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REVIEW 4 major objections 5 minor 54 references

Red blood cells aggregates transport for finite concentration

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims that red blood cell transport through a channel is maximized at a moderate, reversible adhesion energy: weak adhesion raises cell flux, stronger adhesion blocks it.

desk verdict A plausible but statistically thin 2D simulation study; the non-monotonic flux result is interesting, but the physiological claim outruns the data. read the letter →

arxiv 2501.03860 v1 pith:2RC3TCLP submitted 2025-01-07 physics.bio-ph cond-mat.soft

Mehdi Abbasi , Chaouqi Misbah This is my paper · ORCID
classification physics.bio-phcond-mat.soft
keywords redbloodcellaggregationadhesionenergyfluxhematocritmicrocirculationlatticeBoltzmannmethodvesiclemodelhemorheology
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 establish that red blood cell aggregation is not simply harmful: the normalized cell flux $Q_c/Q_0$ in a straight channel rises as weak, reversible adhesion is added and then falls once adhesion grows strong enough to form blocking aggregates. If true, this gives a reason healthy blood keeps aggregation mild and reversible — it improves oxygen delivery — while pathological hyper-aggregation is what impairs perfusion. The case is made with two-dimensional numerical simulations of vesicles carrying bending, stretching, area, and Lennard-Jones adhesion energies, with adhesion calibrated to physiological and pathological fibrinogen levels.

What carries the argument

The machinery is a two-dimensional vesicle suspension in a straight channel, solved by a lattice Boltzmann method coupled to the membranes through an immersed boundary scheme. Each vesicle membrane combines stretching, area, and bending energies with a Lennard-Jones pair potential for adhesion between cells; the control parameter is $\bar{\epsilon}_{adh} = \epsilon_{adh} R_0^2 / k$, calibrated to fibrinogen levels by AFM measurements. The argument is carried by the competition between two effects of aggregates: small reversible aggregates remove dissipative recirculations between cells and increase flux, while large aggregates span the channel and block it. This competition produces the optimal adhesion energy at which $Q_c/Q_0$ is maximal.

What would settle it

Measure, in a microfluidic straight channel at fixed hematocrit and shear rate, the normalized red-cell flux as fibrinogen concentration is increased: if the flux does not first rise then fall, or if including a cytoskeleton in a 3D simulation removes the peak, the central claim is falsified.

Watch

Extended reading notes

Core claim

The central discovery is a non-monotonic dependence: for fixed capillary number and hematocrit, the maximal normalized cell flux $Q_c/Q_0$ first increases with dimensionless adhesion energy $\bar{\epsilon}_{adh}$, reaching a boost of roughly 20–30% over the no-adhesion case, and decreases beyond an optimal adhesion energy. Weak adhesion creates small reversible aggregates that suppress the recirculation zones between cells and lower dissipation, so more cells get carried by the same flow. Stronger adhesion makes aggregates grow laterally until they occupy a substantial part of the channel cross-section and reduce the flux. The effective viscosity shows the mirror image: it drops by up to about 50% as adhesion rises in the moderate range, then increases. The optimal adhesion energy shifts upward with capillary number because stronger flow breaks aggregates and requires stronger adhesion to maintain the benefit.

Load-bearing premise

The load-bearing premise is that a two-dimensional vesicle membrane without a cytoskeleton, with Lennard-Jones adhesion, captures the aggregate shapes and disaggregation behaviour of real red blood cells closely enough that the non-monotonic flux-vs-adhesion trend transfers to three dimensions; the paper itself flags the absent cytoskeleton as a limitation.

Editorial extensions

If this is right

  • At fixed hematocrit and capillary number, both too little and too much adhesion reduce RBC transport; the peak flux sits at a nonzero adhesion energy.
  • The optimal adhesion energy is larger at higher capillary numbers, because stronger flow dissociates aggregates and needs stronger adhesion to keep the beneficial suppression of recirculations.
  • Effective suspension viscosity is non-monotonic in adhesion energy as well, with a minimum that can be about 50% lower than the no-adhesion viscosity.
  • When viscosity contrast is high ($\lambda = 10$), aggregates are robust and hardly break under shear, and the cell flux is dramatically reduced compared with the reversible-aggregation regime.

Reading between the lines

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

  • A direct testable extension: in a microfluidic channel at fixed hematocrit and shear rate, raising fibrinogen concentration should first increase and then decrease the measured RBC flux, with the peak shifting to higher fibrinogen at higher shear rates.
  • If the mechanism survives in three dimensions, therapies for hyper-aggregation should aim at an optimal aggregation window rather than eliminating aggregation entirely, since moderate adhesion is predicted to be beneficial.
  • The blockage term should depend on vessel diameter relative to aggregate size, so the optimal adhesion energy is expected to be lower in narrower vessels where even small aggregates occupy a large fraction of the cross-section; the paper's straight-channel geometry leaves this as a prediction for network studies.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This manuscript reports 2D lattice-Boltzmann simulations of vesicle suspensions as models of red blood cells in a straight channel, with a Lennard-Jones adhesion potential between membranes. The authors vary the dimensionless adhesion energy, capillary number, and volume fraction, and measure the normalized cell flux and effective viscosity. Their central claim is that the maximum cell flux is non-monotonic in adhesion energy: moderate adhesion (claimed to be physiological) increases flux by 20–30% relative to no adhesion, while stronger adhesion reduces it. The proposed mechanism is that small aggregates suppress dissipation in recirculation zones, while large aggregates block the channel. The paper also reports a corresponding minimum in relative viscosity and discusses reversible versus irreversible aggregation at low and high viscosity contrast.

Significance. If the non-monotonic flux result holds, it offers a plausible mechanistic explanation for the presence of reversible RBC aggregation in healthy circulation and a warning that excessive aggregation impairs perfusion. The study is systematic in exploring capillary number and volume fraction, and the no-adhesion limit is checked against the earlier results of Farutin et al. [18]. The simulation setup builds on prior validated work for doublet stability [9] and uses a published conversion from fibrinogen concentration to adhesion energy. The limitations of the 2D vesicle model and the absence of a cytoskeleton are acknowledged in Section IV, which tempers but does not eliminate the physiological relevance claim. The paper's main strength is the counter-intuitive, falsifiable prediction that moderate adhesion can improve transport, which should stimulate further work.

major comments (4)
  1. [Section III.B, Figs. 5–6] The central non-monotonic flux peak is reported from a single time-averaged simulation per parameter point, with no error bars, no ensemble averages, and no statement of the averaging duration or the number of cells. Since the suspension dynamics are chaotic and collective, the 0.3 to 0.4 increase in Qc/Q0 (quoted as a 30% boost) could be within run-to-run variability. Please provide error bars or confidence intervals from at least several independent initial configurations and describe the time-averaging protocol in Section II.C.
  2. [Section III.B and abstract/Introduction/Conclusion] The magnitude of the boost is stated as 'about 20%' in the Introduction (for physiological adhesion) and as '30%' in Section III.B and the Conclusion, while the abstract claims the boost occurs 'within the physiological range.' However, the 30% increase is attributed to ε̄adh ≈ 200 at Ca = 25, which exceeds the largest tabulated value ε̄adh = 147.7 in Table I, a value the table color-codes as pathological. Please reconcile these numbers, specify which data point corresponds to the physiological-range claim, and adjust the abstract and conclusion accordingly.
  3. [Section III.B, Fig. 5] The adhesion-energy scan per capillary number contains only about five hand-picked values, so the existence and the location of the 'optimal' adhesion energy in Fig. 6 are not robustly established. A finer scan with several values near the apparent peak, and across the same capillary numbers, is needed to support the non-monotonic claim and to define the optimal adhesion energy with confidence.
  4. [Section IV] The physiological conclusion that adhesion 'may be beneficial for perfusion' transfers the 2D vesicle result to real 3D RBCs, but the only support cited is the similarity of the doublet phase diagram in Ref. [9]. The recirculation-suppression and blockage mechanisms are sensitive to aggregate morphology and wall interactions, which differ between 2D and 3D. A concrete test would be to perform 3D simulations for the key peak parameters, or to compare with experimental measurements of flux versus aggregation, to assess whether the non-monotonic effect persists.
minor comments (5)
  1. [Fig. 9 caption] The caption states 'ϕ = 0.1%', which appears to be a typographical error; the text elsewhere uses volume fractions of 0.1 and 0.4, so this should probably read 'ϕ = 0.1'.
  2. [Eq. (5)] The equation 'uρ = ...' should be 'ρu = ...' (or 'u = .../ρ'); as written, the left-hand side mixes velocity and density.
  3. [Eqs. (14) and (15)] The notation is inconsistent: Eq. (14) uses Pc and P0, while Eq. (15) defines [η] with ϕ and the text then defines ϕt. Please standardize the concentration symbol throughout.
  4. [Section IV] There is a typo: 'cytoskeletton' should be 'cytoskeleton'; also, in Section III.C 'thee center' should be 'the center'.
  5. [Figs. 2, 3, 7, 8] The color coding is described only in the captions by listing adhesion-energy values; a single consistent legend across figures would help the reader compare the configurations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central flux curve is a direct simulation observable, not a fitted or self-referential quantity.

full rationale

The paper's central claim, that normalized RBC flux Qc/Q0 is non-monotonic in adhesion energy, comes from counting cells crossing a channel section in lattice-Boltzmann simulations (Figs. 5 and 6). The adhesion energy enters as an input parameter (Eq. 9), and the flux is an output; no parameter of the model is fitted to reproduce the peak, and the non-monotonic curve is not implied by the model definition alone. The comparison with Farutin et al. [18] in the zero-adhesion limit is a reproducible prior-work benchmark, and the use of the authors' earlier doublet study [9] for the adhesion-energy conversion and for the stability of high-viscosity-contrast aggregates is calibration and context rather than a derivation of the new flux result. The paper explicitly labels the 2D-to-3D extrapolation as a limitation rather than a derived consequence. Issues such as the absence of error bars, the sparse adhesion grid, and the 20% versus 30% discrepancy are statistical and internal-consistency concerns, not circularity.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The simulations introduce a set of dimensionless parameters (Ca, lambda, reduced area, epsilon_adh) and a discrete scan grid for each. The central claim about an optimal adhesion energy is a function of these chosen scan points, so the ledger records them as free parameters. The main unproved background assumptions are the adequacy of the 2D vesicle model, the Lennard-Jones adhesion representation, and the mapping from fibrinogen measurements to simulation energies. No new particles, forces, or dimensions are invented.

free parameters (7)
  • Dimensionless adhesion energy scan points = 0, 5.2, 15.1, 27.5, 36.81, 53, 61.1, 73.63, 84.33, 105, 147.27, 158, 220.91, 530.18, 1060.37
    Hand-picked grid based on Table I plus extra values; the location and existence of the claimed optimal adhesion energy depend on this grid.
  • Capillary number values = 0.9, 9.0, 25.0, 90.0
    Four discrete flow strengths; the claim that optimal adhesion energy rises with Ca is inferred from these points.
  • Hematocrit (volume fraction) values = roughly 0.1 to 0.46
    Discrete concentration grid; optimal hematocrit shifts and viscosity curves are read off these points.
  • Viscosity contrast values = lambda = 1.0 and 10.0
    Two values chosen to realize reversible versus irreversible aggregation, based on prior doublet work [9].
  • Reduced area = 0.65
    Fixed model parameter representing human RBC in 2D; controls deformability and aggregation geometry.
  • Membrane and adhesion micro-parameters = not reported
    Spring constants, bending constant, area penalty, LJ equilibrium distance sigma, interaction cutoff, channel length, cell number, and runtime are not listed; the quantitative results depend on them.
  • Adhesion energy conversion factor = epsilon_adh = 1.6862 h epsilon (h not defined here)
    Conversion from LJ energies to macroscopic adhesion energy is imported from the authors' prior paper [9]; needed to label physiological and pathological values.
assumptions (6)
  • domain assumption A 2D vesicle model without a cytoskeleton is a sufficient stand-in for the essential mechanics of 3D red blood cells in this flow regime.
    Section II.B introduces vesicles as a 2D RBC model and cites prior 2D studies; Section IV explicitly lists the missing cytoskeleton as a limitation.
  • domain assumption RBC-RBC adhesion is well represented by a Lennard-Jones potential between membrane nodes.
    Equation (9). The potential is a modeling choice; the paper does not derive it from bridging or depletion mechanisms.
  • domain assumption The measured AFM interaction energies at various fibrinogen levels can be mapped onto the 2D simulation's adhesion parameter.
    Table I and Eq. (19) use data from Brust et al. [4] and the authors' prior work [9] to label physiological and pathological ranges.
  • standard math The LBM plus immersed boundary with no-slip coupling gives an accurate solution of the Navier-Stokes equations for these suspensions.
    Section II.A and II.B; the method is standard, but the paper gives no convergence or validation tests against analytic solutions.
  • domain assumption Time-averaged measurements from a single dynamical run are stationary and representative of the suspension.
    Section II.C states averaging over time in steady state, but no multiple runs, error bars, or stationarity checks are shown.
  • domain assumption Poiseuille flow in a straight 2D channel is an adequate proxy for microcirculatory flow for the purpose of flux comparison.
    Eq. (13) and Section IV acknowledge the geometry is far from real networks.

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Pith. "Pith review of Red blood cells aggregates transport for finite concentration." pith.science (2026). https://pith.science/paper/2RC3TCLP

@misc{pith2026250103860,
  author       = {Pith},
  title        = {Pith review of: Red blood cells aggregates transport for finite concentration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2RC3TCLP}},
  note         = {Machine review of arXiv:2501.03860}
}
read the original abstract

Red blood cells (RBCs) are responsible for transporting oxygen and various metabolites to tissues and organs, as well as removing waste. Several cardiovascular diseases can impair these functions. For instance, in diabetes, increased RBC aggregation can lead to blood occlusion, thereby depriving tissues of efficient oxygen delivery. Interestingly, RBC adhesion occurs not only in disease states but also under physiological conditions, with the key difference being that adhesion is reversible in healthy situations. This paper focuses on numerical simulations in 2D, exploring different adhesion energies (both physiological and pathological) alongside varying flow strengths and hematocrit levels. A systematic analysis of RBC flux and viscosity is conducted. A remarkable finding is that moderate adhesion energy (within the physiological range) enhances RBC transport, thereby improving oxygen delivery to tissues. This provides insight into why RBC adhesion is present under normal conditions. Conversely, increasing adhesion energy beyond a certain point causes a collapse in RBC flux, thus reducing oxygen transport. We provide a basic explanation for the non-monotonic effect of adhesion energy on blood flow efficiency. This finding serves as an initial step in understanding the impact (both positive and negative) of RBC adhesion before addressing this issue in complex networks inspired by realistic microvasculatures.

Figures

Figures reproduced from arXiv: 2501.03860 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of the simulation [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Snapshots showing the spatial configurations of the cells at different time steps. a) 1500 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Snapshots showing the spatial configurations of the cells at different time steps. a) 1500 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Normalized cell flow rate as a function of volume fraction of cell for different dimensionless [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Normalized cell flow rate as a function of volume fraction for channels with different dimensionless [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The maximal value of the normalized flow rate as function of the dimensionless macroscopic [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Snapshots showing the spatial configurations of the cells for different macroscopic adhesion energy [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Snapshots showing the spatial configurations of the cells for different macroscopic adhesion energy [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Streamlines (grey lines with arrows) in a comoving frame. Snapshots showing the spatial configu [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Concentration profiles of suspension for different dimensionless adhesion energy values ¯ϵ [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Snapshots showing the spatial configurations of the cells at different time steps. a) 1500 [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. The average velocity of vesicle mass center over cells and time as a function of volume fraction [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. The normalized viscosity as a function of volume fraction for channels with different dimensionless [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. The normalized viscosity as function of the dimensionless macroscopic adhesion energy for [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. The normalized viscosity [ [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]

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