Asbestos body concentrations in human lung: predictions from asbestos body counts in tissue sections with a mathematical model

Our plain-English summary of Asbestos body concentrations in human lung: predictions from asbestos body counts in tissue sections with a mathematical model, by R.T. Vollmer, V.L. Roggli (Human Pathology, 1985).

The study

• Authors: R.T. Vollmer, V.L. Roggli
• Journal: Human Pathology
• Published: 1985;16(7):713-8
• Cited by: 8 articles, as counted by NIH iCite
• Read it: PubMed · Publisher

Abstract

A mathematical model for predicting the concentration (Nv) of asbestos bodies (AB) in human tissue from the count (No) of these bodies in planar tissue sections is presented. The result is the equation Nv = No/[0.54 X A X (La + t)], giving the concentration of AB in numbers per gram of wet lung tissue. La, the average length (in microns) of the AB, is specific for each case; A is the area (square millimeters) of the tissue counted, and t is the thickness of the section (in microns). This equation fits experimental digestion results to a multiplicative error factor of less than 3. When an estimate of La, such as 51.6 microns, is used, the equation is less accurate but probably sufficiently accurate for the screening of lung specimens.

In plain English

This study presented a mathematical model for estimating the number of asbestos bodies (iron-coated asbestos fibers visible under a light microscope) per gram of wet lung tissue from the number counted in a thin microscope section. The authors tested it on lung tissue from nine patients, six of whom had been described in an earlier report. For each patient, asbestos bodies were counted in two ways: after chemically digesting a known volume of lung, and in a measured area of an iron-stained tissue section. Across all cases, the average asbestos body length was 51.6 microns. The authors reported that predictions from the sections generally agreed well with the digestion counts. Using each case's own length measurements fit only mildly better than using the 51.6-micron average, and the simpler version predicted concentrations within an error multiple of 2 or 3 in their cases. The model also indicated that 5,000 or fewer asbestos bodies per gram are unlikely to be detected by casual search of slides. The authors concluded that the simpler version is accurate enough for screening. They noted that the digested and sectioned tissue came from different parts of the lung.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Methods study: a probabilistic (geometric) mathematical model, checked against laboratory counts from nine patients
• Who was studied: Lung tissue from nine patients, six of whom were described in a previous report; place and time of the cases are not stated
• Exposure: Asbestos bodies in lung tissue, counted by digestion of a known volume of lung and in a known area of a tissue section stained with Prussian blue; fiber types and occupational sources of the patients are not reported
• Main results:
  • For the nine cases combined, the mean asbestos body length was 51.6 microns (maximum 229, minimum 10)
  • Average, minimum and maximum lengths differed between cases, and the difference was statistically significant (P = 0.0001)
  • The combined probability that an asbestos body crosses the section and is recognized ranged from 0.22 to 0.40 (average 0.34)
  • Concentrations predicted from tissue-section counts generally agreed with concentrations measured by digestion
  • The equation using each case's full length distribution fit only mildly better than the equation using the single 51.6-micron average length
  • In the nine cases, the equation predicted concentrations to within an error multiple of 2 or 3
  • The model predicted that concentrations of 5,000 asbestos bodies per gram or fewer are unlikely to be detected by casual search, while concentrations above 10,000 per gram should give on average at least one asbestos body in every 18 high-power fields
• The authors' conclusion: The authors concluded that the simpler equation using an estimated average length of 51.6 microns is less accurate but probably accurate enough for screening lung specimens. They believed it accurate to within a multiplicative factor of 10.
• Limitations the authors state:
  • The tissue used for digestion (from the lung periphery) was not the same as the tissue used for sections (from the lung interior)
  • Section thickness was about 6 microns but probably varied from section to section
  • The model relied on simplifying assumptions: fibers evenly located in the lung, straight fibers, and uniform section thickness
  • The shrinkage correction factor may carry a 20 per cent error and the volume-to-wet-weight factor a 14 per cent error
  • A single digestion is less accurate because it samples only one site

Topics

Medical terms in this study, explained in our Lexicon: Asbestos Body Formation, Asbestos Bodies.

Related studies

• Numbers of asbestos bodies on iron-stained tissue sections in relation to asbestos body counts in lung tissue digests — V.L. Roggli, P.C. Pratt (1983)
• Development of a mathematical model for predicting concentrations of small asbestos fibers — R.M. Buchan, D.C. Richardson, et al. (1984)
• Comparison of feasibility and estimates of central and peripheral nitric oxide parameters by different mathematical models — T. Karvonen, H. Kankaanranta, et al. (2017)
• Pleural plaques and exposure to asbestos: a mathematical model — B. Järvholm (1992)
• Reproducibility of asbestos body counts in digestions of autopsy and surgical lung tissue — M.I. Velasco-García, M.J. Cruz, et al. (2011)
• A model to predict the breathing zone concentrations of particles emitted from surfaces — J. Thornburg, J. Kominsky, et al. (2010)

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