Ann. occup. Hyg., Vol. 46, No. 7, pp. 597-607, 2002
© 2002 British Occupational Hygiene Society
Published by Oxford University Press
Estimating the Quartz Exposure of South African Gold Miners
1 Safety Health Environment International Consultants, Suite 101, 38 Athabasca Avenue, Devon, Alberta, Canada T9G 1G2; 2 Marmanet No. 45, PO Box 1549, Kempton Park 1620, South Africa
Received 27 September 2001; in final form 3 July 2002
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ABSTRACT |
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The possibility that dust and silica exposure estimates in epidemiological studies of South African gold miners have been underestimated has been postulated for some years. These exposure estimates were obtained by converting particle number concentrations measured with konimeters and thermal precipitators to respirable mass concentrations, primarily on theoretical considerations. A detailed review of the methodology has revealed that the theoretically based dust and silica estimates were probably underestimated. In the absence of systematic side-by-side thermal precipitator and modern respirable mass measurements in the South African gold mines, the true relationship between the respirable mass concentrations and the theoretically derived concentrations cannot be known. However, with many uncertainties, we estimate that the quartz exposures of South African miners derived from past theoretically based conversions from particle number to respirable mass underestimate the actual quartz exposures by a factor of about 2.
Keywords: conversions; exposure; gold miners; konimeter; quartz; Sichel index; silica; silicosis; South Africa; thermal precipitator
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX. DESCRIPTION OF THE...REFERENCES |
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The objective of this study was to resolve the issue of the possible underestimation of dust and quartz exposures in epidemiological studies of South African gold miners. This is important for two reasons. First, while there have been many studies of silicosis in silica-exposed workers (Finkelstein, 2000; Greaves, 2000), few have quantified quartz exposures or been as comprehensive as those in South Africa. Secondly, for several years there has been some suspicion that silicosis risks in South African studies were overestimated because of underestimates of dust and silica exposure. For example, Hughes and Weill (1995) estimated that the risks of small round opacities of ILO category 1/1 or greater after 40 yr exposure to 100 µg/m3 respirable quartz, based on studies of Ontario miners (Muir et al., 1989) and South African gold miners (Hnizdo and Sluis-Cremer, 1993), were 1.2 and 60%, respectively. They suggested that South African exposures were underestimated, a possibility acknowledged by the original authors, as the average concentration in a dusty stope in 1991 was 0.48 mg/m3 compared with 0.37 mg/m3, the pre-1960 value used in their study. Unfortunately, comparisons between Ontario and South African risk estimates are complicated because of a shorter follow-up period in Ontario, which may, in part, be responsible for the difference in estimates (Finkelstein, 2000). It has also been argued that studies such as those of Steenland and Brown (1995) and Kreiss and Zhen (1996) support the South African risk estimates. However, they also have limitations. The gold miners studied by Steenland and Brown (1995) were also exposed to cummingtonite-grunerite and an unusual combination of factors was used regarding when silicosis first appeared. Kreiss and Zhen (1996) studied about 100 miners in a high altitude community. The effects of altitude, migration and the extent to which those studied were representative of the more than 2000 annual mining workforce are not known.
Nowadays, most silica standards are expressed as the mass concentration of respirable crystalline silica measured using personal size-selective dust samplers. Historically, most silica exposures were assessed using particle count methodologies where exposure–response relationships have been based upon conversions to respirable mass. Methods to achieve these conversions have included side-by-side measurements (see for example Verma et al., 1989), ratios of average concentrations measured using various sampling methods (see for example Seixas et al., 1997) and extrapolation of conversion factors from one industry to another (see, for example, Steenland and Brown, 1995). In contrast, exposures in South African studies have been derived using largely theoretical considerations. Such an approach was dictated, in part, by the limited analytical sensitivity of the older methods of quartz determination. To date, the theoretical conversion of particle number concentrations using thermal precipitators and konimeters to respirable mass concentrations as measured using modern personal cyclone methods has not been validated with measurements. This does not mean that theoretically derived respirable mass concentrations are invalid. Indeed, health outcome rates have been shown to increase in a sensible manner with increasing theoretically derived estimates of respirable silica exposure.
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METHODS |
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Hnizdo and Sluis-Cremer (1993) described the relationship between radiologically defined silicosis (ILO category 1/1 or greater) and cumulative incombustible, acid-insoluble respirable dust exposure expressed in mg/m3-yr. They applied theoretically derived estimates of the respirable mass concentrations associated with various mining occupations (Du Toit, 1991) to the work histories of cohort members. Cumulative respirable quartz exposure was obtained by multiplying the respirable dust exposure estimates by 30%, the percentage of quartz in total, non-incinerated, non-acid washed dust. How the South African dust and quartz exposures were estimated was not fully described in the published literature. Therefore, to clarify key issues, we investigated the methods used to derive exposures and in particular examined the theoretically based exposure estimates in the study by Hnizdo and Sluis-Cremer (1993).
Reasons for the apparently lower respirable dust concentrations in South African gold mines (Page-Shipp and Harris, 1972) compared with those in similar Canadian mines (Verma et al., 1989) were also investigated.
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RESULTS |
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The data used to estimate exposure
The exposure estimates used in epidemiological studies of South African gold miners to date have been based on a survey undertaken in 1956–60 by Beadle (1967). The survey objective was to establish shift-long dust exposures based on measurements in a random sample of 20 gold mines. Standard and modified thermal precipitators and the Witwatersrand type of konimeter were used. Konimeters are ‘spot’ samplers which, as a plunger is released, suck in and deposit dust on a glass plate. The particles are counted under a microscope. The quantities of incombustible and acid-insoluble dust particles (mainly quartz and silicates) were measured in terms of the surface area of the respirable dust (RSA) and the number of respirable particles (diameter 0.5–5 µm) per milliliter. The data from the surveys by Beadle (1967) were summarized by Page-Shipp and Harris (1972). The thermal precipitator results from that report were converted to respirable dust concentrations (in mg/m3) by Du Toit (1991) and used in the study by Hnizdo and Sluis-Cremer (1993) (Table 1).
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Validity of extrapolating results from the ‘Beadle 1956–60 survey’ to all years
Page-Shipp and Harris (1972) assumed that dust conditions had not varied greatly in the period 1935–60 because the mean ‘dust levels’ reported by the South African Chamber of Mines had not altered appreciably in this period. They rejected, for epidemiological purposes, the dust samples collected daily in the gold mines, because they were sampled for purposes other than to estimate worker exposures, such as locating unsatisfactory dust conditions and compliance with legal requirements.
In the 1930s, the South African Government Mines Inspectorate began random dust measurements using konimeters at some 13 types of locations. To develop an index of concentration trends, Du Toit (Beadle, 1967, Discussion), supported by Martinson (1970), reported annual average concentrations at the same six ‘locations’. The locations were: tops and bottoms of downcast shafts; main intake airways away from downcast shafts; working faces of stopes and development ends and bottoms of sinking shafts. While not personal samples, these systematic results are probably the best available barometer of the dust generation and control systems in place in the various years. Dust concentrations in stopes fell from 309 particles/cm3 (p.p.c.c.) in 1931 to 149 p.p.c.c. in 1941, in development ends from 450 p.p.c.c. in 1931 to 147 p.p.c.c. in 1953 and in sinking shafts (excluding blowing over operations) from 330 p.p.c.c. in 1931 to 140 p.p.c.c. in 1956 (Table 2). The overall mean respirable dust concentrations based on the six strategic locations fell steadily from 243 in 1931 to 93 in 1959. The reduction in the mean concentration from 1941 (118 p.p.c.c.) to 1959 (93 p.p.c.c.) was about 22%. In 1960, concentrations began to increase to values similar to those in 1941, most likely due to increased production and better instrumentation and support the earlier observation by Hnizdo and Sluis-Cremer (1993). The exposures of workers prior to about 1940 could have been more than three times those measured in 1957–60 and in some years after 1940 from 0–50% higher depending on work location or job (Table 2).
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As with all particle counting methods, counts obtained using thermal precipitators and konimeters are subject to observer variation, which, in retrospect, is difficult or impossible to quantify. Nevertheless, the pattern of results at the various sites within each year and trends are consistent with what might be anticipated. Thus, the assumption that overall concentrations did not change to a large extent after the 1940s seems to be generally supported. However, exposures before 1940 would have been much higher than estimated.
Mine differences
Page-Shipp and Harris (1972) assumed that miners doing the same type of work in different mines were exposed to the same dust levels. However, dust controls at some mines were considerably better than at others (Du Toit, personal observation based on measurements by Government Inspectors of Mines at the six strategic positions). This could be important epidemiologically, as mine differences were not taken into account when assessing exposures and silicosis rates in the various mines have not been reported.
The mining conditions
Dust concentrations in South African gold mines have always been low for the following reasons: (i) wet mining was introduced by Regulation no. 101 framed under The Mines and Works Act of 1911 to cover rock drilling and the removal of broken rock (Miners' Phthisis Prevention Committee, 1937, p. 223); (ii) the large Witwatersrand gold mining operations involve deep mines. By 1954, stoping was done at a maximum depth of 2749 m and development at a maximum depth of 2960 m [Government Mining Engineer (GME, 1954)]. By 1965, stoping was done at a maximum depth of 3002 m and development at a maximum depth of 3304 m (GME, 1965). In view of the heat in these deep mines, it has always been necessary to use considerable volumes of air to cool the mines and this reduced dust exposures.
Estimating respirable mass concentrations from thermal precipitator and konimeter dust samples
The way in which the airborne respirable dust and quartz concentrations were calculated for the South African studies is described in detail in the Appendix. Du Toit calculated respirable mass concentrations for each occupational group, which were used by Hnizdo and Sluis-Cremer (1993) to estimate worker exposures (Table 1, columns [1] and [2]). These were incinerated, acid-washed respirable dust concentrations (Hnizdo and Sluis-Cremer, 1993). When reviewing the surface area and volume calculations, it was found that a constant, 
/4, had been omitted. On account of this, the diameter was underestimated by 11% (i.e. 1 – /4) and the volume and mass of the particle by a factor of about 1.37 (i.e. 1.113). Adjustments would have increased the estimated exposures somewhat over the original estimates, but this is not important, because, as described in the Appendix, the more appropriate estimates are those for a d-rv/d-rsa ratio of 1.13, where d-rv is the diameter of the volume mean particle and d-rsa the diameter of the surface area mean particle (Table 1, column [4]). These respirable masses have been calculated after incorporating the /4 factor (see Appendix, step 10). Table 1 also shows the shift mean respirable mass concentrations as originally calculated by Beadle, and as calculated using an unpublished formula by the late R. E. G. Rendall. The concentrations in p.p.c.c. on which the respirable masses were based are also shown.
Respirable dust concentration comparisons
The respirable dust concentrations used in the South African gold mining studies were estimated from thermal precipitator samples after incineration and acid washing of the respirable dust (0.5–5 µm) fractions. Respirable dust concentrations measured using cyclones reported the concentration of all the respirable dust. Thus, comparisons between South African studies and other studies become problematic. The South African airborne respirable dust concentrations, as reported in the epidemiological studies by Hnizdo and colleagues, can be adjusted by multiplying them by the ratio of the respirable particle concentrations before acid washing to that after acid washing, using data from Page-Shipp and Harris (1972). In order to estimate the factor to convert post-acid-washed concentrations to pre-acid-washed concentrations, various ratios were examined (Table 3). Pre-acid-treated particle number concentrations were approximately twice the post-acid-treated concentrations. However, not all approaches gave the same ranking of ratios; this indicates that the before and after treatment of ‘all particles’ was not identical to that for the ‘respirable fraction’. A factor of approximately 2 to convert respirable acid-washed concentrations to respirable non-acid-washed gravimetric concentrations assumes that particles removed by acid treatment have the same particle size distribution and densities as the insoluble particles.
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Quartz content of the dust
In this report, the term ‘quartz’ refers to
-quartz. In order to convert the heat-treated, acid-washed respirable dust mass concentrations to respirable quartz concentrations, Hnizdo and Sluis-Cremer (1993) multiplied the former values by 30%, quoting Beadle and Bradley (1970). In fact, the latter reported that the percentage of quartz in total, non-incinerated, non-acid-washed dust was 30%. Measurements using an electrostatic precipitator by the same researchers gave a mean percentage of quartz in the total dust of about 30% (32%). After acid washing and incineration this percentage increased to 54%. This, and other supporting measurements, suggest that applying the percentage of quartz in the total dust (30%) to the incinerated, acid-washed concentrations introduces an underestimation of the quartz exposures by a factor of 54/30 = 1.8. Recent data collected using cyclone respirable dust samplers operating at 1.9 l/min, as opposed to the 1.7 l/min prescribed by the American Conference of Governmental Industrial Hygienists (ACGIH, 2002), have shown that the percentage of crystalline free silica in non-incinerated, non-acid-washed samples ranged from less than 2 to over 83% (personal communication, South African Mines Inspectorate internal data). Measurements based on samples collected and analyzed by individual mining companies at all operating mines over a period of 1 yr gave an overall quartz content of the respirable dust of about 15% (Kielblock et al., 1997). If 15% were used to estimate the quartz content for heat-treated, acid-washed samples, a factor of 15 x 54/30 would need to be used in recalculating the exposures estimated by Hnizdo and Sluis-Cremer (1993). This approximates 30% and is, in fact, the figure they used. However, this 15% value was based upon dusts sampled in the late 1980s to 1990s and collected predominently on workers with different responsibilities than those in the white cohort (Hnizdo and Sluis-Cremer, 1993). We do not know whether changes in mechanization, the nature of the rock, sampling method, particle size distributions or analytical methodological differences (now infra-red, in the past X-ray diffraction) explain the different respirable airborne quartz contents between 1950 and 1990. In summary, if the data by Beadle and Bradley were valid for the time period studied, the estimates of quartz exposure reported by Hnizdo and Sluis-Cremer (1993) were probably underestimated by a factor of 1.8.
The estimated exposures
The estimated exposures from Hnizdo and Sluis-Cremer (1993) are shown in Table 1. These were similar to those originally calculated by Du Toit (1991) except that they were regrouped into nine categories in which shaft sinkers and development miners were assigned the same lower exposure. As the number of shaft sinking miners was small, this is unlikely to have affected the epidemiological study results significantly.
Dust concentrations today
In recent years, airborne respirable quartz concentrations have been measured by individual mining companies and reported to the South African Government. Data were gathered on workers of all races, but the measurements were not classified by occupational groupings in a way that permitted comparison of concentrations in recent years with those used in the South African epidemiological studies. Further, views have been expressed that because compensation levies have been based on dust concentrations (Government of South Africa, 1962; Du Toit, 1968), mining company data were biased towards lower dust concentrations. For that reason, measurements made by the Mines Inspectorate, Chamber of Mines and the survey by Beadle and colleagues have been viewed as more likely to have reflected the actual dust conditions. On the other hand, it was suggested that control efforts, such as keeping rock wet, may have been more rigorously enforced on the days when measurements were made by external authorities. Recent surveys have shown that some silica concentrations could have been (perhaps two to three times) higher than routinely recorded by the mining companies (Kielblock et al., 1997). It seems unlikely that this would have affected the reported percentage of quartz in the sampled dust, but this is unknown. The overall mean quartz concentration based on 13 749 personal respirable dust sample measurements in all mines since 1983 was 0.06 mg/m3 (Kielblock et al., 1997).
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DISCUSSION AND CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSION AND CONCLUSIONSAPPENDIX. DESCRIPTION OF THE...REFERENCES |
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There are many uncertainties associated with the estimation of respirable quartz concentrations in South Africa. This must be borne in mind when comparing the results from different studies. The size selection characteristics of various respirable dust samplers may introduce other differences. The respirable mass studies by Beadle and Bradley were based on horizontally elutriated systems, which met the British Medical Research Council criteria for respirable dust (i.e. an upper cut-off for quartz of 7 µm). In South Africa, the sampling rate used with 10 mm cyclone personal samplers is 1.9 l/min, while dust samples collected in the USA use a sampling rate of 1.7 l/min (ACGIH, 2002). Thus, the definitions of fractions are not the same and should be taken into account when making comparisons.
The estimated concentrations shown in column 4 of Table 4 are probably the closest approximation to those that would be measured using a personal cyclone sampler. As far as respirable quartz concentrations are concerned, the estimates would be as shown in column 6 of Table 4. Values obtained by multiplying the acid-treated respirable dust concentration recalculated by Du Toit (2000) by 0.54 (the value from Beadle and Bradley, 1970) and by 0.15 (the value reported from recent respirable dust measurements) are also shown in columns 7 and 8 of Table 4. The ratios of the values in column 7 to those in column 8 in Table 4 for occupational groups 1–11 ranged from 1.4 to 2.1 for an overall mean of 1.7. The ratios of the values in column 8 to those in column 5 for occupational groups 1–10 ranged from 0.9 to 2.3 with an overall mean of 1.4. The ratios of values in column 7 to those in column 5 for occupational groups 1–10 ranged from 1.7 to 4.1 with an overall mean of 2.3.
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Ideally, conversions from particle number to mass concentrations should be based on side-by-side comparisons. Unfortunately, the only compilation of work in this area appears to be that of the late R. E. G. Rendall, whose work is the subject of a posthumous thesis under consideration at the University of the Witwatersrand. Rogers (personal communication), who plotted South African respirable dust concentrations versus respirable surface areas based upon measurements with thermal precipitators provided by Rendall, reported that they showed considerable scatter and uncertainty from the standpoint of converting particle counts to respirable mass concentrations. Based on what we know to date, the most likely estimates of the respirable quartz exposure of persons in the cohort studied by Hnizdo and Sluis-Cremer are those in columns 7 and 8 of Table 4. This means that, overall, the quartz exposure estimates in the report by Hnizdo and Sluis-Cremer were probably underestimated by a factor of between 1.3 and 2.3. Factors which could be responsible for underestimates of the South African silica exposures are (4/
)1.5 (factor = 1.4), the quartz content of the dust (54/30 = 1.8) and underestimation of the true dust level (say 1.3), which combined indicate that the underestimate could exceed 3. The occupational histories of the cohort members were not available to recalculate exposures. However, Dr Geoffrey Berry (University of Sydney), using the accelerated failure time model fitted by Hnizdo and Sluis-Cremer (1993) and assuming that overall exposure levels were underestimated by a factor of 2, found that a cumulative risk of 1.4% would have corresponded to an exposure of 
2.7 mg/m3-yr respirable silica. This is close to that estimated for the Canadian gold miners by Hughes and Weill (1995) (i.e. 1.2% at an exposure of 4.0 mg/m3-yr of respirable silica exposure). Acknowledgements—We are grateful to Dr David Stanton (South African Chamber of Mines) for meeting with us and for constructive input to our study, to Mr Ralph McIntyre (Inspector of Mines, Department of Minerals and Energy), Mr George Asworth (Technology Manager of Mining Technology, CSIR), Mr Vali Yousefi (National Centre for Occupational Health) and Mr Jan Kielblock for their considerable help in obtaining information to assist us in our work. We specially thank Dr Geoffrey Berry (University of Sydney, Australia), who calculated the adjusted estimates of risk for the South African miners and who, with Dr David C. F. Muir (McMaster University, Canada) provided constructive comments on our draft paper. This work was funded in part by the Silica Coalition.
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APPENDIX. DESCRIPTION OF THE METHODS USED TO ESTIMATE RESPIRABLE MASS CONCENTRATIONS FROM THERMAL PRECIPITATOR DUST SAMPLES IN SOUTH AFRICA |
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Sichel (1957) identified a straight line relationship between the ‘square root of particle size’ (x) and the ‘log percent number frequency of particles per unit interval’ (y). Particle size is the diameter of the circle with area equal to the projected area of the particle.
The size distribution is given by
where A and a are mainly determined by the proportion of particles >0.5 µm, namely rock particles, and where B and b are mainly determined by the proportion of particles <0.5 µm, namely other industrial particles. For the purposes of silicosis risk studies, it was assumed that particles below 0.5 µm contributed relatively little to the surface area of the harmful particles, in comparison with particles with diameters of 0.5–5.0 µm. Hence, the relationship was limited to the straight line for particles >0.5 µm. Having made a size distributed count, the parameters A and a can be computed and the ‘number’, ‘projected surface area’ and ‘volume’ concentrations for any selected size range of particles calculated.
For example, the cumulative number of particles (n) greater than size 
is given by:
n = 2A ÷ a2(1 + a0.5)/ea
The relative surface area mean particle of all particles greater than size is given by:
S = (u5 + 10u3 + 20u2 + 45u + 44)/a4u
where u = 1 + a0.5 [Joffe and Sichel, 1965, equation (2)].
The relative volume mean particle of all particles greater than size is given by:
V = (u7 + 21u5 + 70u4 + 315u3 + 924u2 + 1855u + 1854)/a6u
where u has the same value as that given above (H. S. Sichel, private communication).
The following example is based on the methodology used to convert the number concentrations to mass concentrations by Du Toit (1991, 2000) and uses the data from Page-Shipp and Harris (1972). Airborne particles in the mine atmosphere were collected using a standard thermal precipitator. In our example, the concentration associated with shaft sinkers will be used. As reported by Page-Shipp and Harris (1972), the concentrations in Table 5 were weighted to be the mean daily dust levels and then multiplied by the number of hours spent by workers in the dust-exposed areas based on their job title. Steps in the calculation of the incinerated, acid-washed respirable dust and quartz concentrations were as follows.
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1. The sample on the thermal precipitator glass coverslip was ignited. Counts of particles were made using rules for the truncated multiple traversing technique (Sichel, 1957, fig. 7). Sichel’s (1957) ‘truncated multiple traversing’ (TMT) technique was specifically designed to improve the accuracy of thermal precipitator sample counting. The crux of the TMT technique is to count each of 15 size ranges of particles until a minimum of 20 particles per size range or a maximum of 20 traverses per individual size range have been counted for each of the strips of dust deposited on the two coverslips. Counters classified particles according to size when counting using an eyepiece graticule. The total airborne particle concentration ‘before acid treatment’ was calculated (Table 5, row 1).
2. ‘Respirable’ was defined as particles with diameters in the size range 0.5–5 µm. These were counted. The ‘respirable particle number concentration before acid treatment’ was determined (Table 5, row 3).
3. The thermal precipitator coverslip was acid washed. The number of particles was counted. The total ‘particle concentration after acid treatment’ was determined (Table 5, row 2).
4. Particles with diameters ranging in size from 0.5 to 5 µm were counted after acid treatment of the slide. The ‘respirable particle number concentration after acid treatment’ was determined (Table 5, row 4)
5. The total projected surface area of particles (µm2/cm3) before acid treatment was then calculated (Table 5, row 5). The method used to convert particle number concentrations to surface area and to respirable mass is based largely on the work of Sichel (1957) and Joffe and Sichel (1965), summarized in Appendix II of Page-Shipp and Harris (1972).
6. The total projected surface area of particles (µm2/cm3) after acid treatment was calculated (Table 5, row 6). Having computed the ‘after acid’ ‘’ parameters, the projected surface area of the particles within the selected size range were computed using the same methods as applied in paragraph (5).
7. The respirable surface area (RSA) of particles (µm2/cm3) before acid treatment (RSAba) was calculated (Table 5, row 7). Page-Shipp and Harris (1972) reported that a linear approximation of the sampling curve recommended by the 1959 Johannesburg Pneumoconiosis Conference in a ‘three spot graticule count (which saved much time) (Joffe and Sichel, 1965) could be used to estimate the respirable surface area from the relationship y = 1.02128 – 0.17 021x, where x is the diameter of the particle (projected area diameter) and y is the sampling efficiency.
8. The respirable surface area (RSA) of particles (µm2/cm3) after acid treatment (RSAaa) was calculated (Table 5, row 8).
9. The mean respirable surface area (µm2/cm3) per particle after acid treatment was calculated. This was done by dividing row 8 of Table 5 (4690) by row 4 (870). This gave a value for /4 x the square of the diameter (d) of the respirable surface area mean particle [i.e. /4 x (d-rsa)2 = 5.3908].
10. The diameter of the incinerated, acid-washed respirable surface area mean particle (d-rsa) was then calculated: d-rsa = (5.3908 x 4/)0.5 = (6.8638)0.5 = 2.6199 µm.
11. The value for d-rv (the diameter of the respirable volume mean particle) was now calculated as shown in paragraph 12. In this connection, the following background is relevant. For a dust with a specific size distribution, there is a specific ratio between the diameter of the volume mean particle (d-rv) and the diameter of the surface area mean particle (d-rsa). This index, d-rv/d-rsa, is an index of fineness. For example, for a dust with an ‘’ fineness index of 3, the ratio d-rv/d-rsa for particles in the size range 0.5–5 µm was (via the Sichel formulae) estimated at (1.89/1.61 = 1.17) (Du Toit, 1990).
For a dust such as that found in the Witswatersrand gold mines, the ratio d-rv/d-rsa ranged from 1.13 to 1.36 (Du Toit, 1959). These ratios referred to d-rsa sizes in the range 1.55–1.82 µm. They were applied to the Beadle data whose d-rsa sizes ranged from 2.41 to 2.73 µm. Such an application was based on sound argument as the difference was not due to the coarseness of the airborne dust but to differences in the counting and respirable surface area computation techniques used by Beadle and Du Toit. Du Toit, whose work was carried out prior to the publication of the ‘Johannesburg curve’ in 1959, used ‘Brown’s alveolar deposition curve’, whereas Beadle used the ‘Johannesburg’ curve. The difference between the two estimates may be summarized as follows. For particle sizes of 1, 2, 3, 4, 5, 6 and 7 µm the proportions (%) of particles included in the computation were, respectively: Brown model, 53, 42, 31, 25, 22, 14 and 8; Page-Shipp, 85, 68, 51, 34, 17, 0 and 0.
The data from Page-Shipp and Harris revealed that the d-rv/d-rsa ratio increased the coarser the dust was. The mean Sichel fineness index reported for the values used by Page-Shipp and Harris was 3.05. To convert to mass concentrations, the surface area values determined by Page-Shipp and Harris (1972) were used.
12. In our example, using a d-rv/d-rsa of 1.13, d-rv becomes 1.13 x d-rsa, which is 1.13 x 2.6199 (from paragraph 10) = 2.9605.
13. Dealing with particles that have been heated to 500°C and then acid washed, it was considered that most of the particles would be quartz and silicate particles and a density of 2.7 g/cc was used. This could potentially be in error somewhat, if there were many particles other than quartz and silicates remaining.
14. The shape factor is defined as the inverse of the ratio of the volume of a sphere of diameter d and the volume of a particle with projected surface area equal to that of a circle with diameter d. A shape factor of 0.25 was used. Du Toit (1991) defends the choice of this value as three independent investigations pointed towards such a value (Miners' Phthisis Prevention Committee, 1937, pp. 41 and 43; Dalla Valle, 1943; Talbot, 1958).
15. Given the above parameters, the respirable incinerated, acid-washed mass concentrations were calculated as follows: mass per particle = x d3 x 2.7 x 0.25/6 pg. At d-rv = 2.9605, the mass per particle = x (2.9605)3 x 2.7 x 0.25/6 = 9.1706 pg.
16. As the shift length for a shaft sinker was 7.7 h, the shift number concentration becomes: row 4 (i.e. 870 particles/ml-h) divided by 7.7 = 113 particles/ml.
17. The shift respirable mass concentration = 113 x 9.1706 = 1036 pg/ml. This was converted to mg/m3 by dividing by 1000 = 1.036 mg/m3.
Uncertainties
In the above calculations, the following are the main areas of uncertainty.
1. The particle size distribution. This was taken into account using the index described by Sichel (1957). For quartz concentrations in the gold mines it has been shown that an index of 3–4 takes into account the size distributions appropriate to the dusts to which South African gold miners are exposed.
2. The shape factor. Airborne particles range from almost spheres to flat flakes and have varying densities. If each particle is a cube and its side is 2 µm, its volume is 8 x 10–12 cm3. If its density is 2.65 (e.g. quartz), the mass of the particle is 21.20 x 10–12 g. If the particle is a sphere with a diameter of 2 µm (i.e. radius r = 1), the mass of the sphere would be (4/3r3 x 2.65 = 4/3 x 22/7 x 1 x 10–12 cm3 x 2.65 g/cc = 88/21 x 10–12 x 2.65 
11 x 10–12 g = 11 pg, about one half the mass of a cube of 2 µm. If the particle is a flat flake, its mass could be one-tenth or less of this. Hence, in practice the mass of a 2 µm particle is somewhere between these limits (i.e. 1–20 pg).
As the estimates apply to incinerated and acid-washed particles with diameters ranging from 0.5 to 5 µm, it is likely that the ‘after acid’ particles are quartz, micas and insoluble metal oxides. In order to take this into account, a shape factor is introduced. Witwatersrand quartzite particles have a length to width dimension ratio of ~2:1. The volume (i.e. mass) of a body varies as the cube of any linear dimensional index. Hence, if the linear index is lowered by a factor of 2, its volume will be lowered by a factor of 8. Particles settle on counting slides in stable positions (i.e. flat), giving the particles about 1/8 the mass of a cube of equal greatest diameter, which would be a mass of 1/4 of a sphere of equal diameter, making for a shape factor of ~0.25. This means that a 2 µm particle has a mass of ~ 11/4 = 2.75 pg (i.e. 1 mg/m3 = 364 p.p.c.c.). In the calculations on which the exposures for the epidemiological studies were based, a shape factor of 0.25 was used. This could lead to an under- or an overestimation of the respirable dust mass concentration by a factor of ~2, depending on the correctness of the assumed shape factor.
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* Author to whom correspondence should be addressed. Tel: +1-780-987-2883; fax: +1-780-987-4901; e-mail: sheicons@compusmart.ab.ca
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