The need for invariant assessments in South African education

Graham A Dampier email@example.com
Department of Childhood Education
University of Johannesburg
South Africa

The need for invariant assessments in South African education
09E52A0C7F0220C5169B1B5F7347EE2Dfoundation phase learnersinvariancemathematical competenceRasch Model
Presently, a plethora of instruments designed to assess a mathematical skill, disposition, or competence prevail in South Africa.Yet few of them adhere to the basic requirements of the unidimensionality and invariance of measures.The Marko-D is a mathematical instrument designed to test learners between the ages of 4 and 8.The instrument, thus far, appears to adhere to the central tenets of fundamental measurement, which hold that a test should be invariant across different groups of people and that it should measure a single variable to a level of precision that is useful practically and theoretically.The Marko-D was used to assess the mathematical competence of 249 foundation phase pupils.Even though we cannot conclude at this stage that the Marko-D satisfies the requirements of invariance and unidimensionality completely, this study provides an elucidation of the need for invariant assessments in South African education.

Introduction

The scientific status of the social sciences, or the human sciences, has been called into question since its inception in the 19th century (Hollis, 1994;Winch, 1958;Wittgen-i stein, 1922;Benton & Craib, 2011).Fundamental measurement seeks to address the ii scientific status of various disciplines in the social sciences by attempting to establish instruments of measurement and assessment that are consistent in time and for different cultures (Bond & Fox, 2007).Fundamental measurement is the commitment and endeavour, both within the social sciences and the natural sciences, to establish measures that are obtained directly from the object of study.Andrich (1988) argues that with the careful application of the Rasch model it is possible to attempt to produce fundamental measures of various phenomena in the social sciences.Measures that can be considered fundamental are by and large elusive and necessarily entail developing scales of measurement and instruments of assessment that produce a direct and stable quantification of phenomena that do not waver in consistency, or that have little variation between people of similar ability (Andrich, 1988;Rasch, 1960;Wright, 1994;Wright & Stone, 1979;Wright & Stone, 1999).

Currently, we do not have one test for basic mathematical skills that can be used in different cultures; yet scientific instruments of measurement, such as thermometers and barometers, produce consistent readings and results everywhere on earth.There is, at best, in the field of foundation phase mathematics, a loose collection of tests available in South Africa that are vaguely related by their interest in a particular phenomenon or subject area.We certainly do not lack readily available instruments to test various mathematical skills.We have the Trends in Mathematics and Science (TIMSS), the Annual National Assessments (ANAs), psychological tests such as the Wechsler Individual Achievement Test (WIAT), and many others with which to test the ability of our learners.What we lack is a single reliable measure of what children in the foundation phase can do with numbers.We lack an instrument to determine whether a particular pupil lacks a basic set of mathematical skills that are necessary for progress through the grades that constitute the foundation phase.

Fundamental measurement consists of a set of axioms that are designed to advance the endeavour of measuring phenomenon consistently in time and in different social and cultural contexts (Bond & Fox, 2007).Unidimensionality and invariance are its most important tenets.Unidimensionality holds that only the ability of persons and the difficulty of items should affect the outcome of a test or assessment (Andrich, 1988;DeMars, 2010;De Ayala, 2008;Bond & Fox, 2007).Anything else would be considered noise, hazardous to the accuracy of measurement, and ultimately unscientific (Linacre, 2002).A test that is unidimensional should measure a single variable "to a level of precision that is of some practical or theoretical use" (Andrich, 1988:10).Let us suppose that we have a unidimensional test that claims to measure a core mathematical ability.If this test is translated into three different languages and used to test participants from each, and if each version of the test measures a common latent trait, then the pattern of responses to the items of the test in the different languages should be consistent, given that the population of each language is representative, heterogeneous in terms of ability, and that sample error has been reduced as much as possible.The test should be invariant for those three groups of people and the respective languages should not obscure our ability to measure the latent trait.Allalouf, Hambleton and Sireci (1999) explain that little research has been conducted on why translated tests produce different results in different languages.They argue that few studies have dealt with detecting the causes of variance across different languages, because few studies use translated tests.The linguistic diversity in South Africa requires that any attempt at large scale standardised assessment, in the vein of the TIMSS, Progress in International Reading Literacy Study (PIRLS), and the ANAs, engages in the process of translating tests into various language.The linguistic diversity of South Africa is potentially a rich source of data in cross-cultural test adaptation and the endeavour of producing invariant measures of people.

This article reports on the attempt to arrive at measures of mathematical competence that are invariant and unbiased across three different language groups.I proceed by elucidating, however briefly, unidimensionality and invariance from the perspective of Rasch measurement theory, before conducting tests of invariance and differential item functioning (Clauser & Mazor, 1998;Rudas & Zwick, 1997;Swanson, Clauser, Case, Nungester & Featherman, 2002, Fidalgo, 2011).This is done to establish whether data gathered with the Marko-D adheres to the basic tenets of measurement, i.e. that an instrument should not be easier for one group of people as opposed to another, and that a test should produce measures that do not vary from one group of people to another.Lastly, I evaluate the implications that the invariance of measures has on assessing the mathematical competence of foundation phase learners in South Africa.

The Rasch Model

The pervasive tenet of the Rasch model, and other models of measurement that fall within the ambit of Item Response Theory (IRT), is that a single dimension is accessed when the items of a test measure one discrete construct or latent trait (DeMars, 2010: 38;De Ayala, 2008;Andrich, 1988).Unidimensionality maintains that a single continuous attribute, dimension or construct is the object of study when an instrument, which adheres to this assumption, is used to assess people who possess varying degrees of the construct being measured.Unidimensionality delimits the measurement of a latent trait to the ability of people, and the difficulty of items used to measure the latent trait and discriminate between people of different levels of ability.Instruments remain faithful to this tenet when they distinguish effectively between people of various levels of ability without discriminating at the same time between people of different genders, cultural groups, linguistic backgrounds or socio-economic status.Two variables, then, are used to describe the latent trait, the ability of people and the difficulty of items.

Another inherent requirement of the Rasch model is that a test should not be easier for one group of people than another.The Rasch model holds that items should only discriminate between people according to their ability and not according to their membership of a particular group of people (Bond & Fox, 2007;De Ayala, 2009;Zumbo, 1999;Rudas & Zwick, 1997).A particular item of a test should make a distinction between two people of differing abilities and should not distinguish between two people of the same ability who belong to two different genders or cultural groups, or who speak different languages.Stated differently, if various translations of a test are used to measure a latent trait consistently, then there should be no statistically significant difference in individual responses to the items of each version of the test (given that sample error has been contained as far as possible and that each population is heterogeneous in ability).

In order for a test that was developed in Germany and translated into English, isiZulu and Sesotho to maintain its validity, it must measure the latent trait without discriminating between people of the same ability who speak different languages.It must allow for the possibility that two people of the same ability, who belong to different language groups, will get an item correct.The likelihood of a person getting an item correct should depend only on their level of ability and not on the language they speak.

When a latent trait is measured consistently across different groups of people the Dampier difficulty of the items should remain invariant.There should be no fluctuation in the hierarchical ordering of items from one group of people to the next.When the difficulty of a given item varies from one group of people to the next, and when this variance exceeds model error, its unidimensionality is thereby violated (De Ayala, 2008).This would suggest that different responses would have been elicited not by varying degrees of ability, but by group membership (assuming there is no sampling error from group to group).Bond and Fox (2007:92) explain that the "principles underlying the plots of person and item invariance across testing situations is exactly that underlying the detection of Differential Item Functioning (DIF).When an item's difficulty estimate location varies across samples by more than the modelled error, then prima facie evidence of DIF exists".

In another sense, DIF will be present in the items of a test when the latent trait is measured differently in different languages.If the language of a test improves the likelihood of a person getting an item correct, or if language presents an added dimension of difficulty, one cannot argue that the test is unidimensional (Zumbo, 1999).In this instance the language of a test will either aid or impeded the ability of a person to respond correctly to an item.The test will be measuring two dimensions the latent trait and the language ability of persons being tested.

The property of invariance is essential to fundamental measurement and is intimately related to the reliability and validity of instruments.According to De Ayala (2008:3), instruments with high reliability will yield consistent results over a series of repeated measurements: "...If these repeated measurements varied wildly from one another [...] they would be considered to have low consistency or to have low reliability".The validity of measures are defined by the degree to which they "are actually manifestations of the latent variable" (De Ayala, 2008:3).Even though the invariance of an instrument does not prove that it is valid in the strictest sense, the consistent measurement of a latent trait over a series of testing sessions certainly strengthens the case that an instrument displays content and construct validity (Field, Miles & Field, 2012).De Ayala writes that (2008:3) Thurstone noted that a measuring instrument must not be seriously affected in its measuring function by the object of measurement.In other words, we would like our measurement instrument to be independent of what it is we are measuring.If this is true, then the instrument possesses the property of invariance [italics in the original].

Method Design

The study reported here is part of a larger panel research project, which is concerned with measuring the conceptual growth of learners between the ages of five and nine.

The longitudinal development of mathematical, literacy and science concepts is studied over four years (Henning, 2012).An instrument developed, normed and standardised in Germany is used to assess the mathematical competence of individuals, and to capture their growth.

The authors of the test describe it as a process-orientated diagnostic instrument that can be used to measure an individual's mathematical abilities either repeatedly over time or cross-sectionally (Ricken, Fritz & Balzer, 2011).The "Mathematical and Arithmetic Competence Diagnostic" instrument (or MARKO-D the German acronym) measures ability with a stable "scale of mathematical achievement" that was "developed on the basis of theoretical suppositions and empirical data" (Ricken et al., 2011:256).The MARKO-D was designed and validated with the principles of the Rasch model in mind.Its developers were striving to arrive at a unidimensional test of mathematical competence.The test captures five incremental levels of mathematical ability, which begin with a basic assessment of the ability to use the counting sequence.Level two assesses understanding of the ordinal number line, level three the knowledge of cardinality, level four the use of the part-whole concept of number, and level five the understanding of congruent intervals, which refers to the ability to understand that any given number is constituted by intervals on the number line, for instance the number "9" can be analysed into "3" and "6" or "4" and "5" (Fritz, Ehlert & Balzer, 2013).

Subjects

The research is conducted at an urban South African public school where children receive home language instruction in one of two languages, either isiZulu or Sesotho.The learners at the school are representative of the surrounding community, which includes households that are spread across the socio-economic spectrum.This conveniently sampled population constitutes a heterogeneous testing sample in terms of ability and socio-economic status.

The dataset consists of 249 responses to 54 variables.Two home languages, isiZulu (129) and Sesotho (120), are represented in this data.Learners between the ages of five and seven are tested in their mother tongue (i.e.either in isiZulu or Sesotho), while learners of 8 and 9 years are tested in English.The reason is that at the end of grade 3 learners at this school will be required (in line with the South African curriculum) to switch to the first additional language (FAL), which in this instance is English.To assist with the transition to English, learners are taught mathematical concepts in both their particular home language and the FAL (Henning & Dampier, 2012) in a pedagogical model of translation that spurns the mixing of languages within sentences (Henning, 2012).

In addition, since the school follows the national public school curriculum strictly, grade R learners receive little, if any, guided instruction in mathematics.Our data can, then, be analysed according to (1) the home language of the participants, (2) the language in which they were tested, and (3) exposure to the formal instruction of mathematics.

Preliminary analysis

Before conducting the DIF analysis the Rasch model of measurement was used to determine whether the data fit the assumptions and parameters of a unidimensional model.An initial analysis of the data yielded a near to ideal value for infit (.99), but a high outfit value of 1.05, which indicates that 50% more variation was observed when unexpected responses were elicited by items.Table 1 contains the summary statistics of the MARKO-D before nine items were excluded for eliciting erratic responses from persons at extreme ends of the latent trait continuum.Even though the summary statistics suggest that the items of the instrument are effective in eliciting on target responses, it was decided to forward those items that were eliciting unexpected responses from persons to a panel of experts for review (Linacre, 2002).

The high measure of outfit has been reduced to 1.00 after excluding those items that were most underfitting.Nine underfitting items were excluded on the basis that they all had high outfit measures (>1.02) that were statistically significant (>2.00).When items display a large degree of underfit in the outfit column, it may suggest the presence of an element of noise in those items (Linacre, 2002).This can mean that something other than the latent trait is affected by the way in which people are responding to these items.It is important to note that these items are not excluded from the test entirely and interminably, but that they will be subject to review by a panel of experts (De Ayala, 2008).It is likely that the translation of the construct from the original German to English, and then into isiZulu and Sesotho may have obscured the accuracy of these items.

Data analysis Invariance across the languages and grades

Even though we require more information to establish definitively what the norms and standards of the MARKO-D in South Africa are, its general validity as an instrument iii for testing mathematical competence is being reaffirmed.With the exception of a few, all the items of the MARKO-D fit the assumptions and parameters of the Rasch model.This bodes well for a test that was developed in Germany on the basis of cutting-edge theory and empirical research into the early development of mathematical competence.The theoretical basis of the instrument posits that certain mathematical abilities may be invariant across cultures (Ricken et al., 2011).The test measures mathematical competence according to five levels of ability, which are acquired sequentially over time (Fritz et al., 2013).Each level is embedded in the level(s) above it and an individual learner must acquire the skill associated with level one before they can move on to level two, and so on.

Our analysis of the (in)variance of responses across the different groups of people tested, proceeds with the assumption that the MARKO-D can be used to measure the mathematical competence of this sample at different points in time and arrive at similar results.

The invariance of a test is determined by comparing the responses of one group of people to another.This comparison is represented visually by a scatterplot and is measured statistically with a correlation coefficient.Figure 1.1 represents a comparison of people who speak isiZulu as a home language to people who speak Sesotho.The individual items are plotted between 95% confidence intervals (or bands), which indicate the extent to which individual items are invariant.

Since only four items fall outside of the confidence intervals (á = 0.942), we can argue that the MARKO-D does not violate the assumption of unidimensionality when it is used to measure mathematical competence in isiZulu and Sesotho speaking learners.

A similar picture emerges when we compare people who were tested in English to people who were tested in their home language.Figure 1.2 presents a visual representation of this comparison.Even though the variation between those learners tested in their home language and those tested in English is comparably higher than the juxtaposition of isiZulu and Sesotho speakers (regardless of the language of testing), the degree of variance is slight enough (á = 0.916) to argue that the test remains invariant when learners are tested in different languages.

By contrast, when we compare participants who have not received formal instruction in mathematics (i.e.Grade R learners) to those who have (i.e.Grade one and two learners), the variance between these groups is too large and too significant.This represents the first indication that the MARKO-D is not measuring mathematical competence in a way that is consistent for learners who have received instruction in mathematics (grade ones and twos) and those who have not (grade Rs).There is notably little structure in the response patterns of these two groups to the items, since they are scattered all over the diagram (á = 0.470).

The degree of variance in this comparison is to be expected since Grade R learners have not been taught a formal syllabus of mathematical concepts and skills, while Grade one and two learners have been exposed to the national curriculum.The expectation is that Grade R learners will think differently about mathematics and are likely to react differently to mathematical problems.

To arrive at a more robust idea variance within our data, we conducted a DIF analysis for speakers of the different languages and the participants who belong to different categories of instruction (namely, those with exposure to a formal syllabus and those who have never been exposed to formal instruction in mathematics).

Differential Item Functioning

Conventionally analyses of DIF are used to determine whether a test exhibits bias, which is normally assessed by comparing distinct groups of people defined by a common categorical characteristic, such as gender, culture, language, socio-economic status or even age.According to De Ayala (2008:324), item bias or test bias is defined statistically as "the systematic under-or overestimation of a parameter", which departs from the lay connotation of unjust a priori partiality.Even though bias can be assessed for individual items (DIF), or for a test as a whole (differential test functioning), the psychometric preference falls on analysing the bias of individual items (De Ayala, 2008).However, for practical significance it is useful to analyse the bias of a test more Dampier generally (Camilli & Penfield, 1997), since this will indicate the extent to which, in the main, a test is invariant across different groups of people.For the sake of rigour it is necessary to analyse the parts if one wants to have a complete idea of the whole.

We define DIF in terms of individual items.DIF refers to differences in responses to items garnered from people with the same ability who belong to different groups.Sinharay and Dorans (2010:474) define DIF as referring to "a psychometric difference in how an item functions for two groups," while Van den Noortgate and De Boeck (2005:443) write that, "Differential Item Functioning refers to the phenomenon that, conditionally on the latent ability, the probability of successfully answering a specific item may differ from group to group."The presence of an extraneous variable that causes people from different groups of the same ability to react differently to a single item, violates the tenet of unidimensionality, since it serves as a source of additional difficulty (Zumbo, 1999).

The aim of conducting a DIF analysis is to identify an item or a series of items that are likely to exhibit measurement bias, since these items cast doubt on the invariance of measures.Bond and Fox (2007:70) argue that invariance "remains the exception rather than the rule" in the human sciences.This state of affairs casts doubt on the scientific rigour of instruments used to arrive at context-independent measures of people across a range of latent traits (Bond & Fox, 2007:70): "[t]his contextdependent nature of estimates in human science research, both in terms of who was tested and what test was used, seems to be the complete antithesis of the invariance we expect across thermometers and temperatures".

When an item is identified as exhibiting DIF and for this reason obscuring the accuracy of measures, it is necessary to evaluate whether the variance in responses to the item warrants revision, or, in more drastic situations, omission from the test completely.De Ayala (2008:324) recommends that items exhibiting DIF be "reviewed by a panel of experts to determine whether the source of an item's differential performance is relevant or irrelevant to the construct being measured".

Using the difR 4.3 package (Magis, Beland & Raiche, 2012) we analysed our data according to the specifications of the General Mantel-Haenszel Chi-square statistic to determine which items display notable DIF in: firstly, a comparison of isiZulu and Sesotho speaking pupils; and, secondly, in a comparison of pupils who have not received formal instruction in maths (i.e.Grade R pupils) to pupils who have.We compared results from this analysis to output obtained from Randall Penfield's software package DIFAS 4.0 (Penfield, 2007), as well as output from Winsteps (Linacre, 2009).The results were consistent with the same items flagged for DIF in each software package.We prefer to report the output obtained from R. The reason for this is that R is famous for its visual representation of data.Figures 1.5 and 1.6 are simple, clear indications of the extent to which individual items display DIF.

Home language

Table 3 presents the Mantel-Haenszel Chi-square statistics for an analysis of DIF between isiZulu and Sesotho responses to the items of the Marko-D.

Table 2 A General Mantel-Haenszel analysis of DIF between the home language groups

The threshold for detecting items that were displaying DIF was found to be 3.8415 (with a significance level of 0.05 and below).Items display large DIF when they measure above this threshold, while at the same time obtaining a significant p value.It is evident that items v5 (marginally), v24, v29, v30 and v39 all measure above the threshold, and have statistically significant p-values to boot.These four items are individually more difficult for one language group as opposed to the other.

Figure 1.5 indicates that for the most part, the items of the MARKO-D remain invariant when they are used to measure the mathematical competence of isiZulu and Sesotho home language speakers, which considering the lexical, grammatical and syntactic differences of these languages is significant, as it suggests that the latent trait remains invariant when the home language of the pupil being tested varies.More data will show to what extent this is true for other home languages, including English, Afrikaans and perhaps even German.

Instruction

A comparison of learners who have received formal mathematics instruction with learners who have not, indicates that exposure to the "learning" of mathematics alters responses to the items of the test dramatically.Table 3 presents output of a DIF analysis conducted in R. At a glance, it is evident that many items display significant variation from one group to the next.As many as 18 items display patterns of response that differ significantly from one group to the next, which suggests that the property of invariance is violated when the status of a child's exposure to the formal teaching of mathematics changes.

The threshold of detection was again a measure of above 3.8415.Items were flagged for DIF when they exceeded this Mantel-Haenszel value and when they obtained a p value of 0.05 and below.between the groups of instruction Figure 1.5 is a representation not only of significant variation between the different groups of instruction, but also an indication of the extent to which DIF is detected in particular items.In Figure 1.5 the greatest extent of DIF was detected in item 24 (or variable 29), which exhibited a Mantel-Haenszel value of 6.3193.Interestingly, items 5 (v5), 24 (v29) and 25 (v30) display less DIF when the two groups of instruction are compared than when the home languages are compared.This may negate the possibility that a common source of DIF is present in the two comparisons.We can argue then that the DIF detected in the two comparisons are independent and unique to the groups in question.

Dampier

Discussion

The property of the invariance of instruments used in the social sciences to measure the ability of people or the presence of a latent trait (for example (e.g.) anxiety or stress) has become essential to ensuring that the study of human beings is as scientific and as accurate as the measurement of distance, temperature and weight in physics.This study has illustrated that the linguistic resources of a country, such as South Africa, can be valuable in the attempt to produce invariant measures across different languages, which will enhance our ability to produce invariant measures of unidimensional constructs in different cultures.The process of adapting tests to suit the cultural and linguistic context of a diverse South African society, if done rigorously, can contribute significantly to the process of attaining fundamental measures of people.At least, the work on translated tests that will stem naturally from test adaptation will assist researchers in other social contexts with detecting invariance across languages and in dealing with this productively.

While our findings are by no means conclusive, it appears that the Marko-D may well prove in the future to measure mathematical competence consistently in people who speak different languages and who hail from different cultures.As exciting as this prospect is, we do not claim at this very instant to possess a test that is invariant across different languages.The performance of grade Rs in this test suggests either that more work needs to be done to ensure that the instrument measures that latent trait consistently in people who have not entered school as yet, or it suggests that instruction fundamentally alters the way we do maths.

The jury, we argue, is still out on whether the current approach to instruction improves our ability to think mathematically or whether the language of mathematics we use somehow impedes the fluidity of thinking mathematically -a proclivity we are all born with (Carey, 2009;Dehaene, 2010;Dehaene & Brannon, 2011;Spelke, 2000).In a separate study we argue, in line with the theoretical framework that informs the Marko-D, that all children enter grade R with a more or less similar ability to do maths (Dampier & Mawila, 2012).Differences that are apparent can be addressed at this very early age, since at this point very little formal orientation into the discourse of mathematics, with its cumbersome and confusing terminology, would have taken place.This argument is well rehearsed in continental and American neuropsychology and in the works of various cognitive psychologists, such as Le Corre, Spelke and Carey.What iv is more, the grade Rs in this study managed to get some of the more challenging items of this test right when their older counter parts struggled.

Future studies will confirm whether the property of invariance is something the Marko-D can lay a legitimate claim to and whether instruction in mathematics, as it is currently conceived and conceptualised in South Africa, does indeed impede the ability of children to reason clearly when they are tasked with solving mathematical problems.What is certain, however, is that instruments which are more scientific are required in a country such as South Africa, where ordinary children are given the extraordinary burden of being among the worst performing mathematicians in the world.With more scientific instruments of measurement and assessment we will be able to identify whether performance in our system is the same for all cultures and the various languages of instruction.Our instruments may be faulty, because we assume they assess the same phenomena in different people without exhibiting item bias.

The veritable absence of scientific rigour in the manner of assessment that prevails in South Africa, and elsewhere, is enough to cast sufficient doubt on the validity and reliability of standardised testing of foundation phase pupils.Standardised tests treat different people as being the same.The differences between people are overlooked, which from a statistical point of view amounts to committing a fatal analytic error.This error can only be remedied by following the strict principles of fundamental measurement and reconceptualising our approach to testing accordingly.

Notes

i The various arguments levelled against the claims to scientific status made by the social sciences are perhaps best captured by Wittgenstein's (1922:89) seventh proposition: "What we cannot speak of we must pass over in silence".Hollis (1994:42) argues that the "driving idea of Logical Positivism was that, because claims to knowledge of the world can be justified only by experience, we are never entitled to assert the existence of anything beyond all possible experience.It can never be probable, let alone certain, that there are, for instance, unobservable structures, forces, instincts or dialectical processes".ii This refers to the process of obtaining direct measures or values of a phenomenon or latent trait that does not rely on previous measurements.iii A German acronym for Mathematical and Arithmetic Competence Diagnostic instrument.iv Here it is worth mentioning the work of : Feigenson, Carey and Spelke (2002); Feigenson, Dehaene and Spelker (2004); Le Corre and Carey (2007); Le Corre, Van de Walle, Brannon and Carey (2006);Spelke (2003); Starkey (1990); Carey (2001);and Carey (2004).

Dampier"

Conceptual Development of Children in the Early Grades of School: How Language Features in the Learning of Mathematics".

Table 3 A
3
General Mantel-Haenszel analysis of DIF

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The weight of nations: an estimation of adult human biomass

Sarah Catherine Walpole
David Prieto-Merino
Phil Edwards
John Cleland
Gretchen Stevens
Ian Roberts
The weight of nations: an estimation of adult human biomass
R E S E A R C H A R T I C L E Open Access
Background: The energy requirement of species at each trophic level in an ecological pyramid is a function of the number of organisms and their average mass. Regarding human populations, although considerable attention is given to estimating the number of people, much less is given to estimating average mass, despite evidence that average body mass is increasing. We estimate global human biomass, its distribution by region and the proportion of biomass due to overweight and obesity.Methods: For each country we used data on body mass index (BMI) and height distribution to estimate average adult body mass. We calculated total biomass as the product of population size and average body mass. We estimated the percentage of the population that is overweight (BMI > 25) and obese (BMI > 30) and the biomass due to overweight and obesity.Results: In 2005, global adult human biomass was approximately 287 million tonnes, of which 15 million tonnes were due to overweight (BMI > 25), a mass equivalent to that of 242 million people of average body mass (5% of global human biomass). Biomass due to obesity was 3.5 million tonnes, the mass equivalent of 56 million people of average body mass (1.2% of human biomass). North America has 6% of the world population but 34% of biomass due to obesity. Asia has 61% of the world population but 13% of biomass due to obesity. One tonne of human biomass corresponds to approximately 12 adults in North America and 17 adults in Asia. If all countries had the BMI distribution of the USA, the increase in human biomass of 58 million tonnes would be equivalent in mass to an extra 935 million people of average body mass, and have energy requirements equivalent to that of 473 million adults.Conclusions: Increasing population fatness could have the same implications for world food energy demands as an extra half a billion people living on the earth.

Background

Thomas Malthus' Essay on the Principle of Population warned that population increase would eventually outstrip food supply, resulting in famine [1]. Malthus expressed his concern at a time when the amount of food energy that could be harvested from a given amount of land was constrained by the available agricultural technologies. The Green Revolution of the twentieth century challenged Malthus' grim predictions, as fossil fuel-based fertilizers, pesticides, irrigation and mechanization greatly increased food yields [2]. In the twenty first century, the link between population and ecological sustainability is again coming to the fore, as global food yields are threatened by ecological destruction (including climate change) and as world population grows [2].

The energy requirement of species at each trophic level in an ecological pyramid is a function of the number of organisms and their average mass. In ecology, these factors are often considered together by estimating species biomass, the total mass of living organisms in an ecosystem. In relation to human populations, although much attention is given to the effect of population growth on food energy requirements, much less attention is given to the impact of increasing body mass.

Physical activity accounts for 25-50% of human energy expenditure. Due to the greater energy cost of moving a heavier body, energy use increases with body mass [3]. Resting energy expenditure also increases with body mass, due to the increase in metabolically active lean tissue that accompanies increases in body fat [4]. As for other organisms, the energy requirements of human populations depend on species biomass. Currently, more than a billion adults are overweight and in all regions of the world,, the entire population distribution of body mass is moving upwards [5].

The increased global demand for food arising from the increase in body mass is likely to contribute to higher food prices. Because of the greater purchasing power of more affluent nations (who also have higher average body mass), the worst effects of increasing food prices will be experienced by the world's poor. In this article, we estimate total human biomass, its distribution by world region and the proportion of human biomass attributable to overweight and obesity.

Methods

Data sources

For each country, we obtained estimates of the population in 2005 by age and sex from the United Nations population database [6]. We obtained estimates of mean (and SD) body mass index (BMI) from the WHO SURF2 report [7] and estimates of mean height (and SD) for 190 countries from national health examination surveys, primarily the Demographic and Health Surveys [5]. Because surveys were not conducted in every country, height data were not available by age and sex in some countries. To estimate mean height (and SD) by age and sex in every country using the available data, we built a linear regression model (of age-sex group, average height, WHO region and sub-region) using R open access statistical software. Some countries and territories were excluded from the analysis due to insufficient data on BMI (see Table 1 for a list of these).

Biomass estimation

Total biomass by age-sex group was estimated as the product of the number of people in the group and their average body mass. The formulae for the estimation of body mass are given below Table 1. We also estimated total biomass due to overweight in each age-sex group. We assumed that BMI is normally distributed in the group and estimated the number of people overweight (using prevalence of BMI > 25) and their average BMI. Using their average BMI, we then estimated their average body mass. The biomass of overweight people was calculated as the product of the number of overweight people and their average body mass. Biomass due to overweight was calculated by estimating the biomass of overweight people assuming they had BMI of 25 and subtracting this from their actual biomass. Using a similar method we estimated the biomass due to obesity. We calculated the total biomass of obese people in each age-sex group and subtracted their estimated biomass assuming that they all had a BMI of 30. For each country, we calculated total human biomass, biomass due to overweight and biomass due to obesity by adding the estimates for each age-sex group. Global totals were calculated by summating across countries.

Extreme case scenarios

We estimated global biomass under two hypothetical scenarios. Specifically, we assumed that each country had the same BMI distributions as that of [1] Japan and Formula for estimating the expected (average) weight (W) in a specific age-sex group where mean and variance of BMI and of height. Using the following notation for each individual values of BMI and W:
b ¼ BMI À BMI ð Þand h ¼ H À H ð Þ
The expected weight in a group of individuals would be:
E W ð Þ ¼ E BMI Â H 2 ð Þ¼E BMI þ b ð ÞÂ H þ h ð Þ 2 ¼ E BMI þ b ð ÞÂð H 2 þ h 2 þ 2 HhÞ ¼ E H 2 BMI þ h 2 BMI þ 2 Hh BMI þ H 2 b þ h 2 b þ 2 Hhb ¼ H 2 BMI þ E h 2 ð Þ BMI þ E h ð Þ2 H BMI þ E b ð Þ H 2 þ E bh 2 ð ÞþE hb ð Þ2 H ¼ H 2 BMI þ E h 2 ð Þ BMI þ E bh 2 ð ÞþE hb ð Þ2 H
Assuming that Height and BMI are independent: COV H; BM ð Þ¼0⇒E hb ð Þ ¼ 0 Assuming that the variance of Height is constant in all values of BMI: E bh 2 ð Þ¼0 Therefore the above equation simplifies to:
E W ð Þ ¼ BMI Â H 2 þ V H ð Þ [2]
USA. We used the method outlined above but applied the BMI of the relevant age-sex group from Japan or USA instead of the actual BMI for that age-sex group. These countries were chosen because despite being high income countries with adequate nutrition, they have average BMI values close to global extremes. For each scenario, we calculated the global biomass and biomass due to overweight and obesity.

Population and energy equivalents

We calculated the food energy required to sustain human biomass using formulae and values from the FAO [8]. Physical Activity Level (PAL) values for each age-sex group are based on non-overweight adults in the USA. Total Energy Expenditure (TEE) is estimated as the product of Basal Metabolic Rate (BMR) and PAL (see Table 2). The energy required to sustain the biomass due to overweight, obesity or the change in biomass that would be seen under hypothetical scenarios, was estimated by multiplying the number of kg by weight dependent component of BMR and by the PAL. We did all calculations by country and age-sex group applying the corresponding coefficients. Then we summed across age-sex groups to obtain total energy requirements for each country and for the world. To calculate the number of average adults that could be sustained with a given quantity of biomass we divided the amount of energy required to sustain that biomass by the average food energy requirement of one human.

Results

In 2005, total adult human biomass was approximately 287 million tonnes (Table 3). Biomass due to overweight was 15 million tonnes, the mass equivalent of 242 million people of average body mass (approximately 5% of the world's population in 2005). Biomass due to obesity was 3.5 million tonnes, the mass equivalent of 56 million people of average body mass (1.2% of the world's population). Average body mass globally was 62 kg. North America has the highest average body mass of any continent (80.7 kg). In North America one tonne of human biomass corresponds to 12 adults. More than 70% of the North American population is overweight and biomass due to obesity is 1.2 million tonnes. North America has 6% of the world's population but 34% of world biomass due to obesity. Asia has the lowest average body mass of any continent (57.7 kg). In Asia, one tonne of human biomass corresponds to 17 adults. Asia has 61% of the world's population but 13% of world biomass due to obesity (449 thousand tonnes).

The average BMI in Japan in 2005 was 22.9. If all countries had the same age-sex BMI distribution as Japan, total biomass would fall by 14.6 million tonnes, a 5% reduction in global biomass or the mass equivalent of We extracted the following coefficients for our age-sex groups.

(*) For non overweight adults in USA. The estimation of energy requirements of an individual is: BMR ¼ BMRc þ BMRs x Weight kg ð Þ ! TEE ¼ BMR x PAL For a group of N individuals of the same age-sex group with a total biomass "B", BMR ¼ N x BMRc þ BMRs x BM kg ð Þ ! TEE ¼ BMR x PAL If that same group had a biomass due to overweight (BMI > 25) of "B25", the energy required to feed that biomass would be:
BMR25 ¼ BMRs x B25 kg ð Þ ! TEE25 ¼ BMR25 x PAL

million people of world average body mass in 2005.

This reduction in biomass would decrease energy requirements by an average of 59 kcal/day per adult living on the planet, which is equivalent to the energy requirement of 107 million adults. Biomass due to obesity would be reduced by 93%. The average BMI in USA in 2005 was 28.7. If all countries had the same age-sex BMI distribution as the USA, total human biomass would increase by 58 million tonnes, a 20% increase in global biomass and the equivalent of 935 million people of world average body mass in 2005. This increase in biomass would increase energy requirements by 261 kcal/day/adult, which is equivalent to the energy requirement of 473 million adults. Biomass due to obesity would increase by 434%. Figure 1 shows the distribution of biomass due to obesity for countries with more than 1% of the global human biomass due to obesity. The two scenarios are also reflected. If China had the same BMI distribution as the USA its biomass due only to obesity would be equivalent to 121% of the world total of biomass due to obesity in 2005.

The energy required to maintain obese biomass corresponds to the energy requirements of 24 million adults of world average body mass ( Table 4). The energy required to maintain overweight biomass corresponds to the energy requirements of 111 million average adults. In the United States alone, the energy required to maintain overweight biomass corresponds to the energy requirements of 23 million adults of world average body mass (Table 4). If all countries had the same BMI distribution as USA, the energy required to maintain obese biomass would increase by 481%, corresponding to the energy requirements of 137 million adults. Under this scenario, the energy required to maintain overweight biomass corresponds to the energy requirements of 406 million adults.

Discussion

We estimated global human biomass, its regional distribution and biomass attributable to overweight and obesity. Our results underscore the need to take body mass into account when considering the ecological implications of population growth. UN world population projections suggest that by 2050 there could be an additional 2.3 billion people. [6] The ecological implications of rising population numbers will be exacerbated by increases in average body mass.

Although the largest increase in population numbers is expected in Asia and sub-Saharan Africa, our results suggest that population increases in the USA will carry more weight than would be implied by numbers alone. It is predicted that the US population will increase from 310 million in 2010 to 403 million by 2050 [5]. Most of the increase will be due to migration and to the extent that migrants adopt the diet and lifestyles of the host population, we can reasonably expect that the body mass of migrants will rise. Our results show that this could have important implications for world energy requirements. Figure 1 Human biomass due to BMI > 30 (Countries with more than 1% of human biomass due to BMI > 30).

In Africa and Asia urban populations are increasing more rapidly than rural populations [9]. This will also have implications for average body mass [10]. Given the current trend of rising BMI, our scenario where all countries have a similar BMI distribution to the USA provides an insight into possible future challenges. If global biomass were to increase to a level where all countries had the age-sex BMI distributions of the USA, the biomass increase would be equivalent to an extra billion people of average body mass. Although, this is not the same as an extra billion people in terms of energy requirements, the increase corresponds to the energy requirements of about 473 million adults of current world average body mass.

Our findings should be viewed in the light of the following limitations. Firstly, in countries where data on average BMI, height and its standard deviation were unavailable, we used a regression model to estimate the missing parameters. Due to limited data availability, we assumed that height and BMI are independent variables, and that the mean and standard deviation of height are the same across the distribution of BMI. Furthermore, because of the lack of data describing the distribution of BMI in relation to high, we assumed zero covariance between BMI and height squared. Secondly, we assumed symmetrical (normal) distributions of BMI in each population, when in reality many population distributions will be skewed, with a tail to the right of the distribution comprising a relatively small proportion of people with very high body mass. We may therefore have underestimated total biomass. Finally, we did not estimate biomass in children who comprise a significant proportion of the population in many countries, nor in countries in  There are also limitations in our estimates of energy requirements. We have used FAO data to estimate the BMR but the extent to which they can be applied to all populations is open to question. The assumption of similar physical activity levels in all countries is clearly unrealistic with higher physical activity levels in low income countries. As a result, we will have underestimated energy requirements in some countries. However, this approach is appropriate for comparing different scenarios of BMI distribution and its implications on relative changes in energy requirements.

Conclusions

Increasing biomass will have important implications for global resource requirements, including food demand, and the overall ecological footprint of our species. Future work will investigate the extent to which food demand and carbon emissions are likely to increase with increasing biomass.

Although the concept of biomass is rarely applied to the human species, the ecological implications of increasing body mass are significant and ought to be taken into account when evaluating future trends and planning for future resource challenges. Our scenarios suggest that global trends of increasing body mass will have important resource implications and that unchecked, increasing BMI could have the same implications for world energy requirements as an extra 473 million people. Tackling population fatness may be critical to world food security and ecological sustainability.

Table 1
1List of excluded countries due to insufficient data on BMICountry / Territory
UN code
Adult pop. (2005)

Other non-specified areas (Taiwan)
158
18,405,317

Serbia
688
8,037,649

China, Hong Kong SAR
344
5,840,953

Puerto Rico
630
2,936,606

Occupied Palestinian Territory
275
1,928,679

Réunion
638
582,423

Montenegro
499
502,268

China, Macao SAR
446
401,495

Guadeloupe
312
338,621

Martinique
474
313,280

Western Sahara
732
301,959

French Polynesia
258
185,626

New Caledonia
540
168,610

Netherlands Antilles
530
143,172

French Guiana
254
130,255

Channel Islands
830
124,942

Guam
316
119,046

Mayotte
175
101,272

United States Virgin Islands
850
84,706

Aruba
533
79,238

TOTAL:
40,726,117

Table 2
2Estimation of Basal Metabolic Rate (BMR) and Total Energy Expenditure (TEE) using FAO tablesMen
Women

BMRc
BMRs
PAL(*)
BMRc
BMRs
PAL(*)

age
Kcal
Kcal/kg
Kcal
Kcal/kg

15-29
692.2
15.057
1.75
486.6
14.818
1.79

30-44
873.1
11.472
1.82
845.6
8.126
1.87

45-59
873.1
11.472
1.64
845.6
8.126
1.8

60-69
587.7
11.171
1.61
658.5
9.082
1.69

70-79
587.7
11.171
1.62
658.5
9.082
1.55

80+
587.7
11.171
1.3
658.5
9.082
1.19

Table 3
3Population, body mass and biomass by world region in 2005 and in hypothetical scenariosWHO region
Adult
population
(millions)

Average
body mass
(kg)

Biomass
(million kg)

No of people
overweight /
total population

Biomass due to
BMI > 25
(million kg)

Biomass due to
BMI > 30
(million kg)

Asia
2815
57.7
162408
24.2%
4265
449

Europe
606
70.8
42895
55.6%
3836
910

Africa
535
60.7
32484
28.9%
1464
340

Latin Am. Caribbean
386
67.9
26231
57.9%
2431
585

Northern Am.
263
80.7
21185
73.9%
3297
1187

Oceania
24
74.1
1815
63.3%
191
46

World
4630
62.0
287017
34.7%
15484
3518

Scenario (1): all countries have
BMI distribution of Japan

4630
58.8
272408 (−5%)
22.3%
5630 (−64%)
253 (−93%)

Scenario (2): all countries
have BMI distribution of USA

4630
74.6
345426 (+20%)
74.0%
53090 (+243%)
18789 (+434%)

Table 4
4Adults per tonne biomass and energy used to maintain overweight and obesityAverage energy used to maintain biomass due to BMI > 25 in kcal/day/adult Thousands of adults of average mass that could be maintained by the energy required to maintain (1) tTEE = theoretical Total Energy Expenditure calculated from FAO tables for adults, assuming that Physical Activity Levels (PAL) for each age-sex group in all countries were the same as those reported for USA in the same document. (2) To calculate these two columns we use the average theoretical tTEE of the world in 2005 (2549 kcal/day).Country with more than
100,000 population

Adults per
tonne

Average tTEE[1]
Kcal/day/ adult

BMI >25
BMI >30

Heaviest 10

United States
12.2
2874
243
22,509.2
7,886.6

Kuwait
12.9
2982
233
156.6
53.9

Croatia
13.1
2741
205
300.3
96.0

Qatar
13.0
3007
204
51.6
14.5

Egypt
13.5
2826
192
3,733.5
1,184.2

United Arab Emirates
13.2
3017
188
241.2
62.8

Trinidad and Tobago
13.8
2778
177
71.3
21.7

Argentina
13.8
2718
176
1,967.9
575.7

Greece
13.3
2707
169
636.0
159.3

Bahrain
13.6
2889
168
34.8
9.7

Lightest 10

North Korea
19.0
2348
8
57.5
1.5

Cambodia
17.9
2472
7
23.9
0.2

Burundi
18.5
2421
7
11.4
0.4

Nepal
19.8
2354
7
42.4
0.6

Democ. Rep. of the Congo
18.7
2410
6
71.2
2.2

Bangladesh
20.2
2342
5
178.2
2.7

Sri Lanka
19.8
2318
5
27.5
0.3

Ethiopia
18.9
2408
3
52.9
0.5

Viet Nam
19.7
2341
3
73.7
1.1

Eritrea
19.2
2393
2
2.0
0.0

WORLD 2005
16.1
2549
61
111,346
23,533

Scenario (1) if BMI as Japan in all countries 17.0
2490 (−2.4%)
22
40,519 (−64%)
1,726 (−93%)

Scenario (2) if BMI as USA in all countries
13.4
2810 (+10.2%)
224
406,255 (+265%)
136,721 (+481%)

Table 1 .
1Future work in this area should account for education levels and urbanisation.
http://www.biomedcentral.com/1471-2458/12/439
AcknowledgementsWe thank Marc Levy and Kate Jones for comments on an earlier draft.Competing interestsThe authors declare that they have no competing interests.Authors' contributions GS is a staff member of WHO. The author alone is responsible for the views expressed in this publication and they do not necessarily represent the decisions, policy, or views of WHO. IR devised the study; SW, DP and PE conducted the analyses with input from GS; and all authors contributed to writing and revising the manuscript. All authors read and approved the final manuscript.
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Porous silicon microcavities: synthesis, characterization, and application to photonic barcode devices

Fernando Ramiro-Manzano
Roberto Fenollosa
Elisabet Xifré-Pérez
Moises Garín
Francisco Meseguer
Porous silicon microcavities: synthesis, characterization, and application to photonic barcode devices
N A N O E X P R E S SPorous silicon colloidsPhotoluminescence emissionOptical cavity modes
We have recently developed a new type of porous silicon we name as porous silicon colloids. They consist of almost perfect spherical silicon nanoparticles with a very smooth surface, able to scatter (and also trap) light very efficiently in a large-span frequency range. Porous silicon colloids have unique properties because of the following: (a) they behave as optical microcavities with a high refractive index, and (b) the intrinsic photoluminescence (PL) emission is coupled to the optical modes of the microcavity resulting in a unique luminescence spectrum profile. The PL spectrum constitutes an optical fingerprint identifying each particle, with application for biosensing. In this paper, we review the synthesis of silicon colloids for developing porous nanoparticles. We also report on the optical properties with special emphasis in the PL emission of porous silicon microcavities. Finally, we present the photonic barcode concept.

Background

Silicon is a key material in many industrial sectors as metallurgy, electronics, and photonics. Depending on the applications, different degrees of purity are used. It ranges from the metallurgical grade (MG), solar grade (SG), and electronic grade (EG) silicon. Most applications of MG silicon concerns bulk physico-chemical properties derived from its electronic structure (sp 3 -like bonding). Also, silicon is a semiconductor material, being nowadays the base material for electronics [1][2][3]. Finally, the huge refractive index (n = 3.5) value of silicon has allowed developing new optical devices as photonic crystals [4,5], waveguides, multiplexers [6], and nanolasers [7]. It is well known from the technology sector that silicon can grow spontaneously in the form of small particles as silicon powder [8]. Several groups have reported on the formation of silicon colloids. Korgel et al. [9,10] have developed sub-micrometric colloidal particles of amorphous silicon by the thermal decomposition of trisilane. Our research team has also developed silicon colloids [11] through chemical vapor deposition methods. They are spherical micro-and nanoparticles of polycrystalline [11], amorphous or porous silicon [12] with a diameter size between 0.5 and 5 μm. We have also shown that they work pretty well as optical microcavities in the visible [12] and infrared [11] regions of the optical spectrum. Porous silicon [13] also shows photoluminescence (PL) emission, and it can be used for sensing devices [14,15]. The PL emission of porous colloids resonates with the whispering gallery modes (WGM) of the microcavity resulting in a high PL intensity. The PL spectrum displays a unique photonic profile identifying each particle, which constitutes the basic idea of a new type of photonic bar encoding [16], similar to other previously reported encoding systems [17]. As porous silicon is a biocompatible material, such photonic barcodes are envisaged for applications in the fields of biology and medicine. In this paper, we will review the synthesis procedure of porous silicon colloids. Also, we will report on the optical properties (optical transmission and PL) of both particle ensembles as well as single particles. Finally, we will report on the concept of the photonic barcode concept based on porous silicon microcavities and its potential applications to biosensing.

Methods

Synthesis of silicon colloids based on chemical vapor deposition

The method for obtaining porous silicon microspheres is based on the decomposition of disilane gas (Si 2 H 6 ) by chemical vapor deposition. The gas is introduced in a reactor whose walls are heated at high temperatures during certain time. During this procedure, Si n H m clusters grow into the gas phase, and they become highly spherical micrometer-sized particles, thanks to surface tension forces. At the same time, there is a hydrogen desorption process from the clusters that makes the hydrogen content decrease progressively until they become hydrogenated amorphous silicon (a:Si-H) colloids. Depending on the decomposition time (DT), one can obtain amorphous [11] or porous silicon colloids [12]. Figure 1a shows an optical microscopy image at × 1,000 magnification of porous silicon microspheres obtained by a DT of 1 min and 30 s at 400°C. The particles are polydisperse in size with a diameter value from 0.5 to 5 μm, and they scatter red, orange, and yellow colors when irradiated by white light. For comparison, Figure 1b shows the optical microscopy image, at the same magnification as that of Figure 1a, of amorphous silicon microspheres that were obtained by the same decomposition temperature, but a bit longer DT, i.e., 5 min. In this case, no scattering of visible light occurs due to the absorption of silicon at these wavelengths, and particles look like black. Figure 1c shows a SEM image of a porous silicon microsphere that has a diameter of approximately 2 μm, illustrating its spherical perfection and its surface smoothness. An annealing treatment at 800°C for 1 h in vacuum was used to convert amorphous to polycrystalline silicon [11]. The high spherical perfection and the smooth surface of such particles allow them to scatter light very efficiently in a very broad spectral range covering the ultraviolet (UV), the visible (VIS), and the infrared (IR) range of frequencies [11].

Results and discussion

Optical properties of silicon colloids  Figure 2b), as well as the theoretical fits (red curves) using the Mie theory. We used the refractive index values for crystalline silicon, with the particle diameter as the only fitting parameter [18]. Each dip in transmission corresponds to a resonating mode. They are indicated under their corresponding dip in the case of the larger microcavity (Figure 2a) by letters a (for transversal magnetic modes) and b (for transversal electric modes) and two sub-indexes that account for the different electric field intensity distributions. Figure 2b shows such distributions for modes a 21 , a 31 , and b 41 (from left to right). Of special interest is the optical spectrum of the smaller microcavity. We have been able detecting the lowest modal number modes of the microcavity like b 11 and a 11 , although they are still quite noisy. Low-index modes are very important because of two reasons: (a) the scattering cross-section is extremely large as they confine light very efficiently, and (b) their electric field distribution (see insets of Figure 2) is very similar to those of atomic orbitals. Silicon colloids also grow as particle ensembles forming a three-dimensional arrangement of spheres we call them as a photonic sponge [11]. These particle ensembles have very peculiar optical properties since they block very efficiently the UV, VIS, and IR radiations in a large wavelength region [11]. A 10-μm-thick coating of polydisperse silicon colloids is able to block 99% of the total sun radiation [11]. It may have important applications for both protecting from UV radiation as well as thermal proofing effects in cosmetics [19], paints, and coatings [20]. Figure 3 shows the optical transmission spectrum of a single porous silicon particle. The resonating modes of porous silicon appear in the near-infrared range. Different to the case of polycrystalline silicon colloids, the transmittance spectra of these particles could not be fitted to the Mie theory assuming a simple silicon colloid model with a homogenous value of the refractive index. The porous structure of silicon colloids may be not homogeneously distributed within the particle. In fact, the optical images of porous particles show an onion-like structure within the particle, suggesting a radial dependence of the porosity (see Figure 1). However, a reasonable fit could be achieved for small diameter spheres. This is the case of the spectrum displayed in Figure 3 (black line), which corresponds to a microsphere with a diameter value of 1.910 μm, and fabricated by a DT of 1 min and 10 s. The spectrum is plotted against the wavelength (λ) (upper axis) and size parameter (lower axis) that is defined as π × Φ/λ, Φ, and λ being the diameter  of the particle and the wavelength value. The red line corresponds to the Mie theory fit. Such a fit was achieved by assuming a simple homogeneous distribution of the porosity within the particle and, therefore, a constant value of n = 1.8 in all the measured wavelength range. The agreement between the theory and experiment is reasonable as far as the mode position is concerned. However, some discrepancies between the theory and experiment regarding the absolute optical transmittance values are still present that could be ascribed to the porous silicon inhomogeneity of the microsphere.

The PL spectrum of a coating of porous silicon particles show the typical PL profile [12] shown in bulk porous silicon obtained through electrochemistry methods [14]. However, when we focus on the PL of a single particle, the spectrum changes completely. Figure 4b shows the PL signal of a 4.1-μm microcavity. Figure 4a shows the transmittance spectrum of the same microsphere. Dips in transmittance correspond to peaks in the PL spectrum. The intrinsic luminescence from porous silicon is strongly enhanced at wavelength values corresponding to the optical modes of the microcavity, resulting in a spectral response plenty of pronounced and narrow peaks, some of them with a full width at half maximum (FWHM) of the order of 1 nm. The PL features (Figure 4b) are much more pronounced and narrower than those obtained from optical transmittance (Figure 4a), this being a clear proof of microcavityinduced PL enhancement. Also, narrower peaks appear at the longer wavelength side of the PL spectrum where self-absorption is smaller. It should be mentioned that the optical resonance position blueshifts with the exposure of the microspheres to air due to an oxidation process as we have recently reported [12].

Porous silicon colloids for biosensing: the photonic barcode concept

As porous silicon show PL emission in the transparent region of the biological tissue, they can be used as active particles for sensing applications [14]. The PL emission of a single porous silicon colloid (see Figure 5) is strongly coupled to the resonating modes of the microcavity. It results in a unique PL spectrum with a high quantum yield. This spectrum depends on two factors: the colloid size and the porosity value. The PL spectrum constitutes, therefore, a fingerprint of the particle. From these facts, we propose a photonic encoding procedure where a unique barcode can be assigned to each colloid by means of its PL spectrum. In the most common bar code, the Universal Product Code [21], the 1 and 0 binary numbers are represented by black bars and white voids whose width indicates the number of equal consecutive digits. Figure 5a,b and e,f illustrates how the optical spectra of two different porous silicon colloids, whose optical microscopy images in reflectance and in transmittance are shown in Figure 5c,d, and g,h, respectively, can be associated to two distinct photonic barcodes. One can see in Figures 5a,e that the different bars are located at the wavelength value of each resonance, and the bar width corresponds to the FWHM of its associated resonance. The bottom numbers of the barcode (see Figures 5a,e) indicate the wavelength scale.

In the following, we will discuss on the potential application of porous silicon colloids as sensors for biomedicine and biology. In the last years, great interest has been paid to the development of micro-and nanometersized particles and systems able to act as photonic sensors [15,22,23] for medicine [24] and biology. As porous silicon-based sensors are biocompatible [15], stable [25], and biodegradable [26], photonic barcodes are envisaged for being used in the fields of biology and medicine. We have measured the PL stability of silicon colloids in biological agents such as NADPH aqueous solutions and bovine cultives. Figure 6 shows the PL spectra of a 3.4-μm-diameter porous silicon colloid after being immersed in a 200-μM NADPH-deoxidised aqueous solution for 1 (bottom spectrum) and 5 h (top spectrum). There are no significant differences between both spectra concerning both the overall PL intensity and the relative intensity of Mie PL peaks over the PL background (broad spectrum). Finally, the peak positions of the Mie-induced PL resonances remain unchanged over the period of time tested. Therefore, we can reasonably infer that porous silicon colloids are stable under the NADPH agent. The PL of porous silicon colloids is also stable under other biological environments like Roswell Park Memorial Figure 4 Transmittance (a) and photoluminescence (b) spectra of a porous silicon microsphere of about 4.1-μm diameter. Dips in the transmittance spectrum correspond to the peaks in the photoluminescence spectrum. They are associated to the optical resonances of the microcavity (reprinted with the permission of [16]).

Institute medium with a fetal calf serum [16]. Finally, some of us, in collaboration with Canham et al., have also proved that amorphous silicon colloids quickly biodegrade in a few days [27]. The data suggests that amorphous silicon does not require nanoscale porosification for full in vivo biodegradability.

Conclusions

We have reviewed the synthesis method we have developed for processing amorphous, polycrystalline and porous silicon colloids with diameter values between 0.5 and 5 μm. Because of both their spherical shape and micrometric size, all silicon colloid allotropes work pretty well as optical microcavities in the near-infrared region. Furthermore, the PL emission of porous silicon colloids is greatly enhanced when it resonates with the optical microcavity modes, resulting in a unique photonic fingerprint we call it as the photonic barcode.

Figure 2
2shows the optical transmission spectra (black curves) of two different polycrystalline silicon particles with a diameter of 1,885 (Figure 2a) and 1,050 nm (

Figure 1
1Microscopy images. (a) Optical image of porous silicon microspheres, and (b) optical image of a:Si-H microspheres. While porous silicon microspheres scatter yellow, orange, and red colors when irradiated by white light, a:Si-H microspheres look like black due to the absorption of visible light by silicon. (c) SEM image of a porous silicon microsphere of about 2 μm in diameter (reprinted with the permission of [12]).

Figure 2
2Optical properties of polycrystalline silicon colloids. Optical transmittance (black curves) and the Mie theory fit (red curves) of single silicon colloids of diameter Φ = 1,885 (a) and Φ = 1,050 nm (b). The dips of transmittance correspond to WGM. They are indicated under their corresponding dip in (a) by labels 'b' and 'a' for transversal electric and magnetic modes, respectively. The electric field intensity distribution is shown for modes (from left to right) a 21 , a 31 , and b 41 in (b) (reprinted with the permission of[18]).

Figure 3
3Optical properties of porous silicon colloids. Measured optical transmittance of a 1.910-μm-diameter porous silicon sphere (black curve). The Mie theory fit (red curve) gives a refractive index of 1.8 in all the measured range. The resonant modes are indicated under their corresponding deeps by letters 'a' (for transversal magnetic modes) and 'b' (for transversal electric modes) and two sub-indexes that account for the different electric field intensity distributions.

Figure 5
5Photonic barcodes (a and e) produced by two different porous silicon microspheres. The location and width of the bars are determined by the position and FWHM of the resonances of their PL spectra (b and f, respectively). Optical microscopy images of the microspheres, taken at × 1,000 magnification in reflection (c and g) and in transmission (d and h) modes indicate, within the limited resolution of this technique, sphere diameter values of 4.1 and 3.7 μm, respectively (reprinted with the permission of [16]).

Figure 6
6PL spectra of an about 3.4-μm diameter porous silicon colloid. After being immersed in 200-mM NADPH aqueous solution during 1 (bottom spectrum) and 5 h (top spectrum).
http://www.nanoscalereslett.com/content/7/1/497
AcknowledgmentsThis work has been partially supported by the Spanish CICyT projects, FIS2009-07812, Consolider CSD2007-046, and PROMETEO/2010/043. http://www.nanoscalereslett.com/content/7/1/497Competing interestsThe authors declare that they have no competing interests.Authors' contributions RF and FM designed the experiments presented in this work. RF processed the porous silicon colloids and preformed the scattering properties of particle ensemble. PL of single particles was performed by FRM and EXP. Theoretical calculations have been performed by EXP and MG. FM wrote the paper and all the authors revised it. All authors read and approved the final manuscript.Submit your manuscript to a journal and benefi t from:7 Convenient online submission 7 Rigorous peer review 7 Immediate publication on acceptance 7 Open access: articles freely available online 7 High visibility within the fi eld 7 Retaining the copyright to your article Submit your next manuscript at 7 springeropen.com
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