Estimating the concentration of indoor particles of outdoor origin: A review

Abstract

Recent toxicological results highlight the importance of separating exposure to indoor- and outdoor-generated particles, due to their different physicochemical and toxicological properties. In this framework, a number of studies have attempted to estimate the relative contribution of particles of indoor and outdoor origins to indoor concentrations, using either statistical analysis of indoor and outdoor concentration time-series or mass balance equations. The aim of this work is to review and compare the methodologies developed in order to determine the ambient particle infiltration factor (F _INF) (i.e., the fraction of ambient particles that enter indoors and remains suspended). The different approaches are grouped into four categories according to their methodological principles: (1) steady-state assumption using the steady-state form of the mass balance equation; (2) dynamic solution of the mass balance equation using complex statistical techniques; (3) experimental studies using conditions that simplify model calculations (e.g., decreasing the number of unknowns); and (4) infiltration surrogates using a particulate matter (PM) constituent with no indoor sources to act as surrogate of indoor PM of outdoor origin. Examination of the various methodologies and results reveals that estimating infiltration parameters is still challenging. The main difficulty lies in the separate calculation of penetration efficiency (P) and deposition rate (k). The values for these two parameters that are reported in the literature vary significantly. Deposition rate presents the widest range of values, both between studies and size fractions. Penetration efficiency seems to be more accurately calculated through the application of dynamic models. Overall, estimates of the infiltration factor generated using dynamic models and infiltration surrogates show good agreement. This is a strong argument in favor of the latter methodology, which is simple and easy to apply when chemical speciation data are available.

Implications:

 Taking into account that increased health risks may be related with ambient particles, a reliable estimation of the main parameters governing ambient particle infiltration indoors may assist towards the development of appropriate regulation and control measures, targeted to specific sources/factors contributing to increased exposures. The overall study of the methodological approaches estimating particle infiltration indoors suggests that dynamic models provide a more complete and realistic picture of ambient particle infiltration indoors, whereas the use of specific PM constituents to act as surrogates of indoor particles of outdoor origin seems also a promising new methodology.

Introduction

Numerous investigators have reported associations between exposure to airborne particulate matter (PM) and increases of morbidity and mortality rates from cardiovascular and respiratory diseases (Pope and Dockery, 2006; Pope et al., 2002; Katsouyanni et al., 2001). Toxicological results suggest that specific components of airborne particles may be responsible for specific biological responses (Clarke et al., 2000; Godleski et al., 2000). According to recent studies, the presence of certain chemical species in particulate matter may significantly alter the association between PM concentrations and health effects (Zanobetti et al., 2009; Franklin et al., 2007).

Urban population exposure is mostly linked to indoor microenvironments because, according to time-activity pattern studies, 85–90% of the time is spent indoors (European Collaborative Action [ECA], 2003; Adgate et al., 2002; Klepeis et al., 2001; Brauer et al., 2000). Additionally, indoor air quality studies have demonstrated that concentration levels in typical indoor microenvironments, such as residences, offices, and schools, are significant and may often surpass the corresponding ambient levels (Diapouli et al., 2007; Rojas-Bracho et al., 2004; Leaderer et al., 1999). These findings have led to new approaches to population exposure assessment, challenging the traditional epidemiological methodologies which use ambient concentration levels as a surrogate for personal exposure.

Exposure in indoor microenvironments may be attributed to the generation of particles indoors as well as the infiltration of outdoor particles. Particles of indoor and outdoor origins represent different sources and size distributions and may also differ in their chemical composition and biological effects (Long et al., 2001a; Abt et al., 2000; U.S. Environmental Protection Agency [EPA], 1996). Moreover, the diurnal cycles of indoor and outdoor particle concentrations follow distinct patterns. Particles of outdoor origin are influenced by the prevailing meteorological conditions and the variation of outdoor sources (mainly vehicular traffic). In contrast, concentrations of particles generated indoors are influenced by the daily activities conducted in the indoor microenvironments. Furthermore, it should be noted that differences in size and chemical composition exist even between ambient-generated particles that have infiltrated indoors and their corresponding ambient particles. This may be attributed to the physical loss mechanisms influencing the infiltration of particles of different sizes, as well as chemical transformations affecting specific PM constituents, such as the changes in gas-to-particle partitioning during the infiltration of organic compounds, nitrate, or ammonium (Lunden et al., 2008; Hering et al., 2007).

The relative toxicity of particles of indoor and outdoor origins has not been studied systematically. According to initial research results, it is possible that these two particle categories present very different types and degrees of toxicity (Ebelt et al., 2005; Godleski et al., 2002; Saldiva et al., 2002; Long et al., 2001b). For instance, increased mortality rates have been reported for fine particles from mobile and coal combustion sources, and particularly traffic-related particles were found more strongly associated with cardiovascular deaths (Laden et al., 2000). These results suggest that health risks may increase as the fraction of ambient particles penetrating indoors increases. Myatt et al. (2011), on the other hand, have found evidence of high indoor particle toxicity during indoor combustion activities. Long et al. (2001b) have also reported increased bioactivity of indoor particles and great variation between indoor samples, which may be attributed to fluctuations in type and intensity of indoor activities. Air exchange rate may play a significant role as well, by promoting ambient particle infiltration or favor the accumulation of indoor-generated particles.

All these findings highlight the importance of considering separately the contribution of indoor- and outdoor-generated particles when interpreting epidemiological studies results. In this framework, recent scientific research has focused on investigating the factors influencing particle penetration and on quantifying the relative contribution of particles of indoor and ambient origins to indoor concentration levels.

The basic form of the mass balance equation that describes indoor concentration profiles is:

1

where C _in(t) and C _out(t) are the indoor and outdoor concentrations of particles, respectively (μg/m³); a is the air exchange rate (hr⁻¹); P is the dimensionless penetration efficiency of particles; k the deposition rate of particles (hr⁻¹); V the volume of the indoor area (m³); and Q _is the indoor particle generation rate (μg/hr). Equation 1 assumes perfect mixing. Also, it ignores particle mass losses or gains due to differences in gas-phase concentrations of condensable species and temperature/relative humidity conditions between indoors and outdoors.

The infiltration of ambient air indoors is described by a characteristic parameter, the infiltration factor (F _INF). The infiltration factor corresponds to the fraction of outdoor particles that enter an indoor microenvironment and remain suspended and is defined by the following equation:

2

The quantification of this factor, which essentially determines the contribution of ambient particles to indoor concentration levels, is of major importance when assessing population exposure. Analysis of data from four exposure assessment panel studies conducted in Atlanta, Baltimore, Boston, and Steubenville, U.S.A., revealed that residential variability in F _INF was one of the main factors explaining differences between personal and ambient levels among and within cities (Sarnat et al., 2009). Infiltration factor is determined through three parameters: air exchange rate (a) of the indoor microenvironment, penetration efficiency (P), and deposition rate (k) of the suspended particles. Air exchange rate (a) is a measurable parameter influenced mainly by building construction, residents’ activities, and meteorological conditions. Penetration efficiency (P) and deposition rate (k) are also related to building characteristics and indoor/ambient conditions but depend on particle size, composition, and electrical charge as well. The main difficulty in estimating infiltration of ambient particles indoors lies in the independent determination of P and k.

Over the last two decades, several methodologies have been developed to estimate the P, k, and F _INF and calculate the relative contribution of indoor and outdoor sources to the observed indoor concentration levels. This work reviews and compares different methodologies used to determine ambient particle infiltration. For a more comprehensive presentation, they are grouped into four categories, according to their methodological principles: (1) steady-state assumption; (2) dynamic solution of the mass balance equation; (3) experimental studies using conditions that simplify model calculations; and (4) use of infiltration surrogates.

Methods

Steady-state assumption

The steady-state assumption has been one of the most widely used methodologies, mainly because it simplifies solution of the mass balance equation. Another advantage of this methodology is that it does not require continuous concentration data, which are often difficult to collect.

Dockery and Spengler (1981) first developed the steady-state mass balance equation, by assuming that air exchange rate (a), penetration efficiency (P), and deposition rate (k) remain constant over a given time period Δt:

3

where is the study time period; , , and are the average values of C _in, C _out, and Q _is over Δt; and ΔC = C _in(t ₁) − C _in(t ₀) is the change in indoor concentration over the same time period. The term reflects the time lag of indoor concentration before reaching equilibrium. For measurement periods of 24 hr or more, this term may be assumed negligible. Therefore, the steady-state equation may be expressed as follows:

4

The authors used indoor and outdoor PM_3.5 concentration data collected during the Harvard Six-City study in order to calculate the two unknown parameters F _INF and using a regression technique. The estimated infiltration factor (F _INF) for PM_3.5 was 0.70. Based on theoretical approaches, as well as previous results reported in Dockery's Ph.D. thesis (Dockery, 1979), they then assumed that the fine particle deposition rate is negligible in comparison to air exchange rate (<0.5 hr⁻¹ for PM_3.5 and < 0.05 hr⁻¹ for PM₁). Thus, the slope of the regression line between indoor and outdoor concentrations corresponds also to the penetration efficiency (P):

5

Later, Koutrakis et al. (1992) modified eq 4 to account for the dominant indoor particle sources at typical residences (e.g., smoking and cooking). The final form of the equation they used was

6

where t is the measurement period (hr); N _cig is the number of cigarettes smoked during that time period; S _cig is the mass of particles emitted (μg) per cigarette smoked; Τ _cook is the time period during which cooking took place (min); S _cook is the mass of particles emitted per min from cooking (μg/min); and Q _other is particle mass emitted from other indoor sources (μg/hr).

These authors analyzed data from the New York State Energy Resources and Development Authority (ERDA) study, in order to quantify source strengths for PM_2.5 mass and selected elemental constituents. Air exchange rate was also measured; deposition rate was assumed equal to 0.36 hr⁻¹, based on experimental results by Sinclair et al. (1988). The slope of the regression line of indoor and outdoor concentrations produced an infiltration factor equal to 0.49, whereas the penetration efficiency calculated using eq 2 was 0.84.

Equation 6 was also used a few years later by Ozkaynak et al. (1996), in order to analyze data from the EPA Particle Total Exposure Assessment Methodology (PTEAM) study, where 12-hr PM₁₀ and PM_2.5 indoor and outdoor concentration measurements were conducted in 178 residences in Riverside, California. The unknown parameters P, k, S _cig, S _cook, and Q _other were determined using a nonlinear technique. Input data included the measured indoor and outdoor concentrations, air exchange rates, and room volumes, as well as information regarding smoking and cooking (N _cig, Τ _cook) based on the time-activity diaries.

A summary of their results for parameters F _INF , P, and k is presented in Table 1.

Table 1. Mean values of the infiltration factor, penetration efficiency, and deposition rate for PM₁₀ and PM_2.5 (Ozkaynak et al., 1996)

	F INF	P	k
PM10	0.60	1.00	0.65
PM2.5	0.71	1.00	0.39

Another modification of eq 4 was developed by Abt et al. (2000). Indoor sources were grouped in four categories: cooking, cleaning, indoor activity (ia), and washing. This modified equation was

7

where C _in,ij  is the indoor concentration that corresponds to the jth measurement (based on a 20-min period) of the ith sampling day (μg/m³); T is the number of minutes spent on each activity during the 20-min measurement period (min); β_cook, β_clean, β_ia, and β_wash are the “effective” parameters for each source (μg/[m³ min]); β₀ is the indoor background concentration (μg/m³); ε is the calculation error (μg/m³); and β_out is the infiltration factor (F _INF; dimension-less). The unknown parameters β’s were calculated by multiple regression technique, using a 20-min indoor and outdoor mass concentration and time-activity diary data collected at four residences in Boston during 1996.

Twelve different particle size fractions were studied in the range 0.02–10 μm. The estimated mean values of F _INF (expressed as β_out) for the different size fractions are presented in Figure 1a and b.

Figure 1. (a) and (b) Infiltration factor as a function of particle size (Abt et al., 2000).

The deposition rate was estimated for time periods when there was strong indoor particle generation followed by a period of no indoor generation and relatively stable air exchange rate. The authors assumed that for these periods, infiltration may be considered negligible, because the indoor concentration is very high due to the previous strong indoor generation of particles. Therefore, the major processes influencing the decrease of indoor concentration are deposition and exfiltration:

8

The deposition rate was calculated by regressing ln[C _in(t)/C _in(t − 1)] on time. The deposition rate was equal to the regression slope minus the measured air exchange rate. This methodology assumes constant outdoor concentration and air exchange rate during the study time period. The calculated values of the deposition rate for the different size fractions are presented in Figure 2a and b.

Figure 2. (a) and (b) Deposition rate as a function of particle size (Abt et al., 2000).

Based on the steady-state mass balance equation, Ott et al. (2000) developed the random component superposition (RCS) model, a statistical methodology for calculating the relative contribution of different sources to total personal exposure to PM. The methodology is based on the assumption that personal exposure at an indoor microenvironment may be expressed as the sum of particles of outdoor and indoor origins and the personal cloud:

9

where E is the total personal exposure (μg/m³); C _ig is the concentration of particles generated indoors (μg/m³); and C _pc is the concentration of particles contributed by the personal cloud (μg/m³).

The respective indoor concentration may be estimated as the sum of outdoor- and indoor-generated particle concentrations:

10

where C _og is the concentration of indoor particles generated outdoors (μg/m³).

Regressing indoor concentration on outdoor concentration thus yields estimates of the infiltration factor (slope) and the indoor-generated particle concentration (intercept). The authors used PM₁₀ concentration data (personal, indoor, and outdoor) collected during the Total Human Environmental Exposure Study (THEES) in Phillipsburg, the PTEAM personal exposure field study in Riverside, and the Ethyl Corporation study in Toronto. The respective F _INF values are presented in Table 2.

Table 2. Infiltration factor, calculated as slope of the regression line of indoor or personal on outdoor concentration data (Ott et al., 2000)

	Phillipsburg	Phillipsburg	Riverside	Toronto
	(Indoor)	(Personal)	(Personal)	(Personal)
F INF	0.53	0.54	0.55	0.61

In an effort to calculate parameters P and k separately, Long et al. (2001a) made an interesting modification to the steady-state equation. The authors used indoor and outdoor concentration and air exchange rate data collected at nine residences in the metropolitan Boston area (cold and warm seasons of 1998) during nonsource periods (nighttime, when there is minimal indoor activity) and applied the following equation:

11

The penetration efficiency and deposition rate were determined by regressing the C _out/C _in concentration ratio on 1/a. Because a serves as an independent variable, this method can be applied to data from a single house or a group of houses only when there is some variability in air exchange rate values. Infiltration factors, penetration efficiencies, and deposition rates were calculated for PM_2.5, as well as for 17 size fractions in the range of 0.01–10 μm. The PM_2.5 results are presented in Table 3.

Table 3. Estimated values of F _INF, P, and k for PM_2.5 (Long et al., 2001a)

	P		k
F INF	Summer	Winter	Summer	Winter
0.75	1.11	0.54	0.15	0.10

Williams et al. (2003) studied the steady-state mass balance equation, investigating the results of seven alternative regression scenarios for PM_2.5 indoor and outdoor concentration data:

1.	a single regression line (slope and intercept) for all data;
2.	parallel regression lines, with a common slope but different intercept for each residence;
3.	parallel regression lines, with common slope but different intercepts for randomly selected groups of data;
4.	coincidental regression lines with common intercept but different slope for each residence;
5.	a different regression line (slope and intercept) for each residence;
6.	regression lines with common intercept but different slopes for randomly selected groups of data; and
7.	different regression lines (slope and intercept) for randomly selected groups of data.

The authors found that the best fit resulted from using a different slope and intercept for each residence (scenario 5). The next best fit was found for a common slope but different intercept for each residence (scenario 2). Additionally, the authors generated independent estimates of P and k, using the calculated infiltration factor (from scenario 5) and measured values of the air exchange rate. They applied an iterative procedure by allowing P and k to increment between 0.1 and 1.0 by 0.1. The PM_2.5 concentration data used were collected at 37 residences in North Carolina, during the Research Triangle Park (RTP) PM Panel Study (2000–2001). The regression analysis produced an infiltration factor equal to 0.45. The estimated penetration efficiency and deposition rate values were 0.72 and 0.42, respectively.

Meng et al. (2005b) used four steady-state based techniques to estimate indoor PM_2.5 of outdoor origin, in the framework of the RIOPA (Relationship of Indoor, Outdoor and Personal Air) study. The study was conducted at 212 residences at three U.S. cities: Houston (Texas), Los Angeles (California), and Elizabeth (New Jersey), during 1999–2001. It included measurements of PM_2.5 mass and selected chemical constituents during a 48-hr sampling period at each residence. A brief description of the steady-state techniques applied is given below, whereas their results are presented in Table 4.

1.	Random component superposition (RCS) model developed by Ott et al. (2000), as described above.
2.	Mass balance model (MBM): Constant values of P and k were calculated for all residences, fitting indoor and outdoor concentration and air exchange rate data to eq 4, using nonlinear regression. The main limitation of this technique is that P and k are not estimated independently.
3.	External mixture model (EMM): Suspended particles of outdoor origin are considered a mixture of different chemical species. The particle infiltration factor for each residence is calculated as a linear combination of the corresponding infiltration factors of their chemical constituents: 12 where wi is the mass fraction of the ith constituent of the particle mass. Penetration efficiency and deposition rate for each chemical species are calculated using eq 4, where air exchange rate values and indoor and outdoor concentration data for the specific species are used in the same way as in the MBM method described above. Evidently, this technique does not allow for the independent estimation of P and k for each chemical species.
4.	Microscopic mixture model (MMM): A robust regression technique was applied to indoor and outdoor concentration data of the different chemical species measured concurrently at a single residence, yielding a PM2.5 infiltration factor (slope) for that residence. The presence of some outliers in the regression is indicative of indoor sources for the specific chemical species. The regression methodology used by the authors allows for significantly down-weighting of outliers in the regression, even when as many as half of the data points are outliers. This technique presents another important advantage as well. The day-to-day calculation permits the study of the daily and between-residence variation of the estimated parameters.

Table 4. Application of different steady-state techniques (Meng et al., 2005b)

	RCS	MBM	EMM	MMM
F INF	0.35	0.40 (P = 1, k = 1.5 hr^−1)	0.54	0.69

In another study, Matson (2005) used eq 4 to calculate the deposition rate for nonsource time periods (Q _is = 0), using experimental measurements of indoor and outdoor concentrations and air exchange rate, assuming that the penetration efficiency is equal to 1:

13

Input data were collected in residential and office buildings at urban and rural areas in Sweden between 2002 and 2003. The calculated mean deposition rate for particles in the size range 0.01 to greater than 1 μm was equal to 0.24 hr⁻¹.

The steady-state mass balance equation has been applied in a more recent study as well. Wichmann et al. (2010) used eq 4 to estimate the infiltration factor of PM_2.5 and soot particles in 18 residences, 6 schools, and 10 preschools, in central, suburban, and background sites of the city of Stockholm, Sweden, during 2003–2004. Mean 2-week PM_2.5 indoor and outdoor concentrations, as well as reflectance measurement data from the same samples (as a proxy for soot concentration), were used as input data. Indoor and outdoor reflectance data produced a mean infiltration factor for all sites of 0.55, whereas separate values were calculated for each microenvironmental type (0.65 for residences, 0.45 for schools, and 0.64 for preschools). Regarding PM_2.5 concentration, indoor and outdoor data correlated poorly (R ² equal to 0.27 for residences, 0.04 for schools, and 0.07 for preschools). The calculated residential infiltration factor was 0.42.

Dynamic solution of the mass balance equation

The availability of continuous PM monitors has led to dynamic models based on the mass balance equation of indoor concentration levels. Tung et al. (1999) assumed an initial indoor concentration equal to C _in,0 and used the following equation:

14

where λ is the mixing factor that accounts for nonperfect mixing of the air in the room ( 0 ≤ λ ≤ 1).

As t → ∞, C _in → C _f, which is the final indoor concentration at equilibrium:

15

Thus, eq 14 may be rewritten as follows:

16

The authors used continuous PM₁₀ indoor and outdoor concentration data, as well as air exchange rate data, collected at an office in Hong Kong Polytechnic School. They calculated the decay term −(λ∙a + k) by regressing ln(C _in − C _f) versus time (t). The deposition rate was then calculated based on experimental values for the effective air exchange rate (λ∙a), obtained using a tracer gas decay method. Finally, the penetration efficiency was determined using eq 15:

17

According to their calculations, mean penetration efficiency and deposition rate were equal to 0.78 and 0.06 hr⁻¹, respectively.

Lunden et al. (2003b) studied short-term indoor and outdoor concentration data for different PM_2.5 chemical constituents. They estimated the contribution of outdoor particles to indoor levels for each constituent separately. For nonreactive chemical species with no indoor sources, the dynamic mass balance equation is:

18

For a time interval t _s in which a, P, and k may be considered constant, eq 18 may be written as follows:

19

where and are the average indoor and outdoor concentrations during the time interval t _s . The authors fitted experimental data of indoor and outdoor concentrations and air exchange rate using eq 19. The ratio was calculated from the slope of the regression line of indoor concentration on time, using 5–7 data points. The authors repeated their analysis for different time intervals (10 min to 24 hr). According to their results, for intervals longer than 1–3 hr, the dynamic term becomes negligible and it is safe to assume steady-state conditions.

Allen et al. (2003) developed a different technique in order to solve the dynamic mass balance equation. They applied a recursive mass balance model, where the indoor concentration at a given time period t is equal to the sum of three terms: (1) the fraction of the mean outdoor concentration that infiltrates during t; (2) the fraction of the indoor concentration that remains from the previous time period (t − 1); and (3) the contribution of indoor sources (S _in) during t:

20

where and .

For nonsource periods, when S _in = 0:

21

Parameters a, P, and k were determined through eq 21, by the use of a nonlinear regression model, with bounds 0 ≤ P ≤ 1, a ≥ 0 hr⁻¹, and k ≥ 0 hr⁻¹.

The infiltration factor was calculated: (1) using eq 2: and (2) from eq 21 using linear regression to estimate a ₁ and a ₂, which are subsequently used to determine . The latter methodology is expected to produce more stable results, because only two parameters are being simultaneously estimated. Using continuous (1-hr) indoor and outdoor PM_2.5 concentration data collected at 44 residences in Seattle over 1999–2001, the authors calculated an air exchange rate (a) equal to 0.54 ± 0.60 hr⁻¹, a penetration efficiency (P) equal to 0.94 ± 0.10, a deposition rate (k) equal to 0.20 ± 0.16 hr⁻¹, and an infiltration factor (F _INF) equal to 0.65 ± 0.21.

More recently, the methodology developed by Allen et al. (2003) was applied by Polidori et al. (2007) to hourly indoor and outdoor PM_2.5 concentrations and particle number concentrations, measured at two retirement communities in Los Angeles, California, during 2005–2006. The estimated infiltration factor was 0.61 for particle number concentration data (0.05–3 μm) and 0.47 for PM_2.5, whereas air exchange rate was calculated equal to 0.29 hr⁻¹.

In another study, Schneider et al. (2004) employed a dynamic form of the mass balance equation originally proposed by Switzer and Ott (1992). The equation is valid for time periods with no indoor sources and assumes constant parameters for short time intervals (Δt):

22

Schneider et al. calculated the penetration efficiency (P) by fitting 30-min data of indoor and outdoor number concentrations and air exchange rate, measured at an uninhabited apartment in Copenhagen during fall, winter, and spring of 2001–2002, as well as values of the deposition rate that had been estimated in a previous research work (Thatcher et al., 2002). The estimated penetration efficiency values decreased with increasing particle diameter (d _p), from 0.75 (for d _p = 1 μm) to 0.1 (for d _p = 4 μm).

Zhu et al. (2005) proposed a simplified solution, assuming no indoor sources, of the mass balance eq 1 for discrete time steps (Δt = 20 min):

23

The authors used indoor and outdoor number concentration and air exchange rate data measured at four apartments in Los Angeles, California, during 2003. Values of a · P and – (a + k) were estimated through linear regression of ΔC _in(t)/Δt (as the dependent variable) on two independent variables (C _out(t) and C _in(t)). Penetration efficiency and deposition rate were then calculated using the measured air exchange rate data. For particles in the size range of 6–220 nm, P and k were found to be in the ranges of 0.10–0.55 and 0.60–0.90 hr⁻¹, respectively. Penetration efficiency was maximum at 40–70 nm, whereas the deposition rate presented the largest value around 20 nm.

Another dynamic solution approach was developed by Bennett and Koutrakis (2006). The authors attempted to overcome the problem of the independent estimation of P and k by applying an iterative technique to solve the dynamic mass balance equation, assuming time periods with no indoor sources:

24

Parameters P and k were allowed to vary over a specific range (P = 0–1, with intervals of 0.05 and k = 0–2 hr⁻¹, with intervals of 0.1 hr⁻¹). For each pair of (P, k), indoor concentration over time was calculated based on continuous measurement data of outdoor concentration and air exchange rate. The best values for P and k (thus for ) were determined based on the minimum χ² error between real and calculated indoor concentrations, over a specified time period. The authors applied the methodology using continuous indoor and outdoor number concentration data (for 17 particle size fractions) and air exchange rate data, collected at seven Boston-area residences. The calculated infiltration factors ranged from 0.32 to 0.76, with the minimum and maximum values corresponding to particle diameters of 3–4 and 0.2 μm, respectively. The main advantage of the methodology is that it allows for an independent estimation of P and k, using simple statistical techniques. Nevertheless, according to the initial results, it does not always produce clear values for the unknown parameters, because it may result in a wide range of values that correspond to very low χ² error. This is more often observed when the air exchange rate is very low, which allows the deposition velocity to play a more significant role in the removal process.

The same methodology was later applied in Diapouli's Ph.D. thesis (2008). The calculations were conducted for PM₁₀, PM_2.5, and number concentration of particles with aerodynamic diameter <1 μm. Indoor and outdoor concentrations and air exchange rate were collected at seven residences and one office in Athens, Greece, during the cold and warm periods of 2005 and 2006. The model results for PM₁₀, PM_2.5, and particle number concentration (PNC) are presented in Table 5.

Table 5. Mean values of penetration efficiency (P), deposition rate (k), and infiltration factor (F _INF) for PM₁₀, PM_2.5, and UFPs (Diapouli, 2008)

	PM10	PM2.5	PNC
P	0.76	0.85	0.80
k (hr^−1)	0.29	0.17	0.33
F INF	0.56	0.71	0.60

Rim et al. (2010) proposed a simplified solution to eq 24 for very small time steps (2.5 min), which allowed the exponential decay of the indoor concentration to be approximated using a linear term:

25

The penetration efficiency and deposition rate were determined by fitting eq 25 to indoor and outdoor number-size-resolved concentrations and air exchange rates, measured continuously at a manufactured test house. For closed windows, the penetration efficiency increased from about 0.2 for 10-nm particles to an asymptote around 0.6 for 30–100-nm particles. The respective deposition rate decreased from around 1.5 hr⁻¹ for 10-nm particles to 0.3 hr⁻¹ for 100-nm particles.

Experimental approaches

An alternative approach that attempts to overcome the difficulties in solving the mass balance equation relies on specially designed experimental protocols. Their objective is to create conditions that allow for one of the parameters to be negligible, thus decreasing the number of unknowns. Roed and Cannell (1987) first applied this methodology to study the effect of outdoor pollution on indoor population exposure after the nuclear accident in Chernobyl. The authors initially attempted to eliminate the effect of the penetration efficiency by enabling outdoor air infiltration into the under-study microenvironment through the use of a centrifugal blower. Under these conditions, they assumed that P = 1 and calculated deposition rate (k) using the steady-state equation, indoor/outdoor concentration ratio, and air exchange rate data:

26

The penetration efficiency was then determined with the blower off, using the steady-state equation and the previously calculated value of k. This method assumes that P and k are independent of air exchange rate, because they are estimated under very different conditions.

Alternatively, the authors attempted to eliminate the effect of deposition by using the blower to duct indoor air to the outdoor atmosphere, leading thus to very high air exchange rates (a >3 hr⁻¹) that render deposition rate negligible in comparison. In this case, penetration efficiency was calculated using the following equation:

27

Byrne et al. (1992) proposed another experimental protocol where indoor concentration was increased by generating suspended particles in the indoor microenvironment. Because indoor concentration was larger than the respective outdoor one, outdoor air infiltration was assumed negligible. Generation of particles was ceased and the deposition rate was calculated from the exponential decay of indoor concentration from an initial high value (C _in,0) to a lower background value (C _in,f):

28

where t is the time needed for the indoor concentration to decrease from its initial value to the final background value.

The calculated values of the deposition rate in the case of a furnished apartment were equal to 0.95 and 2.10 hr⁻¹ for particle diameters of 2.49 and 4.30 μm, respectively.

A similar methodology for the estimation of the deposition rate (k) was used by Thatcher and Layton (1995), who increased indoor concentration through intense cleaning activities. In order to minimize outdoor air penetration, all windows and doors were kept closed. Moreover, time periods with low wind speeds and indoor/outdoor temperature gradients were selected for analysis. The deposition rate was estimated through the decay of indoor concentration ( eq 28) after the cleaning activities had stopped. For particles in the size range 1–6 μm, the calculated deposition rates were equal to 0.25–1.78 hr⁻¹, whereas the measured air exchange rate was 0.18–0.30 hr⁻¹. The deposition rate increased with particle size and was slightly higher at lower air exchange rates. The authors calculated P as well, using experimental values for air exchange rate (a) and the calculated deposition rate (k), and by assuming steady-state conditions and no indoor particle generation and/or resuspension:

29

This method produced unacceptable penetration efficiency values (>1), which were attributed to sudden changes of outdoor concentration or to indoor particle generation (due to minor indoor activities such as walking around the experimental site). Another drawback of the method concerns the inability to assess ultrafine particle size ranges (with aerodynamic diameters <0.1 μm), whose indoor concentrations were not affected by the cleaning activities.

Thatcher and Layton's methodology was later applied by Hill et al. (2001) as well. The only difference was the activity used to raise indoor concentration levels (intense walking instead of cleaning). The experiments were conducted in seven residences in northern England and the calculated deposition rate was in the range 0.1–1.0 hr⁻¹ for particle diameters between 1 and 5 μm and in the range 3.8–8.0 hr⁻¹ for particle diameters between 5 and 15 μm. The mean measured air exchange rate was 1.1 hr⁻¹.

A few years later, Thatcher et al. (2003) attempted to separately calculate parameters P and k, by creating such experimental conditions that would render one of the parameters (P or k) negligible. Each time, they used indoor and outdoor concentration and air exchange rate data to calculate the other unknown parameters (k or P) through the following equation:

30

The deposition rate was estimated as described in their earlier research work (Thatcher and Layton, 1995). A different experimental setup was used for the estimation of penetration efficiency. Clean air was pumped into the study room, creating an increased pressure (greater than atmospheric) that hindered the transfer of outdoor particles to the indoor microenvironment, thus leading to decreasing indoor concentration levels. When clean air pumping was ceased, the observed indoor concentration rise could be attributed mainly to the penetration of the outdoor air. According to their calculations, as particles increased in diameter from 0.1 to 10 μm, penetration efficiency ranged from approximately 1.0 to 0.3, and deposition rate from 0.1 to 5 hr⁻¹.

Using a more realistic variation of the same approach, Chao et al. (2003) increased indoor concentration levels, through the opening of windows, which allowed free entrance of the more polluted ambient air. However, during the decay stage (when all windows were closed), outdoor air penetration was not assumed negligible:

31

The term corresponds to the steady-state indoor concentration (C _ss) (when t → ∞), transforming eq 31 as follows:

32

The deposition rate was then calculated through the exponential decay of the difference C _in − C _ss with time, using experimental data for air exchange rate values. Penetration efficiency was also estimated from the steady-state indoor concentration:

33

According to their results, the maximum value of penetration efficiency was 0.79 at the size range of 0.8–1.4 μm and decreased for both smaller and larger particle size ranges (minimum equal to 0.48 for particle size range of 4.7–9.6 μm). The deposition rate was maximum (1.00 hr⁻¹) at the largest particle size range (4.7–9.6 μm) and minimum (0.27 hr⁻¹) at the size range of 0.5–0.8 μm.

This method was later used by Smolik et al. (2005) as well. However, because they lacked air exchange rate data, they calculated the sum (λ = a + k) through eq 32 and then assumed that P = 1 in order to estimate a:

34

The resulting deposition rate values in relation to particle size presented a characteristic U shape, with the largest values corresponding to particles with aerodynamic diameters larger than 5 μm and smaller than 0.01 μm (Riley et al., 2002). Their findings were in accordance with theoretical models where the maximum deposition rates are estimated for coarse particles (due to gravitational settling) and ultrafine particles (due to Brownian diffusion) (Nazaroff, 2004). The estimated air exchange rate was 0.39 ± 0.06 hr⁻¹.

Stephens and Siegel (2012) refined the method developed by Chao et al. (2003), by incorporating simultaneous indoor and outdoor measurements, to account for ambient concentration fluctuation over time. The authors used the portion of indoor decay data that was not affected by ambient particles penetration to estimate the deposition rate (k) and the initial indoor concentration (C _in,t = 0) before the particle concentrations elevation period through eq 35, using a nonlinear least squares regression. This portion of data was identified graphically by plotting ln(C _in) versus time (t) and selecting only the initial section of data that was log-linear. Air exchange rate was measured by CO₂ decay method.

35

Subsequently, penetration efficiency was calculated by including all indoor and outdoor data, along with the known values of k and a, and using a nonlinear least squares estimation of eq 30.

The authors presented results from 18 unoccupied residences in Texas, U.S.A., with heating, ventilation, and air-conditioning (HVAC) systems operating, for particles in the size range of 20 nm to 1 μm. The estimated deposition rate was between 0.31 and 3.24 hr⁻¹ (mean value 1.01 hr⁻¹), for an air exchange rate varying between 0.13 and 0.95 hr⁻¹. Penetration efficiency was calculated to be in the range of 0.17–0.78 (mean value 0.47).

Jamriska and Morawska (2003) based their analysis on eq 28, originally proposed by Byrne et al. (1992), but also included the effect of coagulation processes:

36

The parameter λ expresses the decay rate of particle concentrations due to deposition and coagulation. In the case of mass concentrations, λ = k. However, number concentrations may be greatly affected by coagulation processes. The contribution of surface deposition and coagulation to total particle loss rate was estimated from the evolution of particle volume and number concentrations, which were measured simultaneously. The difference between the loss rates calculated through volume and number concentration provided the coagulation loss rate. All measurements were conducted under close to zero (closed chamber) ventilation conditions. Their calculations, for particles in the size range 0.017–0.898 μm, yielded a total loss rate of 0.16–0.39 hr⁻¹, whereas surface deposition and coagulation accounted for 66% and 34%, respectively.

Ferro et al. (2004) conducted a 5-day experiment in a residence in Redwood City, California, during April 2000. They increased indoor concentrations through prescribed activities that caused mainly particle resuspension and measured indoor and outdoor particle number concentrations for different size ranges. The authors used the initial form of the mass balance eq 1 to express the decay of indoor concentration after each indoor activity event:

37

The deposition rate was calculated through the slope of the regression line of ln[C _in(t) − a∙C _out(t)] versus time, for measured values of air exchange rate, and assuming that P = 1 for all size ranges, because they lacked sufficient data to calculate penetration efficiency as well.

38

where C _in(0) is the initial indoor concentration, immediately after resuspension activity was ended. According to their results, deposition increased with particle diameter. Mean deposition rates varied between 0.14 hr⁻¹ (for the size range 0.3–0.5 μm) and 0.72 hr⁻¹ (for particle diameters larger than 5 μm), whereas measured mean air exchange rate was equal to 0.46 hr⁻¹.

Finally, a very interesting approach, based on specially designed short-term experimental protocols, was presented by Kopperud et al. (2004). The authors conducted a 5-day experimental campaign in a residential microenvironment. During 3 of the 5 days they conducted prescheduled activities, whereas on the last 2 days the study site was left unoccupied. Measurements included indoor and outdoor concentrations, air exchange rate, as well as concentrations of 13 particulate trace elements. They first calculated deposition rate, after the programmed activities took place, using eq 38, assuming that P = 1 (similarly to Ferro et al., 2004). Because this assumption did not produce realistic results (concentration of particles of outdoor origin was calculated greater than the total indoor concentration measured), the authors used the greater values of P (for P < 1) that did not overestimate indoor concentrations, namely, values for which the calculated indoor concentrations did not exceed the ones measured during time periods with no indoor activities.

Alternatively, they developed a chemical mass balance (CMB) model that used the chemical analysis data collected during the experiments. CMB expresses the indoor concentration of each trace element as the sum of two source contributions: outdoor atmosphere and indoor particle resuspension. The concentration attributed to each source is equal to the product of the source profile by the respective contribution. Sums from all elements, as well as their errors, produce a linear equations system, with the source contributions as unknowns, which may be solved using the least squares method. The outdoor particle profiles were represented by outdoor measurements. The indoor source (resuspension) profiles were determined through chemical analysis of particle samples collected using a vacuum cleaner. The advantage of the CMB model is that it does not require repetitive measurements when there are available source profiles for a sufficient number of trace elements; however, the chemical analyses involved may be both time-consuming and expensive.

The two approaches produced comparable results for the fraction of indoor PM_2.5 and PM₅ originating from indoors and outdoors. Infiltration efficiency (F _INF) was calculated in the range 0.47–0.70 for all particle fractions and methods.

Use of infiltration surrogates

This methodological category uses specific chemical species as surrogates of indoor PM of outdoor origin. According to Wilson et al. (2000), the ideal surrogate:

•	does not have indoor sources;
•	may be measured continuously;
•	is found in relatively high levels so as to allow for an accurate measurement; and
•	is chemically stable.

Sulfate (or sulfur), which is a basic particle constituent, has been proposed by several researchers as a surrogate for the infiltration of outdoor-generated PM_2.5 in indoor microenvironments (Meng et al., 2005b; Wallace and Williams, 2005; Sawant et al., 2004; Sarnat et al., 2000, 2002). Particulate sulfate is often mainly of outdoor origin. A number of studies have demonstrated that indoor and personal SO₄ ²⁻ sources are scarce and that indoor and personal concentrations are highly correlated with the respective outdoor concentrations (Diapouli et al., 2008; Ozkaynak et al., 1996; Clayton et al., 1993; Koutrakis et al., 1992). In addition, the size distribution of particulate sulfate is similar to that of the accumulation mode, which constitutes most of the PM_2.5 mass (Tolocka et al., 2001; Whitby, 1978; Long et al., 2001a; Ebelt et al., 2000; Hinds, 1999; Horvath et al., 1996).

Sarnat et al. (2002) were the first to study the use of sulfate as surrogate of indoor PM_2.5 of outdoor origin. They examined the correlation of indoor versus outdoor PM_2.5 sulfate concentrations. The regression line intercept relates to the contribution of indoor sources to the measured indoor levels, whereas the slope corresponds to the infiltration factor (F _INF). The authors suggest that sulfate may be used as an infiltration surrogate for PM_2.5 in areas where ambient PM_2.5 size distribution is similar to that of sulfur and a significant fraction of PM_2.5 consists of sulfur compounds (such as in Boston where on average 40% of PM_2.5 corresponds to ammonium sulfate (NH₄)₂SO₄). Nevertheless, in areas where PM_2.5 is mostly composed of ultrafine or coarse particles, or where the contribution of sulfur to total PM_2.5 mass is relatively low, the use of this specific chemical species as surrogate may not provide reliable results. Sarnat et al. analyzed PM_2.5 and sulfur indoor and outdoor concentration data, collected at six residences in the Boston area. The calculated indoor-to-outdoor concentration (I/O) ratios for sulfur were highly correlated with the respective ones for PM_2.5, suggesting that sulfur could be used as an infiltration surrogate for this area. The slope of the indoor versus outdoor sulfur concentrations regression yielded a PM_2.5 infiltration factor of 0.84.

Hanninen et al. (2004) used an interesting modification of the above method, while analyzing data collected during the Exposures of Adult Urban Populations in Europe (EXPOLIS) study. They proposed the use of a correction factor that would account for the difference in size distributions between PM_2.5 and particulate sulfur. The data used included mean daily indoor and outdoor concentrations of PM_2.5 and particulate sulfur for a group of 290 residences (one measurement per residence) located in four European cities. The infiltration factor for each residence was calculated using the following equation:

39

where is the infiltration factor of sulfur for a residence, calculated as the ratio of the particulate S indoor-to-outdoor concentration ; is the slope of the regression line of PM_2.5 indoor versus outdoor concentrations (for all data collected at the study city); and is the slope of the regression line of particulate S indoor versus outdoor concentrations (for all data collected at the study city).

Because this method does not allow for the separate estimation of the unknown parameters a, P, and k, the authors assumed values for the penetration efficiency (P = 1) and the deposition rate (k = 0.39 hr⁻¹) based on previous studies (Ozkaynak et al., 1996; Wallace, 1996), in order to calculate the air exchange rate for each residence:

40

The estimated mean infiltration factors range from 0.59 (in Helsinki) to 0.70 (in Greece), whereas mean air exchange rates were calculated in the range 0.75–1.30 hr⁻¹.

Sarnat et al.’s method was also applied by Ebelt et al. (2005), who studied the contribution of outdoor-generated particles to total personal exposure. The experimental data analyzed included PM_2.5 and fine particle SO₄ ²⁻ outdoor and personal concentrations in addition to PM₁₀ outdoor concentrations. Personal exposure was calculated according to Wilson et al. (2000):

41

where A is the personal exposure to particles of outdoor origin (μg/m³) and y the fraction of time spent outdoors.

Subsequently, personal exposure to particles of indoor origin (Ν) was calculated as

42

where Τ the measured total personal exposure.

The infiltration factor was estimated by assuming that infiltration of PM_2.5 was equal to that of sulfate:

42a

The infiltration factor of sulfate (F _INF,personal)^SO4 for each day was calculated using the ratio of the respective personal-to-outdoor concentration. In the case of coarse particles (PM_2.5–10) of outdoor origin, the use of sulfate as surrogate was not suitable due to significant differences in size distributions. The authors proceeded using a number of assumptions. They initially calculated (F _INF)^SO4 using eq 41, with input data: (F _INF,personal)^SO4, y, and (C _out)^SO4. Then, a value for the air exchange rate was estimated through the following equation:

43

assuming that P = 1 and k = 0.2 hr⁻¹ for sulfate, according to results presented by Ozkaynak et al. (1996). Finally they calculated F _INF and F _INF,personal for coarse particles, using equation and eq 41, respectively, assuming that for coarse particles P = 1 and k = 1 hr⁻¹, based on results presented by Long et al. (2001a).

Ebelt et al. (2005) also discussed the use of elemental carbon (EC) or black carbon (BC) as an alternative surrogate for PM_2.5. EC is an important constituent of PM_2.5 and is expected to have similar size distribution to that of fine particles. Moreover, it is mainly of outdoor origin (traffic-related), except for the case of significant indoor combustion sources. In residential microenvironments, indoor and outdoor EC or BC concentration levels generally present very good correlation and very low values of the regression line intercept, revealing a significant contribution of the ambient atmosphere to the indoor levels (Diapouli et al., 2008; Cao et al., 2005; Na and Cocker, 2005; Geller et al., 2002; Jones et al., 2000).

An application of BC as surrogate of indoor PM_2.5 of outdoor origin has been recently presented in Diapouli (2008). BC indoor and outdoor concentrations in seven residences and one office were studied through the estimation of the absorption coefficient of PM_2.5 filters. The absorption coefficient presents a very good correlation with particulate EC concentration and is thus considered a reliable proxy for this chemical species (Adams et al., 2002; Kinney et al., 2000; Edwards et al., 1983). A mean PM_2.5 infiltration factor for all sites was estimated from the slope of the regression line of indoor versus outdoor absorption coefficient values. Indoor and outdoor data presented an excellent correlation (r = 0.94) and a very low intercept. Alternatively, PM_2.5 infiltration factor was calculated by the use of sulfate as surrogate. Both the basic method, proposed by Sarnat et al. (2002), and the modification used by Hanninen et al. (2004), were applied.

The results from the three alternative scenarios (using BC, SO₄ ²⁻, and SO₄ ²⁻, with a correction factor for the difference in size distributions), shown in Table 6, were then compared with the mean infiltration factor estimated by the application of the dynamic model proposed by Bennett and Koutrakis (2006), as presented above. The comparison revealed that, for the area of Athens, EC seems to be the most appropriate surrogate of indoor PM_2.5 of outdoor origin. Comparable results were also obtained by Hanninen et al.’s methodology, where a correction factor accounts for the difference in size distributions between PM_2.5 and SO₄ ²⁻. Sulfate may give more accurate results in the case of PM₁, whose size distribution resembles more that of particulate SO₄ ²⁻.

Table 6. Mean values of PM_2.5 infiltration factor (F _INF), calculated by the application of different methodologies (Diapouli, 2008)

Methodology	F INF
BC as surrogate	0.77
SO4 ^2− as surrogate	0.84
SO4 ^2− as surrogate with a correction factor	0.75
Dynamic model	0.75

Noullett et al. (2010) used personal and ambient concentrations of sulfate and elemental carbon (via absorbance) to determine children's exposure to ambient- and indoor-generated PM_2.5 in the city of Prince George, Canada. Ambient-generated exposure (E _ag) for each individual was calculated through the following equation:

44

where Tracer _personal,ij is the personal exposure to the tracer (sulfate or elemental carbon) for subject i on day j; Tracer _ambient,j is the tracer's ambient concentration on the same day; and C _out is the respective PM_2.5 ambient concentration.

The ratio of tracer personal-to-ambient concentration (also called the attenuation factor, AF) was then used in order to calculate a PM_2.5 infiltration factor, as follows:

45

where y is the fraction of time spent outdoors or in a vehicle. The resulting mean infiltration factor was equal to 0.53 and 0.57, when SO₄ ²⁻ or EC was used as a surrogate, respectively.

Comparison of Results

The estimation of the infiltration parameters remains an open scientific challenge. The different methodologies developed give useful insights on various aspects of this issue. The main difficulty lies in generating independent estimates of penetration efficiency (P) and deposition rate (k). The values reported in the literature vary significantly, creating an additional problem when attempting to select appropriate values for these parameters. A summary of results on deposition rate, penetration efficiency, and infiltration factor, estimated using the different approaches, in studies discussed in the previous section, is given in Figures 3, 4, and 5, respectively. Three main size fractions are examined: PM₁₀, PM_2.5, and ultrafine particles (UFPs).

Figure 3. Summary of results on deposition rate (k).

Figure 4. Summary of results on penetration efficiency (P).

Figure 5. Summary of results on infiltration factor (F _INF).

Deposition rate presents the widest range of values, both between studies and size fractions. It has been found that k is greatly influenced both by the building construction characteristics, as well as the indoor or ambient conditions, which may partly explain the high variability of results (Lai, 2002; Abt et al., 2000). In the case of UFPs, aggregation processes may also play a significant role, by decreasing indoor number concentration and thus leading to an apparent increased deposition rate (Jamriska and Morawska, 2003). Experimental and theoretical studies have shown that deposition may increase as well with increasing aerosol charge (Chang et al., 2012). The different methodological approaches contribute also to the observed variability of values. Regarding the three size fractions, the smallest values correspond to PM_2.5, which consist mainly of accumulation mode particles (with diameters in the range 0.1–1.0 μm). Coarse particles deposition is mainly due to gravitational settling, possibly influenced by inertial impaction. Ultrafine particles, on the other hand, are mainly deposited through Brownian diffusion, leading to increased particle deposition onto vertical surfaces as well. Accumulation mode particles do not seem to be influenced significantly by any of the above mechanisms, presenting thus the lowest deposition on indoor surfaces (Nazaroff, 2004; Wallace, 1996).

Penetration efficiency values also present a relatively wide range. The lowest (0.54) and largest (1.00) values correspond to a steady-state model applied for PM_2.5 by Long et al. (2001a) (cold and warm periods, respectively). The very high value of P during warm period is probably due to open windows at this time of the year. Penetration efficiency equal to 1.00 was also reported by Ozkaynak et al. (1996), for both PM₁₀ and PM_2.5. Their methodology seems to overestimate the value of P, especially in the case of PM₁₀, because penetration of coarse particles is expected to be limited due to their relatively large size. The different dynamic solution results seem to agree well, while they are also consistent with theoretical approaches indicating that the largest penetration is expected for accumulation mode particles. This size fraction is not easily removed from the air stream through diffusion or gravitational settling (Liu and Nazaroff, 2003).

The different infiltration factor values reported in the literature present a better agreement in relation to the previous two parameters (P and k). The combination of the three parameters (air exchange rate, penetration efficiency, and deposition rate) in this single infiltration factor reduces the complexity of calculations, leading to acceptable results even when less advanced methodologies are applied. The majority of studies focus on PM_2.5 rather than PM₁₀. Ultrafine particles have also been studied extensively, especially because their increased health effects have been acknowledged (Oberdorster et al., 2005), but comparison of results is not always possible because different size fractions are considered. The reported F _INF values for PM_2.5 are in general in good agreement, presenting a mean value of 0.70. The somewhat larger deviation exhibited by a few values may be also related to ambient conditions, building characteristics, and PM chemical composition and size distribution. For instance, Polidori et al. (2007) attribute the relatively low infiltration factor (0.45) calculated for Los Angeles, California, to the removal of volatile or semivolatile compounds (such as ammonium nitrate, which is known to contribute significantly to ambient PM_2.5 mass in this area), during transfer of particles indoors (Tolocka et al., 2001). The good agreement of results produced by the application of dynamic models and the use of infiltration surrogates presents strong arguments in favor of the latter methodology, which is simple and easy to apply when chemical speciation data are available. The selection of the appropriate surrogate is crucial in this case, as shown by the results of Noullett et al. (2010) and Diapouli (2008). The highest infiltration factor corresponds to BC in the former work and to sulfate in the latter. The chemical species that best characterizes PM_2.5 infiltration indoors depends on the size distribution of fine particles and the presence of indoor sources at the study area.

Conclusion

The present work examines in a systematic manner the different methodologies used to estimate concentrations of indoor particles of outdoor origin. The underlying problem is how to calculate the infiltration factor of outdoor particles (F _INF) or alternatively the three parameters that define it: air exchange rate (a), penetration efficiency (P), and deposition rate (k). Often more attention is given to the estimation of the infiltration factor (because it is a direct measure of the contribution of the ambient atmosphere to the indoor concentration levels), whereas the values of a, P, and k either are not considered at all or are estimated based on assumptions that may not apply under real conditions. Calculating P and k has proven to be especially difficult, because the statistical techniques used fail to provide truly independent values. The use of iterative techniques may be a reliable approach for independent estimation of P and k.

The steady-state approach is widely used, primarily due to its relatively simple application. Nevertheless, it presents a number of disadvantages. It assumes constant values for all parameters, whereas both outdoor concentration and infiltration parameters (a, P, and k) may exhibit significant daily variation. By ignoring changes in outdoor concentration, this approach may overestimate or underestimate the infiltration factor if there is a sharp decrease or increase, respectively, of ambient concentration. Moreover, using nighttime data, which is a common practice in order to minimize the contribution of indoor sources, may not provide a representative infiltration factor during daytime, when conditions may be very different (e.g., higher air exchange rates). This approach must also use relatively long-term input data (of several hours at least) for the steady-state assumption to hold. Because the regression techniques applied require a sufficient number of data points, usually data from different sites are used. In order to calculate the infiltration factor of a specific site, repeated long-term measurements at this site are needed.

Models that use the dynamic solution of the mass balance equation give a more complete and realistic picture of particle behavior when moving in and out of an indoor microenvironment, because they acknowledge the dynamic character of all parameters. They also offer the possibility to study the spatiotemporal variation of the infiltration parameters (a, P, and k) by analyzing data from a specific site and day. The selection of short time periods during data collection may even allow for the short-term calculation of infiltration parameters and infiltration efficiency, thus providing their diurnal variation profiles.

The application of short-term specially designed experiments provides the opportunity to estimate P and k separately. However, these experiments are usually difficult to conduct, especially in a number of different sites and for an extensive time period. What is more important, they estimate values for one of the two unknown parameters (penetration efficiency or deposition rate) that correspond to specific conditions created during the experiments at which the other parameter may be considered negligible. The second parameter is then calculated based on the mass balance equation and the first parameter's results, but under altered conditions. This practice may lead to deviations from the real situation, because all infiltration parameters (a, P, and k) are interrelated and all depend on the experimental conditions.

The use of chemical a species (such as sulfur or EC) as a surrogate for the infiltration of outdoor particles in indoor microenvironments is a promising approach, but it also presents certain limitations. It may require the application of a time-consuming and expensive experimental protocol, because it involves PM chemical composition data. Moreover, the selected surrogate should not have indoor sources, which is not always true. For example, particulate SO₄ ²⁻ with aerodynamic diameters greater than 1 μm may also be of indoor origin, due to resuspension. Indoor generation of particulate SO₄ ²⁻ has been also observed in smoking residences, during gas-cooking and showering and in residences using humidifiers (Brown et al., 2009; Zhou et al., 2007; Cowen and Ollison, 2006; Dockery and Spengler, 1981). Cigarette smoke has been identified as a source for both sulfate and EC. In addition, in areas where sulfate ambient levels are low, even moderate indoor sources of sulfur may lead to an overestimation of the indoor-to-outdoor ratio and thus of the infiltration factor. A characteristic example is the area of California, where the use of sulfate as surrogate for indoor PM_2.5 of outdoor origin was not successful, because ambient PM_2.5 mass is composed mostly of carbon and nitrate, both species exhibiting very different behavior to sulfate (Meng et al., 2005b).

Another important issue when choosing a suitable surrogate is the similarity in size distributions with the particle fraction studied. Sarnat et al. (2002) mention that sulfate's suitability as surrogate for PM_2.5 may be limited when air exchange rate is very low, because at these conditions the infiltration of sulfur may be different than other PM_2.5 constituents. Moreover, in the case of coarse particles, it is difficult to find a suitable surrogate because coarse material of outdoor origin may be easily resuspended in the indoor microenvironment and thus act as an indoor source.

However, when there are available chemical composition data, the use of infiltration surrogates remains a promising approach, because it may provide reliable results. In the case of elemental carbon in particular, the use of the absorption coefficient as proxy for EC concentration further simplifies the application of this method, because the measurement of absorbance is a nondestructive, simple, rapid, and inexpensive technique.

In view of recent toxicological results suggesting that specific components of airborne particulate matter may be responsible for specific biological responses, it becomes clear that population exposure should be considered in relation to the different indoor and outdoor PM sources. Work is still needed in order to reveal the biological mechanisms of the different PM components. Nevertheless, the quantification of the contribution of indoor- and outdoor-generated particles to total personal exposure may enlighten some aspects of the complex relationships between personal/ambient/indoor levels and particle-induced health effects. In addition, taking into account that increased health risks may be related to ambient particles, a reliable estimation of the main parameters governing particle infiltration may assist the development of appropriate regulation and control measures, targeted to specific sources/factors contributing to increased exposures.