Steven G. Ackleson is with Bigelow Laboratory for Ocean Science, ..... References. 1. J. E. Tyler and R. C. Smith, Measurements of Spectral Irradi- ance Under ...
Size and refractive index of individual marine particulates: a flow cytometric approach Steven G. Ackleson and Richard W. Spinrad
Flow cytometric measurements of light scatter, near-forward light scatter ( = 1.5-19°) and side scatter (0 = 73-107°), from individual marine particles is modeled using Mie theory. Particles are assumed to be homogeneousand nearly spherical in shape. Uniform polystyrene microspheres and oil suspensions are used to estimate model accuracy. Within the particle diameter range of 1-32 gm, the mean error for near-forward scatter and side scatter is 16.9% and 30.1%, respectively. The model is used to estimate size and refractive index of several nannoplankton species and the results are compared with microscopic measurements of cell
size and published values of phytoplankton refractive index. Within the refractive-index range of 1.01-1.1, the model may be inverted to yield refractive index with an absolute error of between 0.01 and 0.003. Measurements of particle size distributions in clear ocean water indicate this range accounts for 99% of all nannoplankton and 39% of all particles within the size range from 1 to 10 im.
1.
Introduction
Optical oceanography has progressed to the point where it is now necessary to know the inherent optical properties of individual marine particles. Suspended particles, to a large extent, determine the apparent and inherent optical properties of all but the clearest natural waters. Recently, several research programs have been conducted with the intent of measuring the spatial and temporal variability of inherent and apparent optical properties of natural waters.'-4 These works were concerned with collecting accurate measurements of inherent and apparent optical properties of estuarine, coastal, and open ocean waters. In spite of this high quality optical data representing a large range of water types, our knowledge of the optical properties of individual marine particles remains limited. Historically, the study of single-particle optics has been addressed indirectly by measuring directional scatter from sample volumes containing many particles. The associated inverse problem, determining the optical properties of individual particles from volume scattering measurements, requires a priori knowledge
Steven G. Ackleson is with Bigelow Laboratory for Ocean Science, West Boothbay Harbor, Maine 04575. Richard W. Spinrad is with U.S. Office of Naval Research, 800 N. Quincy Street, Arlington, Virginia, 22217-5000. Received 23 December 1987. 0003-6935/88/071270-08$02.00/0. ( 1988 Optical Society of America. 1270
APPLIEDOPTICS / Vol. 27, No. 7 / 1 April 1988
of the sample, e.g., particle size distribution, shape, and refractive index.5 -7 However, because the volume scattering function represents the cumulative effect of scatter from many particles within the sample volume, any resulting information concerning the scatterers will also be a cumulative measure. Yet, such a measure may not accurately describe the optical properties of a single particle. The greater the diversity of particles within a sample the greater the uncertainty about the optical properties of any single particle within the sample. An additional problem within a suspension rich in particle diversity'is that some particles, e.g., phytoplankton, may change optically as a result of life cycle and environmental factors. Kiefer et al.8 have mea-
sured variability in diffuse absorption and backscatter within cultures of Thalassiosira pseudonana. and Monochrysis lutheri which are related to age and growth rate. Yet, it is likely that such changes in bulk optical properties may only be measured in relatively pure cultures. As the diversity in particle population increases, the overall effect of any one group of particles should be expected to decrease. Spinrad and Yentsch,9 using flow cytometry, were able to measure multiple-angle light scatter from individual cells of marine phytoplankton. By gating on simultaneous measurements of fluorescense, plankton cells could be
distinguished from all other particles and the associated light scatter isolated. Spinrad and Yentsch found, similar to the results of Kiefer et al. 8 based on bulk optical measurements, that single-cell light scatter varies with the cell growth cycle.
54
=1
S3
,1
(
= 73-107")
,)
-,C
,,,
Fig. 1. ;)'))3C'IRATI)N
Coulter EPICS V flow cytometer measures
single-particle near-forward light scatter (S3 = 1.5-19°) and side scatter (OS4 = 73-107°). Individual particles are injected into a fluid stream and
13))
illuminated at right angles with an argon-ion laser
beam operating at 514 am. Light scatter from the air-stream interface is blocked by positioning an obscuration bar across the entrance to each detector.
Flow cytometry, originally developed in the 1960s and 70s for biomedical research, is a procedure to
The laser focusing assembly forms an elliptical beam at the fluid stream having a horizontal dimension of
rapidly measure directional light scatter and fluores-
130 gm and a vertical dimension of 16 Am. Particles
cence from individual particles. Information may be collected rapidly for a large number of discrete parti-
cles-sampling rates exceeding 1000 particles/s and
injected into the stream are illuminated one at a time as they pass through the laser beam. Because the laser beam is Gaussian, particle light scatter is detected by
operating ranges of 1-150 gm are not uncommon.
In
the near-forward and side sensors as an intensity curve
marine research, flow cytometry has been used successfully to identify and sort subpopulations of phytoplankton from samples of seawater based on characteristic scattering and fluorescence.10' 1 1 With particle fluorescence measurements collected simultaneously with light scatter it becomes possible to identify light
with the passage of each particle. Light scatter is recorded as the peak height of the intensity curve. The near-forward detector is a photodiode and scatter signal is amplified using a linear amplifier. The sidescattered light is measured with a photomultiplier tube and the signal may be amplified using either a linear or logarithmic transformation. In all cases data
scatter from pigment-containing
cells. Flow cytome-
tric measurements of multiple-angle light scatter have yielded information concerning the size, shape, and
are stored as channel values ranging from 0 to 255.
ble to translate single particle light scatter measured at
positioning an obscuration bar in front of each collecting lens.
internal geometry of live cells.12-16 Recent flow cytometric studies have shown it possi-
two angles into particle refractive index and size. 17' 18
Tycko and others,18 in their work with near-forward angle light scatter from red blood cells, pointed out
that the range in particle refractive index and size is a function of view angle. The purpose of this work is to
develop a similar two-angle light scatter method employing near-forward light scatter and side scatter to measure the size and refractive index of individual marine particles. II.
Flow Cytometer
The standard Coulter EPICS V flowcytometer measures single-particle light scatter simultaneously in two angular ranges, 0 = 1.5-19° and 0 = 73-107°, denoted here as S3 and S4, respectively (Fig. 1). (In
addition, the flow cytometer is capable of measuring light scatter in two narrow near-forward directions, Si and S2, but these will not be discussed in this work.) Particles are hydrodynamically focused and injected one at a time into the core of a narrow stream of
microfiltered saline solution. The fluid stream containing the procession of particles is then intersected in air at right angles by a narrow argon-ion laser beam polarized parallel to the fluid stream. The laser was operated at 514 nm with a power of 100 mW.
Scatter from the air-fluid interface of the stream is confined to the plane of illumination and is prevented from entering either of the light scatter detectors by
Ill.
Theoretical Considerations
Light scatter from a single particle is defined by the differential scattering cross section, dCsca/dQ(using nomenclature of Bohren and Huffman19 ). Light scatter occurs as a result of discontinuities
in refractive
index, expressed in complex form as n' + in". Light absorption within the particle is accounted for within the imaginary component of the refractive index, n" = aX/47r,where a is the absorption coefficient and Xis the
wavelength of the incident light. The differential scattering cross section is also a function of particle size (D = equivalent spherical di-
ameter), shape, and homogeneity. Within narrow size ranges, depending on particle refractive index, it may be possible to develop linear relationships
between
dCsca/dQand particle size. In general, however, the actual governing relationships are nonlinear. Perhaps the least is known about the effects of particle shape and homogeneity on dCsca/dQ. Within a flow
cytometer, the problem posed by particle shape and homogeneity may be compounded by the orientation of the particle as it is injected into the fluid stream. Presently, these problems lie beyond the scope of this 1 April 1988 / Vol. 27, No. 7 / APPLIEDOPTICS
1271
work and discussions will be limited to the special case of spherical, homogeneous particles. Light scatter measured by the Coulter EPICS V flow cytometer, stored as channel values, is scaled by changing the detector gains and/or the laser intensity.
light ray would be intercepted by a detector. This procedure was repeated 105 times. The number of rays scattered into each increment of 0 was summed as was the associated number of times a ray was collected
Channel values in themselves offer only a relative mea-
ratio of intercepted light scatter to total scattered light for each increment of 0. The total differential scatter-
sure of light scatter. For a detector i, the intensity of scattered light from an unknown particle p, recorded by the flow cytometer, may be expressed as the linear function SW
= X(i)I(i)pG(i)p(dCsca/dQj)p,
by a detector.
ing cross section as measured by each detector was
then computed by summing the product W(6)dCsca/dQ within the range of 0 for each detector: 19°
(1) dCsca/dgs3
where S(i)p is channel value, 1(i) is the laser intensity, G(i) is the detector gain factor, and (dCsca/di)p is the
differential scattering cross section. The term X(i) is a constant and may be thought of as a dustbin into which is swept all other factors pertaining to instrument optics such as filter transmissivity and lens efficiency. A similar relationship may be written for a well-defined reference particle, r, for which size, shape,
and refractive index are known:
Sir = X()I(i)rGj)r(dCsca/dQi)r,
G(i) (dCsca/dQi)r
(2)
Z
=
V.
(5)
Model Verification
A test of the Mie scattering model accuracy requires particles which are spherical and homogeneous and test the effect of particle size, spherical polystyrene particles were used. Samples ranged in size from 1 to
(3)
1.19 relative to water given 514-nm illumination. Hydrocarbon dispersions were used to test the effects of refractive index where n' ranged from 1.044 to 1.069 (Table II). Table 1. Uniform PolystyreneMicrospheres
Coefficient of
Mean Brand PS SER COU COU SER PS SER PIS COU SER PIS SER SER COU PIS
Much of this work is a further
refinement of algorithms developed by Dave.2 0 The model is programmed on a Micro Vacs II computer and
yields differential scattering cross section as measured by the flowcytometer near-forward and side detectors. Effects of the obscuration bar as well as refraction and internal reflection at the fluid-air interface are accounted for.
Differential scattering cross section is computed in 10 increments across the view range of each detector.
Because the particles are assumed spherical, light scatter is constant with respect to azimuth. For each 10
increment, only a portion of the light scattered
Lot no. 42193 4N1A 5010 5055 5MIN 43758 3A2F SR-10 1745 2P2T 36388 4N1B 4N1C 1625 SR-30
Table II.
developed to estimate the percentage of scattered light intercepted by the near-forward and side detectors for each 1 increment in scattering angle. A pair of ran-
APPLIEDOPTICS / Vol. 27, No. 7 / 1 April 1988
(#110256) (#17135) (#187310) (#47864) (#17136) (#47872) (#47880)
S3 (%)
S4 (%)
1.5 2.0 2.02 5.0 5.0 5.6 7.0 9.8 9.88 10.0 10.12 15.0 20.0 20.15 32.2
5.8 3.2 3.0 3.7 3.8 6.1 4.1 18.0 3.7 4.5 11.8 3.1 3.9 6.1 16.5
12.9 11.9 10.2 16.2 15.0 21.3 9.1 25.5 12.2 35.5 21.0 17.2 31.7 12.2 31.4
PIS = Particle Information Services
A Monte Carlo simulation was
dom numbers was generated and used to compute values for and , thus defining a scatter direction. A test was then performed to determine if the scattered
(#17133) (#47831)
variation
Diameter (m)
PS = Polyscience SER = Seragen Diagnostics COU = Coulter
through 3600 azimuth is collected and recorded by either the near-forward or side detector. A portion of the excluded light scatter is intercepted by the obscuration bar and, at the air-stream interface, a portion is internally reflected and a portion is refracted out of the
1272
W(0)dCsca/dQ.
0=73o
The Mie scattering model is based on algorithms developed by Bohren and Huffman'9 for spherical,
range of the detector.
(4)
107°
dCsca/dQs4
Mie Scattering Model
homogeneous particles.
W(O)dCsca/dg,
0=1.5°
37 Am (Table I). The refractive index of polystyrene is
In other words, flow cytometer channel value may be converted to differential scattering cross section using Mie scattering theory tailored to the specific flow cytometer and an appropriate reference particle. IV.
E
=
which are well defined in size and refractive index. To
Combining Eqs. (1) and (2) yields (dCsca/d~2i)p= S(i),I(i)
A function W(6) was then formed as the
*
Refractive Index of HydrocarbonDispersions
Published refractive
Estimated refractive
Hydrocarbon
index*
index
Heptane Nonane Dodecane
1.044 1.057 1.069
1.043 1.054 1.070
CRC HANDBOOK OF CHEMISTRY AND PHYSICS (1975)
5]
43
(n '
3 U.'
0
0 (3
219
1-4
0 -J
-1
-2 -
-11. . 5
10
15
20
25
30
I II . 35
I .I
I III 40
PARTICLE DIAMETER (Urn) Fig. 2. Comparison of measured (data points) and predicted (solid lines) differential scattering cross section from polystyrene particles 0 measured by the Coulter EPICS V flow cytometer. The upper curve is near-forward angle light scatter ( S3 = 1.5-19°) and the lower curve is 6 side scatter ( S4 = 73-107°). Bars indicate the 90% confidence interval for each measurement where the number of observations is 10,000.
A.
Polystyrene Particles
Of the fifteen samples of polystyrene particles, one was selected as the reference particle and used to com-
pute differential scattering cross sections for the remaining fourteen. All the samples appeared to be highly uniform in size, as measured with a Coulter
counter, and shape, as determined with microscopic observations. In each case, light scatter histograms were unimodal and coefficients of variation ranged between 3% and 18%for near-forward scatter and between 9% and 32% for side scatter. Seragen 5.0-gm particles were selected as the reference particle because they produced low coefficients of variation in
both near-forward scatter (4%) and side scatter (15%) and because they were near the middle of the distribution in sample particle size.
Model predictions of differential scattering cross section from polystyrene particles are compared with flow cytometric estimates in Fig. 2. The absorption
coefficient was assumed to be zero. Within the near-
forward direction mean error was 16.9% and r 2 = 0.95. Within the side-direction mean error was 30.1%and r 2 = 0.88. Assuming that errors due to instrument noise and geometry are small, a cause of error within Fig. 2
Gaussian, as in a laser beam. When the particle diameter and the laser beam diameter are of the same order in magnitude it has been demonstrated that Mie theory does not apply.2 2 Since the beam horizontal and vertical dimensions are 130 and 16 gim, respectively,
this would present a problem for larger particles. Error due to an inhomogeneous light field would be ex-
pected to increase with D for particles larger than 16 gim. For the particle size range investigated here, 1.532.2,gm,this error is probably small because the horizontal dimension of the laser beam was large relative to the diameter of the particles. Differences between predicted and observed dCsca/dQdid not increase with particle size. B.
Hydrocarbon Dispersions
Hydrocarbon dispersions of heptane, nonane, and dodecane were prepared by adding one drop of oil-to 10
mliter of microfiltered saline solution and shaking vigorously. This resulted in a suspension of oil droplets, spherical in shape and ranging in size from -1 to 40 gim,as verified with microscopicinspection. The published refractive indices of heptane, nonane, and dodecane are 1.0435, 1.0567, and 1.0689, respectively. 2 3 As
in the polystyrene microspheres, absorption within Each oil sample,
may lie within the assumption of Mie scatter theory, that the spatial distribution of the plane wave imping-
each oil was assumed to be zero.
ing on the particle be homogeneous. 21 This is clearly
therefore, represented a continuum of particle size and constant refractive index. When near-forward light
not the case where the distribution of light intensity is
scatter is plotted vs side scatter, each oil suspension 1 April 1988 / Vol. 27, No. 7 / APPLIEDOPTICS
1273
5
10
8
4
0 1. 09
I1
_
0 o
x 3
- 2 tJ
U
4
2 a_
O
0
a q
1-21I-
1.01 O4
I 0
I
X
1
2
3
I 4
I 6
I 7
CscOM(3)
X 1 7
I 5
I 8
r 9
10
11
12
Fig. 3. Flow cytometric measurements of differential scattering cross section from three oil suspensions: heptane (H, n' = 1.0435); nonane (N, n' = 1.0567); and dodecane (D, n' = 1.0689). The background grid represents Mie scatter computations where solid lines indicate constant
refractive index (n + i) and dashed lines indicate constant droplet size.
produces a characteristic droplet size only.
curve that is a function of
To test the effects of particle refractive index, Seragen 5-gm particles were once again used to convert flow
cytometer channel values of oil droplet light scatter to differential scattering cross sections and the resulting oil suspension curves projected onto a grid showing the model response to changing particle size and refractive index (Fig. 3). Each oil suspension curve projected
parallel to theoretical curves of equal refractive index. The mean refractive index of each oil type was estimated from the representative scatter curves and the results are included in Table II as a comparison with published values. Differences between predicted and published values of refractive index were 0.001, 0.003,
and 0.001 for heptane, nonane, and dodecane, respectively. VI.
Discussion
A weakness within the model may result from the assumptions of particle sphericity and homogeneity, conditions which are not typical of natural populations. An important question at this point concerns how well the model estimates the refractive index and size of near-spherical planktonic cells. To address this question inocula of three phytoplankton species,
Emiliania huxleyi (BT6), Thalassiosirapseudonana (3H), and Dunaliella
tertiolecta
(DUN), were ob-
tained from the Center for the Culture of Marine Phytoplankton, Bigelow Laboratory. Cultures were incubated in 500-mliter glass flasks using sterile F/2 medium2 4 and stored in an illuminated water bath at 1274
APPLIEDOPTICS / Vol. 27, No. 7 / 1 April 1988
20°C with a 14:10-hlight:dark cycle. Light intensities during the light cycle were -4 mW cm 2 . When the cultures were determined to be in exponential growth phase 10-mliter samples were pipetted from each and run through the flow cytometer. Immediately before and after each sample Seragen 5.0-gm polystyrene particles were also run through the flow cytometer and used as a scattering standard. Flow cytometric measurements of cell near-forward scatter (S3) and side scatter (S4) were then converted to differential scattering cross section and the results projected onto a 2D grid of theoretical differential scattering cross sec-
tion in a manner identical to the hydrocarbon suspensions (Fig. 4). The imaginary part of the refractive index used to compute the grid was n" = 0.01, which is identical to values representing phytoplankton reported by Brown and Gordon2 5 and somewhat larger than values reported by Jonasz and Prandke2 6 (0.005), Morel and Bricaud 2 7 (0.003-0.007), Bricaud et 28 al. (0.003-0.005). Using this projection it was possi-
ble to estimate ranges in cell refractive index and size (Table IV). Next, microphotographs were taken of stained samples from each culture and used to estimate cell size (Fig. 5). These results are also shown in
Table IV as a comparison with the flow cytometric estimates of cell size. BT6 is a coccolithophore which, when cultured in F/
2 media, is denuded of calcium carbonate platelets leaving nearly spherical cells with soft membranes. This was confirmed with microscopic analysis and cell diameter was found to be 4.3 gm. The flow cytometric
analysis estimated BT6 cell size to be between 3.6 and
5 j-
40
-
8
1. 09
:
1.05
x 3 -t : 2 00
1.03
Z-
-j
1.01
1-
0-
T-
-.-T--
Csca(S3) Fig. 4.
6
5
3
2
0
7
8
9
10
X 10
Flow cytometric measurements of differential scattering cross section from three species of phytoplankton, Emiliania huxleyi (BT6),
Thalassiosira pseudonana (3H), and Dunaliella tertiolecta (DUN). The background grid represents Mie scatter computations where solid lines indicate constant refractive index (n' + 0.01i) and dashed lines indicate constant cell size.
Table IlIl. Percentage of Sargasso Sea Particles IncludedWithin the Mie Range: D = 1-10 jm andd = 1.01-1.1 ModelSingularity Scattering
0.1-100 (Am) Number of organic particles
0.14%
Number of all particles
0.07
0.5-50 (AM)
1-20
14%
99%
5.9
Flow Cytometric Estimationsof Cell Refractive Index and Size
Table IV.
pseudonana(3H), and Dunallella huxleyl (BT6), Thalasslosira for Emilianla tertlolecta(DUN)
(m)
39
BT6 3H DUN
n'
D (mm)
DM* (m)
1.05-1.058 1.06-1.065 1.062-1.065
3.6-3.9 3.7-4.1 5.0-5.5
4.3 3.4 X 6.0 7.5 X 11.5
* DM = microscopic measurement Volume of organic particles
28
41
69
Volume of all particles
11
16
26
C
0
!0,.
Fig. 5. Microphotographs ofthree speciesofphytoplankton,Emiliania huxleyi (BT6;A),Thalassiosirapseudonana (3H;B), andDunaliella tertiolecta (DUN;C). 1 April 1988 / Vol. 27, No. 7 / APPLIEDOPTICS
1275
3.9 gim. Refractive index ranged between 1.05 and 1.058.
The diatom 3H has a pillbox structure composed of silica and microscopic analysis estimated a size dimension of 3.4-gm diameter and 6.0-gm length. This compares with a flow cytometric estimate of cell size between 3.7 and 4.1 gim. Flow cytometric estimation of
3H refractive index ranged between 1.06 and 1.065. DUN is an elliptical, soft membraned cell of slightly larger dimension than either BT6 or 3H, 7.5 by 11.5 im, as indicated by microscopic analysis.
Flow cyto-
metric analysis estimated cell size of DUN to range between 5.0 and 5.5 gm and n' = 1.062-1.065. Within natural waters the real component, n', for organic particles is believed to range between 1.01and 1.09 while, for inorganic particles, n' > 1.15.6,7,29 Within the organic particle range, phytoplankton having skeletal material composed of calcium carbonate or silica would be expected to have higher refractive indi-
ces while cells containing no skeletal material should
exhibit lower refractive indices.
Spinrad and
Brown,'7 using the slope of the distribution of log(S3) vs S4, estimated the refractive index of six species of marine algae and n ranged between 1.047and 1.086. These observations agree, in general, with the flow cytometric results presented here. The diatom 3H has a hard silica test while BT6, although similar in size, was denuded of any hard structures. It follows,therefore, that the refractive index of 3H should be greater than BT6, which is consistent with the flow cytometric results. DUN, on the other hand, has no hard structure yet the refractive index appears to be similar to 3H.
Although some interspecies differences in cell refractive index may be related to the amount of hard structural material present, other factors probably play equally important roles. Intraspecies changes in differential scattering cross section have been attributed to rearrangements of internal structures.12'3 0 Some intracellular structures have higher refractive indices than others and so cell refractive index should not only be a function of how these structures
are
arranged within a cell but the type and amount of structural material present. Carder and others6 attributed the greatest intracellular refractive index to the cell wall. It seems reasonable that other cellular membranes, e.g., those of the nucleus and chloroplasts, would also account for larger refractive indices. It is possible that the higher refractive index of DUN relative to 3H may be the result of a higher percentage of cellular membranes, but clearly more work must be conducted to further our understanding of the optical effects of internal cellular structure. It appears possible that flow cytometric measurements of near-forward light scatter (S3) and side scatter (S4) may be used to invert the Mie scatter model within the particle size range of 1-10 m and refractive index range of 1.01-1.1 when cells may be assumed
spherical and homogeneous. With larger particle size and refractive index the model is not singular and the doublet S3:S4 does not necessarily yield a unique dou1276
APPLIEDOPTICS / Vol. 27, No. 7 / 1 April 1988
blet D:n'. Particles of
