Quantitative Phase Imaging Flow Cytometry

• Quantitative Phase Imaging Flow Cytometry is a label-free technique that combines phase imaging with flow cytometry to quantify cell biophysical features like refractive index and dry mass.
• It employs advanced optical methods such as off-axis interferometry, digital holography, and tomographic phase microscopy to enable high-throughput 3D imaging.
• Integrated machine learning pipelines enhance real-time cell classification and diagnostics, paving the way for precise liquid biopsies and functional phenotyping.

Quantitative phase imaging flow cytometry (QPI-FC) refers to the integration of quantitative phase imaging techniques into the high-throughput, rapid, and objective framework of flow cytometry, most often for the analysis of label-free cells in suspension. QPI-FC exploits the ability of phase-sensitive optical modalities to resolve intrinsic morphological and biophysical cell features—including refractive index (RI), dry mass, shape, and compartmentalization—by measuring optical path delay (OPD) or by reconstructing three-dimensional refractive index distributions with high precision. Recent advances extend traditional 2D and 1D signal-based flow cytometry to three-dimensional, label-free, and sub-cellular resolution by leveraging digital holography, tomographic phase microscopy, machine learning, and deep-learning-enhanced image and data pipelines.

1. Underlying Principles of Quantitative Phase Imaging in Flow Cytometry

QPI-FC is fundamentally based on the detection of phase shifts induced by transparent or semi-transparent biological samples as light traverses them. The resulting OPD encodes the integral of the refractive index variation along the optical path—i.e.,

$\mathrm{OPD}(x, y) = \int [n(x, y, z) - n_m] dz$

where $n(x, y, z)$ denotes the 3D RI distribution and $n_m$ is the RI of the surrounding medium (Roitshtain et al., 2019, Dardikman et al., 2019).

Unlike conventional flow cytometry, which uses forward (FSC) and side scatter (SSC) as proxies for size and granularity, respectively, QPI-FC directly quantifies physical properties, such as cell thickness and RI, without labeling. Modern approaches use interferometric (off-axis digital holography), transport of intensity equation (TIE), or optical sectioning (light-sheet or tomographic) to reconstruct these parameters for each cell in a high-throughput flow environment (Han et al., 2019, Morales et al., 2021, Jo et al., 28 Aug 2024).

2. Instrumental Approaches and 3D Imaging Methodologies

Multiple instrumental configurations have been adopted to realize QPI-FC, each exploiting distinct phase-imaging modalities:

• Off-axis interferometric phase microscopy (IPM): Mach–Zehnder–based off-axis setups enable single-exposure acquisition of the complex optical field, facilitating rapid OPD map extraction for each flowing cell. This supports dynamic imaging at throughputs suitable for cytometric analysis (Roitshtain et al., 2019, Nissim et al., 2021, Delikoyun et al., 11 Aug 2025).
• Cameraless optical sectioning with single-pixel detection: A light-sheet, scanned along the $z$-axis by an acousto-optic deflector (AOD), excites serial optical sections while a pinhole array encodes the $x$-axis; as each cell flows along $y$ at velocity $v_c$, a photodetector records the corresponding voxel intensities, enabling high-throughput 3D reconstructions (Han et al., 2019). The signal is mathematically described by:

$$S(t) = \iint \int C \left( x, y - v_c t, z \right) I(z, t) \cdot psf(x, y, z) \cdot F(Mx, My) dx \, dy \, dz$$

where $C$ is the cell intensity profile, $I$ the light-sheet illumination patterned as a traveling Gaussian, and $F$ the spatial filter.

• Holotomography and Fourier Transform Light Scattering (FTLS): Off-axis holography with programmable angle illumination reconstructs 3D RI tomograms. FTLS applies a Fourier transform to retrieve the cell's far-field angular scattering spectrum, directly correlating RI structure with forward and side scatter signals (Jo et al., 28 Aug 2024).
• Multimodal QPI and fluorescence co-registration: Simultaneously acquired phase and fluorescence images facilitate morphological compartment segmentation and integral RI quantification (notably, nuclear vs. cytoplasmic) with ellipsoid and spherical geometrical modeling (Dardikman et al., 2019).
• Continuous-wave multi-pass phase cytometry: By redirecting the illumination beam to interrogate the sample multiple times (e.g., four-pass architecture), both the signal-to-noise ratio (SNR) and contrast are enhanced—approaching quantum sensitivity limits, with SNR scaling as $\sqrt{m}$ for $m$ passes (Israel et al., 2022).

A comparative overview is provided below:

Detection Scheme	Phase Retrieval Principle	Dimensionality	Throughput/Speed
Off-axis DHM/IPM	Fourier-based or TIE	2D/3D	Up to 15 cells/s (Nissim et al., 2021)
Cameraless light-sheet sectioning	Optical/mechanical scanning	3D	500 cells/s (Han et al., 2019)
Holotomography + FTLS	Oblique angle stitching + FFT	3D	Sample-dependent, high
Multi-pass imaging	Multiple re-entry of CW beam	2D	Enhanced SNR at high speed (Israel et al., 2022)

3. Data Analysis, Feature Extraction, and Machine Learning Integration

QPI-FC enables extraction of numerous high-content features from acquired OPD or RI datasets. Conventional and deep-learning-driven analysis pipelines include:

• Feature computation: Morphological and biophysical parameters such as dry mass ($M = \alpha \iint OPD(x, y) dx dy$), phase volume, surface area, sphericity, statistical moments (variance, skewness, kurtosis), textural features (energy, entropy), and shape ratios (Roitshtain et al., 2019, Nissim et al., 2021). For 3D reconstructions and tomograms, volumetric Zernike moment encodings further capture morphological signatures in a highly compressed descriptor string with quasi-lossless fidelity (NRMSE < 1%) (Memmolo et al., 2022).
• Classification frameworks: Principal component analysis (PCA) reduces dimensionality, followed by supervised algorithms (linear SVM, hierarchical multi-step SVM, or deep convolutional networks) for phenotypic discrimination. Reported sensitivities/specificities reach up to 93%/99% for cancer cell subtyping (Roitshtain et al., 2019), and overall multiclass accuracy of 92.56% for simultaneous blood and tumor cell classification (Nissim et al., 2021).
• Real-time and on-the-fly workflows: Recent RT-HAD (Real-Time Haematology Aggregate Detector) pipelines incorporate off-axis DHM, rapid physics-consistent neural hologram reconstruction (OAH-Net), YOLOv8x-p2 object detection (with high-res P2 branch), and graph-based cell-aggregate classification—enabling <10 ms per frame analysis and >99% data reduction via ROI-based storage (Delikoyun et al., 11 Aug 2025).

4. Quantitative Phase Cytometry for Cell Classification and Diagnostics

QPI-FC provides quantitative, label-free cytometric signatures beyond classical flow cytometry (FSC/SSC), directly extracting intrinsic biophysical phenotypes:

• Cancer diagnosis and cell staging: 3D/2D OPD metrics differentiate healthy, primary, and metastatic cancer cells with high statistical significance, even in suspension, and facilitate real-time liquid biopsy staging (Roitshtain et al., 2019).
• Haematological diagnostics and cell aggregate detection: RT-HAD captures blood aggregates—diagnostic of thrombo-inflammation, sepsis, and COVID-19 complications—with 8.9% error rate in platelet aggregate detection, matching laboratory error benchmarks. Functional biomarkers previously missed or flagged by standard cytometers are detected autonomously (Delikoyun et al., 11 Aug 2025).
• Tomographic scattering-based analysis: By extracting digital FSC, SSC, and intermediate scattering channels from 3D RI distributions (holotomography), QPI-FC enables morphology-based cell segmentation and refined type classification, outperforming conventional scatter-based gates (Jo et al., 28 Aug 2024).

5. Computational Innovations and Data Management

The proliferation of 3D phase and tomographic data in high-throughput QPI-FC poses significant data storage, management, and processing challenges. Addressed solutions include:

• Compression via orthonormal basis encoding: 3D Zernike descriptors provide quasi-lossless data reduction—compressing each 50×50×50 RI tomogram to a 1D vector of coefficients (space savings >95%), retaining biovolume, RI, and other markers (Memmolo et al., 2022).
• On-the-fly, region-of-interest storage: RT-HAD only stores phase/image ROIs for target cells or aggregates, minimizing storage from 30 GB (raw) to ~15 MB per patient (Delikoyun et al., 11 Aug 2025).
• End-to-end deep learning pipelines: Integration of AI-based phase recovery, object detection, and morphometric/aggregate analysis supports real-time operation, obviating the need for offline post-processing and manual review (Kandel et al., 2020, Delikoyun et al., 11 Aug 2025).

6. Advances in Optical Hardware and Computational Architectures

Emerging hardware and hybrid computational architectures are further transforming QPI-FC:

• All-optical diffractive processing: Deep-learning-optimized multi-layer diffractive networks replace digital phase recovery by performing the phase-to-intensity transformation at the speed of light, with high compactness and power efficiency (~200 wavelengths in optical path length). Normalized QPI signals are rendered directly on the output plane (Mengu et al., 2022, Li et al., 2023).
• Generalized reciprocal diffractive imaging (RDI): Stand-alone, reference-free, single-shot quantitative phase imaging is achieved by Fourier plane modulation with non-centrosymmetric masks and neutral density filtering, extending applicability beyond diffusive samples to biological specimens and supporting phase retrieval with only an intensity image (Oh et al., 17 Mar 2025).

7. Future Directions and Limitations

Anticipated enhancements include higher spatial resolution, increased throughput (via optical or electronic multiplexing), integration of image-based sorting, and expansion to multi-modal (fluorescence, QPI, scatter) digital cytometry (Han et al., 2019, Delikoyun et al., 11 Aug 2025). Algorithmic advances—such as further model quantization, hybrid hardware-digital approaches, adaptive mask/filter design, and expanded color/contrast multiplexing—may drive adoption in both core labs and point-of-care applications.

Current limitations include:

• Dependence on approximations for 3D RI or nuclear/cytoplasmic geometry (e.g., sphere/ellipsoid models) (Dardikman et al., 2019);
• Potential loss of high-frequency detail or lower SNR with aggressive Fourier filtering or single-shot RDI approaches (Oh et al., 17 Mar 2025);
• Data curation and model robustness across diverse clinical data sources.

A plausible implication is that with continued integration of advanced deep learning, optics, and compression schemes, QPI-FC will support clinically actionable, label-free, and information-rich flow cytometry—enhancing precision diagnostics, functional phenotyping, and real-time decision making in biomedical sciences.