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Correcting the Relative Bias of Light Obscuration and Flow Imaging Particle Counters

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Abstract

Purpose

Industry and regulatory bodies desire more accurate methods for counting and characterizing particles. Measurements of proteinaceous-particle concentrations by light obscuration and flow imaging can differ by factors of ten or more.

Methods

We propose methods to correct the diameters reported by light obscuration and flow imaging instruments. For light obscuration, diameters were rescaled based on characterization of the refractive index of typical particles and a light scattering model for the extinction efficiency factor. The light obscuration models are applicable for either homogeneous materials (e.g., silicone oil) or for chemically homogeneous, but spatially non-uniform aggregates (e.g., protein aggregates). For flow imaging, the method relied on calibration of the instrument with silica beads suspended in water-glycerol mixtures.

Results

These methods were applied to a silicone-oil droplet suspension and four particle suspensions containing particles produced from heat stressed and agitated human serum albumin, agitated polyclonal immunoglobulin, and abraded ethylene tetrafluoroethylene polymer. All suspensions were measured by two flow imaging and one light obscuration apparatus. Prior to correction, results from the three instruments disagreed by a factor ranging from 3.1 to 48 in particle concentration over the size range from 2 to 20 μm. Bias corrections reduced the disagreement from an average factor of 14 down to an average factor of 1.5.

Conclusions

The methods presented show promise in reducing the relative bias between light obscuration and flow imaging.

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Notes

  1. Certain commercial equipment, instruments, or materials are identified in this document. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the products identified are necessarily the best available for the purpose.

Abbreviations

a 1 … a 4 :

Parameters in Eq. 10

A p :

Projected area of a particle

b :

Feret diameter

b max :

Maximum Feret diameter of a particle consistent with constructive interference of light scattering

c :

Measured diameter minus actual diameter of silica beads

C d :

Correction factor for refractive index related to particle diameter, Eq. 3

C sca :

Scattering cross section

C w/t :

Correction factor for refractive index related to particle width-to-thickness ratio, Eq. 3

d :

Diameter

d act :

Actual diameter

d c :

Cut-off diameter, above which Q is obtained by a scaling relation

d meas :

Measured diameter

d trans :

Transformed diameter

F :

Fraction of pixels with largest absolute magnitude of ϕ

G :

Parameter to assess validity of RGD theory, G = 2kl(m – 1)

k :

Wavenumber, equal to 2π/l

l :

Largest characteristic length of a particle

m :

Reduced refractive index, equal to the ratio of the refractive index to the refractive index of the matrix liquid

n p :

Average refractive index of a particle immersed in a matrix liquid

n l :

refractive index of the matrix liquid

N(d):

Cumulative particle size distribution, equal to the number of particles per unit volume of equivalent diameter d or larger

Q :

Extinction efficiency factor

Q PSL :

Extinction efficiency factor for polystyrene latex beads

Q’:

Modified extinction efficiency factor equal to the total scattering beyond the aperture angle, divided by the average projected area of a randomly oriented spheroid.

r ij :

Distance between spheres i and j

R N :

Ratio of the maximum and minimum values of N(d)

x,y :

Orthogonal distances perpendicular to the optical axis

t :

Particle thickness of a gravitationally settled particle

w :

Particle width, equal to the minimum Feret diameter, of a gravitationally settled particle

z :

Distance along the optical axis

z p :

Thickness of a particle in the z direction

α :

Minimum angle for light to be scattered out of a light-obscuration detector

Δn :

Refractive index of a particle minus the refractive index of the matrix fluid

η :

Aspect ratio of minor to major axis.

θ :

Scattering angle

λ 0 :

Wavelength in vacuum

λ :

Wavelength in the matrix fluid

ϕ :

Optical phase thickness

ETFE:

Ethylene tetrafluoroethylene

FI:

Flow imaging

HEPES:

2-[4-(2-hydroxyethyl)piperazin-1-yl]ethanesulfonic acid

HSA:

Human serum albumin

IgG:

Immunoglobulin G

LO:

Light obscuration

PFA:

Perfluorinated alkoxy

PMMA:

Poly(methyl methacrylate)

PSL:

Polystyrene latex

PVDF:

Polyvinylidene fluoride

QPI:

Quantitative phase imaging

RGD:

Rayleigh-Gans-Debye

SDS:

Sodium dodecyl sulfate

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ACKNOWLEDGMENTS AND DISCLOSURES

We thank Wyatt Vreeland of the National Institute of Standards and Technology for helpful comments, Robert Fletcher of the National Institute of Standards and Technology for assistance with aperture measurements, and Nathan Vandesteeg of Baxter Healthcare for further details of his work.

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Authors and Affiliations

  1. Biomolecular Measurement Division, National Institute of Standards and Technology, Gaithersburg, Maryland, USA

    Dean C. Ripple

  2. Center for Computational and Systems Biology, Institute of Biophysics, Chinese Academy of Sciences, Beijing, China

    Zhishang Hu

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  1. Dean C. Ripple
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Correspondence to Dean C. Ripple.

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Ripple, D.C., Hu, Z. Correcting the Relative Bias of Light Obscuration and Flow Imaging Particle Counters. Pharm Res 33, 653–672 (2016). https://doi.org/10.1007/s11095-015-1817-9

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