Pith. sign in

REVIEW 2 major objections 4 minor 101 references

Flow in a porous non-axisymmetric annular conduit: Coupling wall compliance and peristalsis

T0 review · 2 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A reduced-order model claims that wall compliance suppresses net peristaltic pumping in porous, eccentric annular conduits by orders of magnitude once the resistance-scaled compliance number exceeds one, even for walls that seem nearly rigi

desk verdict Solid reduced-order model with a clean closed-form answer; the math holds up, but the physiological punchline leans on a compliance closure that needs a caveat. read the letter →

arxiv 2607.15239 v1 pith:IHTITFZ2 submitted 2026-07-16 physics.flu-dyn physics.med-ph

Nishanth Surianarayanan , Ivan C. Christov This is my paper · ORCID
classification physics.flu-dynphysics.med-ph MSC 76Z0576S0574F1076D08 PACS 47.15.gm47.56.+r47.63.-b
keywords peristalticpumpingperiarterialspaceglymphaticsystemporousmediaflowwallcompliancelubricationapproximationeccentricannulusfluid–structureinteraction
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 builds a two-way-coupled model of peristaltic pumping in a porous, eccentric annular conduit with an elastic outer wall, motivated by cerebrospinal fluid flow in the brain's periarterial spaces. It reduces the lubrication equations to a single nonlinear pressure equation and, for small wave amplitudes, derives the closed-form net pumping rate: ⟨Q⟩ = πεΔ1 / (1 + (2πR0R_{e,0}β)²). The key prediction is that because porous drag makes the base hydraulic resistance R0 large, the effective compliance parameter B = 2πR0R_{e,0}β exceeds unity even for physiologically tiny wall compliance, so the system sits in the β⁻² tail and pumping is strongly suppressed. If true, this means rigid-wall models overestimate glymphatic pumping in penetrating perivascular spaces, and wall stiffness is a first-order control on transport.

What carries the argument

The load-bearing object is a single nonlinear partial differential equation for the axial pressure, obtained by integrating the lubrication equations over the eccentric annular cross-section: ∂/∂Z(R⁻¹ ∂P/∂Z) − 2π(1+εT)T′ − 2π(R_{e,0}+εβP)β ∂P/∂T = 0, together with the resistance expansion R = R0(1 + Δ1εT + Δ2εβP). The compliance closure u_e = C(p−p_ref) introduces the dimensionless compliance number β = Cμω/(κ²r0³); the product B = 2πR0R_{e,0}β controls all compliant effects, including the pumping suppression and the pressure-flow phase lag.

What would settle it

Measure the cycle-averaged flow rate in a porous eccentric annular conduit with an elastic outer wall as wall stiffness is varied; if the ratio of net pumping at finite compliance to that in the rigid limit does not equal 1/(1+(2πR0R_{e,0}β)²) using independently measured R0 and β, the local-compliance closure is wrong. Alternatively, measure the phase shift of the pressure gradient relative to the peristaltic wave and check whether it saturates toward −π/2 as β increases across the predicted crossover B ≈ 1.

Watch

Extended reading notes

Core claim

The central claim is that in a non-axisymmetric annular conduit filled with a porous medium and bounded by a compliant outer wall, the cycle-averaged peristaltic pumping rate obeys ⟨Q⟩ = πεΔ1 / (1 + (2πR0R_{e,0}β)²), where β is the dimensionless compliance number, R0 is the base hydraulic resistance of the undeformed cross-section, R_{e,0} is the dimensionless equilibrium outer radius, and Δ1 is a geometric resistance-perturbation coefficient. Because R0 scales inversely with the Darcy number in the porous regime, B = 2πR0R_{e,0}β becomes large for β values well below the physiological range, so even a very weakly compliant endfeet layer suppresses net pumping by orders of magnitude relative

Load-bearing premise

The prediction stands on the closure that the outer wall deforms locally as a linearly elastic, pressure-loaded membrane under uniform cross-sectional pressure (plane strain, homogeneous tissue); if real endfeet deformation is bending-dominated, viscoelastic, or coupled along the axial direction, the suppression law would change.

Editorial extensions

If this is right

  • The rigid-wall peristaltic pumping result is recovered as β → 0, so the model unifies open and porous, rigid and compliant descriptions of annular peristaltic pumps.
  • For the physiological parameter ranges tabulated in the paper, even endfeet compliance values one might dismiss as negligible put the system in the β⁻² tail, so net pumping is orders of magnitude smaller than rigid-wall estimates.
  • The phase of the pressure gradient relative to the arterial wave is set by B = 2πR0R_{e,0}β, providing a measurable link between waveform lag and tissue compliance.
  • Net pumping grows strongly as the space becomes more open: for small Darcy number, ⟨Q⟩ ∝ Da² in the compliant regime, so porosity itself inhibits transport.
  • Eccentricity reduces net pumping for all porosities and compliances, because it alters both the resistance R0 and the perturbation coefficient Δ1.

Reading between the lines

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

  • If this suppression mechanism operates in vivo, peristaltic pumping alone may be insufficient to drive glymphatic exchange in penetrating spaces; other drivers such as vasomotion, respiration, or transient (non-cycle-averaged) flow would need to dominate.
  • The 1/(1+B²) law could serve as a design rule for soft microfluidic peristaltic pumps: the same compliant wall that shields tissue in vivo acts as a gain-kill switch whose threshold is set by hydraulic resistance, not stiffness alone.
  • The predicted saturation of the pressure-flow phase lag could be tested with in vivo or in vitro waveform measurements, offering a way to infer endfeet stiffness from flow phasing without direct elasticity measurements.
  • Non-sinusoidal waves with a nonzero mean (e.g., functional hyperemia) may partially evade the suppression: the oscillatory component should still decay as 1/(1+B²), but a mean wave component could produce a baseline flow that the current sinusoidal analysis misses.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper develops a reduced-order lubrication model for peristaltic pumping in an eccentric annular conduit whose interior is a Darcy–Brinkman porous medium and whose outer wall is linearly compliant. The inner wall executes a traveling-wave displacement; the outer wall displacement is coupled to the local pressure through u_e = C(p - p_ref). After solving the cross-sectional velocity problem numerically, the hydraulic resistance is expanded about the undeformed state, leading to a one-dimensional nonlinear PDE for the axial pressure, Eq. (2.9). For sinusoidal waves and periodic boundary conditions, a small-amplitude expansion yields the analytical pressure waveform (2.10) and the net pumping rate <Q> = pi eps Delta1 / [1 + (2 pi R0 R_e0 beta)^2], Eq. (3.2). Numerical solutions of (2.9) are used to verify the expansion and to study the effects of eccentricity, Darcy number, and compliance number. The central physiological conclusion is that wall compliance suppresses net pumping by orders of magnitude in porous penetrating periarterial spaces.

Significance. The paper fills a genuine gap by simultaneously accounting for non-axisymmetric geometry, porous drag, and wall compliance in a peristaltic annulus, and it reduces the problem to a tractable PDE plus an explicit analytical formula. The derivation is internally consistent and carefully benchmarked: the rigid-wall limit reproduces Coenen et al., the concentric-annulus velocity field is validated against a Bessel-function solution, the finite-element mesh and time-step convergence studies are documented, and Eq. (3.1) provides an a posteriori check that the wall displacement remains small. No target quantity is fitted; model parameters are taken from the literature. The analytical result (3.2) is a useful design and interpretation tool for glymphatic-flow modeling. The main risk is that the physiological inference depends on the local compliance closure and on how the physiological parameter ranges are translated into the compliance-number range; these issues are addressable and should be made explicit in a revision.

major comments (2)
  1. [§2.2 and Eq. (2.5b)]
  2. [§3.3 and Table 1]
minor comments (4)
  1. [§3.2]
  2. [Eq. (2.10b)]
  3. [Figure 6]
  4. [Table 1]

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central pumping formula is derived from the stated model and verified against the rigid-wall limit, with the compliance closure a transparent modeling assumption rather than a fitted target.

full rationale

The derivation chain is self-contained in the modeling sense: the cross-sectional velocity problem (2.3) is solved by FEM to obtain the resistance R0 and the perturbation coefficients Δ1, Δ2 (2.6); these enter the pressure PDE (2.9), whose leading-order solution (2.10) yields the net pumping formula (3.2). No target quantity is fitted: R0 and Δ1 are computed from the stated geometry and Darcy equation with literature parameter ranges, and the β→0 limit recovers Coenen et al.'s equation (4.5), with numerical verification against an independent implementation of that rigid-wall model in Appendix B.3. The only self-cited ingredient is the standard linear-elastic compliance closure u_e = C(p − p_ref) in §2.2, supported by Christov (2022), Rallabandi (2024), Wang et al. (2022), and Takagi et al. (2024). This closure is an explicitly stated constitutive assumption, not a hidden ansatz or a fitted value, and the paper itself flags its limitations in §4 (e.g., transverse pressure variations could cause non-uniform deformation). The physiological conclusion is contingent on that closure, but contingency on an openly stated model assumption is not circularity. No step reduces by construction to its own input.

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

All parameters are taken from the physiological literature (Table 1) rather than fitted to the authors' own target results. The model rests on standard lubrication theory plus a linear compliance closure; the latter is the main assumption that the reader 'pays for upstream' and that is not independently validated in this paper.

assumptions (6)
  • domain assumption Lubrication/long-wave approximation: (κr0)^2 ≪ 1 and Wo^2 ≪ 1, so inertial terms and axial viscous diffusion are dropped.
    Invoked in §2.1 and justified by parameter ranges in Table 1; central to reducing the momentum equation to a 2D cross-sectional problem.
  • domain assumption Outer wall deformation is local, linear, and purely radial: u_e = C(p - p_ref), with C = r0/E_endfeet estimated from a homogeneous isotropic plane-strain elastic model.
    Introduced in §2.2 (Eq. 2.5b and following). This is the key biomechanical closure, but brain tissue is viscoelastic and heterogeneous; the authors acknowledge non-uniform deformation as a future extension.
  • domain assumption Both inner and outer walls are impermeable to the flow.
    Stated in §2. The model captures porous drag in the interior but not transmural flow through the endfeet layer, which is a known feature of PAS physiology.
  • domain assumption Small-amplitude expansion: ε ≪ 1, and the domain-perturbation expansion of resistance (2.6) is valid with εβP small compared to R_e,0.
    Used throughout §2.3 and Appendix A. The authors provide an a posteriori check for sinusoidal waves in Eq. (3.1), but the check does not cover arbitrary waveforms.
  • domain assumption Periodic boundary conditions and sinusoidal peristaltic waveform for the analytical solution.
    In §2.4 and Appendix A.3; the conduit length is taken as 2λ, which the authors note is longer than typical PAS segments.
  • domain assumption The porous medium is described by a Darcy–Brinkman term with uniform permeability and porosity, with no-slip at the solid walls.
    Equation (2.3) and surrounding text; standard for reduced-order porous flow models but does not resolve pore-scale structure.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Flow in a porous non-axisymmetric annular conduit: Coupling wall compliance and peristalsis." pith.science (2026). https://pith.science/paper/IHTITFZ2

@misc{pith2026260715239,
  author       = {Pith},
  title        = {Pith review of: Flow in a porous non-axisymmetric annular conduit: Coupling wall compliance and peristalsis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IHTITFZ2}},
  note         = {Machine review of arXiv:2607.15239}
}
read the original abstract

Coenen \textit{et al.}\ (\textit{J. Fluid Mech.}, vol.~921, 2021, p.~R2) developed a reduced-order model of peristaltic pumping in non-axisymmetric annular conduits with rigid walls, in the context of periarterial space (PAS) flows. \textit{In vivo} studies show that the PAS's outer wall undergoes significant displacement due to flow within and that the penetrating PASs form a porous pathway. To account for these biomechanical aspects, we revisit the problem of flow in an eccentric annular conduit and incorporate porous drag and two-way-coupled fluid--structure interaction between the compliant outer wall and the cerebrospinal fluid flow within. A Darcy--Brinkman term in the axial momentum equation accounts for drag due to the porous medium. We account for changes in hydraulic resistance due to peristalsis and compliant-wall displacements perturbatively, thereby reducing the problem to a single nonlinear partial differential equation for the axial pressure. This reduced-order model allows us to build a mechanistic understanding of flow through a porous penetrating PAS and enables parametric studies. For small-amplitude peristaltic waves, analytical solutions are possible.

Figures

Figures reproduced from arXiv: 2607.15239 by the authors.

Figure 1
Figure 1. Schematic of the model porous domain, with non-axisymmetric cross-section 𝛺cs, and associated mathematical notation. The boundary of each cross-section, 𝜕𝛺cs, consists of the outer wall (“endfeet layer” with radius𝑟𝑒 with respect to its own axis), which is always centered at the axis, and the inner cylinder (“artery ’ with radius𝑟𝑎 with respect to its own axis), which is offset from the former’s axis, leading to a n… view at source ↗
Figure 2
Figure 2. Contours of the axial velocity 𝑉ˆ 𝑍 variation in the eccentric annular cross-section for (a,b) 𝐷𝑎 = 10−1 (weak porous drag, approaching an “open space”) and (c,d) 𝐷𝑎 = 10−3 (representative of a porous medium), at two eccentricities each. non-axisymmetric (eccentric annular) domain 𝛺cs. For our problem, 𝜕𝛺cs consists of two circles. In the outer-wall-centered coordinate system of figure 1, the inner part of 𝜕𝛺cs is t… view at source ↗
Figure 3
Figure 3. Computed dependence of the resistance perturbation expansion parameters, R0, 𝛥1, and 𝛥2 from (2.6), on the eccentricity, 𝑒𝑐𝑐, for selected values of the Darcy number, 𝐷𝑎 = 10−5 , 10−3 , 5 × 10−3 , 10−2 , 3 × 10−2 , 10−1 , and 105 (light to dark curves). and 𝛥2 ∼ −2𝜋𝑅𝑒,0/𝐴 ≈ −2.05, independent of 𝑒𝑐𝑐 as 𝐷𝑎 → 0, precisely matching the small-𝐷𝑎 curves’ plateaus seen in figure 3(b,c), respectively. Finally, from figure … view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Effect of eccentricity on the flow metrics for (a) 𝐷𝑎 = 10−3 (note that all curves overlap), (b) 𝐷𝑎 = 10−2 , and (c) 𝐷𝑎 = 10−1 . Each column corresponds to a Darcy number, while the rows represent flow metrics, with resistance in the top row, and the pressure gradient …
Figure 5
Figure 5. Figure 5: Effect of compliance on flow metrics. Time series of (a) resistance R, (b) pressure gradient −𝜕𝑃/𝜕𝑍 and flow rate 𝑄. The driving peristaltic wave profile, T, is shown above each plot. In (b), the −𝜕𝑃/𝜕𝑍 and 𝑄 curves corresponding to 𝛽 = 100 are multiplied by a factor o…
Figure 6
Figure 6. Figure 6: Pumping (space-time or cycle averaged) flow rate as a function of (a) eccentricity, 𝑒𝑐𝑐, (b) compliance, 𝛽, and (c) Darcy number, 𝐷𝑎. The darker (purple) curves are based on the analytical approximation (3.2) for 𝜖 ≪ 1. Cases with 𝛽 = 10−10 represent the rigid limit ev…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

101 extracted references · 67 canonical work pages

  1. [1]

    and Pandolfino, John E

    Acharya, Shashank and Halder, Sourav and Kou, Wenjun and Kahrilas, Peter J. and Pandolfino, John E. and Patankar, Neelesh A. , month =. 2022 , journal =. doi:10.1016/j.compbiomed.2021.104948 , issn =

    arXiv 2022

  2. [2]

    and Bork, Peter A.R

    Tithof, Jeffrey and Boster, Kimberly A.S. and Bork, Peter A.R. and Nedergaard, Maiken and Thomas, John H. and Kelley, Douglas H. , number =. 2022 , journal =. doi:10.1016/j.isci.2022.104258 , issn =

    arXiv 2022

  3. [4]

    and Wang, Minghuan and Liao, Yonghong and Plogg, Benjamin A

    Iliff, Jeffrey J. and Wang, Minghuan and Liao, Yonghong and Plogg, Benjamin A. and Peng, Weiguo and Gundersen, Georg A. and Benveniste, Helene and Vates, G. Edward and Deane, Rashid and Goldman, Steven A. and Nagelhus, Erlend A. and Nedergaard, Maiken , number =. 2012 , journal =. doi:10.1126/scitranslmed.3003748 , issn =

    doi:10.1126/scitranslmed.3003748 2012

  4. [5]

    2021 , journal =

    Roy-O’Reilly, Meaghan and Mulavara, Ajitkumar and Williams, Thomas , month =. 2021 , journal =. doi:10.1038/s41526-021-00133-z , issn =

    work page doi:10.1038/s41526-021-00133-z 2021

  5. [6]

    , number =

    Takaddus, Ahmed Tasnub and Chandy, Abhilash J. , number =. 2018 , journal =. doi:10.1080/10255842.2018.1516764 , issn =

    arXiv 2018

  6. [7]

    and Thomas, John H

    Guo, Yisen and Quirk, Keelin and Kelley, Douglas H. and Thomas, John H. , number =. 2025 , journal =. doi:10.1098/rsif.2025.0010 , issn =

    arXiv 2025

  7. [8]

    2020 , journal =

    Wang, Xiaowei and Lou, Nanhong and Eberhardt, Allison and Yang, Yujia and Kusk, Peter and Xu, Qiwu and F. 2020 , journal =. doi:10.1126/scitranslmed.aaw3210 , issn =

    work page doi:10.1126/scitranslmed.aaw3210 2020

  8. [9]

    and Heys, Jeffrey J

    Ray, Lori and Iliff, Jeffrey J. and Heys, Jeffrey J. , month =. 2019 , journal =. doi:10.1186/s12987-019-0126-9 , issn =

    doi:10.1186/s12987-019-0126-9 2019

Show all 101 references
  1. [10]

    and Coenen, Wilfried and Haughton, Victor and S

    Nozaleda, Guillermo L. and Coenen, Wilfried and Haughton, Victor and S. 2025 , journal =. doi:10.1038/s41598-025-97631-x , issn =

    2025 doi

  2. [11]

    Lee, Stuart M. C. and Ribeiro, L. Christine and Martin, David S. and Zwart, Sara R. and Feiveson, Alan H. and Laurie, Steven S. and Macias, Brandon R. and Crucian, Brian E. and Krieger, Stephanie and Weber, Daniela and Grune, Tilman and Platts, Steven H. and Smith, Scott M. an...

    2020

  3. [12]

    and Costanzo, Francesco , month =

    Kedarasetti, Ravi Teja and Drew, Patrick J. and Costanzo, Francesco , month =. 2022 , journal =. doi:10.1186/s12987-022-00326-y , issn =

    2022 doi

  4. [13]

    Boster, Kimberly A. S. and Cai, Shengze and Ladr. 2023 , journal =. doi:10.1073/pnas.2217744120 , issn =

    2023 doi

  5. [14]

    and Alferova, Irina V

    Marshall-Goebel, Karina and Laurie, Steven S. and Alferova, Irina V. and Arbeille, Philippe and Au. 2019 , journal =. doi:10.1001/jamanetworkopen.2019.15011 , issn =

    2019

  6. [15]

    Bork, Peter A. R. and Ladr. 2023 , journal =. doi:10.1098/rsif.2023.0050 , issn =

    2023

  7. [16]

    and Sepehrband, Farshid and Toga, Arthur W

    Lynch, Kirsten M. and Sepehrband, Farshid and Toga, Arthur W. and Choupan, Jeiran , month =. 2023 , journal =. doi:10.1016/j.neuroimage.2023.120009 , issn =

    2023

  8. [17]

    , month =

    Menon, Karthik and Hu, Zinan and Marsden, Alison L. , month =. 2024 , journal =. doi:10.1017/flo.2024.5 , issn =

    2024 doi

  9. [18]

    and Thomas, John H

    Kelley, Douglas H. and Thomas, John H. , month =. 2023 , journal =. doi:10.1146/annurev-fluid-120720-011638 , issn =

    2023 doi

  10. [19]

    2020 , journal =

    Cl. 2020 , journal =. doi:10.1152/jn.00476.2019 , issn =

    2020

  11. [20]

    2023 , journal =

    Park, Chang‐hyun and Shin, Na‐Young and Nam, Yoonho and Yoon, Uicheul and Ahn, Kookjin and Lee, Seung‐Koo , number =. 2023 , journal =. doi:10.1002/hbm.26277 , issn =

    2023 doi

  12. [21]

    and Cohen-Gadol, Aaron A

    Shidhore, Tanmay C. and Cohen-Gadol, Aaron A. and Rayz, Vitaliy L. and Christov, Ivan C. , number =. 2023 , journal =. doi:10.1115/1.4056317 , issn =

    2023 doi

  13. [22]

    2020 , journal =

    Xue, Yang and Liu, Na and Zhang, Miaoyi and Ren, Xue and Tang, Jie and Fu, Jianhui , month =. 2020 , journal =. doi:10.1016/j.brainresbull.2020.04.008 , issn =

    2020 doi

  14. [23]

    and Melo-Carrillo, Agustin and Strassman, Andrew M

    Schain, Aaron J. and Melo-Carrillo, Agustin and Strassman, Andrew M. and Burstein, Rami , number =. 2017 , journal =. doi:10.1523/JNEUROSCI.3390-16.2017 , issn =

    2017 doi

  15. [24]

    2022 , journal =

    Wostyn, Peter and Mader, Thomas H and Gibson, Charles Robert and Nedergaard, Maiken , month =. 2022 , journal =. doi:10.2147/EB.S354710 , issn =

    2022 doi

  16. [25]

    Williams, J. G. and Turney, B. W. and Moulton, D. E. and Waters, S. L. , month =. 2020 , journal =. doi:10.1017/jfm.2020.121 , issn =

    2020 doi

  17. [26]

    and Johnston, I.H

    Bloomfield, I.G. and Johnston, I.H. and Bilston, L.E. , number =. 1998 , journal =. doi:10.1159/000028659 , issn =

    1998 doi

  18. [27]

    2024 , journal =

    Luo, Jilong and Yang, Jing and Zhao, Juan and Cui, Bin and Cui, Yaoyuan and Tang, Shiyi and Wang, Anqing and Chen, Yu and Wang, Junxiao and Yan, Junhao and Wang, Guan and Han, Hongbin and Du, Jichen , month =. 2024 , journal =. doi:10.1016/j.actaastro.2023.12.004 , issn =

    2024 doi

  19. [28]

    and Rallabandi, B

    Zhang, X. and Rallabandi, B. , month =. 2024 , journal =. doi:10.1017/jfm.2024.612 , issn =

    2024 doi

  20. [29]

    and Olveda, Genaro and Thomas, John H

    Mestre, Humberto and Tithof, Jeffrey and Du, Ting and Song, Wei and Peng, Weiguo and Sweeney, Amanda M. and Olveda, Genaro and Thomas, John H. and Nedergaard, Maiken and Kelley, Douglas H. , month =. 2018 , journal =. doi:10.1038/s41467-018-07318-3 , issn =

    2018 doi

  21. [30]

    , number =

    Thomas, John H. , number =. 2019 , journal =. doi:10.1098/rsif.2019.0572 , issn =

    2019

  22. [31]

    2024 , journal =

    Rallabandi, Bhargav , month =. 2024 , journal =. doi:10.1146/annurev-fluid-120720-024426 , issn =

    2024 doi

  23. [32]

    2023 , journal =

    Li, Penghui and Guo, Weiqi and Fan, Jinbo and Su, Chen and Zhao, Xiuguo and Xu, Xinxi , month =. 2023 , journal =. doi:10.1016/j.jaerosci.2023.106166 , issn =

    2023

  24. [33]

    , month =

    Heil, Matthias and Hazel, Andrew L. , month =. 2011 , journal =. doi:10.1146/annurev-fluid-122109-160703 , issn =

    2011 doi

  25. [34]

    doi:10.1007/978-3-0348-0822-4

    2014 , booktitle =. doi:10.1007/978-3-0348-0822-4

    2014 doi

  26. [35]

    and Echagarruga, Christina and Gluckman, Bruce J

    Kedarasetti, Ravi Teja and Turner, Kevin L. and Echagarruga, Christina and Gluckman, Bruce J. and Drew, Patrick J. and Costanzo, Francesco , month =. 2020 , journal =. doi:10.1186/s12987-020-00214-3 , issn =

    2020 doi

  27. [36]

    and Kelley, Douglas H

    Gan, Yiming and Thomas, John H. and Kelley, Douglas H. , number =. 2024 , journal =. doi:10.1098/rsif.2023.0659 , issn =

    2024

  28. [37]

    and Li, Baoman and Peng, Weiguo and Verghese, Philip B

    Achariyar, Thiyagaragan M. and Li, Baoman and Peng, Weiguo and Verghese, Philip B. and Shi, Yang and McConnell, Evan and Benraiss, Abdellatif and Kasper, Tristan and Song, Wei and Takano, Takahiro and Holtzman, David M. and Nedergaard, Maiken and Deane, Rashid , month =. 2016 ...

    2016 doi

  29. [38]

    2023 , journal =

    Holstein-R. 2023 , journal =. doi:10.1038/s41593-023-01327-2 , issn =

    2023 doi

  30. [39]

    2022 , journal =

    Jirak, Peter and Mirna, Moritz and Rezar, Richard and Motloch, Lukas J and Lichtenauer, Michael and Jordan, Jens and Binneboessel, Stephan and Tank, Jens and Limper, Ulrich and Jung, Christian , number =. 2022 , journal =. doi:10.1093/eurjpc/zwac029 , issn =

    2022 doi

  31. [40]

    and Mestre, Humberto and Nedergaard, Maiken and Thomas, John H

    Tithof, Jeffrey and Kelley, Douglas H. and Mestre, Humberto and Nedergaard, Maiken and Thomas, John H. , month =. 2019 , journal =. doi:10.1186/s12987-019-0140-y , issn =

    2019 doi

  32. [41]

    and Mukhopadhyay, Debduti and Nagpal, Sagar and Osmond, Peter , number =

    Izzo, Joseph L. and Mukhopadhyay, Debduti and Nagpal, Sagar and Osmond, Peter , number =. 2022 , journal =. doi:10.1038/s41371-022-00791-w , issn =

    2022 doi

  33. [42]

    and Hupfeld, Kathleen E

    McGregor, Heather R. and Hupfeld, Kathleen E. and Pasternak, Ofer and Beltran, Nichole E. and De Dios, Yiri E. and Bloomberg, Jacob J. and Wood, Scott J. and Mulavara, Ajitkumar P. and Riascos, Roy F. and Reuter-Lorenz, Patricia A. and Seidler, Rachael D. , month =. 2023 , jou...

    2023 doi

  34. [43]

    and Robertson, Andrew D

    Hughson, Richard L. and Robertson, Andrew D. and Arbeille, Philippe and Shoemaker, J. Kevin and Rush, James W. E. and Fraser, Katelyn S. and Greaves, Danielle K. , number =. 2016 , journal =. doi:10.1152/ajpheart.00802.2015 , issn =

    2016 arXiv

  35. [44]

    , number =

    Basser, Peter J. , number =. 1992 , journal =. doi:10.1016/0026-2862(92)90077-3 , issn =

    1992 doi

  36. [45]

    2019 , journal =

    Yamada, Shigeki and Ishikawa, Masatsune and Yamamoto, Kazuo and Yamaguchi, Makoto and Oshima, Marie , month =. 2019 , journal =. doi:10.1016/j.jns.2019.01.022 , issn =

    2019 doi

  37. [46]

    and Taylor, J.A

    Tidwell, J.B. and Taylor, J.A. and Collins, H.R. and Chamberlin, J.H. and Barisano, G. and Sepehrband, F. and Turner, M.D. and Gauthier, G. and Mulder, E.R. and Gerlach, D.A. and Roberts, D.R. , number =. 2023 , journal =. doi:10.3174/ajnr.A7949 , issn =

    2023 doi

  38. [47]

    and Richmond, Sutton B

    Hupfeld, Kathleen E. and Richmond, Sutton B. and McGregor, Heather R. and Schwartz, Daniel L. and Luther, Madison N. and Beltran, Nichole E. and Kofman, Igor S. and De Dios, Yiri E. and Riascos, Roy F. and Wood, Scott J. and Bloomberg, Jacob J. and Mulavara, Ajitkumar P. and S...

    2022 doi

  39. [48]

    and Zenit, Roberto and Rodriguez, Mauro , number =

    Trevino, Avery and Powers, Thomas R. and Zenit, Roberto and Rodriguez, Mauro , number =. 2025 , journal =. doi:10.1103/PhysRevFluids.10.054003 , issn =

    2025 doi

  40. [49]

    and Zhang, X

    Coenen, W. and Zhang, X. and S. 2021 , journal =. doi:10.1017/jfm.2021.525 , issn =

    2021 doi

  41. [50]

    and Bertram, Christopher D

    Moore, James E. and Bertram, Christopher D. , month =. 2018 , journal =. doi:10.1146/annurev-fluid-122316-045259 , issn =

    2018 doi

  42. [51]

    and McGregor, H.R

    Hupfeld, K.E. and McGregor, H.R. and Reuter-Lorenz, P.A. and Seidler, R.D. , month =. 2021 , journal =. doi:10.1016/j.neubiorev.2020.11.017 , issn =

    2021 doi

  43. [52]

    and Phillips, Scott D

    Buckey, Jay C. and Phillips, Scott D. and Anderson, Allison P. and Chepko, Ariane B. and Archambault-Leger, Veronique and Gui, Jiang and Fellows, Abigail M. , number =. 2018 , journal =. doi:10.1152/ajpregu.00086.2018 , issn =

    2018

  44. [53]

    and Bifulco, Savannah F

    Gonzalo, Alejandro and Augustin, Christoph M. and Bifulco, Savannah F. and Telle, Åshild and Chahine, Yaacoub and Kassar, Ahmad and Guerrero‐Hurtado, Manuel and Dur. 2024 , journal =. doi:10.1113/JP287011 , issn =

    2024 doi

  45. [54]

    and Andersen, Mie and Tokarska, Klaudia and Radovanovic, Tessa and Kjaerby, Celia and S

    Hauglund, Natalie L. and Andersen, Mie and Tokarska, Klaudia and Radovanovic, Tessa and Kjaerby, Celia and S. 2025 , journal =. doi:10.1016/j.cell.2024.11.027 , issn =

    2025 doi

  46. [55]

    2018 , journal =

    S. 2018 , journal =. doi:10.1017/jfm.2018.67 , issn =

    2018 doi

  47. [56]

    2009 , journal =

    Wittek, Adam and Hawkins, Trent and Miller, Karol , month =. 2009 , journal =. doi:10.1007/s10237-008-0118-1 , issn =

    2009 doi

  48. [57]

    2024 , journal =

    Winn, Aaron and Katifori, Eleni , month =. 2024 , journal =. doi:10.1017/jfm.2024.480 , issn =

    2024 doi

  49. [58]

    2017 , journal =

    Bedussi, Beatrice and van der Wel, Nicole N and de Vos, Judith and van Veen, Henk and Siebes, Maria and VanBavel, Ed and Bakker, Erik NTP , number =. 2017 , journal =. doi:10.1177/0271678X16655550 , issn =

    2017 doi

  50. [59]

    2018 , journal =

    Bedussi, Beatrice and Almasian, Mitra and de Vos, Judith and VanBavel, Ed and Bakker, Erik NTP , number =. 2018 , journal =. doi:10.1177/0271678X17737984 , issn =

    2018 doi

  51. [60]

    and Lin, LiJing A

    Mestre, Humberto and Verma, Natasha and Greene, Thom D. and Lin, LiJing A. and Ladron-de-Guevara, Antonio and Sweeney, Amanda M. and Liu, Guojun and Thomas, V. Kaye and Galloway, Chad A. and de Mesy Bentley, Karen L. and Nedergaard, Maiken and Mehta, Rupal I. , month =. 2022 ,...

    2022 doi

  52. [61]

    2020 , journal =

    Roman. 2020 , journal =. doi:10.1038/s41598-020-77787-4 , issn =

    2020 doi

  53. [62]

    1971 , journal =

    Jaffrin, M Y and Shapiro, A H , month =. 1971 , journal =. doi:10.1146/annurev.fl.03.010171.000305 , issn =

    1971

  54. [63]

    and Balmforth, N.J

    Takagi, D. and Balmforth, N.J. and Llewellyn Smith, Stefan G. , month =. 2024 , journal =. doi:10.1017/jfm.2024.386 , issn =

    2024 doi

  55. [64]

    Brennen and Thomas, John H

    Carr, J. Brennen and Thomas, John H. and Liu, Jia and Shang, Jessica K. , month =. 2021 , journal =. doi:10.1017/jfm.2021.277 , issn =

    2021 doi

  56. [65]

    and Balmforth, N

    Takagi, D. and Balmforth, N. J. , month =. 2011 , journal =. doi:10.1017/S0022112010005914 , issn =

    2011 doi

  57. [66]

    2026 , journal =

    Trevino, Avery and Zenit, Roberto and Rodriguez, Mauro , month =. 2026 , journal =. doi:10.48550/arXiv.2604.04779 , arxivId =

    2026 doi arXiv

  58. [67]

    and Pandey, S.K

    Misra, J.C. and Pandey, S.K. , number =. 2002 , journal =. doi:10.1016/S0898-1221(02)80022-0 , issn =

    2002 doi

  59. [68]

    , month =

    Li, Chenji and Dabiri, Sadegh and Ardekani, Arezoo M. , month =. 2025 , journal =. doi:10.1186/s12987-025-00668-3 , issn =

    2025 doi

  60. [69]

    2022 , journal =

    Ladr. 2022 , journal =. doi:10.1016/j.jtbi.2022.111103 , issn =

    2022

  61. [70]

    2023 , journal =

    Gan, Yiming and Holstein-R. 2023 , journal =. doi:10.1098/rsif.2023.0288 , issn =

    2023

  62. [71]

    2012 , journal =

    Alastruey, Jordi and Passerini, Tiziano and Formaggia, Luca and Peir. 2012 , journal =. doi:10.1007/s10665-012-9555-z , issn =

    2012 doi

  63. [72]

    and Christov, Ivan C

    Pande, Shrihari D. and Christov, Ivan C. , month =. 2025 , journal =. doi:10.1016/j.jnnfm.2024.105347 , issn =

    2025

  64. [73]

    Grotberg, J. B. , month =. 1994 , journal =. doi:10.1146/annurev.fl.26.010194.002525 , issn =

    1994

  65. [74]

    and Pike, Martin and Simon, Matthew and Iliff, Jeffrey J

    Ray, Lori A. and Pike, Martin and Simon, Matthew and Iliff, Jeffrey J. and Heys, Jeffrey J. , month =. 2021 , journal =. doi:10.1186/s12987-021-00290-z , issn =

    2021 doi

  66. [75]

    2017 , journal =

    Leizea, Ibai and Mendizabal, Ainitze and Alvarez, Hugo and Aguinaga, Iker and Borro, Diego and Sanchez, Emilio , number =. 2017 , journal =. doi:10.1109/MCG.2015.96 , issn =

    2017 doi

  67. [76]

    and Blair, Gordon W

    Jochems, Angela C.C. and Blair, Gordon W. and Stringer, Michael S. and Thrippleton, Michael J. and Clancy, Una and Chappell, Francesca M. and Brown, Rosalind and Jaime Garcia, Daniela and Hamilton, Olivia K.L. and Morgan, Alasdair G. and Marshall, Ian and Hetherington, Kirstie...

    2020 doi

  68. [77]

    and Wuyts, Floris L

    Barisano, Giuseppe and Tomilovskaya, Elena and Roberts, Donna R. and Wuyts, Floris L. , number =. 2022 , journal =. doi:10.1073/pnas.2208241119 , issn =

    2022 doi

  69. [78]

    Boster, Kimberly A. S. and Tithof, Jeffrey and Cook, Douglas D. and Thomas, John H. and Kelley, Douglas H. , number =. 2022 , journal =. doi:10.1098/rsif.2022.0257 , issn =

    2022

  70. [79]

    and Ladr

    Raicevic, Nikola and Forer, Jarod M. and Ladr. 2023 , journal =. doi:10.1186/s12987-023-00454-z , issn =

    2023 doi

  71. [80]

    , number =

    Nguyen, Tuan and Ong, Joshua and Waisberg, Ethan and Lee, Andrew G. , number =. 2024 , journal =. doi:10.1038/s41433-024-03119-9 , issn =

    2024 doi

  72. [81]

    2023 , journal =

    Bojarskaite, Laura and Vallet, Alexandra and Bj. 2023 , journal =. doi:10.1038/s41467-023-36643-5 , issn =

    2023 doi

  73. [82]

    2022 , journal =

    Christov, Ivan C , number =. 2022 , journal =. doi:10.1088/1361-648X/ac327d , issn =

    2022 doi

  74. [83]

    and Alaminos-Quesada, Javier and Guti

    Nozaleda, Guillermo L. and Alaminos-Quesada, Javier and Guti. 2025 , journal =. doi:10.1103/89kj-npfn , issn =

    2025 doi

  75. [84]

    2017 , journal =

    Meurer, Aaron and Smith, Christopher P and Paprocki, Mateusz and. 2017 , journal =. doi:10.7717/peerj-cs.103 , keywords =

    2017 doi

  76. [85]

    2026 , journal =

    Covarrubias, Geraldy and Bautista, Oscar and Arcos, José and M. 2026 , journal =. doi:10.1017/jfm.2026.11286 , issn =

    2026

  77. [86]

    and Gibson, Charles Robert and Nedergaard, Maiken , number =

    Wostyn, Peter and Mader, Thomas H. and Gibson, Charles Robert and Nedergaard, Maiken , number =. 2022 , journal =. doi:10.1073/pnas.2207724119 , issn =

    2022 doi

  78. [87]

    and Jillings, Steven and Jeurissen, Ben and Taylor, James A

    Barisano, Giuseppe and Sepehrband, Farshid and Collins, Heather R. and Jillings, Steven and Jeurissen, Ben and Taylor, James A. and Schoenmaekers, Catho and De Laet, Chloë and Rukavishnikov, Ilya and Nosikova, Inna and Litvinova, Liudmila and Rumshiskaya, Alena and Annen, Jitk...

    2022

  79. [88]

    and Waters, S.L

    Cummings, L.J. and Waters, S.L. and Wattis, J.A.D. and Graham, S.J. , month =. 2004 , journal =. doi:10.1007/s00285-003-0252-4 , issn =

    2004 doi

  80. [89]

    2015 , journal =

    Alnaes, Martin S and Blechta, Jan and Hake, Johan and Johansson, August and Kehlet, Benjamin and Logg, Anders and Richardson, Chris and Ring, Johannes and Rognes, Marie E and Wells, Garth N , number =. 2015 , journal =. doi:10.11588/ans.2015.100.20553 , issn =

    2015 doi

  81. [90]

    and Baumer, Alexa C

    Leftwich, Megan C. and Baumer, Alexa C. , month =. 2024 , journal =. doi:10.1146/annurev-fluid-121021-033738 , issn =

    2024 doi

  82. [91]

    and Lilius, Tuomas O

    Lohela, Terhi J. and Lilius, Tuomas O. and Nedergaard, Maiken , number =. 2022 , journal =. doi:10.1038/s41573-022-00500-9 , issn =

    2022 doi

  83. [92]

    2020 , journal =

    Hupfeld, Kathleen E and McGregor, Heather R and Lee, Jessica K and Beltran, Nichole E and Kofman, Igor S and De Dios, Yiri E and Reuter-Lorenz, Patti A and Riascos, Roy F and Pasternak, Ofer and Wood, Scott J and Bloomberg, Jacob J and Mulavara, Ajitkumar P and Seidler, Rachae...

    2020 doi

  84. [93]

    and Linninger, Andreas , number =

    Penn, Richard D. and Linninger, Andreas , number =. 2009 , journal =. doi:10.1159/000218198 , issn =

    2009 doi

  85. [94]

    2006 , journal =

    Lu, Yun-Bi and Franze, Kristian and Seifert, Gerald and Steinh. 2006 , journal =. doi:10.1073/pnas.0606150103 , issn =

    2006 doi

  86. [95]

    and Biessels, Geert Jan and Kuijf, Hugo J

    Bouvy, Willem H. and Biessels, Geert Jan and Kuijf, Hugo J. and Kappelle, L. Jaap and Luijten, Peter R. and Zwanenburg, Jaco J.M. , number =. 2014 , journal =. doi:10.1097/RLI.0000000000000027 , issn =

    2014 doi

  87. [96]

    and Costanzo, Francesco , month =

    Kedarasetti, Ravi Teja and Drew, Patrick J. and Costanzo, Francesco , month =. 2020 , journal =. doi:10.1038/s41598-020-66887-w , issn =

    2020 doi

  88. [97]

    2026 , journal =

    Sarkar, Drik and Mukherjee, Saikat , month =. 2026 , journal =. doi:10.1017/jfm.2026.11573 , issn =

    2026

  89. [98]

    and Pande, S

    Wang, X. and Pande, S. D. and Christov, I. C. , pages =. 2022 , journal =. doi:10.1016/j.mechrescom.2022.104016 , arxivId =

    2022

  90. [99]

    2026 , journal =

    Winn, Aaron and Katifori, Eleni , number =. 2026 , journal =. doi:10.1103/pw9s-vvf4 , issn =

    2026 doi

  91. [100]

    and Iliff, Jeffrey J

    Kress, Benjamin T. and Iliff, Jeffrey J. and Xia, Maosheng and Wang, Minghuan and Wei, Helen S. and Zeppenfeld, Douglas and Xie, Lulu and Kang, Hongyi and Xu, Qiwu and Liew, Jason A. and Plog, Benjamin A. and Ding, Fengfei and Deane, Rashid and Nedergaard, Maiken , number =. 2...

    2014 doi

  92. [101]

    and Jaitner, Noah and Fedders, Michael and G

    Schattenfroh, Jakob and Meyer, Tom and Aghamiry, Hossein S. and Jaitner, Noah and Fedders, Michael and G. 2026 , journal =. doi:10.1016/j.actbio.2026.02.002 , issn =

    2026 doi

  93. [102]

    Womersley, J. R. , number =. 1957 , journal =. doi:10.1088/0031-9155/2/2/305 , issn =

    1957 doi

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.