Spatial Encoding with Amplitude Modulation in Serial Flow Cytometry

Highlights

What are the main findings?

• We validate amplitude modulation–enabled frequency multiplexing of multiple-region flow cytometry to a single photodetector as a solution to reduce serial cytometer complexity, bulk and cost.
• Detected particles were measured with over 97% analysis yield and imprecisions in the range of 0.53% to 2% despite using reduced excitation power.

What are the implications of the main findings?

• Amplitude modulation is shown to be compatible with serial flow cytometry, including particle region decoding and uncertainty quantification.
• This technology simplifies optofluidic design for multi-region optical readouts and enables approaches using single detectors and wide-field detection.

Abstract

Serial flow cytometry was recently introduced as a method that can estimate measurement uncertainty (i.e., imprecision, the coefficient of variation of repeated measurements of individual particles) independent from population characteristics. Replication of light sources and detectors at multiple sites along a flow cytometer’s microchannel requires more equipment and can complicate detector synchronization. Here, we introduce amplitude modulation to encode each region of a serial cytometer with a unique carrier frequency, which enables demultiplexing of the combined signal incident on a single photodetector by fast Fourier transform (FFT) peak magnitude. To facilitate validation of detection, matching, and uncertainty quantification of fluorescence signals, we designed a microfluidic amplitude modulation (AM) serial flow cytometer that has ground truth detectors on individual regions (serial cytometry) in parallel with the combined channel detection for AM demultiplexing. With this report, we present metrics for event detection and dynamic range, prevalence and processing of overlapping detections, region-decoding accuracy, process yield, and uncertainty quantification on a brightness ladder of calibration microspheres. Despite being operated with reduced light intensities, the AM cytometer was capable of high-fidelity performance in comparison to conventional serial cytometry. For events above the detection limit, over 97% were analyzed. Both conventional and AM serial cytometers achieved median imprecisions in the range of 0.53% to 2.1% after outlier removal, which was well below the inherent intensity distribution of any of the microsphere subpopulations. Overall, AM cytometry supports uncertainty quantification and temporal analyses of serial cytometry data with a reduced number of photodetectors, which offers simplification of chip design with multiple measurement regions and wide-field detectors.

1. Introduction

Flow cytometry is an indispensable tool that supports high-throughput data collection for numerous applications in biomanufacturing, immunological therapeutics, and biomedical research [1,2,3,4,5]. The technology is of high value in the development of drugs and immunotherapies and the detection of cancer, and ultimately it enables decision-making that affects life and death [6,7]. At its core, flow cytometry addresses classification problems, i.e., challenges of identifying to which group or class a particular sample belongs, a crucial step in detecting, characterizing, or purifying cells with desired properties. In conventional cytometry, population variability is confounded with measurement uncertainty, which leads to challenges interpreting data from different instruments, as our research group has recently highlighted [8,9]. In flow cytometry, a stream of particles (e.g., cells) typically flows single file through an illuminated measurement region. The particles may be labeled with fluorescent dyes (often attached to antibodies) to reveal the presence or activity of a particular biomarker. Emitted, transmitted, and scattered light are collected, providing estimates of per-particle fluorophore abundance, size, and granularity [10]. Improvements in flow cytometry have historically expanded upon the technology’s fundamental strengths of throughput, breadth of categorization, and types of sample [11].

Modern commercial instruments continue to gain new functions and technologies which can fundamentally change metrological performance [12]. New functions include spectral cytometry [13] and imaging cytometry [14], as well as inertial [15], acoustic [16], and viscoelastic focusing [17] that augment or replace hydrodynamic focusing. Instruments now leverage optofluidic technologies [18,19,20,21,22,23,24,25,26,27] and advances in high time-resolution photoelectronics [28,29,30]. Additional techniques include new spectral barcoding approaches for metasurface-enabled fluorophore detection [31] and multi-pass particle identification [32]. Such modifications empower instruments for new applications, but perturbations in the design and configuration of cytometers can also modify fundamental measurement performance in unpredictable ways. For example, spectral flow cytometry requires spectral unmixing, which progressively reduces signal-to-noise ratios with increasing numbers of fluorophores, necessitating new studies and tools to design labeling panels compatible with the instruments [33]. As another example, we have demonstrated that under many conditions, inertial flow-focusing effects can dominate hydrodynamic effects in flow cytometers, which greatly reduces measurement precision [34]. Thus, there is a persistent need for uncertainty quantification (UQ) to understand, validate, and optimize measurements from flow cytometers as their designs evolve.

We have reported a new approach to flow cytometry, called serial (or multiple-region) flow cytometry, that performs UQ by quantifying the precision of replicated optical measurements of individual particles tracked across sequential measurement regions [9,34]. Serial cytometry directly extracts measurement variability, independent from population-based variability, which improves the interpretability of biological effects from flow cytometry measurements. We have also reported the extension of serial flow cytometry and UQ for modeling particle shapes and sizes [28], instrument comparability [8,9], and dynamic measurements to characterize material properties [35]. However, a downside to previous serial cytometers was that the entire measurement apparatus (i.e., integrated optics, photodetectors, and digital signal channels) of a cytometer was replicated at each measurement region. As a result of this design, serial cytometers would become increasingly complex, bulky, and expensive to operate if more replicate measurements were desired. In this paper we report a new design for serial cytometry that reduces the amount of hardware required for repeating measurements. Our key innovation was to apply amplitude modulation (AM) to light sources to spatially encode signals from each region by the frequency of the modulation, which permitted multiplexing and combination of the light from all regions into a single collected-emission detector.

Light modulation has previously been applied in flow cytometry, providing a number of opportunities to encode or extract measurement signals. When excitation illumination is modulated at high speeds (e.g., 10 × 10⁶ cycles s⁻¹), emission phase shift and amplitude modulation diminution can be used to calculate the lifetime of fluorophores’ fluorescence decay [36,37,38,39,40]. This approach has been employed to observe fluorescence lifetime shifts in an autofluorescent metabolite during apoptosis [41]. Dadesh and Basu produced a system to multiplex detection of two fluorophores, illustrating the potential for multiplexed laser excitation to reduce detector count and still distinguish fluorophores with overlapping emission spectra [42]. Tovar et al. multiplexed lasers with four different wavelengths at distinct modulation frequencies to distinguish the illuminated fluorophores when emissions were collected to a single detector [43]. By separating fluorescent colors in this way, Tovar et al. achieved multiparametric signal detection with reduced complexity, increased setup flexibility, and improved sensitivity. Similarly, Kierzek et al. reported a stopped-flow cytometry system in which they distinguished fluorophores with overlapping emission spectra by oscillating the excitation light [44]. These three studies, from Dadesh and Basu, Tovar et al., and Kierzek et al., were enabled by lock-in amplifiers that linked the excitation light’s modulation to detected emissions for pulse waveform extraction. Additionally, optical encoding has been achieved using micropattern-based spatial encoding of light, rather than by modulating the laser intensities, which allowed for reconstruction of cell images in a flow cytometer from a single-pixel photomultiplier tube [45].

In this paper we present a basic evaluation of the feasibility of using AM with frequency encoding for multiple-region cytometry. As others have done with AM encoding schemes, we used a single detector in place of multiple dedicated detectors. However, our approach used multiplexing to combine spatial regions (not colors) to a single detector, performed offline digital signal processing on the detected emission light to remove the need for lock-in amplifiers and to further reduce hardware requirements, and preserved a previously published serial cytometry matching and uncertainty quantification pipeline [34]. We report the impacts of modulation-based encoding on measurement, such as accuracy of region decoding and the impact on uncertainty of the measured value. We also characterize the resilience of the method to possible pulse overlaps. AM serial cytometry is validated as an approach that can reduce the complexity, bulk, and cost of multiple-region flow cytometry by reducing hardware requirements to only a single photodetector for fluorescence, while retaining advantages in a serial cytometry application such as comparable imprecision of fluorescence measurements.

2. Materials and Methods

2.1. Cytometer Fabrication and Instrumentation

A serial cytometer takes repeated fluorescence and scatter measurements as particles pass a series of optical measurement regions. This allows for measurement of instrument variation that is independent of population variation. For this study, an AM serial flow cytometer was designed with fluidic inlets, debris traps, a flow-focusing region, two replicated optical measurement regions, and a fluidic outlet to waste.

The design included a previously reported three-dimensional hydrodynamic and inertial particle focuser to consistently position particles within the 100 μm tall by 40 μm wide flow channel, as discussed in detail by DiSalvo et al. [34]. In brief, the focuser positioned sheath flows above, below, and on both sides of the sample flow, resulting in hydrodynamic and inertial focusing of the particle-containing sample core. Modification of the sheath flows enabled cross-sectional positioning of the sample core within the flow channel. The flow channel departed from the flow focuser and passed through two repeated optical measurement regions, each of which contained one excitation waveguide, two fluorescence collection waveguides (permitting two collections in parallel from each measurement region: one ground truth and one multiplexed), and one transmission collection waveguide. Each waveguide was designed to couple an optical fiber from a light source or detector to align with the measurement region in the flow channel of the chip. The two regions were spaced sequentially along the flow channel 19.8 mm apart and were surrounded by light-obstruction channels.

The cytometer was constructed as a two-layer chip, as previously described [34,46]. The design was transferred by direct-write photolithography to a silicon wafer coated with 100 μm thick photoresist, followed by heat curing and photoresist development. Apposing poly(dimethylsiloxane) (PDMS) (Sylgard 184, Dow, Midland, MI, USA) layers were molded from the photoresist templates via soft lithography [47,48], aligned, and bonded using crosslinking agent. The light-blocking channels were filled with light-absorptive black PDMS. The waveguide channels were filled with optical adhesive (Norland Optical Adhesive 88, Jamesburg, NJ, USA), multimode optical fibers were inserted, and the adhesive was cured with UV light. Finally, fluidic connections joined the fluid channels (inlets and outlet) to off-chip syringe pumps.

To operate the device, fluids were delivered to the cytometer by syringe pumps (30 μm min⁻¹ minimum pulse-free actuation speed) through the fluidic inlets to control the various sample and focusing streams. Experiments were run at a total flow rate of 37 μL min⁻¹ with dimensionless flow rate ratios of the 5 inlets [SampleCore:Above:Below:Left:Right] of [1:4:4:20:8]. These ratios were used to rapidly pre-position particles at a stable inertial focusing node [49], as these values minimized variations in particle streamlines in this system [34]. These flow rates positioned our core particle-containing stream 6.5 μm from the channel center, which located 10.4 μm diameter microspheres such that their closest distance to the channel wall was 8.3 μm. The cytometer was connected to two excitation lasers (488 nm, 200 mW diodes, and up to 150 × 10⁶ cycles s⁻¹ modulation) by waveguide-coupled fiber optics of numerical aperture (NA) 0.1. The first laser was modulated sinusoidally at a frequency of 125,200 cycles s⁻¹ and the second laser was modulated at a frequency of 200,000 cycles s⁻¹. These were selected to avoid interference between carrier and harmonic frequencies, to encode optical pulses in the cytometer with at least 30 carrier periods to ensure analysis could demodulate the signal envelopes, and to ensure the sampling rate exceeded the maximum carrier frequency by a factor of at least 10 to detect the carrier frequencies without aliasing. Output modulation was set for full-range depth with no clipping of the highs or lows of the modulated laser. Fiber optics of NA 0.22 were used to collect fluorescence emission to filtered (520 nm ± 20 nm bandpass) photomultiplier tube (PMT) photodetectors (0.57 ns rise time; radiant sensitivity on the order of 78 mA/W over a range of 450 nm to 700 nm; connected to transimpedance amplifiers with limiting bandwidth set to 1 × 10⁶ cycles s⁻¹) and to collect transmitted light into silicon photodetectors (measurable power range 20 pW to 2 W). One emission optical fiber from each region went directly to a photodetector for use as ground truth. Two emission optical fibers, one from each region, were combined with a splitter/combiner to join their outputs to a single photodetector for AM serial flow cytometry. The signals from all PMT photodetectors’ transimpedance amplifiers were digitized at 2 × 10⁶ samples s⁻¹ with 16 bit resolution, after which a previously described [34] in-house software application performed instrument control, data monitoring, and recordings from cytometry experiments.

2.2. AM Flow Cytometry

Specific procedures were developed for flow cytometry using the AM microcytometer, involving (1) sample preparation, (2) detector adjustment, (3) triggering, and (4) gating. Many of the key parameters described below are replicated in Table S1.

2.2.1. Sample Preparation

Multi-fluorochrome labeled polystyrene microspheres (10.4 μm nominal diameter) in a logarithmically scaled brightness ladder (URCP-100-2H microspheres, Lot #AP01, Spherotech, Lake Forest, IL, USA) were made neutrally buoyant in a sample fluid consisting of water (59% to 68%), Triton-X 100 (0.1%), stock microsphere solution with 10,000,000 microspheres per milliliter (8% to 10%, sourced from a dropper bottle, hence the ranges in the buoyancy recipe), and saturated sodium chloride salt solution (24% to 30%); all percents are reported as volume fractions. Particle concentrations in the sample fluid were prepared within a range of 500,000 microspheres per milliliter to 2,000,000 microspheres per milliliter, which produced event rates on the order of 20 particles s⁻¹ for a cytometry run approximately 3 min in duration.

2.2.2. Detector Adjustment

Gain voltages on the photodetectors were adjusted such that the AM combined channel’s maximum voltage response from the brightest microsphere of the nine-level calibration ladder was beneath half the saturation limit of the detector. These settings ensured that the combined detector did not saturate during the coincident detection of two of the brightest microspheres. Gain voltages on the photodetectors for the ground truth channels were set so the maximum voltage response was nearly the full saturation limit of the detectors.

2.2.3. Instrument Triggering

The cytometer recordings were triggered similarly to a previously described method, with modification of specific values necessary to allow for modulated signals [34]. Briefly, signal was recorded as an event whenever the smoothed signal (40 μs moving average) exceeded a threshold value for a duration of 0.75 ms. The threshold was set to the moving average background level (median over 10 ms) plus a factor of two times the estimated standard deviation of the noise ((moving median absolute deviation over 10 ms) × 1.4826). The recording acquired additional background signal before and after the event, with a background duration equal to ten times the event duration.

Events were compared to thresholds to separate analyzable pulses from noise-induced data or passages of microspheres too dim to distinguish from the background. For pulses in the ground truth channels, the thresholds were determined by manual threshold setting on per-region histograms of the pulse integrated areas. For the AM channel, thresholds were determined by manual threshold setting on per-region histograms produced from the peak magnitudes of fast Fourier transforms (FFTs) of every AM pulse. The thresholds were chosen to separate dim microspheres (and noise) from bright, distinct microsphere subpopulations; see Figure S1.

2.2.4. Population Gating

Gating was performed on flow cytometry data to exclude noise and identify each particle type. Noise gating was performed manually to identify signal pulses with distinct “magnitudes” (defined here as integrated area for ground truth channel data or FFT peak magnitudes for AM combined-region data). Gating of particle subpopulation (i.e., corresponding to each intensity of a multi-brightness calibration particle ladder) was also performed manually. Ground truth channels were gated into subpopulations on two-dimensional scatterplots derived from principal component analysis (PCA) of the pulse area, width, and height. AM combined-region channels were gated into subpopulations on histograms of the FFT peak magnitude. See Figure S2 for manual subpopulation gating details.

2.3. Signal Processing and Analysis

The digitized data contained 5 channels composed of the 2 transmission measurements, 2 ground truth measurements, and the singular AM measurement combined from the two interrogation regions. Each channel contained a series of pulses. Due to the modulation in the pulses from the AM laser illumination, novel analyses were required to process the data in the context of serial flow cytometry. These analyses included: (1) pulse metric extraction, (2) overlaps/coincident events, (3) region decoding, and (4) signal matching.

2.3.1. Signal Metrics

For the ground truth channels, signal intensities at each region were measured by the time-integrated area under the pulse’s voltage level above background for the channel (i.e., fluorescence integrated area). Also measured for ground truth were pulse width and maximum height. For the AM channel, FFT-based measurements of signal brightness at the two laser carrier frequencies were collected as follows. The signal voltage was smoothed to produce a single rise-and-fall shape from the modulated pulse. The full width half maximum (FWHM) of the smoothed pulse was used to find the pulse’s center. A window having a width of 5000 samples (2.5 ms) was collected from the AM channel centered on the pulse’s center. The FFT of this data window was collected, and the magnitudes of the FFT peaks at both regions’ carrier frequencies were found.

2.3.2. Overlapping Event Demodulation

We mitigated the risk of detector saturation for concurrent pulses in two regions by tuning the gains of the detectors and attenuations along the emission light paths so that two microspheres of maximum intensity could be detected without saturation. We also kept a low sample microsphere concentration to maintain a low chance of multiple pulses occurring simultaneously (see Supplemental Information D: Overlaps for more details).

We used an approximate demodulation algorithm to qualitatively demonstrate the feasibility of separating overlapped pulse waveforms. This algorithm was separate from our main, demodulation-free region decoding pipeline (detailed below in Section 2.3.3). To demodulate selected overlapping waveforms, at each AM oscillation frequency f, we multiplied the waveform trace pointwise by a cosine function of frequency f with phase shift φ. The result was processed by a fast Fourier transform (Equation (1)) into the frequency domain, where we applied a low pass cutoff filter by removing all but the lowest ten modes. We then took the inverse fast Fourier transform (Equation (2)) of this frequency spectrum to produce the demodulated waveform. Carrier frequencies f = 125,200 cycles s⁻¹ and f = 200,000 cycles s⁻¹ were used for regions 1 and 2, respectively. The appropriate phase shift φ depended on the relative phase of the AM carrier wave with the pulse waveform and was found by an optimization algorithm that maximized the pulse area after demodulation. To produce demodulated pulses equal in magnitude to their ground truth equivalents, a scale factor was found that related each demodulated pulse’s height to the height of its ground truth channel’s pulse.

The fast Fourier transform was performed as

$$Y\left(k\right)={\sum }_{j=1}^{n}X\left(j\right)W_n^{(j-1)(k-1)},\mathrm{with} W_n=e^{(-2\pi i)/n},$$

(1)

where X(j) are time-domain samples of a waveform of length n = 5000 samples long. Y(k) are frequency-domain spectrum amplitudes. The inverse fast Fourier transform was performed as

$$X\left(j\right)={\displaystyle \frac{1}{n}}{\sum }_{k=1}^{n}Y\left(k\right)W_n^{-(j-1)(k-1)},\mathrm{with}{W}_n=e^{(-2\pi i)/n}$$

(2)

with the same term definitions as Equation (1).

2.3.3. Region Decoding

Each pulse was classified per the ground truth channels, with each ground truth channel’s pulse’s area compared to its region’s noise threshold. Any pulse with an area greater than the comparable threshold was classified as being: (i) a falsely triggered pulse or one too dim to detect, denoted (0,0); (ii) a pulse in region 1, denoted (1,0); (iii) a pulse in region 2, denoted (0,1); or (iv) simultaneous pulses occurring in both region 1 and 2 at the same time (an overlap), denoted (1,1).

To decode a windowed AM pulse and determine its region of origin, we compared the magnitudes at the two carrier frequencies’ peaks to each region’s noise threshold value and the pulse was classified as occurring in (i) neither, (ii) region one, (iii) region two, or (iv) both regions. From the two classification procedures, ground truth and AM, we produced a confusion matrix of classifications as either correct or mistaken for the AM classification as validated by ground truth, divided into subpopulation groups.

For some subpopulations of microsphere, pulse brightness was above the noise threshold in ground truth channels but not in the AM combined channel. For these events, the AM region decoding algorithm was adapted to use event triggering from the ground truth channels and perform classification through a simple comparison of AM and FFT peak magnitudes. The region with the higher FFT peak magnitude was selected as the decoded region, (1,0) or (0,1), with no assignments to classifications (0,0) or (1,1). This enabled a limited region classification that could still be validated against ground truth to investigate the utility of the FFT peak magnitudes to decode data below the detection threshold.

2.3.4. Signal Matching and Uncertainty Quantification

With the pulses’ regions of origin classified, the data was matched and serialized. For ground truth data, the matching and serialization analysis was equivalent to that of a serial cytometer with separate detection paths for each region, as previously described [9,34]. Briefly, a rough time of flight was estimated for all the pulses by cross-correlation, then the region 1 data was projected forward by the time of flight to generate time intervals in which each particle was expected to arrive in region 2. Most pulses were matched in this way, and additional accuracy was attained by refining the forward projection times per particle and by addressing intervals that had multiple pulses.

For matching and serialization, the AM combined data channel was also separated into two regions, each including pulses recognized as originating from its region. Noise (0,0) signals were excluded, and overlap (1,1) pulses were included in both regions’ pulse series. From this point, the two generated pulse series were input into the previously described serial cytometry data processing pipeline.

Once matching was complete, the signal strengths of the matched pulses from regions 1 and 2 were normalized and averaged to generate serialized signal strengths per pulse, for both the ground truth approach and the AM combined-region approach. The serialized measurements were reported per calibration particle brightness subpopulation, including the average signal strength, the robust coefficient of variation of pulse integrated area, and area imprecision, which was defined as the percent coefficient of variation of the serial pulse area measurements combined by averaging.

3. Results

3.1. Spatial Encoding Using Amplitude Modulation

A serial flow cytometer repeats fluorescence and scatter light measurements on individual particles. The per-particle distribution of these repeat measurements represents instrument-dependent variation that is independent of the heterogeneity of the particles. A serial flow cytometry system was used to test spatial encoding by amplitude modulation (Figure 1). The system was designed for dual emission waveguides from each spatial measurement region to serve as equivalent signals for validating AM decoded measurements against ground truth. The microfluidic flow cytometer is shown in Figure 1A, with a micrograph of the optical measurement region showing the two emission waveguides. A schematic of the flow channel, two measurement regions, their waveguides, and off-chip fiber optics is shown in Figure 1B. Figure 1C provides an overview of the detection, validation, and matching process for particles transiting between two regions. Figure 1D–G show representative time traces of pulses from a microsphere with brightness level 7 (out of 9) as it passes the two ground truth detectors, while panel 1H shows the FFT of these two pulses. With AM carrier frequencies set at 125,200 cycles s⁻¹ and 200,000 cycles s⁻¹ for regions 1 and 2, respectively, and flow rates set according to the methods described above, we found a median full width half maximum pulse duration of 0.76 ms (1525 samples), which results in 95 or 153 oscillations per pulse and 16 or 10 samples per oscillation in each region, respectively.

3.1.1. Detection and Noise Thresholding

When the sample brightness dependence of region decoding was tested using a conventional nine-brightness fluorescence intensity calibration ladder, we found that the dynamic range of detection did not cover the full dynamic range of the microsphere set. The ground truth pulses’ integrated area measurements were distinct from background for the seven brightest microsphere subpopulations. In the combined channel, the five brightest microsphere subpopulations were clearly distinct from background (see Figure S2).

From the 3755 pulses collected in one experimental run (detections triggered from any channel result in collection of data in all channels), applied noise thresholds (see Methods) for each of the ground truth channels identified 2239 pulses in the five brightest microsphere subpopulations. Similar thresholding in the AM combined channel detected 2229 pulses.

To understand the limitations and differences in pulse detection between the AM combined channel and the ground truth channels, we plotted the FFT magnitudes corresponding to each region (by carrier frequency) in the combined channel data (Figure 2A). Using ground truth detections as a basis and with noise thresholds set per region, pulses from each decoded region of the combined channel were validated against detection in the appropriate ground truth channel. In addition, the simultaneous measurement of the ground truth channel allowed for the detection of missed pulses in the combined channel. The plot in Figure 2A identifies pulses that were either missed (in red) or spurious (in blue) detections in the combined channel. Overall, these disagreements accounted for approximately 0.4% of all detections and only existed near the noise floor.

3.1.2. Coincident Pulse Detections

Given that AM cytometry involves simultaneous collection of two regions to a single detector, overlapping detections should occur with some regularity. Figure 2B shows overlapping detection of two microspheres from the brightest subpopulations in regions 1 and 2. Demodulation of the signal at the two carrier frequencies separated the region 1 and region 2 signals (Figure 2C), which appropriately matched the ground truth–detected signals in shape and timing (Figure 2D,E). The upper right quadrant of Figure 2A shows 27 pulses above the detection threshold in both regions, suggesting these were coincident microsphere detections, accounting for 1.21% of all detections. This matched well with the calculation of 1.47% expected coincident pulse detections, detailed in Supplemental Information D: Overlaps.

3.1.3. Region Decoding Accuracy

Accuracy of region decoding was validated by comparing AM region classification to ground truth detections. Of those pulses whose intensities were above the manual gating threshold that separated the lowest-intensity detected subpopulation from background in the AM channel, 99.3% (2223/2239, with binomial fit 95% confidence interval [98.8%, 99.6%]) were accurately assigned to a region.

As region decoding accuracy depended on the magnitude of the pulses, accuracy was validated per microsphere brightness subpopulation, using gating strategies described in the Materials and Methods Section. To approximate decoding accuracy for the five brightest subpopulations, we subtracted the counts of spurious and missing pulses (the red asterisks and blue crosses in Figure 2A, respectively) and incorrectly decoded pulses from the number of ground truth pulses and divided by the number of ground truth pulses (Figure 3 and

Table 1. Table of data presented in Figure 3.

Microsphere Brightness	15K	42K	130K	380K	1.0M	3.0M	7.4M
Accuracy, %	60.4	90.9	97.7	99.5	99.1	99.6	99.7
N	101	593	304	607	225	473	630
Confidence Interval, [%, %]	[50.2, 70.0]	[88.3, 93.1]	[95.3, 99.1]	[98.6, 99.9]	[96.8, 99.9]	[98.5, 100.0]	[98.9, 100.0]

).

Even for those subpopulations that could not be classified for intensity because they were below the threshold for combined-region pulse detection (see Figure S2), it was still possible to assess region decoding accuracy. We calculated region decoding accuracy of dim signals (e.g., subpopulations 3 and 4 detected in ground truth channels) by taking the count of pulses for which the FFT peak amplitude for the appropriate region encoding frequency was larger than the FFT peak amplitude of the frequency that encoded the other region and dividing by the total number of dim signal detections in ground truth. Detections coincident to both regions were thus counted as correct insofar as at least one region was decoded correctly. We note the ability to assess region accuracy when we cannot assess subpopulation accuracy seems to imply there are future opportunities for improving detection and classification. As seen in Figure 3, bright microspheres are easily decoded, but accuracy decreases with decreasing microsphere brightness. The microsphere subpopulation with a brightness of 42,000 molecules of equivalent fluorescein (MEFL, provided as nominal values by the manufacturer) was decoded with 90.9% accuracy or, as represented by a 95% confidence interval generated from a binomial fit, with [88.3% to 93.1%] accuracy. Therefore, a reasonable cutoff value for 90% region identification accuracy is above 42,000 MEFL for this optical power and gain configuration.

Based on the pulse classifications described above, a confusion matrix was generated for each brightness subpopulation to understand the types of inaccuracies in region decoding (

Table 2. Confusion matrices presenting region-decoding accuracy in a 3755-pulse dataset (2933 ground truth–detected pulses above a minimum detection threshold), grouped into subpopulations by ground truth microsphere brightness, with numbers of detected pulses reported per subpopulation as (ground truth/missing/spurious/combined-region pulses). The entries in the confusion matrix refer to the ground truth data detections. Rows of the tables indicate combined channel (i.e., spatially encoded) classifications, and columns indicate ground truth channel (i.e., validation channel) classification. Classifications indicate the pulse was identified in neither region (0,0), region 1 only (1,0), region 2 only (0,1), or regions 1 and 2 simultaneously (1,1). All entries are normalized to the total number of events for each ground truth (column) classification. The dashed line–enclosed center-diagonal table entries indicate the accuracy proportion of the combined channel to the ground truth channel for single-region pulses. Microspheres 3 and 4 could only be classified in rows as (1,0) or (0,1) by direct comparison of their combined channel FFT peak magnitudes, because these magnitudes were indistinguishable from noise. Microspheres 1 and 2 were too dim to detect.

	Ground Truth Classification					Ground Truth Classification					Ground Truth Classification
	Microsphere 1 (below detection threshold)					Microsphere 2 (below detection threshold)					Microsphere 3 (101 pulses)
Combined Classification (by FFT Peak Magnitude)												(0,0)	(1,0)	(0,1)	(1,1)
			N/A					N/A			(1,0)		0.48	0.28	0.50
											(0,1)		0.52	0.72	0.50
											42 of 101 misclassified (or overlaps), 40.4%
	Microsphere 4 (593 pulses)					Microsphere 5 (304/7/4/301 pulses)					Microsphere 6 (607/3/0/604 pulses)
Combined Classification (by FFT Peak Magnitude)		(0,0)	(1,0)	(0,1)	(1,1)		(0,0)	(1,0)	(0,1)	(1,1)		(0,0)	(1,0)	(0,1)	(1,1)
						(0,0)		0.01	0.03		(0,0)		0.01
	(1,0)		0.93	0.11	0.67	(1,0)		0.99			(1,0)		0.99
	(0,1)		0.07	0.89	0.33	(0,1)			0.97	0.29	(0,1)			1.00
						(1,1)				0.71	(1,1)				1.00
	66 of 593 misclassified (or overlaps), 11.1%					7 of 304 misclassified, 2.30%					3 of 607 misclassified, 0.49%
	Microsphere 7 (225/2/0/223 pulses)					Microsphere 8 (473/1/0/472 pulses)					Microsphere 9 (630/1/0/629 pulses)
Combined Classification (by FFT Peak Magnitude)		(0,0)	(1,0)	(0,1)	(1,1)		(0,0)	(1,0)	(0,1)	(1,1)		(0,0)	(1,0)	(0,1)	(1,1)
	(0,0)			0.02		(0,0)		0.00			(0,0)			0.00
	(1,0)		1.00			(1,0)		1.00			(1,0)		1.00
	(0,1)			0.98		(0,1)			1.00	0.07	(0,1)			1.00	0.05
	(1,1)				1.00	(1,1)				0.93	(1,1)				0.95
	2 of 225 misclassified, 0.89%					2 of 473 misclassified, 0.42%					2 of 630 misclassified, 0.32%

). Each pulse, in both the ground truth and the combined channel, was scored as a detection in region 1 (1,0), region 2 (0,1), both regions (1,1) or as below the detection thresholds (0,0). The likelihood of inaccuracy was equivalent between the two regions. However, we did find less accurate decoding for overlapped events compared to single-region events. It is instructive to note that coincident events are reported in the table based on the subpopulation nearest to their summed intensity, which is most likely the brightest of the two microspheres.

3.2. Region-to-Region Matching and Yield

Region-to-region particle matching is required for serial cytometry, which provides both increased confidence in particle detection and the ability to estimate imprecision. Pulses were matched across both ground truth regions as well as from both decoded regions using time-of-flight projections (as described in DiSalvo et al. [34]).

Our analysis found that there were an additional 5 out of 3755 (0.13%) events whose pulses were truncated too narrowly to allow for FFT analysis. The remaining failure modes affecting yields included missed events, mis-triggered noise events, and multi-candidate matching failures.

Table 3. Data processing yields. Yields reported are percentages from the prior (i.e., above) row; for the missed and spurious columns, they are percentages of the ground truth channel counts. Region-separated over-threshold counts and accurate decoding counts are equal, i.e., post-detection yield of accurate region decoding is 100%. Serialized pulses’ yields were calculated based on the lower of the per-region counts. The provision of 95% confidence intervals was based on a binomial distribution fit.

	Event Count (Yield)
	Ground Truth Channel	Combined AM Channels
		Missed (−)	Spurious (+)	Net
Total Pulses	3755
Over-Threshold Brightness Confidence Interval [%, %]	2239 (59.6%) [58.0, 61.2]	14 (0.63%)	4 (0.18%)	2229 (59.4%) [57.8, 60.9]
Over-Threshold Per-Region (Region 1:Region 2)	1119:1120	7:7 (0.63%:0.63%)	0:4 (0%:0.36%)	1112:1117
Accurate Region Decoding	2239			2229
Accurate Per-Region (Region 1:Region 2)	1119:1120	7:7 (0.63%:0.63%)	0:4 (0%:0.36%)	1112:1117
Matched and Serialized Confidence Interval [%, %]	1110 (99.2%) [98.5, 99.6]			1088 (97.8%) [96.8, 98.6]

summarizes the yields from each step of pulse processing using the AM serial cytometer dataset gated for the top five microsphere subpopulation intensities. The data in Table 3 compares ground truth detections to detections in the combined channel, now fully decoded, validated, and matched. Overall, more than 97% of pulses above the combined-region detection threshold were successfully serialized.

3.3. Uncertainty Quantification of Serial Cytometry

Repeated measurements provide opportunities to estimate uncertainties on a per-particle basis [34]. We defined imprecision, calculated as the coefficient of variation of the per-particle repeat measurements, as a useful metric for uncertainty quantification. Imprecision was plotted in Figure 4.

Table 4. Median relative fluorescence brightness (RFB), measured as the waveform area under the pulse, subpopulation robust coefficients of variation (rCVs) for brightness measurements (RFB area), and median imprecision for particles as determined by the serial cytometry measurements, excluding outliers as shown in Figure 4. Each metric’s 95% confidence intervals are shown in the second line of each table cell in square brackets, as calculated using the BC_a bootstrapping confidence interval method with N = 100 [51].

	Ground Truth					AM Combined
Brightness Subpopulation:	5	6	7	8	9	5	6	7	8	9
Median RFB (V·s × 10−6), (Area)	5.25 [5.19, 5.30]	15.3 [15.2, 15.5]	41.4 [40.6, 42.1]	124 [123, 125]	340 [337, 342]	1.57 [1.55, 1.59]	4.67 [4.63, 4.70]	12.6 [12.5, 12.7]	38.0 [37.6, 38.3]	106 [106, 107]
Population rCV (%), (Area)	6.65 [5.43, 7.97]	6.86 [6.25, 7.49]	8.09 [6.44, 10.4]	7.81 [6.88, 8.81]	6.24 [5.60, 6.92]	6.96 [5.62, 8.47]	6.53 [5.74, 7.48]	6.10 [4.44, 7.79]	7.52 [6.60, 8.93]	5.28 [4.65, 5.83]
Imprecision (%), (Area)	1.31 [0.96, 1.49]	0.89 [0.77, 1.05]	0.73 [0.61, 0.82]	0.71 [0.59, 0.83]	0.78 [0.67, 0.89]	2.05 [1.79, 3.02]	1.25 [1.05, 1.38]	0.69 [0.55, 0.84]	0.53 [0.44, 0.61]	0.53 [0.47, 0.62]

summarizes several measures relevant to cytometer performance and uncertainty quantification. For each intensity subpopulation, Table 4 presents medians of the pulse fluorescence integrated area, the subpopulation’s robust coefficients of variation (rCVs) for the fluorescence integrated area for ground truth and combined AM channels, and imprecisions from serialized measurements. Ground truth imprecision medians ranged from 1.31% to 0.71% across microspheres 5 to 9 of the nine-brightness ladder, whereas decoded combined-region medians decreased from 2.05% to 0.53% over the same microsphere brightness range. There were statistically significant differences at both the high and low ends of this microsphere brightness range. Demonstrating the value of serial cytometry, which separates the measurement uncertainty from the inherent population variability, the ranges of imprecisions were much lower than that of per-subpopulation rCVs from the ground truth data, which spanned from 8.09% to 6.24% on the same intensity range.

4. Discussion

The goal of this study was to develop and validate the measurement capabilities of an AM serial flow cytometer using frequency encoding to combine optical signals generated at different locations within the devices. Our validation method provided access to independent ground truth signals, enabling an unambiguous and quantitative comparison of cytometer performance with and without frequency decoding. AM serial cytometry achieved high yield (>97%) and low fluorescence area measurement imprecision (<2.1%) across all five microsphere fluorescence intensities considered in this study, demonstrating the feasibility of this technology. This performance was similar to the estimated imprecision using the ground truth data (Table 4), with improved imprecision for the ground truth channels at low brightnesses and for the AM combined channel at high brightnesses, perhaps due to measurement sensitivity effects at lower and higher measured brightnesses from integration bound-finding and detector sensitivity, respectively. We observed that combining optical signals to the AM detector using optical fiber combiners introduced a linear decrease in conveyed optical power (Supplemental Information E: Power Attenuation at Fiber Combiner). The decrease in optical power (approximately −7 dB) was sufficient to prevent concurrent detections of the brightest bead intensity from saturating our combined-region photodetector, and no comparative adjustments were made to the gains of the photodetectors. The reduction in optical power could be offset in future work by using higher-power lasers and more efficient methods for light/fiber recombining or increasing the detector gains [8]. However, our data showed that despite the reduced fluorescence intensities, the various functions of the instrument, including region decoding, matching, and uncertainty quantification, were largely unaffected.

Although this work only utilized two-region encoding with AM, the framework presented here allows future studies to test cytometer performance with region encoding at greater scales. Encoding even more regions is of high interest, not only to improve the uncertainty quantifications offered by serial cytometers (i.e., by increasing the repetitions of measurements of the same cell) but also to enable novel measurements. For example, separation of measurements in space permits investigation of time-dependent phenomena, such as cell deformation-induced streamline migrations [35], kinetic measurements of reactions in droplets, and dynamics of cellular responses as these materials transit the flow cell.

Some practical limitations remain regarding the addition of more regions in an AM serial cytometer. For every scale-up of a factor of two in the number of regions, the attenuation necessary to prevent saturation of coincident events is 50% (or −3 dB). More generally, increasing the number of regions from N to N + 1 will require modifications in laser power or gain to preserve maximum pulse intensity by dividing signal strength by (N + 1)/N. This design rule ensures that concurrent detections of the brightest possible samples at all regions will avoid saturation of the detectors. Alternatively, a more effective preservation of signal over noise could include a statistical analysis to weigh the benefits of capturing overlaps on-scale against the loss in dynamic range and signal-to-noise ratio, with adjustment of overall risk by attenuation/gain adjustment.

AM-enabled spatial encoding requires multiple lasers and signal generators to create high frequency oscillation within each excitation region. With the advent of microfabricated lasers and other light sources (e.g., nanoLEDs [52,53,54]), on-chip excitation promises improved optical integration and opens the door for more cost-effective scale-up of multiple measurements. Each additional AM signal added to a detector raises the likelihood of concurrent pulses and detector saturation, though opportunities exist to mitigate some of this concern by controlling microsphere-to-region density (Supplemental Information D: Overlaps). If the likelihood of coincident pulses is low or if saturation-related inaccuracies can be tolerated, the sensitivity of the combined region could be improved by increasing the detector gain [8]. Also, with each added AM carrier frequency, we must ensure that harmonics are isolated so that FFT spectra do not interfere. Fortunately, our analog-to-digital convertor operating at 2 × 10⁶ samples s⁻¹ provides plenty of bandwidth for added carrier frequencies between and beneath this study’s selected 200,000 s⁻¹ and 125,200 s⁻¹ carrier frequencies. Complexities associated with combining more regions into a single detector, such as by fiber combiners, could lead to further loss of optical power. A potential solution could be to support the flow system over a large-area photodetector, which could both improve collection efficiency and simplify detector channel-balancing.

Our intention with this study was to validate spatial encoding of cytometry pulses with AM onto a single detection channel for the realization of an AM serial cytometer. Overlapping signals were detected and separated, although their prevalence was maintained at a relatively low level (<2%) to facilitate clear and unambiguous separation. Future work is aimed at validating performance with more demanding cytometry scenarios comprising higher event rates, additional regions, and biological samples with significantly more heterogeneity. Regarding the development of a system that can handle commercial throughput rates, DAQ modules are available that operate at speeds above 2 × 10⁶ samples s⁻¹, which would enable event rates of 1000 events s⁻¹.

Although others have used AM with encoding to reduce hardware complexity for multi-color flow cytometry [43], there are limitations involving spectral mixing caused by combining multiple lasers colors into a single excitation path. In contrast, multi-region AM flow cytometry could be repurposed for multi-color cytometry with each color being spatially separated into different regions of the flow cell. Spatial separation is now used in commercial systems, and multi-region encoding would offer reduced system complexity and cost alongside the elimination of spectral bleed-through. A notable difference between our approach and those that make use of lock-in amplifiers for demodulation [42,43,55,56] is that we collect full time series of pulses for offline signal processing. This strategy saves hardware complexity at the cost of computation, which offers additional benefits of more refined signal processing and performance analysis. Indeed, additional computational analyses may improve upon the metrics we developed to analyze AM pulses, thereby enabling detection of dimmer particles or widening the system’s dynamic range. For example, one could improve upon the detection threshold tuning algorithm, integrate more of the signal spectrum around the FFT peak, and/or use both the DC and AC components of the pulse to estimate pulse brightness (once overlaps are ruled out). We save such pursuits for future work.

Amplitude modulation in flow cytometry is also useful for measurement of fluorescence lifetimes. The phase shift induced by the fluorescence decay of a fluorophore stimulated with a modulated laser, combined with the accordant decrease in modulation depth, can be used to calculate the time constants of decays with multiple exponential time constants [36,39,57,58]. This approach has been adapted to a series of laser excitation and measurement regions to screen large libraries of cells for genetically encoded fluorophores, which ultimately led to the engineering of a brighter variant of the FusionRed protein and a deeper understanding of protein structure–function relationships that govern fluorescent protein brightness [23,59,60,61]. These studies are relevant both because of their implementation of fluorescence lifetime measurements using amplitude modulation of excitation illumination and their use of multiple measurement regions that could benefit from AM frequency multiplexing.

Lastly, a direction of future work involves adapting newly developed models of signal shape [28] and noise-to-signal ratio [8,9] into analysis of AM flow cytometer performance. By modeling noise contributors to the population spread, it may be possible to attribute sources of measurement variation within the experimental setup and facilitate quantitative comparison of the AM serial cytometer to other cytometers.

5. Conclusions

This paper describes AM-enabled spatial encoding flow cytometry as realized on a microfluidic chip that can accomplish and validate various pulse detection and analytical processes fundamental to the technique. The goal was to achieve the inherent capabilities of serial cytometry, such as uncertainty quantification and dynamic measurements, while preserving flow cytometry’s inherent advantages of sample sensitivity, dynamic range and throughput, with a single photodetector for fluorescence. We found that single photodetector collection of spatially encoded excitation light using amplitude modulation multiplexing is a viable strategy for (1) pulse detection, (2) overlap separation, (3) region decoding, and (4) matching. These operations are required for serial cytometry yet may have other applications in spectral cytometry, imaging, and applications involving fluorescence lifetimes. Future studies with signal analysis and alternative system components may help ameliorate losses in brightness and dynamic range, in addition to offering further opportunities to reduce hardware complexity, bulk, and cost.