Refractive index properties of calcined silica submicrometer spheres[END_REF]. Fig. 6. Radiation pressure force variation versus the radius R of silica-gold raspberries predicted by Mie theory (red curve: φ = 0.45% as a mean between 0.43% (sample γ) and 0.47% (sample α), green curve: φ = 0.20%) and measured experimentally in the three raspberries samples (black-gray dots). Also shown for the comparison, are the calculation and measurements on core silica particles (black curve and empty circles respectively). The dashed curve represents the forces in the ray optics approximation for silica particles. Error bars also appear on calculations (just represented for silica particles for the sake of clearness) to take into account the weak beam size variation over the Rayleigh length during the particle displacement in the microchannel.

Finally, to compare with classical optical chromatography schemes [START_REF] Hart | Refractive-index-driven separation of colloidal polymer particles using optical chromatography[END_REF][START_REF] Kaneta | Theory of optical chromatography[END_REF], we present in Fig. 6 calculations in the ray optics approximation for silica particles in water, using already mentioned optical indexes. They fairly approximate Mie calculations for the investigated particle radii. They also show the robustness of this approximation beyond its size range validity (here R ~λ0 while R >> λ 0 would be required), and thus enlighten the traditional use of ray optics in optical chromatography. Thus, our results demonstrate that quantitative predictions can indeed be advanced for both core and much more complex core-shell micro materials when the Maxwell-Garnett formulation of the refractive index is applicable. Consequently, our experiments and calculations open the route for the study and the manipulation of hybrid particles with tunable optical properties such as multiple shell objects, micro-nano hybrids where nanometric tags present specific and tunable SPR [START_REF] Hu | Optical properties of gold-silica-gold multilayer nanoshells[END_REF][START_REF] Padmanabhan | A facile method for the synthesis of highly monodisperse silica@gold@silica core-shell-shell particles and their use in the fabrication of three-dimensional metallodielectric photonic crystals[END_REF], or complex engineered biological system [START_REF] Kumara | Bioengineered flagella protein nanotubes with cysteine loops: self-assembly and manipulation in an optical trap[END_REF].They also show the way to increase the magnitude of optical forces for particle actuation in microfluidic environments.

Conclusion

Using an optical chromatography setup, we investigated optical forces on dielectric core microparticles and hybrid dielectric-metal micro-nano raspberries based on the same silica core. We measured the enhancement of the optical force due to the metallic shell of the raspberries and found good quantitative agreement with a numerical simulation based on Mie theory. We also showed that even at very low metallic concentrations (down to 0.2%) we can definitively differentiate the particles through optical forces, thus demonstrating that nano metallic tags can significantly increase the magnitude of optical forces at the microscale. Consequently, using these "micron-sized nanoparticles", one can associate ease of manipulation and benefit from nano-engineered materials used as tags where the micrometric range is dedicated to transportation and where the nanometric range offers specific and tunable optical, chemical or biological properties. These results also open up new opportunities in the field of plasmonic particles manipulation and sorting, as dielectric-metal microparticles could be easily differentiated according to their metal concentration in a very fine way. One can imagine using an optical chromatography setup to discriminate mixtures of inhomogeneously decorated particles and create ultra pure sets of similar raspberries with enhanced spectral properties.

Fig. 1 .

 1 Fig. 1. (a) Scheme of the experimental chromatography setup. (b) Illustration of flowing particles in the microchannel; particles are magnified by the scattering of the green laser light (c) TEM image of a silica-gold raspberry particle with core diameter D = 1.17 µm and adsorbed gold nanosdots of diameter d = 15 nm (sample α, Table1.).

1 R

 1 particle radius R is very small compared to the beam waist (i.e. ω << ), the plane wave approximation applies and the beam intensity distribution can be reduced to

  [START_REF] Bashkatov | Water refractive index in dependence on temperature and wavelength: a simple approximation[END_REF]. The dielectric constant used for the core is taken from measurements performed on similar silica particles cross-sections is performed using a Matlab code for core-shell particles with the previously mentioned dielectric constants.The optical force F rp is then estimated from measurements of the particle velocity υ and from the second Newton law, 0

Fig. 3 .

 3 Fig. 3. Velocity as function of the incident laser beam power measured for different types of particles. (a) Core dielectric particles with a diameter of 1.17µm (black empty squares) and SiO 2 @Au raspberries sample α (blue squares). (b) Core particles with a diameter of 1.46µm (black empty circles) and raspberries (green and red circles correspond to sample β and γ respectively). Error bars represent standard deviations. The linear fits are guides for the eye.

Fig. 4 .

 4 Fig. 4. Wavelength dependence of the radiation pressure cross section C rp of silica-gold raspberries calculated using Mie theory for silica core diameter D = 1.46 µm, and d = 15 nm thick composite shell composed of water and gold nanodots with volume fraction φ = 0.20% (green), 0.45% (red), 1% (blue) and 2% (cyan). The behavior in black describes the silica core case. The vertical dashed line indicates the optical excitation wavelength of 532 nm. The Inset represents the evolution of the enhancement factor, i.e. the ratio of C rp for raspberries over C rp core for silica core as a function of the metal volume fraction φ.

Table 1 . Data on raspberries samples: diameter of the core silica microparticles, gold volume fraction φ 100% estimated from quantities used in chemical synthesis, gold volume fraction φ deduced from cross section calculations and measured enhancement factor of optical forces compared to silica core

 1

	SiO 2 @Au Raspberries samples	SiO 2 microparticle diameter D	Gold volume fraction φ 100% (synthesis)	Experimental optical forces enhancement factor	Gold volume fraction φ (Mie calculation)
	α	1.17 µm	1.1%	1.93	0.47%
	β	1.46 µm	0.45%	1.39	0.20%
	γ	1.46 µm	0.9%	1.83	0.43%

Acknowledgments

The authors acknowledge the scientific program Advanced Materials in Aquitaine (GIS Matériaux) and the Conseil Régional d'Aquitaine (Project Nano-Trans N# 20111101010) for funding. The authors would also like to acknowledge networking support by the COST Actions MP 1202 (http://www.cost-hint.cnrs.fr) and MP 1205 (http://costmp1205.eu).

In order to estimate the radiation pressure forces experimentally, we have in the other hand to consider the temperature dependence of the viscosity within the Stokes drag expression and consequently the temperature at the vicinity of the particle which is directly related to the gold volume fraction of the shell. We proceed by dichotomy in volume fraction φ. This procedure is illustrated in Fig. 5. Given a value of φ, we calculate the absorbed power and the corresponding laser overheating (Fig. 5(a)), we deduce the water viscosity at the raspberry surface from the Vogel-Fulcher empiric law (Fig. 5(b)). We apply this procedure to the set of investigated laser powers and then we fit the experimental data with a linear law to get the slope rp F P (as in Fig. 5(d)). We then compare the enhancement factor on the force ( ) ( ) core rp rp F P F P (relatively to measurements in silica core particles with same core diameter) to the numerically calculated one at the same φ. The process is iterated in φ up to equality between the two approaches (Fig. 5(c)). The optimal values of φ (enhancement factor matching) are summarized in Table 1 and The estimated volume fractions are almost half of φ 100% , those suggested from the synthesis with an expected 100% adsorption yield (Table 1). Similarly, the enhancement factor for the smallest silica core (D = 1.17 µm, sample α, Table 1) leads to a metal contribution φ = 0.47%. Note for instance that φ = 0.47% correspond to an inter-particle


Yue Kang

Danilo Alves De Lima

Alessandro Corrêa

An approach of human driving behavior correction based on Dynamic Window Approach

Keywords: ADAS, Human Driving Behavior, Driving Safety, Dynamic Window Approach

This paper presents the approach of an applicable safety driving methodology for human drivers based on Dynamic Window Approach (DWA), as an implementation of Advanced Driving Assist Systems (ADASs). The human driving behaviors are modelled for the design of controller, refined by referential paths using evasive trajectory model, and the linear and angular velocities are limited and corrected by DWA which performed as an obstacle avoidance strategy. Results of trajectory following and obstacle avoidance are compared with the visual servoing (VS) controller as a corresponding approach of autonomous control pattern.

I. INTRODUCTION

Safety has been of major and critical interest to the automation systems since the dawn of the automotive industry. Developing effective active safety devices has gained emphasis within the last decades for accident prevention and harm reduction [START_REF] Ghandour | Risk indicators evaluation based on anticipated vehicle dynamics parameters[END_REF]. A large number of road accidents occur on the main and secondary roads each year, and driver error is one of the reasons with evident importance [START_REF] Lotz | System architectures for automated vehicle guidance concepts[END_REF]. A growing number of applicable approaches has been brought out in the progress of various modelings of driving behavior. For instance, a similar system is proposed in [START_REF] Glaser | Speed limitation based on an advanced curve warning system[END_REF] which takes into account vehicle dynamics and driver behavior as coefficient that express how much acceleration the driver could accept. Another approach of software-based collision avoidance system was implemented to a dedicated shortrange vehicle-to-vehicle communication for better mitigating accident collisions [START_REF] Tang | Collision avoidance timing analysis of dsrcbased vehicles[END_REF]. More recently in [START_REF] Wang | A safety-based approaching behavioural model with various driving characteristics[END_REF] a safety-based approaching behavioural model was proposed for the driver's car-following behavior with various driving characteristics, deducted from an integrated driving behavior modeling framework in previous works [START_REF] Toledo | Integrated driving behavior modeling[END_REF] [START_REF]Estimation of an integrated driving behavior model[END_REF].

However, these achievements focusing on modeling the characteristics and behavior of intelligent vehicles rarely employ the driver's control instructions to the vehicles. Taking a step backwards, fully autonomous vehicles are currently available in rather ideal and constrained experimental environment, and human effect during the driving has failed to be taken into sufficient consideration while human drivers' repulsive controlling characteristics are still major causes of road crashes [START_REF] Isermann | Collision-avoidance systems proreta: Situation analysis and intervention control[END_REF]. Consequently, approaches of applicable detection and correction for human decision

The authors are with Heudiasyc UMR CNRS 7253 Université de Technologie de Compiègne. Yue Kang holds a Ph.D scholarship from Chinese Scolarship Council and Picardi region in France. Contact authors yue.kang@hds.utc.fr faults, as a supplementary driving assistance system, are in extreme need.

Traditional Advanced Driver Assistance Systems (ADASs) have been exceedingly advanced over the past few decades [START_REF] Lotz | System architectures for automated vehicle guidance concepts[END_REF]. From the first generation described by "lateral and longitudinal stabilization and control" and represented by the renowned Anti-lock Braking System (ABS) and the Electronic Stability Control (ESC) system, to the later "careful active actions and warnings" generation with the Adaptive Cruise Control (ACC) [START_REF] Vahidi | Research advances in intelligent collision avoidance and adaptive cruise control[END_REF], Lane Departure Warning (LDW) [START_REF] Suzuki | An analysis of drivers steering behaviour during auditory or haptic warnings for the designing of lane departure warning system[END_REF] and Lane Keeping Support (LKS) systems [START_REF] Tsogas | Using digital maps to enhance lane keeping support systems[END_REF] [START_REF] Minoiu Enache | Driver steering assistance for lane departure avoidance[END_REF], till the last generation characterized by "warnings and full active actions" for which the Mitigation to effects of Collisions (CM) or Collisions Avoidance (CAV) [START_REF] Isermann | Collision-avoidance systems proreta: Situation analysis and intervention control[END_REF] by emergency braking or steering holds the reputation, the ADASs have been playing without doubt a rewarding and efficient role in the autonomous driving industry. Our work continues in the same directions leaded by previous approaches while emphasizing human drivers' controlling characteristics.

As a complement of ADAS with focus on the judgement and correction of human drivers' behavior, our approach possesses a close relation with teleoperation systems. In [START_REF] Hokayem | Bilateral teleoperation: An historical survey[END_REF] a detailed survey of bilateral teleoperation is performed along with interactions between human operators, masterslave robotic servo systems and the operation environment. In more recent works as in [START_REF] Theriault | Design and development of an affordable haptic robot with force-feedback and compliant actuation to improve therapy for patients with severe hemiparesis[END_REF] and [START_REF] Renon | Haptic interaction between human and virtual icub robot using novint falcon with chai3d and matlab[END_REF], haptic robotic systems interact with human users by force feedback and tactile sensation feedback such that operators amend and correct their actions in teleoperation. Quite a few related approaches harbor the significance on operational humanrobot interactions, which is also acknowledged in the domain of ADAS as human-vehicle interactions. In our work, this interaction, which is performed as the correction of the human drivers' decision faults, is of essential importance.

The objective of our approach is to simulate and correct the human drivers' decision faults, which is accomplished by applying the Dynamic Window Approach (DWA) [START_REF] Fox | The dynamic window approach to collision avoidance[END_REF]. The human decision faults are modelled as a Human Driving Behavior (HDB) controller with predefined trajectory paths where potential collisions and crashes occur. This approach is emerged from the approach of our previous work [START_REF] Lima | Navigation of an autonomous car using vector fields and the dynamic window approach[END_REF], where the DWA method was applied with an image-based Visual Servoing (VS) controller [START_REF] Cherubini | Visual servoing for path reaching with nonholonomic robots[END_REF] to perform the autonomous road lane following task while avoiding obstacles. A detailed explanation of this method can be referred in the other paper submitted by the same authors. While working outstandingly for the trajectory navigation tasks, the VS control fails to guarantee the safety of driving with the lack of obstacle avoidance. In the current approach we focus on the correction of the human decision faults in the same driving environment of the autonomous VS-DWA cooperative control pattern, and a comparaison of performance between the two controllers.

In order to present this methodology, this article is organized as follows: in Section II, we present the robot model and the simulation environment; in Section III, we illustrate our design of control pattern in the perspective of humanvehicle interactions with a short introduction of DWA-VS controller used for the comparaison, and the evasive trajectory as the reference for the design of HDB controller; finally experimental results with performance analysis are presented in section IV.

II. GENERAL DEFINITIONS

The robot in this work is considered to move in a planar workspace, similar to the one described in [START_REF] Cherubini | Visual servoing for path reaching with nonholonomic robots[END_REF], where the road lane center defines a path once differentiable in IR 2 . The robot follows the path according to the kinematic model of a front wheel car [START_REF] Luca | Robot Motion Planning and Control[END_REF] as:

    ẋr ẏr θ φ     =     cos θ cos φ sin θ cos φ sin φ/l 0     v 1 +     0 0 0 1     v 2 , (1)
where the vehicle configuration is given by q = [x r y r θ φ] T , with the position (x r , y r ) and orientation (θ) of the car's reference frame {R} in relation to a static world reference frame {O}, and φ is the average steering angle of each front wheel by the Ackerman's approximation. The orientation and steering angles (θ and φ) are positive counter-clockwise, with θ ∈] -π, π] and φ ∈ [-φ max , φ max ]. The variables are illustrated in the Figure 1.

The control input for the vehicle of the model ( 1) is u = [v 1 v 2 ] T , which consists of respectively the linear velocity v 1 and the steering velocity v 2 of the front wheels. With the relationship between linear velocity v and front wheels velocity v 1 as v = v 1 cos(φ), as well as the angular velocity θ = v 1 cos(φ)/r 1 = ω and the steering angle, it is possible to choose the robot control input as u r = [v ω] T . For the presentation of Visual Servoing (VS) control used for further comparaisons in the Section III and IV, the Figure 1 also represents the camera frame {C} with optical center position in (x c , y c , z c ) = (t x , t y , t z ) in the robot frame and a constant tilt offset 0 < ρ < π 2 related to the x r axis. The camera's image frame {I} is represented in the Figure 2, with defined size as (2X I , 2Y I ).

The obstacles on the road are represented as blocks with similar size to our vehicle, as in the Figure 3. An example from the camera point of view is also represented in the Figure 2. To simplify the problem, we assume that the obstacles are in two dimensions, rectangle-shaped and can be detected by exteroceptive sensors, for instance, LIDAR. This assumption helps reduce the difficulty of establishing the simulating and experimental environment while maintain the feasibility and reliability of the obstacle avoidance required by the Dynamic Window Approach (DWA).

III. HUMAN-VEHICLE INTERACTIONS

Recalling the principal aim of our work, we propose an autonomous correction mechanisme to the driving behaviors based on the Dynamic Window Approach (DWA). With the interaction between human drivers and the vehicle, the driving behaviors which are represented by the vehicle configuration q = [x r y r θ φ] T defined in the Section II, are revised and optimized by the application of the new control input u = [v 1 v 2 ] T calculated by DWA.

A. Dynamic Window Approach

The Dynamic Window Approach is a reactive obstacle avoidance technique proposed originally by [START_REF] Fox | The dynamic window approach to collision avoidance[END_REF], with a modification for car-like robots presented in [START_REF] Rebai | Car-like robot navigation at high speed[END_REF], This approach optimize an objective function [START_REF] Lotz | System architectures for automated vehicle guidance concepts[END_REF] in order to select the best control input regarding the desired configuration to the robot. The objective fonction is constituted with three weighted components: the goal position (heading), the obstacle distance (dist) and the final linear velocity (velocity), represented as:

DW A(v, ω) =α • heading(v, ω) + β • dist(v, ω) + γ • velocity(v, ω). (2)
Initially, for the actual velocity of the robot (v a , ω a ), the dynamic window V d is defined for all reachable velocities in a time interval △t as:

V d = {(v, ω)| v ∈ [v a -v△t, v a + v△t] , ω ∈ [ω a -ω△t, ω a + ω△t]} (3)
where v and ω are respectively the linear and angular acceleration of the robot. Following, each reachable velocity must be classified as admissible or not depending on the obstacle distance (dist) and the robot maximum breaking accelerations ( vb , ωb ). The velocity is guaranteed as admissible if the distance to the obstacle in a circular trajectory exceeds the distance required to stop safely the vehicle. The collision detection algorithm implemented in the function dist(v, ω) is the one proposed by [START_REF] Arras | Real-time obstacle avoidance for polygonal robots with a reduced dynamic window[END_REF] for polygonal robots, which defines the set of admissible velocities:

V a = {(v, ω)| v ≤ 2 • dist(v, ω) • vb , ω ≤ 2 • dist(v, ω) • ωb } . (4)
Finally, V s is defined to satisfy the maximum acceleration constraints vmax and ωmax . The dynamic window search space, which considers the actual speed of the vehicle, its accelerations, the obstacles in the workspace, and also the physical limits of the vehicle is consequently generated as:

V DW = V d ∩ V a ∩ V s . (5)

B. Design of Control Pattern

According to the control input for the vehicle defined in the Section II as u = [v 1 v 2 ] T , we simplify the human control pattern. In an ideal driving environment where no obstacles are involved, the obstacle distance (dist) in the objective function is omitted. Naturally human driver conducts the vehicle in the center of the road lanes, with which the goal position (heading) in the objective function 2 is determined. The linear and the angular speeds depend on the maximum velocity constrain of the vehicle, the legal speed limitions of the road and the road conditions (turnings, intersections, etc.). In a simplified experimental circle track, the linear velocity v 1 and the steering velocity v 2 are constrained respecting these elements.

In general, human drivers avoid the collision with two principal reactions: decelerating and turning. Without any auxiliary perception of the environment, these reactions depend only on the individual judgement of the human drivers [START_REF] Ranney | Models of driving behavior: a review of their evolution[END_REF]. Consequently, the DWA guarantees a limitation of the input velocities with the help of the obstacle avoidance and the implement of the obstacle distance (dist). Nonetheless, apart form the obstacle avoidance, the essential aim of human drivers is still guiding the vehicle in the center of the road, and the the goal position (heading) remains unchanged.

As a contrast to the human control pattern, we apply the Visual Servoing (VS) strategy carried out by Cherubini et al [START_REF] Cherubini | Visual servoing for path reaching with nonholonomic robots[END_REF], in which two non-linear feedback controllers are designed for the propose of following a line path projected in the camera image. With the absence of the capacity to guarantee the safety of driving, a correction by an obstacle avoidance technique, in this case the DWA, is consequently necessary. Omitting the detail of visual perception and projection, the design of the feedback control of VS is represented as:

ω = -B + c (λe + A c v d ), (6)
where ω is the feedback gain of the controller, e is the state error calculated according to the visual characteristics from the projected image, A c and B c are matrixes from the kinematic model ( 1) transformed to the image frame, and v d is the desired linear velocity of the tracking control. For more details of the implementation and stability analysis see [START_REF] Cherubini | An image-based visual servoing scheme for following paths with nonholonomic mobile robots[END_REF].

To imitate the behavior of human driving, we propose an ordinary but practicable design of feedback control according to the Euclidean distance between the position (x r , y r ) of the vehicle and a predefined referential trajectory path which represents the desired driving route. This design of feedback control, namely human driving behavior (HDB) controller is represented as:

ω = v d v l (x r -x p ) 2 + (y r -y p ) 2 + β, (7)
where ω is the feedback gain of the controller, v d is the desired linear velocity of the tracking control, v l is the velocity limitation of the vehicle, (x r , y r ) are coordinates of the position of the vehicle, (x p , y p ) are coordinates of the corresponding point on the referential path, and β is an additive white Gaussian noise (AWGN) which represents inaccuracy of human drivers' control. Noted that this controller involves no angular information. This omission is acceptable in the circumstance where human drivers are rarely aware of the precise drift angle of the vehicle [START_REF] Keller | Active pedestrian safety by automatic braking and evasive steering[END_REF].

C. Referential Path Modeling

For the requirement of predefinition of the referential path in the design of HDB controller, a mathematical model of driving trajectory is essential. From the approach of vehicle trajectory prediction [START_REF] Houenou | Vehicle trajectory prediction based on motion model and maneuver recognition[END_REF] we are confirmed that, in an appropriately simplified driving circumstance, modeling the human drivers' behaviors with an ensemble of data, including the vehicle position coordinates which consist of a discrete path, and the linear and angular velocities representing the decision of acceleration, brake and steering, is practical and adequate. In an obstacle-free circumstance this path is located in the middle of the drivable road, in the form of segments in a straight line or an arc, depending on the road driving condition characteristics. With obstacles involved, this geometrical layout of driving path is inadequate. In our approach, an evasive trajectory [START_REF] Isermann | Collision-avoidance systems proreta: Situation analysis and intervention control[END_REF] is applied in the task of obstacle avoidance. This trajectory is described by a sigmoid curve in the form as:

y(x) = y m 1 + e -a(x-c) , ( 8
)
where y m is the maximum y-value, a defines the slope at x = c of the sigmoid curve and c defines the position of the inflection point of the curve, therefore the total length as s = 2c. The curve of the trajectory along with its parameters is presented in the Figure 4. Noted that the definition of the evasive trajectory is not a function of time (i.e. an abuse of the naming "trajectory"), we utilize henceforth this model as a segment of a referential path. For the determination of the referential path in the task of obstacle avoidance for HDB controller, we manually revise the initial path, which is obtained in the obstacle-free circumstance, at the segments where obstacles occupy the initial path, as presented in the Figure 5.

IV. EXPERIMENTAL RESULTS

A. Validation

Our first experiment aims at validating the design of imitational feedback controlling mechanism of the HDB controller that mimics the driving behaviors of humankind. The vehicle is set in a closed-loop athletic-track-shaped environment as workspace without obstacles, in which a referential clockwise path in the middle of the right-side road is predefined. The vehicle succeeded the path following task in accordance with the HDB controller applied to the kinematic model ( 1), as represented in the Figure 6.

The results in the Figure 6(a) demonstrated the driving route by HDB controller with an ideal referential path, while the Figure 6 vehicle left the curve and entered the straight road. This phenomenon is due to the absence of angular information in the design of the HDB controller, which causes time delay of establishing the steady angular state. It also reflects the common failure of the judgement by the human drivers as incorrect estimation of the actual steering angle of the vehicle.

B. Comparison with VS

For the purpose of proving the feasibility and reliability of our methodology in the sense of safety driving, we set up obstacles showed in the Figure 3 in the simulation environment, and apply DWA method to both HDB and VS controllers. The results are presented in the Figure 7.

The routing result presented in the Figure 7(a) demonstrated that both controllers succeeded in guiding the robot to avoid obstacles with the application of DWA. Although the difference between the two routes did not prove adequately the advantage of our approach, the Figure 7(b) demonstrated that, after an essential deceleration before engaging the avoidance, the vehicle applied with the HDB controller passed the obstacle while maintaining a relatively high linear velocity. In contrast, with a sharp drop followed by a long period of low-speed forwarding, the robot guided by the VS controller failed to retain the velocity during a passing manoeuvre, which demanded a consequently long passing time and an increase of energy consuming.

In addition, the Figure 7(c) illustrated that HDB controller guaranteed the smoothness of turning procedure. The angular velocity of the robot calculated by HDB controller remained (a) HDB control driving route (in blue, hereinafter) and VS control driving route (in green, hereinafter), both in portion. in a suitable interval. As a contrast, with the guidance of the VS controller, the angular velocity rapidly flipped with peak values considerably larger than those calculated by HDB controller. The experimental result proved HDB controller available and feasible with the cooperation of DWA method and a predefined referential path, while reducing the demand of deceleration in comparison with the VS controller.

C. Danger Behaviors Correction

In this experimental section, the performance of our methodology is examined in the circumstance where human drivers adopt danger behaviors while driving. For the purpose of representing the danger behaviors, the referential path is adjusted according to the evasive trajectory presented in the Section III-C. Firstly we postpone the turning of the path before bypassing an obstacle to simulate the delayed steering decision of human drivers. Another danger behavior is presented as a wrong turning which leads to a potential thread of collision. Both adjustments of the referential path are presented in the Figure 8(a).

The experimental result of the route, also presented in the Figure 8(a), illustrated that the robot successfully avoided the potential danger of collision with the application of HDB controller and VS-DWA method. The route taken by the robot applying the HDB controller held a safe distance from the obstacles and simultaneously remained smooth and stable from the perspective of the reference frame. In addition, the Figure 8(b) reclaimed the maintenance of linear velocity during the bypass period, as is mentioned in the Section IV-B. Although a larger interval of angular velocity is observed in the Figure 8(c), in comparison with the result in the Figure 7(c), the peaks during the first period of steering is decreased, and a smooth passing manoeuvre is consequently guaranteed.

Referential Path Correction

(a) Referential path with danger behaviors (in red) and corrected route by HDB controller (in blue), both in portion. In the following experiment, we took a step further to enlarge excessively the hazard of danger driving behavior by canceling the turning of the path before passing an obstacle. In such circumstance the obstacle occupies and blocks completely the referential pas as presented in the Figure 9(a).

The results presented in the Figure 9(a) revealed again a smooth and stable trajectory from the perspective of the reference frame with the manoeuvre of obstacle avoidance. The maintenance of linear velocity during the bypass period is also observed in such circumstance as illustrated in the Figure 9(b). The major concern in this part of experiment lies in the result of the angular velocity showed in the Figure 9(c). In comparison with the results from the previous experiments in the Figure 7(c) and 8(c), the angular velocity by HDB controller in such circumstance revealed a smooth process of steering with minor values of the angular velocity and fewer peaks. Due to the curve characteristics of the referential path, we conclude that the quality of the referential path influences considerably the behavior of HDB controller, thus affecting consequently the outcome of the practical control of the robot.

V. CONCLUSION

In this paper we have presented an approach of modeling the behaviors and decisions of human drivers, which has established the foundation of a simplified control pattern of human drivers' behaviors. With the application of DWA providing the validation of the linear and angular velocities of the vehicle, potential dangerous behaviors of human drivers have been refrained and corrected. Safety of driving in such circumstance has been therefore guaranteed. In comparison with the experimental results of VS controller, our control pattern with the focus on human-vehicle interaction have proved its superiority in maintaining the smoothness and stability of the obstacle passing manoeuvre. Control strategies determined by human drivers, or in our approach by HDB controller, with both absolute values and smoothness of the control variables being promising, have also been confirmed as practical and applicable on actual intelligent vehicles.

Our approach has yet called for quite a few further progresses. The most apparent shortcoming of our design is the indispensable predefinition of the referential path or trajectory. A real-time calculation to achieve the referential trajectory from the perspective of human drivers, and a reliable localisation method to guarantee the acquisition of the position of the vehicle, are consequently desired. The characteristics of the referential path has also revealed its significance to the performance of the HDB controller. Therefore . These current deficiencies will point out the direction of our future research.

Fig. 1 .

 1 Fig. 1. Cinematic model diagram for a front wheel car-like robot. In this model the vehicle reference frame R performs circular trajectories related to the instantaneous center of curvature (ICC). The pinhole camera frame is also represented in C.

Fig. 2 .

 2 Fig. 2. Image frame {I} with the road lane center projection P (in red) related to the boundaries δ 1 and δ 2 (in yellow), its tangent Γ (in dark blue) at the point D and the angle offset Θ of Γ to the axis -Y .

Fig. 3 .

 3 Fig. 3. Obstacles represented in world frame {W} (in blue), with detection of obstacles and also navigable zone boundaries (in pink).

Fig. 4 .

 4 Fig. 4. Evasive trajectory for obstacle avoidance.

Fig. 5 .

 5 Fig. 5. Referential path revision using evasive trajectory.

  (b) illustrated the divergence of the coordinates of the actual driving route in comparison with the reference. While the overall route converged to the referential path, the largest deviation of the driving route occurred when the Reference route Actual driving route (a) Reference path (in red, hereinafter) and actual driving route by HDB controller (in blue, hereinafter).

  of ref. Coor. x of actual driving Coor. y of ref. Coor. y of actual driving (b) Contrast of coordinates X and Y of the two routes.

Fig. 6 .

 6 Fig. 6. Validation of HDB controller design.

  Comparison of linear velocities.

  Comparison of angular velocities.

Fig. 7 .

 7 Fig. 7. Comparison of performance in obstacle avoidance.

  Linear velocity calculated by HDB controller.

  /s) (c) Angular velocity calculated by HDB controller.

Fig. 8 .

 8 Fig. 8. Result of danger behaviors correction performed by HDB controller.

  (a) Referential path with inevitable collision (in red) and corrected route by HDB controller (in blue), both in portion.

  Linear velocity calculated by HDB controller.

  /s) (c) Angular velocity calculated by HDB controller.

Fig. 9 .

 9 Fig. 9. Result of danger behaviors correction performed by HDB controller.