Integral refractive index imaging of flowing cell nuclei using quantitative phase microscopy combined with fluorescence microscopy

Barham Javidi; Gili Dardikman; Gyanendra Singh; Itay Barnea; Natan T. Shaked; Nir A. Turko; Yoav N. Nygate

REVIEW 3 major objections 4 minor 35 references

Integral refractive index imaging of flowing cell nuclei using quantitative phase microscopy combined with fluorescence microscopy

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A quantitative phase image plus a fluorescence snapshot can recover the thickness-averaged refractive index of a suspended cell's nucleus without 3D tomography.

desk verdict A credible methods paper for measuring nuclear integral RI by combining IPM and fluorescence, but the single-cell demonstration without reported RI values leaves the central claim unquantified. read the letter →

arxiv 1910.00108 v1 pith:3PTDKYSS submitted 2019-09-03 physics.bio-ph physics.optics

Gili Dardikman , Yoav N. Nygate , Itay Barnea , Nir A. Turko , Gyanendra Singh , Barham Javidi , Natan T. Shaked This is my paper · ORCID

classification physics.bio-phphysics.optics

keywords quantitativephasemicroscopyintegralrefractiveindexcellnucleusfluorescenceellipsoidmodelflowcytometrydigitalholographicopticalpathdelay

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that the thickness-averaged (integral) refractive index of a cell nucleus can be measured from a single quantitative phase image plus a simultaneous fluorescence snapshot, without 3D tomography. The fluorescence channel localizes the stained nucleus and supplies its in-plane radii, while the phase channel supplies the optical path delay of the whole cell. Under the assumption that the suspended cell is spherical or ellipsoidal and the nucleus is ellipsoidal, these 2D data are enough to build thickness maps and subtract the cytoplasm contribution, yielding the nucleus's integral RI profile pixel by pixel. Demonstrating on SW480 cancer cells, the paper obtains nuclear RI values lower than cytoplasmic RI, matching recent findings. If the method is right, flow cytometry could gain a nuclear-RI readout at camera frame rates, something tomographic phase microscopy cannot currently provide during flow.

What carries the argument

The engine of the method is the ellipsoid thickness model: from the in-plane radii $R_1,R_2$ of an area, the axial radius is estimated as $R_3 = (R_1+R_2)/2$, giving a 3D ellipsoid whose thickness $h(i,j)$ is computed by summing the ellipsoid's intersection with each pixel column. That thickness feeds the organelle-resolved optical path delay identity $\mathrm{OPD}(i,j) = h_c(n_c-n_m) + h_n(n_n-n_m)$, which the paper solves for the nucleus integral RI profile $n_n(i,j)$ after estimating the cytoplasmic RI from pixels outside the nucleus. The ellipsoid model is what turns a single 2D snapshot into a 3D thickness map, and the OPD identity is what separates nucleus and cytoplasm contributions.

What would settle it

Compare single-snapshot nuclear RI values with 3D tomographic phase microscopy on the same cells whose ellipsoid orientation is known from confocal imaging; if the RI deviation systematically exceeds the predicted worst-case value of about 0.008 RI units for central pixels (for an OPD of 0.4 μm and a small-axis radius of 4 μm), the axial-radius averaging model is wrong.

Watch

Extended reading notes

Core claim

The central claim is that the thickness–RI coupling problem for a suspended cell can be resolved from a single measurement direction: one off-axis phase image and one fluorescence image of the nucleus. For every pixel inside the nucleus the paper writes $\mathrm{OPD}(i,j) = h_c(i,j)\,(n_c(i,j)-n_m) + h_n(i,j)\,(n_n(i,j)-n_m)$, where $h_c$ and $h_n$ are the thickness of cytoplasm and nucleus along the illumination axis, $n_m$ is the medium RI, and $n_c$ is estimated from pixels outside the nucleus. The thicknesses come from fitting an ellipse to each 2D boundary and treating the missing axial radius as the average of the two in-plane radii, producing a 3D ellipsoid whose projected thickness is integrated numerically. The paper validates the ellipsoidal-nucleus assumption offline with 3D confocal fluorescence microscopy and with 2D fluorescence tracking of rotating cells in flow, and reports a worst-case orientation error of about 20% in the axial radius. Applying the method to SW480 cells gives a nuclear integral RI lower than the cytoplasmic RI, with nucleoli appearing as higher-RI features.

Load-bearing premise

The load-bearing premise is that the front-to-back radius of the nucleus (and of the whole cell) can be estimated as the average of the two radii seen in a single 2D projection, even though the true orientation of the ellipsoid relative to the camera is unknown for each cell.

Editorial extensions

If this is right

A nuclear refractive index readout becomes available in imaging flow cytometry at the camera frame rate, since both images are acquired simultaneously and no multi-angle acquisition or cell tracking is required.
The method self-selects valid cells: fluorescence shape can flag non-ellipsoidal (for example dividing) nuclei and exclude them from the measurement.
For a given cell type, a one-time offline characterization of nuclear ellipsoid ratios bounds the expected RI error, making the online single-shot measurement quantitative.
Even though the profile is thickness-averaged and loses some 3D detail, it retains local features such as nucleoli and remains a practical alternative when full tomography is too slow.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Inference: if the flow-regime-dependent orientation of the ellipsoid is modeled, the axial radius could be estimated by a scaling factor other than the simple average (the paper itself notes a factor of 0.88 for one orientation), so a calibration step per channel geometry could shrink the worst-case error further.
Inference: the same subtraction logic could be applied to any fluorescently labeled organelle whose shape is approximated by a convex ellipsoid, extending the method beyond nuclei.
Inference: because the acquisition is single-exposure, the technique could be paired with high-speed cameras to follow fast nuclear dynamics in suspension, where tomographic methods cannot keep up.
Inference: if the lower nuclear RI relative to cytoplasm is confirmed across cell lines, it would sharpen the interpretation of light-scattering signals from cell suspensions, where nuclear RI contrast is a major contributor.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a sensible incremental technique. They combine simultaneous quantitative phase and fluorescence imaging to localize the nucleus in a phase image, assume the cell and nucleus are ellipsoids, estimate the out-of-plane radius from the average of the two in-plane radii, and compute a thickness-averaged nuclear RI. That specific combination is new relative to the earlier spherical models and phase-only nucleus localization, and it is a plausible route toward label-free nuclear RI in flow.

The mathematical core (Eqs. 1-9) is standard and correct. The shape model is backed by confocal 3D fluorescence and by tracking 30 rotating cells in flow; that is real effort, and they are upfront about needing to select cells with elliptic nuclei. They also honestly note the method is best for near-spherical shapes.

The soft spots are mostly in the demonstration. First, they never report the actual nuclear and cytoplasmic RI values for the cell shown in Fig. 7. The claim that the nucleus RI is lower than the cytoplasm is supported only by a color image and a citation to prior work. Without numbers, a reader cannot tell whether the measured difference is larger than the method's own error. That is the biggest weakness. Second, the demonstration is a single static cell, not a flowing cell, even though flow is the motivation. The rotation validation was fluorescence-only. Third, the R3 estimation is the least secure link: they average the two in-plane ellipse radii to get the out-of-plane radius, and Table 2 bounds the error for two principal-axis alignments but does not prove these are global worst cases over all orientations. My sense is that for typical aspect ratios the principal-axis cases are likely the worst, but the paper doesn't show it. More importantly, the error analysis isn't connected to the experimental result. Fourth, the '10 frames' rule of thumb is unproven, though it is peripheral to the actual measurement.

None of these are fatal. The method is plausible and the analysis is careful up to the final step. But as it stands, this is a promising methods proposal, not a validated quantitative measurement.

Who gets value: researchers working on quantitative phase imaging, label-free flow cytometry, or nuclear refractive index as a biomarker. It deserves a serious referee. My recommendation: send it to review, but require the authors to report the actual RI values with multiple cells, add uncertainty quantification, and either demonstrate on a flowing cell or temper the title's claim. Those are addressable, and the underlying idea is worth keeping.

Referee Report

3 major / 4 minor

Summary. The paper introduces a multimodal technique for measuring the integral (thickness-averaged) refractive index (RI) of cell nuclei in suspension by combining quantitative phase microscopy (QPM) with simultaneous 2-D fluorescence microscopy. The method uses fluorescence to localize the nucleus and measure its in-plane radii, assumes the nucleus is an ellipsoid and the whole cell an ellipsoid/sphere, estimates the z-axis radius as the average of the two in-plane radii, computes thickness distributions, and solves for the nuclear RI using the cytoplasm as a reference. The ellipsoid assumption is validated offline by 3-D confocal fluorescence microscopy and by 2-D fluorescence tracking of cells rotating in flow. A demonstration on one SW480 cancer cell yields nuclear RI values lower than cytoplasmic RI, consistent with recent findings. The authors position the technique as a single-exposure alternative to tomographic phase microscopy for flow cytometry applications.

Significance. If the result holds, the technique provides a practical high-throughput route to nuclear integral RI in flowing cells, where full tomographic phase microscopy is too slow. The mathematical derivation (Eqs. 1-9) is straightforward and clearly presented, and the error analysis for the shape model is a useful contribution that quantifies the effect of the z-axis radius uncertainty. The paper also benefits from two independent morphological validation approaches (confocal and rotational fluorescence) and from consistency with the recent observation that nuclear RI can be lower than cytoplasmic RI. However, the quantitative demonstration is limited to a single cell, and the numerical values of the measured RI difference and its uncertainty are not reported, so the central claim that the method can reliably distinguish nuclear from cytoplasmic RI is not yet fully demonstrated.

major comments (3)

[Section 2.2, Table 2, Eq. (12)] The error analysis for the z-axis radius R3 is restricted to two orientations in which the projection axes coincide with the principal axes of the ellipsoid. For a randomly oriented nucleus, the projected major and minor axes are generally not the true principal axes, and the estimator R3 = (R_proj_major + R_proj_minor)/2 has an error that is not proven to be bounded by the 0.205 and 0.2 values in Table 2. The sentence after Eq. (12) that the RI error is 'bounded by the latter for all possible orientations' is therefore not established by the presented analysis. Since the estimated RI error of 0.0076-0.0086 is comparable to typical nuclear-cytoplasmic RI differences reported in the literature, this gap is load-bearing for the central claim that the method can distinguish nuclear from cytoplasmic RI.
[Section 3.3, Fig. 7] The demonstration reports no numerical values for the measured nuclear and cytoplasmic integral RI, nor their difference or uncertainty. Without these values, the reader cannot verify that the method's accuracy, as estimated in Section 3.2, is sufficient to distinguish nucleus from cytoplasm. In addition, the demonstrated cell is nearly spherical (nucleus in-plane radii 3.27 and 2.99 μm; cell 4.17 and 3.84 μm), so it does not exercise the error model for the more elongated nuclei represented by the Table 1 average aspect ratios. Please add the numerical results for the Fig. 7 cell, an uncertainty budget for the nuclear-cytoplasmic difference, and preferably data from additional cells with a range of aspect ratios.
[Section 3.2, Figs. 3-4] The flow-rotation validation of nuclear ellipsoidality uses cells selected for having elliptic nuclei, as stated: 'the 2-D fluorescence measurement can be used to select those cells with elliptic nuclei.' This selection means the validation does not quantify the probability that a randomly encountered non-dividing cell in suspension has an ellipsoidal nucleus, which is what the RI extraction assumes for every measured cell. The paper should report the fraction of nuclei excluded by this criterion or otherwise justify that the selection does not bias the prevalence claim. The confocal validation, consisting of a single representative cell (Fig. 3), does not on its own establish the statistical prevalence of ellipsoidal nuclei.

minor comments (4)

[Abstract and Section 2.2] The abstract states that the entire cell can be assumed to be a sphere, while Section 2.2 states that both the cell and the nucleus are modeled as ellipsoids; please reconcile these descriptions.
[Section 3.2] The assertion that 'as few as 10 frames taken in equal temporal increments during a full revolution' suffice for radius estimation with an error of up to 5% is presented without derivation or simulation. Please provide supporting evidence or soften the claim to a heuristic.
[Throughout] There are typographical errors: 'in-plain radii' should be 'in-plane radii' in the abstract and text, and the Fig. 2 caption 'tilted versus untitled ellipsoid' should be 'tilted versus untilted ellipsoid'.
[Appendix/Equations] The equation formatting in the provided manuscript is garbled (e.g., ' )1(' instead of numbered equations); if this reflects the version of record, the typesetting should be corrected so that equation references are unambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the nuclear RI estimate is obtained from an independently validated geometric thickness model, and no fitted parameter or self-citation forces the result.

full rationale

The derivation chain is self-contained. The OPD is decomposed into nuclear and cytoplasmic contributions in Eq. (6), and Eq. (7) solves for the nuclear integral RI using the measured OPD, the known medium RI, the geometric thicknesses h_n and h_c, and the cytoplasmic RI estimated from non-nuclear pixels via Eq. (8). The thickness model in Section 2.2 is geometric: the z-axis radius R3 is estimated as the average of the two in-plane radii, and this estimate is not fitted to the RI outcome. The ellipsoid assumption is validated independently in Section 3.2 by 3D confocal fluorescence microscopy and by rotational 2D fluorescence measurements, and the resulting orientation-induced thickness and RI errors are propagated in Table 2 and Eq. (12) as an error analysis, not used to tune the reported nuclear RI. The only hand-chosen element is the R3-average rule, which is explicitly characterized as an approximation with quantified worst-case error; this is an accuracy limitation, not a circular construction. Self-citations in the paper concern the interferometric setup [2,30] and phase reconstruction [31,32], none of which is load-bearing for the nuclear RI claim. The biological comparison to previous reports of lower nuclear RI rests on external references [11,12,20,21]. No equation reduces by construction to an input, and no fitted parameter is renamed as a prediction. The paper would benefit from reporting the actual measured nuclear and cytoplasmic RI values and from testing the R3 error over fully random 3D orientations, but those are correctness/validation concerns, not circularity.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The only free parameter is the hand-chosen z-axis radius estimate. No new physical entities are postulated. The ellipsoid shape and homogeneous cytoplasm are domain assumptions, with dependence on the specific cell type and flow regime.

free parameters (1)

z-axis radius R3 of cell and nucleus = (R1+R2)/2 from in-plane radii
The third radius is estimated as the average of the measured in-plane major and minor axes for both the cell and the nucleus. This is a hand-chosen model assumption that directly determines the thickness profiles h_c and h_n used in Eqs. 7-9. The paper quantifies the resulting error in Fig. 5 and Table 2 but does not measure the actual orientation.

assumptions (6)

domain assumption The nucleus of a suspended cell not in division is an ellipsoid.
Section 3.2 validates this by confocal and rotational fluorescence on 30 SW480 nuclei, but the validation excludes cells with non-elliptic nuclei, and a single orientation is used in the measurement.
domain assumption The entire cell in suspension is a sphere (or more generally an ellipsoid).
Section 2.2 cites refs 15-21; this is a standard assumption for suspended cells, though the paper uses an ellipsoid fit to the 2D projection.
domain assumption The cytoplasm RI is homogeneous, so the value estimated from the cytoplasm-only region can be used for pixels containing the nucleus.
Section 2.1 after Eq. 9 states 'Assuming that the RI of the cytoplasm is largely homogenous.' This is necessary to evaluate Eq. 7.
standard math Light passing through the nucleus region also passes through a cytoplasm layer (Eq. 6).
Geometric decomposition of the sample into two compartments along the optical axis; standard in cell phase modeling.
ad hoc to paper As few as 10 frames per revolution suffice for estimating ellipsoid radii to within 5% error.
Section 3.2 states this as a rule of thumb without derivation or simulation; it supports the validity of the rotational validation but is not rigorously justified.
domain assumption Cells rotating in low confinement flow can be treated as rigid bodies.
Section 3.2 cites refs 13, 14, 29; this is needed to interpret 2D projections as those of a static ellipsoid.

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Cite this review

Pith. "Pith review of Integral refractive index imaging of flowing cell nuclei using quantitative phase microscopy combined with fluorescence microscopy." pith.science (2026). https://pith.science/paper/3PTDKYSS

@misc{pith2026191000108,
  author       = {Pith},
  title        = {Pith review of: Integral refractive index imaging of flowing cell nuclei using quantitative phase microscopy combined with fluorescence microscopy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3PTDKYSS}},
  note         = {Machine review of arXiv:1910.00108}
}

read the original abstract

We suggest a new multimodal imaging technique for quantitatively measuring the integral (thickness-average) refractive index of the nuclei of live biological cells in suspension. For this aim, we combined quantitative phase microscopy with simultaneous 2-D fluorescence microscopy. We used 2-D fluorescence microscopy to localize the nucleus inside the quantitative phase map of the cell, as well as for measuring the nucleus radii. As verified offline by both 3-D confocal fluorescence microscopy and by 2-D fluorescence microscopy while rotating the cells during flow, the nucleus of cells in suspension that are not during division can be assumed to be an ellipsoid. The entire shape of a cell in suspension can be assumed to be a sphere. Then, the cell and nucleus 3-D shapes can be evaluated based on their in-plain radii available from the 2-D phase and fluorescent measurements, respectively. Finally, the nucleus integral refractive index profile is calculated. We demonstrate the new technique on cancer cells, obtaining nucleus refractive index values that are lower than those of the cytoplasm, coinciding with recent findings. We believe that the proposed technique has the potential to be used for flow cytometry, where full 3-D refractive index tomography is too slow to be implemented during flow.

Figures

Figures reproduced from arXiv: 1910.00108 by the authors.

**Figure 3.** 3-D rendering of a representative SW480 cancer cell nucleus, using 3- [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 6.** Scheme of the combined IPM-epifluorescence setup used for imaging. IPM beams [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

Figures from the paper (1 more)

**Figure 7.** Figure 7: Steps in extraction of the integral RI profile of a cell nucleus from the combined [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Introduction Measurements of refractive index (RI) of biological cells in vitro , indicating their inner content and spatial arrangement, provide invaluable information for both medical diagnosis and biological research. Interferometric phase microcopy (IPM) enables imaging of...

2018
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Methods 2.1 Theory A transmission mode interferometric imaging system captures the phase difference between a beam that passes through a sample ( a sample beam) and a beam that did not ( a reference beam), by recording their interference pattern on a digital camera. The phase ...

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The cells were grown in DMEM medium supplemented with 10% fetal bovine serum, antibiotics and glutamine (Biological Industries, Beit HaEmeq, Israel)

Results 3.1 Sample preparation We imaged human colorectal adenocarcinoma colon cells, SW480 (CCL- 228, ATCC). The cells were grown in DMEM medium supplemented with 10% fetal bovine serum, antibiotics and glutamine (Biological Industries, Beit HaEmeq, Israel). The cells were cu...

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The results agree well with recent findings regarding the RI values of the nucleus

Discussion and conclusions We presented a new technique for measuring the nucleus integral RI distribution of suspended cells by combining IPM with simultaneous 2-D fluorescence microscopy, and demonstrated it on cancer cells. The results agree well with recent findings regard...

2018

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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Quantitative Analysis of Biological Cells Using Digital Holographic Microscopy,

N. T. Shaked, L. L. Satterwhite, M. T. Rinehart, and A. Wax, "Quantitative Analysis of Biological Cells Using Digital Holographic Microscopy," In Holography, Research and Technologies , J. Rosen Ed., (InTech, 2011), 219–236

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Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy,

B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. J. Magistretti , "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express. 13(23), 9361–9373 (2005)

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Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye-enhanced dispersion of perfusion medium,

B. Rappaz, F. Charrière, C. Depeursinge, P. J. Magistretti, and P. Marquet, "Simultaneous cell morphometry and refractive index measurement with dual-wavelength digital holographic microscopy and dye-enhanced dispersion of perfusion medium," Opt. Lett. 33(7), 744–746 (2008). 6. B. Rappaz, A. Barbul, Y. Emery, R. Korenstein, C. Depeursinge, P. J. Magistret...

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Refractive index measurement in viable cells using quantitative phase‐amplitude microscopy and confocal microscopy,

C. L. Curl, C. J. Bellair, T. Harris, B. E Allman, P. J. Harris, A. G. Stewart, A. Roberts, K. A. Nugent, and L. Delbridge, "Refractive index measurement in viable cells using quantitative phase‐amplitude microscopy and confocal microscopy," Cytometry A 65(1), 88–92 (2005). Accepted to Biomedical Optics Express, January 2018. OSA©

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Development of a digital holographic microscopy system integrated with atomic force microscope,

N. Cardenas, N. Ingle, L. Yu, and S. Mohanty, "Development of a digital holographic microscopy system integrated with atomic force microscope," Proc. SPIE 7904, 790409 (2011)

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Localized measurements of physical parameters within human sperm cells obtained with wide‐field interferometry,

M. Balberg, M. Levi, K. Kalinowski, I. Barnea, S. K. Mirsky, and N. T. Shaked, "Localized measurements of physical parameters within human sperm cells obtained with wide‐field interferometry," J. Biophotonics 10(10), 1305–1314 (2017)

work page 2017