2.1.

Scanning Flow Cytometer

An SFC (Cytonova LLC Company, Novosibirsk, Russia) was used to measure standard FSC and SSC, as well as angular dependence of the intensity of the scattered light in a wide range of polar angles, or angle-resolved LSPs, of individual particles.³¹ Technical features of the SFC were described in detail elsewhere.^27,28 LSPs of individual particles in flow were generated with a 405 nm laser (30 mW, Radius, Coherent Inc., Santa Clara, USA), and FSC and SSC were measured at 488 nm (15 mW laser, FCD488-020, JDS Uniphase Corporation, Milpitas). By considering only the latter signals, we emulate a representative example of a standard flow cytometer. Note, however, that the FSC/SSC collection angles vary a great deal among existing instruments, so the specific gating results of this paper should be generalized with caution. In particular, SFC has the FSC detector integrating over a polar angle of 14.2 to 23 deg and the SSC detector with an NA of 0.5. The corresponding collection angular ranges both for FSC and SSC were estimated from analysis of a mixture of different PS microspheres, similar to that proposed by Fattaccioli et al.,³² and summarized in Table 1.

Table 1

Optical models, methods, and system parameters, used for light-scattering simulations of reference microspheres and plasma MPs.

Within the Mueller-matrix formalism³³ for description of light scattering, the LSP, FSC, and SSC intensities (FSC/SSC peak amplitudes) measured by the SFC are expressed as

The operational angular range in which SFC measures angle-resolved light-scattering information, or LSP, was determined from analysis of $1.87\mu \mathrm{m}$ PS microspheres, as described elsewhere,³⁷ to be from 15 to 50 deg with a resolution of 0.5 deg (Table 1). FSC and SSC threshold levels were set to two standard deviations of the noise in corresponding channels. FSC provided a wider detection range for single-spherical particles (see Fig. 1), and, therefore, was used to trigger the electronics of the SFC. Moreover, we discarded particles with $S/N$ for the LSP signal $<1$ to avoid accidental detection of background noise. Since the LSP is originally a time-resolved signal measured over $600\mu \mathrm{s}$,²⁸ as compared to $<10\mu \mathrm{s}$ for FSC/SSC signals, it allows us to reliably detect coincident events (so-called, swarm detection) and to remove them from further consideration.

Fig. 1

(a) Standard MP gating based on FSC and SSC levels equal to that of an equivalent sphere—gray-colored and hatched regions, respectively. Dashed lines are the FSC (black) and SSC (gray) detection limits, solid lines are upper limits, corresponding to the signal of $1\text{-}\mu \mathrm{m}$ particle with RI of 1.47. The experimental data to illustrate the gating are for three reference PS beads (0.4, 0.7, and $1\mu \mathrm{m}$) and for a spherical fraction of plasma particles, identified using their LSPs. (b) The same gates, but in coordinates of RI versus diameter, computed using the Mie theory. Corresponding particle characteristics are obtained through the solution of the ILS problem.

2.2.

Plasma Microparticles and Reference Particles

To eliminate the impact of preanalytical steps, including loss of MPs during centrifugation, and to preserve natural MP characteristics, we performed MP measurements directly in fresh platelet-rich plasma as described previously.³⁰ The whole blood sample was obtained after informed consent from a healthy volunteer and collected in a vacuum citrate tube (BD Vacutainer Systems, BD, UK). A supernatant of platelet-rich plasma formed in a tube within 2 h of the collection by natural precipitation was carefully collected and diluted by 30-fold in $0.2\mu \mathrm{m}$ filtered (Sartorius Stedim Biotech GmbH, Goettingen, Germany) 0.9% saline containing preliminarily added 0.7 and $1.87\mu \mathrm{m}$ reference PS microspheres. While platelets are removed from consideration after LSP processing based on their size and shape,³⁰ the remaining events may comprise plasma components other than MPs, such as lipoprotein particles (LPs), including chylomicrons, the largest and least dense lipoprotein species.³⁸

We used nonfluorescent polystyrene (PS) microspheres, including Molecular Probes 0.4, 0.7, 1, and $3\mu \mathrm{m}$, and Thermo Scientific $1.87\mu \mathrm{m}$, to determine LSP, FSC, and SSC light acceptance angular ranges, as well as in actual measurements together with MPs. As optical models for both reference beads and MPs, we considered spheres and bispheres—their characteristics and corresponding light-scattering simulation methods are summarized in Table 1.

2.3.

FSC/SSC-Based Particle Characterization

Once intrinsic technical characteristics of FCM are determined, the scatter signals for a homogeneous spherical particle depend only on diameter and RI. Therefore, particle characterization, the so-called inverse Mie problem, boils down to solving the following system of two equations

2.4.

Particle Characterization From Angle-Resolved Scatter Measurements

A more advanced approach is based on simultaneous fitting of experimental LSPs, FSC, and SSC signals by theoretical ones. Unfortunately, the FSC and SSC amplitudes can be used only for spherical particles, because otherwise they depend on the azimuthal orientation angle (in addition to the polar orientation angle $\beta$), in contrast to the LSP, which is integrated over the azimuthal scattering angle [see Eq. (1)]. The inverse light-scattering (ILS) problem was transformed into the global minimization of the following weighted sum of residual squares:

Two global optimization algorithms were used to minimize $S(\mathbf{Q})$: DiRect^37,39 for spheres and nearest-neighbor interpolation using the precalculated database of LSPs for bispheres.⁴⁰ Both algorithms not only determine the best-fit characteristics or their mathematical expectations, but also estimate their errors based on the Bayesian method.⁴⁰ Moreover, estimated uncertainties adequately respond (by larger errors of characteristics) to model errors, e.g., when a nonspherical particle is fitted by a spherical model.³⁷ Applying both shape models to each MP and PS microsphere, we chose the best model based on goodness of LSP fit using the Bayesian information criterion.³⁰

Using the signals for two wavelengths is complicated by the dispersion of RI. To keep the number of characteristics low, we assume that RI at 488 nm is fully determined by its value at 405 nm. In particular, we assume the constant difference for PS microspheres according to the bulk values,⁴¹ i.e., $n(488\mathrm{nm})=n(405\mathrm{nm})-0.023$. By contrast, for MP, we assume the RI dispersion to be comparable to that of the medium, i.e., $n(488\mathrm{nm})=0.99554\times n(405\mathrm{nm})$, which is equivalent to considering a constant RI relative to the medium. To allow direct intercomparison of our results, we further report only $n(405\mathrm{nm})$, even when the originally determined characteristic is $n(488\mathrm{nm})$.

3.1.

FSC/SSC-Based Triggering and Gating

Consider the gating strategy^10,42 based on setting the FSC and/or SSC levels equal to that of a sphere with specific size and RI. We illustrate this strategy in Fig. 1(a), assuming $d=1\mu \mathrm{m}$ and $n=1.47$, together with detection (noise) thresholds. Typically, the values from 1.38 to 1.4 are used as RI of MPs^16,17,26 with no convincing justification. Although the distribution of MPs over RI were obtained with the NTA,⁴³ they are too wide (1.36–1.55) for practical usage. Since this width is due to the uncertainty of single measurements, even mean and mode values of the distributions may be significantly biased. However, there are evidences that in fresh platelet-rich plasma MPs are commonly accompanied by LPs, which have larger RI.²⁴ Hence, we used the value of $n=1.47$ as a tentative upper limit for MPs, e.g., to separate them from LPs.⁴⁴

In the FSC/SSC [Fig. 1(a)] map, we show three reference PS microspheres (0.4, 0.7, and $1\mu \mathrm{m}$) and all spherical plasma particles, identified and characterized using their LSPs. The measurements for PS beads are adequately positioned with respect to the gates, considering the larger RI of PS. Being mapped to size/RI coordinates [Fig. 1(b)], these gates represent curved regions that clearly demonstrate the nonlinear (not even monotonous) dependence of the FSC/SSC signals on particle characteristics. For our instrument, the FSC provides a wider (than SSC) detection range with 200-nm PS microspheres and 300-nm MP at its edge. Size/RI representation of the FSC-based gate is elongated along RI and does not allow one to select particles in a specific range, e.g., plasma MPs with $\mathrm{RI}<1.47$ or in a particular size range. Thus, Fig. 1(b) shows serious limitations of the standard gating strategy, but immediately points to evident improvement, which we name “absolute gating.” The latter operates directly in size/RI coordinates [Fig. 2(a)] and is further transformed into the instrument-specific scatter gates [Fig. 2(b)]. First, we constructed a regular coordinate grid in size/RI and transformed it into the scatter coordinates, showing the complexity of the underlying Mie mapping. In particular, the mapping is not injective; hence, some of the grid lines intersect. Second, we show three exemplary gates: one for $0.4\mu \mathrm{m}$ microspheres and two RI-based gates for the plasma constituents. As mentioned above, the RI values of MPs and their relation to that of LPs are known very poorly. We leave a detailed study of this interesting issue for future research; here we specify the RI ranges ([1.37,1.47] and [1.47,1.58] for MPs and LPs, respectively) rather arbitrarily just to illustrate the capabilities of this strategy. Other meaningful gates can be constructed analogously if a more detailed specification of size and RI ranges is available. The LSP-based sizing is robust but it does not exactly conserve FSC and SSC values, which explains why 15% of plasma components seemingly fall into the wrong FSC/SSC gates.

Fig. 2

Absolute MP gating strategy in terms of size/RI. Three gates are defined in (a): ${\mathrm{G}}_{0.4}$ is $[0.36,0.43]\mu \mathrm{m}$ for diameter and [1.58,1.65] for RI, tentative MP and LP gates (${\mathrm{G}}_{\mathrm{MP}}$ and ${\mathrm{G}}_{\mathrm{LP}}$) are defined by RI ranges [1.37,1.47] and [1.47,1.58], respectively, upper size limit of $1\mu \mathrm{m}$, and lower size limit along the FSC threshold. (b) The same gates in FSC/SSC coordinates together with grid lines of constant size and RI (dashed lines). The experimental data to illustrate the gating are for $0.4\text{-}\mu \mathrm{m}$ PS beads and for a spherical fraction of plasma particles, including MPs and LPs, processed using their LSPs.

Finally, the proposed gating strategy does not always require both FSC and SSC signals to be above the noise thresholds. For instance, a single significant signal (FSC) is sufficient to detect a nonnoise event, and the specific SSC value (up to a noise threshold) does not matter as long as it falls inside the gate [as with ${\mathrm{G}}_{\mathrm{MP}}$ in Fig. 2(b)].

3.2.

Is it Possible to Determine Size and RI from FSC/SSC Measurements?

The natural next step is to invert the Mie mapping from size/RI to FSC/SSC and use it to determine the former characteristics for each measured particle. We theoretically analyzed the feasibility of such a characterization approach in the range $d\in [0.1,1.5]\mu \mathrm{m}$ and $n\in [1.35,1.7]$, covering both MPs and reference PS microspheres. We sampled this range with a $100\times 100$ grid and computed the scatter signals for each grid point. Equations (4) and (5) were then solved, and the resulting number of solutions is shown in Fig. 3(a). For the current SFC optical configuration, the solution is unique only for a limited range of characteristics, part of which is below the instrument detection limits. Even if a solution is unique or a proper one can be selected based on a priori information, such as a narrow size or RI range, its usefulness is determined by estimation uncertainties. The latter are plotted in Figs. 3(b) and 3(c), showing that for single-spherical particles with $n\ge 1.5$, including silica or PS microspheres, size, and RI could be deduced with relative standard deviation less than 10%. However, in the range of MPs, uncertainties may exceed 30%, mostly due to the $S/N$ ratio decreasing with both size and RI. There is also an inherent limitation related to the Rayleigh scattering regime (particles much smaller than the wavelength), at which all optical properties are determined by particle polarizability.³³ The latter is a function of size and RI, which cannot be discerned individually from any optical measurements (with a given wavelength). More specifically, the relative sensitivity of inverse mapping (uncertainties for a constant $S/N$ ratio) increases approximately as $d^{-2}$ (considering only the first two terms of the Mie series). Coupled with $d^6$ scaling of the scatter signals, it results in very unfavorable scaling of uncertainties as $d^{-8}$ for a constant noise level. While there is no hard boundary, we calculated a tentative one corresponding to 100% uncertainties of either $d$ or RI for a noise level ${10}^4$ times smaller than the current one. It is indicated by the black color in Figs. 3(a)–3(c).

Fig. 3

(a) Contour plot of number of solutions (ambiguity) of inverse Mie problem for a sphere from FSC/SSC measurements versus its size and RI. Current FSC and SSC detection limits are also shown. (b) and (c) are same as (a), but for relative uncertainty (standard deviations) of size (top) and RI (bottom) estimates, assuming constant noise amplitudes in scatter channels (based on experimental data). (d)–(g) Typical examples illustrating the cases of unique and multiple solutions, including single PS microspheres [$d=0.4$, 0.71, and $0.9\mu \mathrm{m}$ with $n=1.628$—(d), (f), and (e) respectively] and a potential MP (g) with $d=0.7\mu \mathrm{m}$ and $n=1.45$. The solutions are shown as intersections of constant-level curves for FSC and SSC.

Finally, Figs. 3(d)–3(g) show typical examples corresponding to different multiplicities of the solution. For instance, the SFC cannot resolve a $0.71\text{-}\mu \mathrm{m}$ PS microsphere and a particle of $d=1.32\mu \mathrm{m}$ and $n=1.515$ based on FSC/SSC measurements. However, the ambiguity can be removed if one assumes the material to be PS (hence, restricting RI to a narrow range). For a $0.9\text{-}\mu \mathrm{m}$ microsphere, a second solution is closer and cannot be easily gated out. The number of solutions generally increases with decreasing RI; an example of a potential MP is given with four solutions, three of them forming a single-confidence region.

3.3.

Characterization of Single Particles: FSC/SSC versus Angle-Resolved Light Scattering

The goal of this section is to show the effect of particle shape (nonsphericity) on the characterization results. For that, we applied both FSC/SSC- and LSP-based approaches to characterize measured PS microspheres (0.4 and $0.7\mu \mathrm{m}$) and plasma MPs. MPs are known to be present in plasma not only as spheres, but also as dimers (doublets) of spheres and more complicated shapes.^24,25,30 Similarly, 5% of PS microspheres were in a form of dimers, despite sonication. We show in Fig. 4 several illustrative examples from our data that were unambiguously identified as either monomer or dimer of spheres, based on their LSP. For presented single-spherical particles, both FSC and SSC signals were above the noise threshold, and the solution of the corresponding inverse Mie problem is either unique or can be made such by prior RI gating. Moreover, both approaches led to similar results for size and RI within their uncertainties.

Fig. 4

Application of FSC/SSC-based (g)–(i) and angle-resolved LSP-based (a)–(f) characterization to single-submicron particles, including 0.7 (top) and $0.4\mu \mathrm{m}$ (middle) PS microspheres, and plasma MPs (bottom). The solutions of corresponding ILS problems are demonstrated for single-spherical particles (a)–(c) and their dimers (d)–(f). Experimental and best-fit theoretical LSPs (for sphere and dimer models), as well as estimates of particle characteristics (mathematical expectation ± standard deviation) of the best-fit model are also shown. (g)–(i) FSC/SSC-based solutions shown as intersections of constant-level curves of FSC/SSC scatter intensities. In (i), those curves are almost the same for the considered particles.

By contrast, dimers highlight the difference between the two approaches. LSP measurements allow one to identify and accurately characterize those dimers, while FSC/SSC approach results in a predictable failure. For presented dimers of 0.4- and $0.7\text{-}\mu \mathrm{m}$ PS spheres, both the resulting size and RI are wrong. In principle, the presence of dimers of PS beads (or other monodisperse particles) is not an issue, since those dimers can be easily identified and removed from consideration based on their larger FSC and SSC intensities or on resulting characteristics falling outside of the expected range [Figs. 4(g) and 4(h)]. The situation is markedly different for polydisperse samples, such as MPs. We have chosen two events, corresponding to a dimer of MPs and a single denser spherical MP (probably, an LP one), having almost the same FSC and SSC signals [overlapping constant-level FSC/SSC curves in Fig. 4(i)]. Hence, FSC/SSC-based characterization has no capabilities whatsoever to distinguish between those two events.