F Jaillet

Neo: a Data Model for Electrophysiological Data Representation and its Python Implementation

(1) , S. Garcia

(2) , A. P. Davison

(3) , L. Estebanez

(3) and P. Yger

(3)

(1) The objective of Neo is to facilitate the cooperation between independent software projects working on simulation, modeling, representation and analysis of electrophysiological signals in electroencephalography or intracellular and extracellular electrophysiology. For this, Neo provides a common representation of the core data in order to improve the reusability of the developed tools and share data between dierent projects. It also provides a common layer for datale and database reading and writing through its IO modules.

The core objects and IO modules provided in the Neo 0.2 implementation are described below.

Brief history of the project

The need for a common data model appeared in the NeuralEnsemble community (neuralensemble.org). The specication process started by considering the available data models in existing NeuralEnsemble tools for processing of experimental data (OpenElectrophy, NeuroTools) and for simulation (PyNN). Other projects with related goals were also considered, in particular the Neuroshare project (neuroshare.sourceforge.net). In this process, the limits of the data models in these dierent projects as well as the current and future uncovered needs were identied.

RecordingChannelGroup

The core objects available in Neo 0.2 are:

• Block: Main container gathering all the data for a given setup, which can be viewed as a list of Segments.

• Segment: Container for heterogeneous data objects sharing a common time base, generally acquired during the same time period.

• AnalogSignal: A regular sampling of a continuous signal.

• AnalogSignalArray: A regular sampling of a multichannel continuous signal.

• IrregularlySampledSignal: An irregular sampling of a continuous signal.

• RecordingChannel: A physical location identifying the recorded data (for example the position of the electrode).

• RecordingChannelGroup: A set of physical locations identifying the recorded data (for example the positions of the electrodes).

• SpikeTrain: A set of action potential times (with optional waveforms)

emitted by the same cell in a given time period.

• Spike: One action potential characterized by its time and waveform.

• Unit: A Unit gathers all the SpikeTrain objects within a common Block, across several Segments, that have been emitted by the same cell.

• Event: Point-like time event (triggers, stimulus,...)

  INCM, CNRS UMR 6193 -Université de la Méditerranée, Marseille, France, (2) CRNL, INSERM U1028 - CNRS UMR 5292 -Université Claude Bernard, Lyon, France, (3) UNIC, CNRS UPR 3293, Gif-sur-Yvette, FranceNeo and its objectiveNeo is a hierarchical data model for the representation of intracellular and extracellular electrophysiology data with support for multi-electrodes (for example tetrodes) and EEG data. The Neo project distributes an implementation of this model with a set of input/output (IO) modules for various le formats, as an open-source, multi-platform Python package under a BSD license. It is available at

http://pypi.python.org/pypi/neo.

  After discussions between Neural Ensemble members, a rst implementation in Python of Neo (version 0.1) was produced during summer 2010 as part of the rewriting from scratch of OpenElectrophy. To respond to the needs of new projects interested in using Neo, some discussions took place in February 2011 for the specication of Neo 0.2. The main improvements introduced in Neo 0.2 are the possibility to handle physical quantities and the possibility to represent data items individually or grouped in arrays for improved processing eciency and better handling of multichannel data.

		Architecture
	Block
	Event	EventArray
	Segment
	AnalogSignal
	IrregularlySampledSignal
	Spike
	AnalogSignalArray
	RecordingChannel
	SpikeTrain
	Unit
	Epoch
	EpochArray
	Neo 0.2 architecture

  Neo provides of a set of IO modules to convert data from/to many le formats used for multichannel recordings of electrophysiological data. The IO module API also enables access to databases for the storage of Neo objects. Compared to other projects, Neo has the specicity to provide these converters as free and open-source pure Python code, which ensures transparent multiplatform use and upgradability.

	• EpochArray: A set of Epochs
	Input/output modules
	The le formats currently supported in Neo 0.2 are: ASCII, Axon, EEGLAB, Elan, HFD5, Micromed, NeuroExplorer, Plexon, PyNN, raw, Spike2, TDT,
	WinEDR, WinWCP, Neuroshare (win32 only).
	Some new IO modules are currently in development or planned (AlphaOmega, Brainvision, EDF, Elphy), and others will be added in the future.
	Projects using Neo

• EventArray: A set of Events • Epoch: Similar to Event but with a duration (period, state of a subject,...) http://packages.python.org/OpenElectrophy http://neuralensemble.org/NeuroTools http://www.g-node.org http://www.thevirtualbrain.org Perspectives Neo 0.2 is currently in development and will be released towards the end of this summer. Neo is a young project which is still open to evolution and welcomes new contributions. You can join the Neo initiative by: • Participating in the Neural Ensemble online discussion group (groups.google.com/group/neuralensemble) and shaping the evolution of Neo. • Using Neo classes in your projects. • Implementing IO modules for new data le formats and databases.


PhD Catherine Pellenq

MPH Susan Gunn

Ali Mohammed Vaqas

PhD Mohammed Vaqas Ali

How do Working Children Feel About Their Lives? And Why it Matters That We Know

A child's story … "I am Sarswati. I am 15 years old. I dropped out of school at grade 6 when my family became so poor we could no longer afford two meals a day. This is the second year I have come with my father to the brick kilns and I plan to come again next year. I must, because this way my little sister can go to school. My day is usually like this: I wake up at 2 AM and mold bricks using a flashlight for light until the day breaks. I keep doing this until 11 AM and then go quickly to make lunch for my father and me. Then I take a nap, do the dishes and other housework and at 1 PM start to work again. This time, my task is stacking up the bricks that have been drying. At 7 PM I go back to cook dinner and go to bed about 9 PM. Yes, I know that some people say this work is dangerous, but it's okay for me, because the other workers take care of us. The only time I got hurt was when I dropped a brick on my bare foot." (ILO, 2014).

Yet when we analyzed Sarswati's psychosocial profile, it tells a different story. The heavy sense of obligation for her family's welfare was creating a serious level of depression, anxiety and stress. Most of all, Sarswati does not feel she has a choice and the future looks bleak.

It is not only adults who work, nor the youthful population of underdeveloped countries.

Everywhere in the world, from household chores to steady jobs, work is part of the life experience of children. Depending on the conditions and nature of this work activity and the age of the young person involved, it may be classified as child labour, youth employment, or just 'helping out', but regardless of its designation there are health risks involved. Most countries have ratified international agreements against child labour1 because people recognize that work can be dangerous and one naturally recoils at images of children slaving in the hot sun instead of sitting in school. But there has been a tendency to look at the risks through an adult occupational and safety health (OSH) lens, focusing on hazards which are physical, observable, and perhaps more typical of the workplaces common in industrial societies.

We know comparatively little about the costs to the mind and body of a person in the full throes of growth and maturation who is being exposed to industry's recent chemical wonders or to repetitive, mind-numbing tasks, or to constant humiliation [START_REF] Sudhinaraset | The unique developmental considerations of youthrelated work injuries[END_REF]. We know little because it has been a challenge to measure such impacts … much easier to dispense with the problem by legislating that children should not work. Making work illegal, off-limits, however, does not solve the problem, as older children (above 15 years of age; 14 in some countries) are usually of legal age for a regular job, young children are often engaged in some form of household support, and those in between want to work a few hours a week outside of school for pocket money and experience. An estimated 62.088 million children, age 5-17, are doing age-appropriate work and household chores. On the other hand, 160 million children are doing work that is considered child labour in that it poses a potential threat to their health and well-being (ILO & UNICEF, 2021).

We must remember too, that a lens focused on dangers, risks, and vulnerabilities gives us only a blurry image, if any, on well-being. What is the other side of the coin? What offers a child strength, support, and solace? This chapter offers an example from the brick manufacturing sector to illustrate the value of eliciting the children's own view of their mental and physical state and the situation in which they find themselves. It shows how this child-oriented (rather than adult-oriented) perspective on risks and well-being can be measured on a population basis and, as such, how it can be the entry point to more appropriate policies, whether of protection or prohibition. It argues that, for project and policy guidance, the methods for assessing children's psychosocial well-being are not the same as those required for diagnosis and treatment of pathology, which are individualistic by necessity. Instead, these are methods which can and must be incorporated in routine surveys or preparatory studies for large-scale projects. Through them, we can gain a broader picture of how a particular group of children feel, and we avoid making interventions that, to our eyes, give them a "better" childhood but which, to their eyes, are not helpful at all.

Background

Some of the earliest Conventions adopted by the Member States of the International Labour Organization (ILO) aimed at protecting children from abusive work. 2 In fact, it was the visual and literary depictions of the horrors to which child miners or factory workers in Europe were subjected that contributed to calls for universal rules or labour standards in general. In these Conventions, which serve as guides to national laws, health is embedded in the very definition of child labour, for example, "work which by its nature or the circumstances in which it is carried out is likely to jeopardise the health, safety or morals of young persons shall not be less than 18 years". 3 In the non-binding Recommendation (R.190) that accompanies the most recent of the child labour Conventions (C.182), these risks are spelled out in some detail: While the work which poses physical risks is laid out clearly enough and relatively easy to identify, what is the "psychological abuse" that (a) above refers to? How is it determined?

There has been a tendency to shrug and say "you'll know it when you see it" but all too often, it is not seen. Children who work behind closed doors as maids, for example, one of the most common forms of child work, may not suffer physical harm, but social isolation can cause them a great deal of mental harm. In fact, children are often sought for workby parents as well as outside employersbecause they are compliant, wanting to please, fearful of what might happen if they did not workwhich leaves the impacts experienced by the young person largely invisible. For this reason, ILO Recommendation 190 calls for special attention to be given to "the problem of hidden work situations, in which girls are at special risk".

To understand, then, whether child workers are experiencing "psychological abuse" and are therefore victims of child labour, a risk assessment cannot confine itself to safety and health hazards as is typically done with adult workers, but must also include measures of children's psychological development and functioning. Since the areas where child labour occurs most frequently are areas where health or research professionals tend to be less frequent, the assessment tools and methods also need to be practical.

Meeting such requirements may seem daunting but the rewards can be extremely important.

There is good reason to suspect that, in the case of children, psychological risks can be equally or even more important than physical ones due to the fact their brains, intellectual capacity, and social skills are all in a stage of rapid development. In addition, government policy and parental decisions are based on what they understand is the likelihood that children will be hurt or alternatively, their life chances enhanced, by the activities in which the children are engaging.

If the information that policy-makers and parents have is incomplete, and is limited to whether or not a work situation might cause injury, for example, their actions will reflect this and the children will not receive the protection they need. Add, then, to this lack of relevant and up-to-date information, the powerful forces of poverty.

We tend to assume that putting a child to work is not a matter of decision but of necessity. True, poverty is certainly a dominant factor but it is important not to forget that there are others, gender discrimination being one example. Addressing poverty and the other root causes of child labour is extremely important, but long roots take a long time to extricate, whereas working children are facing risks now. It can be argued that what is most urgent is not trying to determine the type and relative strength of the different causal factors of child work, but rather to determine the type and relative strength of the risks involved in the work the children are doing.

In short, whether work will either exacerbate the conditions under which a child lives or ameliorate them, whether parents will be convinced that their children should or should not work, whether governments will decide to proscribe or allow a particular type of work for persons under 18, the full range of risks and advantagespsychological as well as physicalmust be known.

The Challenges of Measuring Physical and Psychological Risks

What is OK or not OK for children to do? Commonly accepted standards of risk have been developed for a wide range of chemical and physical exposures. They allow us to say that concentrations above a certain level have been shown to affect health and should be avoided.

However, these standards are only for adults and only for physical risks. There are no such risk standards for persons under 18 years of age, 4 nor should there be, given that children have different vulnerabilities at different points in their development. Hence, governments have resorted to using age as the common standard for lawschildren of the age to go to school (normally 5-15 years), should be in school, not at work.

In spite of the fact that there are no health risk standards to guide the decision on whether children should work or not, the methods do exist for at least measuring the physical risks, and this is occasionally done. (These are not done with the intention of establishing standards for children, but of highlighting where interventions might be needed). On the other hand, the methods for measuring psychological risks and impacts of work relevant to children have received very little attention. The best known work has been with the comparatively small and specific populations of child soldiers and children exploited in sex work, with the notable exception of a significant study on child domestic workers [START_REF] Hesketh | The psychosocial impact of child domestic work: A study from India and the Philippines[END_REF] Our objective, therefore, has been to develop, test and validate methods of measuring psychological risks and impacts of work on young persons, and to thereby demonstrate the importance of the information which can be gained. The methodological criteria we set were that the tools could be used (a) cross-culturally, (b) with children of the age range 11-17, 5 (c) 4 For example, Threshold Limit Values (TLVs) for chemical exposures and Biological Exposure Indices (BEIs). 5 children within this age group have likely already been working for some time and have the maturity to reflect on their experience and express themselves accordingly.

with groups of adequate size that statistical inferences could be drawn, and (d) by persons who were not psychological professionals.

We chose the construction sector, specifically handmade brick manufacture, for our initial focus. Not only is it large, employing an estimated 5 million children in over 20 countries, but it is growing, thanks to the demand for bricks in the rapidly growing cities of the developing world. In South Asia overall, almost 20 percent of the total work force employed at brick kilns is under 18 years of age [START_REF] Khan | Measuring children's work in South Asia: perspectives from national household surveys[END_REF]. However, this ratio is not equally distributed across the region. For example, it is estimated that 30% of the brick workers in Nepal are children (ILO, 2014a) and in some Pakistan brick factories, a majority of the workers are under 18 years of age (ILO, 2013). In Afghanistan, some children as young as 4 years old were observed working in the brick factories (ILO, 2015a). In Bangladesh, 86% of the children were working over 8 hours per day (ILO, 2014b). This sector is important for another reason as well: like waste-picking, this is an occupation of the poorest of the poorpeople who, due to debt, drought, war, or other dislocation have exhausted all other options to put food on the table. Because of this extreme poverty, one must be very careful with interventions so as not to inflict greater harm on people who have no cushion. This is why it matters to have the children's subjective view of their situation. They see the world and their work through very different eyes than ours.

The study was carried out in four countries -Afghanistan, Bangladesh, Nepal, and Pakistanwith a total of 915 child brick workers, and a comparison group of 638 children from the same areas and socio-economic level who did not do this work. The psychosocial component was one part of a larger occupational health study aimed at understanding the actual environmental, physical, economic, educational, and social situation of the children so that appropriate assistance could be provided. (ILO, 2015b)

The Research Methodology

The tool that was developed for the psychosocial component is called the "Instrument for Psychosocial Assessment of Working Children" (IPAW). The questions are answered using a visual device corresponding to a Likert scale of four options. Some questions relate to the work situation, others to general psychological development and functioning. (For further information on the design, process and sources used in developing the IPAW, see [START_REF] Hofman | Toil in soil: Impact of work at brick kilns on heath of children and youth -Report of research in 5 districts of Pakistan[END_REF].

The IPAW draws on three bodies of literature: (1) Martin Woodhead's conceptual frameworks identifying the multiple ways, both positive and negative, in which work is likely to affect children's psychological well-being [START_REF] Woodhead | Psychosocial impacts of child work: a framework for research, monitoring and intervention[END_REF], (2) studies in child development and child psychology, such as the Strengths & Difficulties Questionnaire [START_REF] Goodman | The Strengths and Difficulties Questionnaire: A Research Note[END_REF] as well as instruments which have been used with discrete populations, such child soldiers [START_REF] Jordans | Development and validation of the child psychosocial distress screener in Burundi[END_REF], and (3) measures for assessing psychological well-being of adult workers. It was expected that the latter two would yield appropriate instruments which had already been validated. However, after testing with child workers, it was clear that while these helped to define the areas of inquiry, there were substantial gaps, 6 requiring that a new instrument be developed [START_REF] Leka | Assessing psychosocial hazards and impact of child work[END_REF].

The IPAW, currently 38 items, has been demonstrated to have the properties and metrics of a reliable assessment tool [START_REF] Pellenq | The psychological health of children working in brick kilns: A classification tree analysis[END_REF]. These items are structured into different factors which are capable of revealing and confirming the multiple psychosocial dimensions of child workers' well-being [START_REF] Pellenq | The psychological health and well-being of children working in the brick industry: A comparative study[END_REF]. The psychological domains they reflect are: Stress at work, Self-esteem at work, Supervision at work, Negative emotions, Personal security, and sense of Maltreatment and abuse (see Figure 1). These domains were found to be the ones that are both, those most relevant for working children and the minimum necessary for understanding the children's subjective well-being. Although there are additional domains that could be included, there is a trade-off between what can be practically included in a child's interview along with all the other demographic and social information required. Because this paper reports on how children who work in brick factories differ from those who are not engaged in this work, the following analysis is limited to these three latter factors.

Of particular concern in this paper is the factor "personal security" which is directly related, in its negative connotations, to the concept of perceived risk and vulnerability and in its positive connotations to a sense of ease and comfort in the environment.

Results and Their Implications

The results of the physical health component of the larger occupational health study more or less confirmed the expected risks and impacts, which were primarily musculo-skeletal strain from carrying too much weight, and secondarily, injuries to feet, legs and hands from dropping bricks or stumbling over them [START_REF] Graves | Occupational injuries among child labourers: Preliminary results from a study of the brick manufacturing industry in four countries[END_REF]. It showed, also, that parents and brick kiln owners were largely aware of and concerned about the risks to the children and took measures to reduce the risk of injury, such as ensuring that the children were kept a safe distance from the burning kilns. Given these findings, it would not be unreasonable for parents to conclude that the infrequent injuries were not so serious as to offset the important contribution that the children made in supporting the adults' work and rendering it more efficient by, for example, turning the bricks to dry in the sun. Nor would it be unreasonable for policy-makers to decide that there was insufficient evidence to justify brick-making as a "hazardous occupation" which would make it off-limits for anyone under 18 years of age. Taking account, too, that many of these families were fleeing war or forced into such labour through years, sometimes generations, of accumulated debt, it might seem to them more humane not to put undue and unenforceable restrictions on them by declaring all aspects of brick manufacturing as "hazardous child labour". What was not expected, however, were the disturbing results gained from the psychosocial component of the study, and in particular, how the children viewed their situation [START_REF] Pellenq | The psychological health of children working in brick kilns: A classification tree analysis[END_REF][START_REF] Pellenq | The psychological health and well-being of children working in the brick industry: A comparative study[END_REF].

In this chapter, we report on the role that work and schooling plays in the lives of the children working in the brick-kilns of the four countries, and then present new evidence on the effects of gender and age and how these differ among the countries studied.

Working Children vis-à-vis Their Peers

We find marked differences between how child workers say they feel, and how children who do not work in the brick factories say they feel. The brick workers evidence a higher prevalence of negative emotions (e.g., sadness and fear), a greater sense of being mistreated or bullied, and a substantial feeling of personal insecurity. In the statistical analysis, being a child worker is a powerful predictor of negative outcomes (see figure 2). We expected that work might have a deleterious effect on certain factors, but we were not prepared for the magnitude of the effects, especially on the factor Personal Security. There appears to be relatively little documentation on this in the occupational health literature, suggesting that perhaps Personal Security is more salient for child workers than adult workers. Support for this interpretation comes from recent research which provides evidence that security is an especially important dimension for children in general (Bhomi, 2021 and[START_REF] Tonon | Children's feeling of security[END_REF].

The Effect of Education

Some child brick kiln workers are currently attending school or had done so previously. A surprising finding was that, when schooling is taken into account in the analysis, it effectively 'erases' the negative effects of the work variable on the child's sense of insecurity. It also reduces the effect of work on fear and other, so-called negative emotions. These data indicate that simply the fact of attending school has a mediating effect on the child workers' psychosocial well-being, reducing or deleting the negative impact of work.

Figure 3

Effect of Work and School on Three Dimensions of Well-being (standardized coefficient β).

Adapted from Pellenq et al.2021. ** p < .00, * p< .05

In other words, it appears that schoolindependent of its quality, and possibly even durationhas somewhat of a protective effect on the working children's psychological well-being. This is a critical area that needs to be more fully examined to see what is operating here. Is it the opportunity to play and socialize, the cognitive stimulation offered by the classes, the vision of an alternative future, or simply the chance to be away from dull and grinding work?

The Effects of Gender, age, and Local Culture

All four study countries exhibit the same general profile of results with respect to two variables: gender and age. Overall, being a girl and increasing age have predictive value regarding the expressions of distress and fear, and the sense of feeling mistreated.

But there are differences between the countries which may be evidence of the influence of context-specific factors, such as culture and environment on the child workers' perception of well-being. To further examine these inter-country differences, we undertook a new analysis of the total sample (all four countries) of 1553 children (i.e., both the brick kiln workers and the children who do not do this work). The total sample is composed of 672 girls and 881 boys, all within the age group 11 to 18 (Figure 4).

Figure 4

Age of Girls and Boys

To do this, we stratified the data by country and undertook a regression analysis with seven predictors: gender, age, working/not working, attending/not attending school, injuries, migration, living with family or not. Table 1 presents the effects of two of these predictors -gender and age --while controlling for the other variables. a girl is detrimental with respect to general well-being in Pakistan and Afghanistan, whereas the effect is not significant in Nepal.

Age is more complicated. Younger children differ from older children on the factor of "emotions", with the younger children expressing less negativity and depression, but this is significant only for Nepal and Afghanistan. On the factor of "maltreatment", it is the younger children who feel more mistreated than the older ones, but again only in the case of Pakistan and Nepal. Are younger children more likely to be mistreated? Are they less able or willing to acknowledge maltreatment due to their age? Or perhaps these two findings about the younger children (less depressed but having a sense of being treated poorly) suggest that they externalize or do not see where to attribute the causes of what is happening to them, whereas older children internalize these causes. With the data currently available, it is difficult to explain the local variations and further research is needed.

What is interesting is that age and gender do not seem to be having an effect on the factor "Security". In other words, (and this is an important finding) it demonstrates that all of the children studied, regardless of their age or gender, regardless of whether they work or not, suffer from a high sense of insecurity. They feel precarious in their day to day lives. The most likely explanation is that is associated with the poverty in which both the working children and the comparison group are living. However, the children in the brick factories are faced with an additional factorwork --which exacerbates and compounds this sense of insecurity, the exception being those fortunate enough to go to school.

To summarize, our analysis has investigated the determinants of well-being at three levels. At a micro level we have isolated the effects of two key socio-demographic variablesage and genderfinding that girls scored more negatively than boys. At the meso level we examined the effects of work and school, with the results showing that working children scored more negatively than those who did not, except in the case of those children who combined work and school. Finally, at the macro level we considered the effects of culture and locality, finding that there were, indeed, significant differences by country. The variables at these three levels all interact with each other simultaneously, and all are made more complex by the extreme poverty in which these children live. Some individuals are vulnerable in three or four ways at the same time: being a child, a female, a worker, and living in a certain cultural or environmental context.

It is these children whose situation is most worrying. The potentially compounding effects of age, gender, working conditions and country, suggest numerous questions which could be answered with further study. For example, why are some older girls more positive about working than their male comrades? Do they feel that work might protect them from early marriage? Do they see it as a path out into the world from an otherwise restricted life? Or do they just feel safer at work than at home? These are things we need to know.

Because we used a comparative method, matching a population of working children with their peers who do not do this work, both living in extreme poverty and exposed to similar social and environmental conditions, we were able to isolate the effects that are related to the work itself, independent of other factors. Our data have shown that work was the agent that had the most detrimental effect on child workers' subjective well-being. Work increases children's negative emotions and their sense of maltreatment and, although both groups of children experienced considerable insecurity due to the poor circumstances in which they lived, the sense of insecurity was even more pronounced on the part of the brick working children. Furthermore, work influences the children's ability to have harmonious relationships with their peers and others, and to envision the possibility of a better, more positive future for themselves.

The findings regarding gender which we present here demonstrate that the psycho-social situation of girls in some countries is very troubling. Work compounds the disadvantages they inherit from their society, putting them into a situation of extreme vulnerability. This study provides empirical, objective evidence for putting priority on girls in all interventions, and in particular, for putting maximum effort to getting them into school in a culturally sensitive manner.

It is also important to note that, while the gender effect is consistent across all four countries, there is some variation between countries, even between those which are similar with respect to culture and economic development. This suggests that girls' vulnerability is situational, not inevitable, and therefore subject to influence. Hopefully, such findings "can provide a fresh impetus within the countries where there are gender differences to try to understand and tackle the sources of these inequalities" (Rees, 2017, p.78).

Probably the finding which is unique and has the greatest significance is that school appears to play a mediating role in two of the three factors of well-being by either reducing or eliminating the negative burden of work. In effect, it seems that school is protective. Since the number of child workers who attend school in the brick manufacturing population tends to be relatively small, it is crucial that this be explored further in future large-scale studies and with other economic sectors. New studies should compare child workers who are attending school with children who are neither working nor attending school.

Since the COVID-19 pandemic forced schools to close in many countries, including those in this study, we can surmise that the loss of the chance to go to school may have had a disproportionately negative effect on the well-being of working children as they see this window of protection and opportunity closing before them. The pandemic may well have increased their levels of anxiety and fear incorporated in the factor "negative emotions" as well heightened the sense of precariousness measured by the factor "security".

The negative consequences may also be long term. Recent interviews conducted with brick workers in Pakistan 7 have revealed that since the schools have been closed for over a year, some previously school-going children have returned to working full-time. These children may be less likely to return to school after schools reopen, as families may have come to rely on the added income provided by the children. Inflation and the resulting increase in cost of living further exacerbate this risk. In addition, the loss of adult employment in other occupational sectors during the pandemic and lack of access to "welfare safety nets" [START_REF] Daly | Breaking the child labour cycle through education: issues and impacts of the COVID-19 pandemic on children of incountry seasonal migrant workers in the brick kilns of Nepal, Children's Geographies[END_REF] has led to more families becoming indebted and more families turning to brick manufacturing as a job of last resort, such that the cultural milieu in which the child workers live is also becoming more fraught.

In conclusion, understanding how children view their work, how their work is situated within their lives, and how it makes them feel about their future is key to offering them options that make sense to them. Yet very few research projects and project baseline studies make more than a cursory attempt to do this essential listening. Using a standardized instrument is crucial for cross-national comparisons. As we have seen with the comparison between working girls in Nepal and Afghanistan, their experience is very different. It throws into sharp relief differences which might otherwise be masked or glossed over and which demand further attention. Instruments designed for use on a population basis throw up questions that deeper, more qualitative investigations can explore. Results from this study suggest that a potentially fruitful area for study are the culture-specific aspects of child labour, such as the world view that a culture engenders in working children, and the psychological strengths or vulnerabilities that may derive from it. Child labour is a complex phenomenon. It may be that the psychosocial impacts of child labour are best understood by looking at them within a specific geographical context as well as in comparison with cross-cultural commonalities.

The IPAW questionnaire has been demonstrated to be a reliable tool for obtainingnot a diagnosisbut a sense of the general psychological state of children who live in very difficult conditions and who work hard to provide for themselves and their families. One of its strengths is that it is able to elicit children's own feelings regarding personal security, a dimension which

  (a) "work which exposes children to physical, psychological or sexual abuse; (b) work underground, under water, at dangerous heights or in confined spaces; (c) work with dangerous machinery, equipment and tools, or which involves the manual handling or transport of heavy loads; (d) work in an unhealthy environment which may, for example, expose children to hazardous substances, agents or processes, or to temperatures, noise levels, or vibrations damaging to their health; (e) work under particularly difficult conditions such as work for long hours or during the night or work where the child is unreasonably confined to the premises of the employer."

  Culture has traditionally been a reliable guide for families to know what is good or bad for children. It offers powerful arguments in favour of child work: training in technical skills, entry to future employment, development of confidence and desirable habits, and possibly provision of food and shelter as well. But tradition is no longer so reliable in a rapidly globalizing world where there are new stresses, new toxic materials, new forms of work (think of e-waste recycling) and work in which new, non-traditional skills are required.

Figure 1 6

 1 Figure1

Factorial

  Structure of the IPAW Of these six dimensions of subjective well-being, three are related to the working conditions of the children (Stress, Self-esteem and Supervision at work) and the questions related to these are administered just to working children. The other three (Negative Emotions, Personal Security and Maltreatment) focus on general psychological functioning and in a comparative study such as this, are administered to both the study population and the control or comparison group.

Figure 2

 2 Figure2

7

  as part of an ongoing pilot project proposing to provide technical training skills to adolescent girls from brick worker families in Lahore, Pakistan.

  Figure 4

Table 1

 1 Standardized Beta of Gender and Age on Each of the 3 Factors of Well-Being by Country

		Pakistan	Nepal	Bangladesh	Afghanistan
	Negative Emotions
	Female	.293***	-.048	.096	.309***
	Age	.027	.130**	-.119	.170***
	Personal Security
	Female	.057	-.047	.049	-.040
	Age	-.011	-.023	-.097	.034
	Maltreatment
	Female	.168**	.029	.041	.150***
	Age	-.255***	-.114*	-.080	-.046
	Note: *** p<.001,** p < .05, * .05 < p < .10.

In this model, gender is shown to have a significant effect in at least two of the three countries for which there are adequate data. (There were too few girls in the Bangladesh sample from which to draw a statistical conclusion, but the fact that girls did not work in the brick factories after a certain age suggests that gender is playing a role there as well). As Table

1

shows, being

For example, the United Nations (UN) Convention on the Rights of the Child, or the Conventions of the International Labour Organization (ILO)

ILO Convention No. 5 -Minimum Age (Industry), 1919; ILO Convention No. 7 -Minimum Age (Sea), 1920; ILO Convention No. 10 -Minimum Age (Agriculture), 1921; ILO Convention No.

on Minimum Age (Non-Industrial Employment), 1932. 3 ILO Convention No. 138, Article 3

is increasingly being seen as critical to both children's current well-being as well as their future development.


Annemie Van Hirtum

Mohammad Ahmad

Raphael Chottin

Annemie Van

Hirtum Mohammad

Ahmad Raphaël

Chottin Xavier

A Composite Analogy to

Keywords: Effective linear Young's modulus, Equivalent multi-layer composite representation, Speech sound production

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

Introduction

The human larynx, situated between the trachea and the vocal tract, is a complex organ with major functions related to airway protection and speech sound production [START_REF] Rosen | Operative techniques in laryngology[END_REF]. For phonation or voiced speech sound production, the presence of two apposed vocal folds (VFs) is crucial. The fluid-structure interaction between airflow coming from the lungs and the deformable VFs tissues, positioned on each side of the glottal constriction as depicted in Fig. 2, can result in sustained VFs auto-oscillation which is the major sound source for voiced speech [START_REF] Rosen | Operative techniques in laryngology[END_REF][START_REF] O'shaughnessy | Speech Communication Human and Machine[END_REF]. As a consequence, the role of normal (healthy) and abnormal (pathological) VF structural properties on the fluid-structure interaction underlying VFs auto-oscillation and sound production is i May 2, 2023 15:57 ws-ijam ii Van Hirtum, Ahmad, Chottin, Pelorson an ongoing research subject [START_REF] Rosen | Operative techniques in laryngology[END_REF][START_REF] Hirano | Vocal fold physiology: contempory research and clinical issues, chap. Growth, development and aging of human vocal folds[END_REF][START_REF] Alipour | Elastic models of vocal fold tissues[END_REF][START_REF] Berke | Laryngeal biomechanics: an overview of mucosal wave mechanics[END_REF][START_REF] Min | Stress-strain response of the human vocal ligament[END_REF][START_REF] Chan | Relative contributions of collagen and elastin to elasticity of the vocal fold under tension[END_REF][START_REF] Murray | Vibratory responses of synthetic, self-oscillating vocal fold models[END_REF][START_REF] Riede | Body size, vocal fold length, and fundamental frequency: implications for mammal vocal communication[END_REF][START_REF] Mobashir | Linear measurements of vocal folds and laryngeal dimensions in freshly excised human larynges[END_REF][START_REF] Alexander | Volumetric analysis of the vocal folds using computed tomography: effects of age, height, and gender[END_REF].

Physical studies of the VFs auto-oscillation rely on deformable mechanical VF replicas. Replicas for which the structural properties can be systematically altered are of interest to reproduce the mechanical action regulating function of the vocal ligament and vocalis muscle as well as to explore the influence of structural abnormalities on the fluid-structure interaction and subsequent VFs autooscillation [START_REF] Cisonni | The influence of geometrical and mechanical input parameters on theoretical models of phonation[END_REF][START_REF] Luizard | Threshold of oscillation of a vocal folds replica with unilateral surface growths[END_REF][START_REF] Tokuda | Effect of level difference between left and right vocal folds on phonation: Physical experiment and theoretical study[END_REF]Bouvet et al., 2020b;[START_REF] Lucero | Phonation threshold pressure at large asymmetries of the vocal folds[END_REF]. One such mechanical VF replica, depicted in Fig. 2 and further detailed in Section 2, is obtained by representing each VF as a pressurised latex tube (PLT). Its mechanical action can be regulated by varying the height of a water column, which imposes the internal pressure P P LT of the replica.

Regardless of the extensive and ongoing use, for more than two decades, of the PLT type of VF replicas in physical studies of phonation [START_REF] Cullen | Brass instruments: linear stability analysis and experiments with an artificial mouth[END_REF]; Lopez [START_REF] Lopez | Physical modelling of buzzing artificial lips: the effect of acoustical feedback[END_REF][START_REF] Ruty | An in-vitro setup to test the relevance and the accuracy of low-order models of the vocal folds[END_REF][START_REF] Cisonni | The influence of geometrical and mechanical input parameters on theoretical models of phonation[END_REF]Bouvet et al., 2020a;[START_REF] Luizard | Threshold of oscillation of a vocal folds replica with unilateral surface growths[END_REF][START_REF] Van Hirtum | High-speed imaging to study an autooscillating vocal fold replica for different initial conditions[END_REF], no systematic study of the stress-strain relationship between its internal pressure and its deformation has yet been assessed. Therefore, a main objective of this work is to experimentally investigate the elastic stress-strain relationship. An imaging approach is outlined in Section 2 in order to measure the effective low-strain Young's modulus E ef f and thus to contribute to the mechanical characterisation of the PLT replica. It is noted that the low-strain range is pertinent for small deformations generally associated with normal VF auto-oscillation [START_REF] Ishizaka | Synthesis of voiced sounds from a two-mass model of the vocal cords[END_REF][START_REF] Titze | The physics of small-amplitude oscillation of the vocal folds[END_REF][START_REF] Ruty | An in-vitro setup to test the relevance and the accuracy of low-order models of the vocal folds[END_REF].

From Fig. 2 is seen that the PLT vocal fold replica can be thought of as a composite consisting of water and latex. This idea is exploited in Section 5 to formulate a composite analogy. The analogy relies on an analytical model of the effective low-strain elastic Young's modulus of a multi-layer composite as a function of its layer compositions, i.e. Young's modulus, dimensions and stacking orientation with respect to adjacent layers [START_REF] Ahmad | Modelling and validation of the elasticity parameters of multi-layer specimens pertinent to silicone vocal fold replicas[END_REF][START_REF] Ahmad | Low-strain effective Young's modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions[END_REF]. The composite analogy in combination with the measured effective Young's modulus E ef f allows then to consider the PLT replica as a de-homogenised equivalent multi-layer material. An equivalent low-strain Young's modulus can then be associated with each equivalent layer.

Next, the influence of design changes to the obtained equivalent multi-layer representations can then be used to assess the influence on its overall effective Young's modulus, i.e. associated with the homogenised replica. This is illustrated in Section 6 considering the influence of the outer latex layer design properties on the modelled effective Young's modulus of the PLT replica. May 2, 2023 15:57 ws-ijam iv Van Hirtum, Ahmad, Chottin, Pelorson Table 1. Overall characteristics of the PLT replica for P P LT = 0 Pa and values reported for a male adult [START_REF] Hirano | Vocal fold physiology: contempory research and clinical issues, chap. Growth, development and aging of human vocal folds[END_REF][START_REF] Plant | Direct measurement of onset and offset phonation threshold pressure in normal subjects[END_REF][START_REF] Mobashir | Linear measurements of vocal folds and laryngeal dimensions in freshly excised human larynges[END_REF][START_REF] Alexander | Volumetric analysis of the vocal folds using computed tomography: effects of age, height, and gender[END_REF] using soft tissue density 1.03 g/cm 3 [START_REF] Riede | Body size, vocal fold length, and fundamental frequency: implications for mammal vocal communication[END_REF][START_REF] Titze | Vocal fold mass is not a useful quantify for describing f 0 in vocalization[END_REF]: right-left length Lx, posterior-anterior length Ly, inferior-superior length Lz, volume V V F and mass m V F .

Lx [mm] Ly [mm] Lz [mm] V V F [mm 3 ] m V F [
= 998 kg•m -3 , dynamic viscosity coefficient µ L = 1.0 × 10 -3 Pa•s).
The water inlet (internal diameter 4 mm) is connected to a water column whose height determines the internal pressure P P LT within the latex tube. The PLT VF replica dimensions L x , L y and L z , volume V V F and mass m V F (see Fig. 1) for P P LT = 0 Pa are summarised in Table 1. Reference values reported for the VF of a male adult are indicated as well [START_REF] Hirano | Vocal fold physiology: contempory research and clinical issues, chap. Growth, development and aging of human vocal folds[END_REF][START_REF] Plant | Direct measurement of onset and offset phonation threshold pressure in normal subjects[END_REF][START_REF] Mobashir | Linear measurements of vocal folds and laryngeal dimensions in freshly excised human larynges[END_REF][START_REF] Alexander | Volumetric analysis of the vocal folds using computed tomography: effects of age, height, and gender[END_REF]. The internal pressure of the PLT VF replica varies with the imposed P P LT and thus with the height of the water column [START_REF] Cisonni | The influence of geometrical and mechanical input parameters on theoretical models of phonation[END_REF]. Concretely, in this work internal pressure P P LT is systematically increased (↑) and decreased (↓) between 450 Pa and 6500 Pa with steps of about 100 Pa. This corresponds to a water column range of about 60 cmH 2 O. All experiments are performed at room temperature (21

± 1 • C).
The right PLT VF is positioned in a rigid frame, as depicted in Fig. 3, in the same way as during fluid-structure interaction experiments [Bouvet et al., 2020a;[START_REF] Van Hirtum | High-speed imaging to study an autooscillating vocal fold replica for different initial conditions[END_REF]. The metal support part is immobilised whereas the unconstrained deformable portion faces the medio-sagittal y-z plane. The frame allows simultaneous camera observation of the VF along the sagittal y-z plane (side view in Fig. 3, Nikon AF-S Nikkor 18-70 mm, shutter time 2 ms, aperture 4.3 mm, 0.037 mm/px) and along the transverse x-y plane (top view in Fig. 3, Motion Blitz Eosens Cube 7, shutter time 726 µs, aperture 11 mm, 0.049 mm/px). It is noted that the main oscillation occurs within the transverse plane as indicated in Fig. 1.

Increasing (or decreasing) the internal water pressure P P LT expands (or shrinks) the radius of the PLT replica with respect to the posterior-anterior y-axis depicted in Fig. 1

Stress-strain data

Extracted replica edges as a function of y/L y (with L y = 42 mm indicated in Fig. 2) are illustrated in Fig. 5 top (or side) view imaging is then obtained for each imposed P P LT as

ε x t = ln L x L x,min and ε z t = ln L z L z,min (1a)
with L x,min (or L z,min ) denoting values associated with the lowest assessed P P LT ≈ 450 Pa. The stress σ t along both radial directions is set by the imposed internal pressure so that σ t = P P LT holds. Resulting measured stress-strain data σ t (ε x t ) (top view) and σ t (ε z t ) (side view) are plotted in Fig. 6. Different datasets of ε x t and ε z t are obtained for each of the four ∆y/L y -intervals used to determine mean values L x and L z . Overall, strain ranges ε x t ≤ 0.15 and ε z t ≤ 0.12 are associated with stresses σ t up to 6.5 kPa.

Measured effective low-strain Young's moduli

Linear fits (lines) to the measured stress-strain curves σ t (ε x t ) and σ t (ε z t ) and their accuracies (coefficient of determination R 2 in %) are illustrated in Fig. 6. For each data curve, the linear fit accuracy yields R 2 ≥ 98%. Therefore, it is reasonable to assume that measured strains, up to ε x t ≤ 0.15 and up to ε z t ≤ 0.12, are within the linear elastic range for both the transverse x and streamwise z direction. Effective elastic low-strain transverse Young's modulus E x ef f and low-strain streamwise Young's modulus E z ef f are then estimated as the slope of the linear fit following Hooke's law of linear elastic deformation [START_REF] Strobl | The Physics of Polymers[END_REF]]

E x ef f = σ t ε x t and E z ef f = σ t ε z t . ( 2
)
Measured effective Young's moduli E x ef f and E z ef f are plotted in Fig. 7. Values obtained for increasing (σ t (ε z t ) ↑ , σ t (ε x t ) ↑ ) and decreasing (σ t (ε z t ) ↓ , σ t (ε x t ) ↓ ) internal pressure for each of the assessed ∆y/L y intervals are indicated. For each ∆y/L y interval, it is seen that the influence of increasing (↑) or decreasing (↓) the water May 2, 2023 15:57 ws-ijam viii Van Hirtum, Ahmad, Chottin, Pelorson pressure P P LT is negligible as estimated E x ef f and E z ef f are affected with less than 1.5%. This confirms the hypothesis of linear elastic deformation expressed in Eq. 2 for the assessed strain range.

The influence of the exact position of the local (4 mm) intervals centered around y/L y ∈ {0.4, 0.5, 0.6} is negligible as it is less than 2% with respect to the value at y/L y = 0.5. The means and standard deviations for these local intervals yield

E x ef f = 44 ± 1 kPa and E z ef f = 49 ± 1 kPa. Consequently, E z ef f is increased with 11% compared to E x ef f .
The boundary conditions at the extremities affect E ef f determined on the whole y-range (0 ≤ y/L y ≤ 1) as E x ef f decreases with 7% (to 41 kPa) and the overall mean E z ef f increases with 12% (to 55 kPa) compared to mean values obtained on the local intervals. Therefore, values obtained on the whole interval are further disregarded.

Composite analogy: equivalent multi-layer representation

Three equivalent multi-layer (ML) representations of the deformable portion of the PLT replica are obtained by considering an equivalent composite with two (2L), three (3L) or four (4L) perfectly bounded adjacent layers within the rectangle enveloping the coronal (medio-frontal) section along the x-z plane of the PLT replica. Equivalent representations are illustrated in Fig. 8. The rigid non-deformable part of the PLT replica, corresponding to the metal support in Fig. 2, is excluded so that equivalent representations are rectangular with transverse length l = 6.6 mm along the x-direction and streamwise length h = 11.4 mm along the z-direction. The deformable portion of the PLT replica (water and latex envelop) is thus represented as a multi-layer material composed of an inner layer adjacent to one (for the 2L representation), two (for the 3L representation) or three (for the 4L representation) thin latex (natural rubber [START_REF] Bouvet | Experimental and theoretical contribution to the analysis and the modelling of the vocal folds vibration[END_REF]) outer layers. The latex outer layers have thickness 0.2 mm (l 2 , h 1 and h 3 in Fig. 8) and Young's modulus E r = 1.1 MPa (see Section 2). Dimensions of the inner layer for each representation are indicated in Fig. 8 and its equivalent Young's moduli along the transverse x-direction (E x 2L , E x 3L and E x 4L ) and streamwise z-direction (E z 2L , E z 3L and E z 4L ) are unknown and need thus to be modelled.

Each equivalent representation depicted in Fig. 8 consists of serial (⊥) or parallel ( ) stacked layers with respect to the force (F) direction, which is either transverse (F x ) or streamwise (F z ). When the layers stacking orientation is known, the relationship between the effective Young's modulus E ef f of the homogenised composite can be expressed analytically as a function of the equivalent Young's moduli and dimensions of its individual layers [START_REF] Ahmad | Modelling and validation of the elasticity parameters of multi-layer specimens pertinent to silicone vocal fold replicas[END_REF][START_REF] Ahmad | Low-strain effective Young's modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions[END_REF].

For k serial (⊥) stacked layers with respect to the force direction, the effective Young's modulus E ⊥ ef f is expressed as the harmonic mean of the layers Young's moduli E i weighted with their lengths in the force direction following the Reuss hypothesis of homogeneous stress [START_REF] Reuss | Berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle[END_REF][START_REF] Ahmad | Modelling and validation of the elasticity parameters of multi-layer specimens pertinent to silicone vocal fold replicas[END_REF][START_REF] Ahmad | Low-strain effective Young's modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions[END_REF]. For transverse May 2, 2023 15:57 ws-ijam

x Van Hirtum, Ahmad, Chottin, Pelorson F x and streamwise F z forces this becomes respectively

E ⊥,x ef f = k i=1 l i k i=1 l i E i and E ⊥,z ef f = k i=1 h i k i=1 h i E i . ( 3
) with l = k i=1 l i , h = k i=1 h i .
For k parallel ( ) stacked layers with respect to the force direction, the effective Young's modulus E ef f of the homogenised composite is obtained as the arithmetic mean of the layers Young's moduli E i weighted with their heights perpendicular to the force direction following the Voigt hypothesis of homogeneous strain [START_REF] Voigt | Ueber die beziehung zwischen den beiden elasticitätsconstanten isotroper körper[END_REF][START_REF] Ahmad | Modelling and validation of the elasticity parameters of multi-layer specimens pertinent to silicone vocal fold replicas[END_REF][START_REF] Ahmad | Low-strain effective Young's modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions[END_REF]. For transverse F x and streamwise F z forces this becomes respectively

E ,x ef f = k i=1 h i E i k i=1 h i and E ,z ef f = k i=1 l i E i k i=1 l i . ( 4
)
When layers are stacked both parallel and serial, i.e. combined stacking ( ⊥), with respect to the force direction, firstly adjacent parallel stacked layers are homogenised using Eq. ( 4) and then the remaining serial stack is homogenised using Eq. ( 3) [START_REF] Ahmad | Modelling and validation of the elasticity parameters of multi-layer specimens pertinent to silicone vocal fold replicas[END_REF][START_REF] Ahmad | Low-strain effective Young's modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions[END_REF].

Analytical expressions of effective Young's moduli of each homogenised equivalent multi-layer representation are then set to match measured values E x ef f = 44 kPa (for F x ) and E z ef f = 49 kPa (for F z ) (Section 4). This way, analytical expressions of the effective Young's modulus of each homogenised equivalent composite (2L, 3L or 4L) subjected to a transverse force F x (or streamwise force F z ) reduce to first-order linear equations whose unknown is the equivalent Young's modulus E x

•

(or E z • ) of the inner layer (Fig. 8). Analytical expressions for E x 2L and E z 2L for the 4L (E x 4L and E z 4L ) composite representation. Measured effective Young's moduli E x ef f and E z ef f for the PLT replica (Section 4) and Er for the outer latex layer(s) (natural rubber [START_REF] Bouvet | Experimental and theoretical contribution to the analysis and the modelling of the vocal folds vibration[END_REF]) are given.

E x • [kPa] E z • [kPa] inner layer, 2L E x 2L = 42.7 † E z 2L = 15.1 inner layer, 3L E x 3L = 4.1 E z 3L = 47.4 † inner layer, 4L E x 4L = 4.3 E z 4L = 14.5 outer latex layer Er = 1100 Er = 1100 homogenised ‡ E x ef f = 44 E z ef f = 49 ‡ set to match E x
ef f and E z ef f measured on the PLT replica. † robust representation (Er-variation), serial (⊥) stack.

design representation (known Er), combined ( ⊥) stack.

2L representation, E x 3L and E z 3L for the 3L representation and E x 4L and E z 4L for the 4L representation are given in A. Resulting values are presented in Table 2. As a reference, imposed effective Young's moduli E x ef f and E z ef f for the homogenised equivalent representations are indicated as well.

Resulting E x ef f and E z ef f in Table 2, either measured on the PLT replica (Section 4) or modelled E x

• and E z • for each of the equivalent mutli-layer composite representations, are within the range (up to 65 kPa) reported for the normal VF layer structure of a male adult [START_REF] Hirano | Vocal fold physiology: contempory research and clinical issues, chap. Growth, development and aging of human vocal folds[END_REF][START_REF] Alipour | Elastic models of vocal fold tissues[END_REF][START_REF] Min | Stress-strain response of the human vocal ligament[END_REF][START_REF] Chan | Relative contributions of collagen and elastin to elasticity of the vocal fold under tension[END_REF][START_REF] Chhetri | Measurement of Young's modulus of vocal folds by indentation[END_REF][START_REF] Miri | Mechanical characterization of vocal fold tissue: a review study[END_REF][START_REF] Zhang | Biaxial mechanical properties of human vocal fold cover under fold elongation[END_REF], i.e. muscle, vocalis ligament, superficial layer and epithelium. Therefore, Young's moduli associated with the homogenised (E x ef f and E z ef f ) and the inner layer (E x

• and E z • ) of the equivalent composite representations are also within the range characterising molded multi-layer silicone VF replicas designed to mimick up to some extent the anatomical multi-layer structure of a normal VF [START_REF] Pickup | Flow-induced vibratory response of idealized versus magnetic resonance imaging-based synthetic vocal fold models[END_REF]Murray andThomson, 2011, 2012;[START_REF] Tokuda | Effect of level difference between left and right vocal folds on phonation: Physical experiment and theoretical study[END_REF]Bouvet et al., 2020b;[START_REF] Ahmad | Low-strain effective Young's modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions[END_REF]. Note, that Young's modulus E r = 1.1 MPa of the outer latex layer is out of this range as its value is much greater (factor 17) than 65 kPa corresponding to the upper limit of the range commonly associated with anatomical VF layers.

Influence of outer latex layer characteristics

From Table 2 is seen that for all equivalent composite representations (2L, 3L or 4L), outer latex layer(s) Young's modulus E r is much larger (by a factor 20 up to 270) than inner layer Young's moduli E x

• and E z • . Since the arithmetic mean for parallel layer stacking (Eq. ( 4)) is more affected by layers with high Young's modulus than the harmonic mean for serial layer stacking (Eq. ( 3)), serial layer stacks are expected to be somewhat robust with respect to variations of outer latex layer characteristics, i.e. dimensions (l 2 , h 1 , h 3 ) and Young's modulus E r . From Fig. 8 is seen that purely serial layer stacking occurs only for the 2L representation in the case of a transverse force F x (E x 2L , Fig. 8(a)) and for the 3L representation in the case of a streamwise force F z (E z 3L , Fig. 8(a)). Consequently, these representations, and thus resulting E x

2L and E z 3L , are most robust with respect to outer latex layer characteristics. This is further illustrated in Fig. 9 where E x • and E z • (using Eq. (A.1), Eq. (A.2) and Eq. (A.3)) are plotted for varying E r (Fig. 9(a)) and varying outer latex layer dimensions l 2 , h 1 , h 3 (Fig. 9(b)) while still imposing measured effective Young's moduli E x ef f = 44 kPa and E z ef f = 49 kPa for the effective homogenised representation moduli. As a reference values E r = 1.1 MPa and l 2 = h 1 = h 3 = 0.2 mm used in the equivalent representations shown in Fig. 8 are indicated (dotted vertical lines). The outer layer Young's modulus E r is varied between 0.4 MPa and 2.0 MPa, which spans the range reported for natural rubber [START_REF] Department | Materials data book[END_REF][START_REF] Strobl | The Physics of Polymers[END_REF] (Piercan Ltd.) and outer latex layer dimensions (l 2 , h 1 , h 3 ) are varied from 0.01 mm up to 1 mm. It is seen that E x

2L and E z 3L are indeed least affected (with less than 10 kPa) when outer layer characteristics (E r and l 2 , h 1 , h 3 ) are varied as their value remains near E x ef f and E z ef f characterising the homogenised composite representations. It follows that E x

2L and E z 3L are most robust to changes of the latex outer layer(s) characteristics. All other representations contain a parallel stacked outer latex layer, so that inner layer Young's moduli E x

• and E z • decrease rapidly when E r or outer layers dimension (l 2 , h 1 , h 3 ) are increased.

In Fig. 9 (and in Table 2) is further seen that E x 3L ≈ E x 4L and E z 2L ≈ E z 4L . This is due to the similar transverse 3L and 4L parallel layer stacks and the similar streamwise 2L and 4L parallel layer stacks (as depicted in Fig. 8) whereas the remaining serial stacking part for the 4L representation is, again due to the harmonic mean, only marginally affected by the thin latex outer layer with high E r .

Overall, the equivalent 4L composite representation seems most rigorous on the condition that E x 4L > 0 and E z 4L > 0. Indeed, the 4L representation applies to both force directions, either transverse or streamwise, and resulting inner layer Young's moduli (E x 4L < E z 4L ) reflect the anisotropy between both force directions observed for the measured effective Young's moduli (E x ef f < E z ef f ). Moreover, the inner layer of the 4L representation only concerns the water portion of the PLT replica so that E x

4L and E z 4L might be exploited in order to vary the latex outer layers characteristics (E r or/and its length) in order to approximate a prescribed effective Young's moduli for the homogenised equivalent 4L composite. This way, the 4L representation might potentially contribute to PLT replica design. On the other hand, representations as-May 2, 2023 15:57

ws-ijam

Composite analogy xiii sociated with E x 2L and E z 3L are of interest when latex outer layer characteristics are either not accurately known or out of the working range of the 4L representation, which requires E x 4L > 0 and E z 4L > 0.

Discussion and conclusion

The effective linear elastic Young's modulus of the PLT vocal fold replica is measured along the transverse right-left (x) and the streamwise inferior-superior (z) direction. Measured E x ef f = 44 kPa and E z ef f = 49 kPa exhibit an anisotropy of 11% with respect to E x ef f characterising the main auto-oscillation direction. These values are within the range, up to 65 kPa, reported for anatomical layers of a male adult human VF. Equivalent 2L, 3L and 4L composite representations of the PLT replica are introduced consisting of an equivalent inner layer with unknown Young's modulus to which one, two or three outer latex layers are added. The effective linear Young's modulus of each homogenised equivalent representation is set to match measured effective Young's moduli E x ef f = 44 kPa and E z ef f = 49 kPa observed on the PLT replica. Unknown Young's moduli of the equivalent inner layer are then obtained analytically using a composite analogy. The assessed 4L representation is most rigorous as it applies to both force directions and its inner layer does not involve outer latex layer characteristics. Associated E x 4L = 4.3 kPa and E z 4L = 14.5 kPa reflect the anisotropy between both force directions observed for the measured effective Young's moduli E ef f on the PLT replica. It is argued that this representation might be exploited for PLT replica design where the outer latex layer characteristics can be adapted in order to attain a prescribed effective Young's modulus. On the other hand, the transverse 2L (E x 2L = 42.7 kPa) and streamwise 3L (E z 3L = 47.4 kPa) representations with serial stacking are most robust with respect to outer latex layer characteristics. These representations remain valid in case that outer layer characteristics are not accurately known. Regardless of the applied representation, found linear Young's moduli for the inner layer are within the range associated with human VF layers. Thus the equivalent multi-layer representations present itself as a tool for PLT replica design in terms of its linear stress-strain behaviour. Besides design purposes, equivalent multi-layer representations favour the comparison with the stress-strain behaviour of other types of deformable multi-layer VF replicas such as molded multi-layer silicone replicas, which are designed to mimic the multi-layer anatomical structure of a human VF.

Appendix

A. Analytical expressions of Young's moduli of inner layer of ML representations

The layers of the 2L representation (Fig. 8(a)) are stacked serial for a force along the x-dimension and parallel for a force along the z-dimension so that unknowns E x 2L and E z 2L are expressed as

E x 2L = l 1 α 1,x 1 - l 2 E r α 1,x and E z 2L = α 1,z l 1 - l 2 E r l 1 (A.1)
with α 1,x = E x ef f /l, α 1,z = E z ef f l and l = l 1 + l 2 . The layers of the 3L representation (Fig. 8(b)) are stacked parallel for a force along the x-dimension and serial for a force along the z-dimension so that unknowns E x 3L and E z 3L are expressed as

E x 3L = α 2,x h 2 - 2 h 1 E r h 2 and E z 3L = h 2 α 2,z 1 - 2 h 1 α 2,z E r (A.2)
with α 2,x = E x ef f h, α 2,z = E z ef f /h and h = 2 h 1 + h 2 since h 1 = h 3 . The layers of the 4L representation (Fig. 8(c)) are stacked parallel and serial for both force directions so that unknowns E x 4L and E z 4L are obtained combining expressions in Eq. (A.1) and in Eq. (A.2) as .3)

E x 4L = h h 2      l 1 α 1,x 1 - l 2 E r α 1,x - 2 h 1 E r h      and E z 4L = l l 1      h 2 α 2,z 1 - 2 h 1 α 2,z E r - l 2 E r l      . (A

Fig. 1 .Fig. 2 .

 12 Fig. 1. Schematic overview of the time-varying glottal constriction area Ac(t) and main VF characteristics (dimensions Lx, Ly, Lz and mass m V F ) during VF auto-oscillation.

Fig. 3 .

 3 Fig. 3. Spatial positioning of right PLT VF replica and camera views (side and top).

  Fig. 4. Illustration of edge detection from right PLT VF imaging and extracted Lx(y) (a: top view) and Lz(y) (b: side view) for different P P LT (Pa).

  (a) for top view images and in Fig.5(b) for side view images for increasing P P LT . For each image, and hence imposed P P LT , mean L x (top view) and L z (side view) are quantified on four different ∆y/L y intervals. The overall mean (0 ≤ y/L y ≤ 1 or interval length ∆y/L y = 1, standard deviation less than 2.5%) and three local mean values on 4 mm ranges (interval length ∆y/L y = 0.1, standard deviation less than 0.2%) with center values set 2.4 mm apart at y/L y = 0.5 (center, 0.45 ≤ y/L y ≤ 0.55), y/L y = 0.4 (towards the water inlet, 0.35 ≤ y/L y ≤ 0.45) or y/L y = 0.6 (away from the water inlet, 0.55 ≤ y/L y ≤ 0.65) are assessed. Quantified L x (P P LT ) (top view) and L z (P P LT ) (side view) and standard deviations (bars) are plotted in Fig.5(c) and Fig.5(d). Increasing (or decreasing) P P LT also increases (or decreases) the mean characteristic lengths L z (side view) and L x (top view) associated with expansion (or shrinking) of the PLT replica. For each imposed P P LT , L x and L z of different ∆y/L y -intervals agree to within 0.25 mm and to within 0.1 mm considering only the local intervals (∆y/L y = 0.1 or ∆y = 4 mm).The strain ε x t (or ε z t ) along the transverse x (or streamwise z)

  Fig. 5. Characteristic lengths characterisation of PLT replica from imaging: a,b) Lx(y/Ly) (top view) and Lz(y/Ly) (side view) for increasing P P LT (lighter in color) and c,d) mean (symbols) and standard deviation (vertical bars) of Lx(P P LT ) (top view) and Lz(P P LT ) (side view) for 4 ∆y/Ly-ranges. Dashed line indicates reference values for P P LT = 0 Pa associated with either the latex tube outer radius of 11.2 mm (in a,c) or the metal support diameter of 12.0 mm (in b,d).

Fig. 7 .

 7 Fig. 7. Effective elastic Young's modulus E x ef f (and E z ef f ) estimated as the linear slope to curves σt(ε x t ) ↑ and σt(ε x t ) ↓ (and σt(ε z t ) ↑ and σt(ε z t ) ↓ ). Different ∆y/Ly intervals (symbols) used to determine ε x t and ε z t are indicated. Mean values for σt(ε x t ) and σt(ε z t ) for the local intervals, thus excluding values for y/Ly ∈ [0 1], are indicated (dashed lines).

  Fig. 8. Equivalent multi-layer composite PLT replica representations with effective Young's modulus E x ef f = 44 kPa and E z ef f = 49 kPa: a) two-layer (2L), b) three-layer (3L) and c) four-layer (4L). Top: coronal replica section at P P LT = 0 kPa. Bottom: equivalent composite (dimensions in mm) excluding the rigid metal support portion. Layer orientations (serial ⊥, parallel , combined ⊥) with respect to a transverse Fx or streamwise Fz force are indicated. The Young's moduli of the equivalent thin (0.2 mm) outer latex layers yields Er = 1.1 MPa. The sought transverse E x• and streamwise E z • equivalent Young's modulus of each inner layer is modelled exploiting the composite analogy.

  Fig. 9. Influence of outer latex layer characteristics on inner layer E x • (black symbols) and E z • (gray symbols) of the equivalent 2L ( ), 3L (•) and 4L (+) composite representations of the PLT VF replica while imposing homogenised effective Young's moduli E x ef f = 44 kPa and E z ef f = 49 kPa (dashed horizontal lines): a) latex Young's modulus Er, b) outer latex layer dimension l 2 , h 1 , h 3 . Replica values Er = 1100 kPa and l 2 = h 1 = h 3 = 0.2 mm (dotted vertical lines) are shown.

Table 2

 2

	. Equivalent Young's moduli E x • and E z • of the inner layer of the equivalent 2L (E x 2L and E z 2L ), 3L (E x 3L and E z 3L ) and

Acknowledgements

Financial support from the CNRS through the 80|Prime program (InteracSon) and from the French National Research Agency (Full3DTalkingHead, ANR-20-CE23-0008-03) is acknowledged.