Red blood cell partitioning and segregation through vascular bifurcations in a model of sickle cell disease

Christina Caruso; Michael D. Graham; Wilbur A. Lam; Xiaopo Cheng

REVIEW 3 major objections 6 minor 13 references

Red blood cell partitioning and segregation through vascular bifurcations in a model of sickle cell disease

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Simulations show stiff sickle cells prefer the low-flow branch at vascular bifurcations, reversing the Zweifach-Fung effect for normal red cells.

desk verdict Stiff sickle cells preferring the low-flow branch is a plausible and nicely explained qualitative result, but the extreme 20%-volume cell model and lack of error bars cap how far the quantitative claims should be trusted. read the letter →

arxiv 2501.04017 v1 pith:LBSZDHOW submitted 2024-12-23 physics.bio-ph physics.comp-ph

Xiaopo Cheng , Christina Caruso , Wilbur A. Lam , Michael D. Graham This is my paper · ORCID

classification physics.bio-phphysics.comp-ph

keywords sicklecelldiseaseredbloodmarginationZweifach-Fungeffectanti-Zweifach-Fungcell-freelayerwallshearstressvascularbifurcationcomputationalsimulation

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

This paper uses three-dimensional simulations of a binary red blood cell suspension to argue that stiff sickle-shaped cells reverse a well-known microcirculation rule. Healthy red cells drift to the vessel center and, at a fork, preferentially enter the higher-flow branch—the Zweifach-Fung effect. Sickle cells, being stiffer and smaller, marginate to the cell-free layer near the wall, and when the flow split is unequal they preferentially enter the lower-flow branch instead. The paper further shows this upstream segregation persists downstream, concentrates sickle cells on outer branch walls, and increases the frequency of high wall-shear-stress events, offering a physical route by which blood disorders damage endothelium.

What carries the argument

The load-bearing object is the separatrix, the dividing surface in the parent vessel that marks whether a cell's trajectory ends in the left or right daughter branch, together with the cell-free layer (CFL), the near-wall region depleted of healthy red cells. The argument works because healthy cells are concentrated at the channel center, sickle cells are marginated in the CFL, and shifting the separatrix under unequal flow sends the CFL preferentially into the low-flow branch. The sickle cell itself is modeled as a stiff capsule with a curved prolate spheroidal rest shape, roughly 20% of normal cell volume and five times the membrane shear modulus.

What would settle it

Measure, in a microfluidic Y-junction with physiological flow splits and a suspension of stiffened or sickled red cells, the cell partition ratio into the high-flow branch: if the ratio equals or exceeds the fluid partition ratio for the high-flow branch at flow splits of 0.7 and 0.9, the central claim is contradicted. A complementary observation would be imaging the parent-vessel cell distribution and showing that stiff cells do not concentrate in the cell-free layer upstream of the bifurcation.

Watch

Extended reading notes

Core claim

The central claim is that margination inverts the Zweifach-Fung effect for aberrant red blood cells. In a simulated binary suspension of 90% normal and 10% sickle cells flowing through a symmetric bifurcation, normal cells follow the classical rule (cell partition ratio exceeds fluid partition ratio when a branch receives more flow), while sickle cells show an anti-Zweifach-Fung effect: they preferentially enter the low-flow branch. The mechanism is spatial: upstream of the fork, normal cells occupy the channel center while sickle cells reside in the cell-free layer, and the separatrix—the surface dividing fluid that enters each daughter branch—shifts toward the high-flow side when flow is asymmetric, sweeping the near-wall cell-free layer into the low-flow branch. The segregation persists downstream, with sickle cells accumulating on the outer walls of daughter branches, and this accumulation increases the probability of large wall-shear-stress events, particularly on the outer side of the high-velocity branch. In geometrically asymmetric bifurcations, cells of both types favor the larger-radius branch at equal flow, and sickle cells still exhibit the anti-Zweifach-Fung effect.

Load-bearing premise

Everything hinges on the idealized sickle cell: stiff, small, and curved enough to marginate strongly into the cell-free layer; if real sickle cells in a patient are softer or heterogeneous enough not to marginate, the anti-Zweifach-Fung effect and the wall-stress consequences would weaken or disappear.

Editorial extensions

If this is right

In mixed sickle-cell blood, downstream branches with lower flow will receive a disproportionate share of sickle cells, concentrating stiff cells where flow is already sluggish.
The outer walls of daughter branches, especially the high-velocity branch, see more high wall-shear-stress events in sickle-cell suspensions than in healthy suspensions.
Geometric asymmetry alone biases cell entry toward the larger-radius branch even when flow rates are equal, and this bias compounds the flow-driven partitioning.
The anti-Zweifach-Fung effect provides a purely physical, non-adhesive mechanism connecting margination to endothelial stress, complementing experiments showing that sickle-cell margination upregulates an endothelial dysfunction marker.

Reading between the lines

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

If real sickle-cell populations contain many cells that only partially stiffen, the magnitude of the anti-Zweifach-Fung effect may be weaker or distributed across a spectrum of partition ratios, since the current model uses a single idealized sickle cell.
The same separatrix-shift logic should apply to other marginated blood elements such as platelets, white cells, or rigid inclusions, so bifurcations may generally sort stiff or small particles into low-flow branches—a possible design principle for microfluidic separators.
A testable extension is to measure the cell partition ratio at varying flow splits in a microfluidic Y-junction with stiffened or sickled cells; the crossover where the cell partition ratio drops below the fluid partition ratio for the high-flow branch would confirm the mechanism.
The wall-shear-stress increase is reported as event frequency at fixed points; mapping these events to endothelial calcium signals or adhesion-molecule expression would connect the physical mechanism to tissue-level pathology.

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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

The paper has one central idea: normal RBCs show the classic Zweifach-Fung effect at a bifurcation, while stiff, marginated sickle cells do the opposite and preferentially enter the low-flow branch. That anti-Zweifach effect is mechanistically explained through the cell-free layer and the shifted separatrix, and the explanation is clean and convincing. The authors also show the segregation persists downstream, with sickle cells piling up on outer walls and raising the frequency of high wall shear stress events. That is new context — the malaria work of Li et al. already showed stiff cells going to low-flow branches, but the SCD-specific binary mixture, the ηN versus ηQ mapping, the downstream wall concentration statistics, and the WSS probability distributions are all new content. The healthy-cell validation against the experimental Zweifach-Fung data is solid, and the model is based on an established immersed boundary method.

The soft spots are in the quantitative extrapolation. The sickle cell model uses a rest volume about 20% of a normal RBC. Real dense sickle cells are typically 60-80% of normal volume, so 20% is extreme, and smaller and stiffer particles marginate more strongly. The headline anti-Zweifach effect depends on that strong margination. The authors state this is a simplification and they do cite the heterogeneity of real SCD populations, but they run no sensitivity analysis on volume, stiffness, or sickled fraction. Without that, we don't know if the magnitude of the effect (or even its existence) holds at physiologically representative sickle cell properties. The qualitative effect is probably robust — the malaria-infected cell simulations also showed stiff cells preferring low-flow branches — but the quantitative curves in Figures 2 and 5 need to be seen as illustrative, not predictive. Also, all partitioning and WSS statistics are presented without error bars or replicate runs, which makes it hard to judge the significance of the differences they report. The code and data are not released, despite a data availability statement that says "all data needed... are present."

The citation pattern is honest; they explicitly cite Li et al. for the prior stiff-cell-to-low-flow-branch observation and position their contribution as extending it. No signs of overclaiming novelty on that front.

Who should read this? Microcirculation modelers and people who care about the physics of cell segregation in bifurcating vessels. It is a useful computational study, not a paradigm shift. It deserves a serious referee, but the referee should push for sensitivity analysis and error bars. If the authors can show the effect survives at more realistic sickle cell volumes, the paper becomes much stronger.

Recommendation: send to peer review, with a request for sensitivity runs and uncertainty quantification.

Referee Report

3 major / 6 minor

Summary. This paper presents immersed-boundary simulations of binary red blood cell (RBC) suspensions in model vascular bifurcations, with one population of normal biconcave capsules and one population of stiff, smaller, curved prolate spheroidal capsules intended to represent sickle RBCs. The authors report that normal RBCs reproduce the classical Zweifach-Fung effect, preferentially entering the higher-flow branch, while the model sickle cells instead preferentially enter the lower-flow branch—an 'anti-Zweifach-Fung effect'—which they attribute to the marginated position of the stiff cells in the cell-free layer coupled with the flow-dependent shift of the separatrix. Downstream of the bifurcation, sickle cells accumulate along the outer branch walls, and the simulations show that the SCD suspension produces a higher probability of elevated wall shear stress events than a healthy suspension, especially on the outer side of high-velocity branches. An additional set of simulations in a geometrically asymmetric bifurcation shows that cells preferentially enter the larger-radius branch and that the anti-Zweifach-Fung effect persists.

Significance. If the central finding is robust, it is novel and potentially clinically relevant: it provides a mechanistic, purely hydrodynamic explanation for how a stiff, marginating RBC subpopulation could be routed to low-flow branches in the microcirculation and how this could locally amplify wall shear stress fluctuations, contributing to endothelial dysfunction in sickle cell disease. The paper's strengths include validation of the healthy-cell partitioning behavior against published experimental microcirculation data (Fig. 1B, Ref. 61), a clear mechanistic account of the partitioning via the separatrix and the cell-free layer, and the use of an established simulation method (the authors' prior Science Advances work, Ref. 18). The anti-Zweifach-Fung effect emerges from the simulations rather than being imposed as an input, which is a genuine model output. However, the sickle cell is represented by a single, strongly marginating parameter set, and the quantitative claims are not supported by sensitivity analysis or uncertainty quantification, so the breadth of the physiological conclusion currently outruns the evidence.

major comments (3)

[Formulation] The sickle cell model uses a rest volume approximately 20% that of the normal RBC and a membrane shear modulus five times larger. This parameter choice is physiologically extreme: reported sickle RBC volumes are typically 60–80% of normal, not 20%. Because the entire anti-Zweifach-Fung mechanism rests on the near-wall (cell-free layer) location of sickle cells, and because smaller, stiffer particles marginate more strongly, this extreme parameter set likely inflates the reported effect. The authors themselves call the single-class representation 'a substantial simplification,' yet they provide no sensitivity analysis in cell volume, stiffness ratio, or aberrant-cell fraction. Without such a test (e.g., repeating the key partitioning simulations at 50% and 75% of normal volume, or at stiffness ratios of 2 and 3), the reader cannot tell whether the anti-Zweifach-Fung effect is a robust feature of diseased RBCs or an artifact of the chosen idealized parameter point. This is the load-bearing assumption for the paper's headline result, so the omission is a major gap.
[Results, Partitioning and Wall Shear Stress] No uncertainty quantification or replicate statistics are provided for any of the central quantitative claims. Figures 2(B), 4(D–F), and 5(B) show smooth curves and probability densities from what appear to be single simulations per condition, with no error bars, confidence bands, or indication of run-to-run variability. Given that cell trajectories through a bifurcation are stochastic, the statements that ηN for sickle cells lies below ηQ for ηQ > 0.5 (and above for ηQ < 0.5), and that the SCD suspension raises the probability of high WSS events, cannot be assessed for statistical significance as presented. At a minimum, the authors should report the number of independent simulations or the length of the stationary time window, and provide bootstrap or replicate-based error estimates on ηN and on the WSS probability distributions. This is necessary to support the quantitative, and especially the inverted-branch-preference, claim.
[Results, Geometrically Asymmetric Bifurcation] The asymmetric-bifurcation result that cells preferentially enter the larger-radius branch even at equal volumetric flow (ηQ = 0.5) is presented without any sensitivity to the degree of geometric asymmetry. Only one pair of daughter radii (14 µm and 11 µm) is reported, and the claim that 'the geometric asymmetry of the bifurcation increases the curvature of the separatrix, further amplifying the uneven distribution' is not backed by a systematic variation of the radius ratio or bifurcation angle. Because the separatrix curvature is the proposed explanation, the lack of a parameter sweep leaves the generality of this secondary conclusion unsupported, even if the symmetric-bifurcation mechanism is accepted.

minor comments (6)

[Discussion] The word 'modling' in the first paragraph of the Discussion should be 'modeling'; the same paragraph also contains a missing article ('this is an anti-Zweifach-Fung effect' reads awkwardly in context).
[Formulation] The sentence 'The Chorin projection method is utilized to advance the velocity field u. This method involves solving an advection-diffusion equation...' repeats the earlier statement about the projection method; the redundancy should be removed.
[Results, Validation] In Fig. 1(B), the experimental data from Ref. 61 are plotted without error bars; reproducing the experimental uncertainty would help the reader judge the agreement quantitatively.
[Results, Wall Shear Stress] The claim that 'the average WSS at point a remains close to zero' should be supported by a numerical value, since the distribution in Fig. 4(D) is broad and symmetric but the mean is not reported.
[Results, Cell Distribution and Segregation] The 'regions of interest' (ROI) in Fig. 3(A) are only defined in the caption; the main text should state the axial extent of the ROI and how the cross-sectional number density is normalized.
[Formulation] The verification at Re = 0.05 is mentioned only as a sentence without any results; a supplementary figure or a quantitative statement of the change in ηN would make this verification credible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the anti-Zweifach-Fung effect is an emergent simulation result, and the model is validated against independent experimental data.

full rationale

The paper is a computational experiment, not a derivation. The sickle-cell model inputs (rest volume ~20% of normal, fivefold membrane stiffness) are physiological assumptions, not the target outcome. The headline anti-Zweifach-Fung effect is measured from simulation outputs (ηN vs ηQ) and is not encoded in the inputs; it emerges from the simulated marginated distribution interacting with the flow separatrix. The healthy-cell case is validated against independent experimental results (Pries et al., ref. 61; Fig. 1B), breaking any self-referential loop. The separatrix analysis is a post-hoc logistic-regression diagnostic fitted to trajectory data; it is used to explain the measured partitioning, not to generate the predicted partition ratios, so it does not reduce to a fitted-parameter-as-prediction step. Self-citations to the authors' prior work (ref. 18) provide the numerical method and previous validation, but the current paper contains its own external benchmark, so those citations are not load-bearing. No uniqueness theorem or ansatz is smuggled in via self-citation, and the 'anti-Zweifach-Fung effect' naming is contextualized by earlier observations of low-flow-branch preference for stiff cells (refs. 48, 62). No step reduces by construction to its own inputs.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central results rest on standard microfluidic biomechanics plus a simplified sickle cell model; the sickle cell idealization is the main additional assumption, with several computational parameters chosen for tractability.

free parameters (5)

Sickle cell membrane stiffness ratio = 5x normal RBC
Set to model stiff SCD RBCs; directly controls margination and therefore the reported anti-Zweifach-Fung effect. Chosen based on physiology, not fitted to target outcomes.
Sickle cell volume ratio = 0.2x normal RBC
Models dehydrated SCD RBCs; affects margination and cell-free layer position.
Aberrant cell number fraction = 0.1
Binary-mixture simplification; changing this fraction could alter CFL and partitioning quantitatively.
Viscosity ratio (internal to plasma) = 1
Computational simplification; authors cite prior studies for qualitative robustness.
Particle Reynolds number Rep = 0.1
Compromise between accuracy and cost; verified at 0.05 with no change to conclusions.

assumptions (4)

standard math Plasma is an incompressible Newtonian fluid obeying the Navier-Stokes equations.
Assumed throughout Formulation; standard for microcirculatory simulations.
domain assumption Normal RBCs can be represented as deformable biconcave capsules with shear and bending elasticity.
Model from prior work (refs 57,58); not re-derived here.
ad hoc to paper Sickle RBCs can be represented as a single class of stiff, smaller prolate spheroidal capsules.
Idealization stated in Formulation; real SCD populations are heterogeneous, and this assumption drives margination.
domain assumption Inflow/outflow single-phase zones with Dirichlet velocity boundary conditions produce fully developed particulate flow at the bifurcation.
Method from Liu et al. (ref 53); assumed not to perturb bifurcation region.

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Pith. "Pith review of Red blood cell partitioning and segregation through vascular bifurcations in a model of sickle cell disease." pith.science (2026). https://pith.science/paper/LBSZDHOW

@misc{pith2026250104017,
  author       = {Pith},
  title        = {Pith review of: Red blood cell partitioning and segregation through vascular bifurcations in a model of sickle cell disease},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LBSZDHOW}},
  note         = {Machine review of arXiv:2501.04017}
}

read the original abstract

The impact of cell segregation and margination in blood disorders on microcirculatory hemodynamics within bifurcated vessels are physiologically significant, yet poorly understood. This study presents a comprehensive computational investigation of red blood cell (RBC) suspension dynamics, with a focus on a model of sickle cell disease (SCD) as an example of a disorder associated with subpopulations of aberrant RBCs. The findings reveal how cell margination influences cellular partitioning and distributions as well as vessel wall shear stress (WSS) at vascular bifurcations. Normal RBCs, which migrate toward the channel center, exhibit the Zweifach-Fung effect, preferentially entering high-flow-rate branches. In contrast, sickle cells, which marginate near the vessel wall, demonstrate an anti-Zweifach-Fung effect, favoring lower-flow-rate branches due to their position within the cell-free layer (CFL). The upstream segregation of cells remains downstream through the bifurcation, where sickle cells accumulate along the outer branch walls. This accumulation of sickle cells increases the frequency of high WSS events via direct physical interactions, particularly on the outer side of high-velocity branches, potentially contributing to the vascular damage and endothelial disruption observed in many disorders that affect RBCs. In geometrically asymmetric bifurcations, cells preferentially enter branches with larger radii, underscoring the influence of geometric complexity on microcirculatory blood flow. These findings provide insights into microvascular hemodynamics in SCD and other blood disorders.

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Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

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Red blood cell partitioning and segregation through vascular bifurcations in a model of sickle cell disease

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Red blood cell partitioning and segregation through vascular bifurcations in a model of sickle cell disease

Red blood cell partitioning and segregation through vas- cular bifurcations in a model of sickle cell disease Xiaopo Cheng, a Christina Caruso , b Wilbur A. Lam, bc and Michael D. Graham ∗a The impact of cell segregation and margination in blood disorders on microcirculatory hemodynamics within bifurcated vessels are physiologically significant, yet poorl...

work page Pith review arXiv 2024

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Kumar and M

10 A. Kumar and M. D. Graham, Physical Review Letters , 2012, 109, 108102. 11 V. Narsimhan, H. Zhao and E. S. G. Shaqfeh, Physics of Fluids, 8 | 1–10 + P V S O B M / B N F < Z F B S > < W P M > 2013, 25, 061901. 12 R. G. Henríquez Rivera, K. Sinha and M. D. Graham, Physical Review Letters, 2015, 114, 188101. 13 R. G. Henríquez Rivera, X. Zhang and M. D. G...

work page 2012

[3] [18]

As depicted in Fig

To gain a comprehensive under- standing of the hydrodynamic ramifications associated with cell margination and segregation at the vascular surface, we conduct an evaluation of the WSS near the bifurcation. As depicted in Fig. 4 (A), illustrating the transient distribution of WSS on the bifurcated vessel surface, distinct positive local WSS fluctuations ar...

work page 1971

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Zhang, W

55 X. Zhang, W. A. Lam and M. D. Graham, Physical Review Flu- ids, 2019, 4, 043103. 56 D. A. Reasor, M. Mehrabadi, D. N. Ku and C. K. Aidun, Annals of Biomedical Engineering, 2013, 41, 238

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Sinha and M

57 K. Sinha and M. D. Graham, Physical Review E , 2015, 92, 042710. 58 E. Evans and Y.-C. Fung, Microvascular Research , 1972, 4, 335–347. 59 P. Balogh and P. Bagchi, Journal of Computational Physics , 2017, 334, 280–307. 60 R. Mittal, H. Dong, M. Bozkurttas, F. Najjar, A. Vargas and A. Von Loebbecke, Journal of Computational Physics , 2008, 227, 4825–485...

work page 2015

[6] [425]

Sun and L

43 C. Sun and L. L. Munn, Computers & Mathematics with Appli- cations, 2008, 55, 1594–1600. 44 S. S. Shevkoplyas, T. Yoshida, L. L. Munn and M. W. Bitensky , Analytical chemistry, 2005, 77, 933–937. 45 H. Wei Hou, H. Y. Gan, A. A. S. Bhagat, L. D. Li, C. T. Lim and J. Han, Biomicrofluidics, 2012, 6, 024115. 46 R. Enjalbert, D. Hardman, T. Krüger and M. O....

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7 K. Sinha and M. D. Graham, Soft Matter , 2016, 12, 1683–

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16 X. Zhang, C. Caruso, W. A. Lam and M. D. Graham, Physical Review Fluids, 2020, 5, 053101. 17 C. Caruso, M. E. Fay , X. Cheng, A. Y. Liu, S. I. Park, T. A. Sulchek, M. D. Graham and W. A. Lam, iScience, 2022, 25, 104606. 18 X. Cheng, C. Caruso, W. A. Lam and M. D. Graham, Science Advances, 2023, 9, eadj6423. 19 A. Pries, T. W. Secomb and P. Gaehtgens, C...

work page 2020