A Lattice Boltzmann Method for Non-Newtonian Blood Flow in Coiled Intracranial Aneurysms

Barbara Wohlmuth; Dmytro Sytnyk; Medeea Horvat; Stephan B. Lunowa

arxiv: 2402.10809 · v2 · pith:WP2ICLTPnew · submitted 2024-02-16 · 🧮 math.NA · cs.NA· physics.flu-dyn

A Lattice Boltzmann Method for Non-Newtonian Blood Flow in Coiled Intracranial Aneurysms

Medeea Horvat , Stephan B. Lunowa , Dmytro Sytnyk , Barbara Wohlmuth This is my paper

Pith reviewed 2026-05-24 03:14 UTC · model grok-4.3

classification 🧮 math.NA cs.NAphysics.flu-dyn

keywords lattice Boltzmann methodvolume-averaged Navier-Stokesporous mediumintracranial aneurysmscoil embolizationnon-Newtonian blood flowpatient-specific modelinghemodynamics

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The pith

A lattice Boltzmann method with volume-averaged Navier-Stokes equations models non-Newtonian blood flow through coiled aneurysms by treating the coil as an inhomogeneous porous medium.

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

The paper develops a computational workflow that incorporates patient-specific aneurysm geometries and parameters to simulate how coil embolization alters blood flow. Coils are represented as an inhomogeneous porous medium within the volume-averaged Navier-Stokes equations that include non-Newtonian blood rheology. These equations are discretized and solved with a problem-adapted lattice Boltzmann method. Direct comparison of the resulting flow fields against fully resolved simulations supports the approach as a practical way to assess treatment effects without resolving every coil wire.

Core claim

The central claim is that the volume-averaged Navier-Stokes equations for non-Newtonian blood, closed by an inhomogeneous porous-medium representation of the coil, can be solved with a lattice Boltzmann method on patient-derived geometries to produce flow predictions whose essential features match those obtained from fully resolved simulations, thereby enabling patient-specific assessment of flow changes induced by coil insertion.

What carries the argument

Volume-averaged Navier-Stokes equations closed by an inhomogeneous porous-medium model for the coil and discretized by a problem-adapted lattice Boltzmann method.

If this is right

Flow predictions for coiled aneurysms become feasible on patient-specific meshes without explicit resolution of individual coil filaments.
The same workflow can be used to compare alternative coil placements or packing densities before intervention.
Non-Newtonian rheology is retained throughout the porous-medium region, so shear-thinning effects remain present after treatment.
The lattice Boltzmann discretization handles the transition between free-flow and porous regions without additional interface conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could be combined with time-resolved imaging to update permeability parameters from post-treatment angiograms and thereby refine predictions for follow-up interventions.
Because the porous-medium description is local, the framework extends in principle to other endovascular devices such as flow-diverter stents whose effective permeability can be calibrated similarly.
If the permeability maps can be derived from coil packing density alone, the workflow becomes a candidate for rapid in-clinic estimation of hemodynamic risk after embolization.

Load-bearing premise

Representing the coil as an inhomogeneous porous medium with suitable permeability parameters, together with the volume-averaged Navier-Stokes equations, sufficiently captures the essential flow changes caused by coil insertion.

What would settle it

A side-by-side comparison in the same patient geometry in which the volume-averaged model produces statistically significant differences in wall shear stress, intra-aneurysmal velocity, or recirculation patterns relative to both fully resolved simulations and available experimental data would falsify the validity statement.

read the original abstract

Intracranial aneurysms are the leading cause of hemorrhagic stroke. One of the established treatment approaches is the embolization induced by coil insertion. However, the prediction of treatment and subsequent changed flow characteristics in the aneurysm is still an open problem. In this work, we present an approach based on a patient-specific geometry and parameters including a coil representation as inhomogeneous porous medium. The model consists of the volume-averaged Navier-Stokes equations for a non-Newtonian blood rheology. We solve these equations using a problem-adapted lattice Boltzmann method and present a comparison between fully-resolved and volume-averaged simulations. The results indicate the validity of the model. Overall, this workflow allows for patient specific assessment of the flow due to potential treatment.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper combines LBM with volume-averaged non-Newtonian flow and an inhomogeneous porous coil model for patient-specific aneurysms, but the abstract's validity claim rests on an unquantified comparison to fully-resolved runs.

read the letter

This paper takes established lattice Boltzmann techniques and volume-averaged Navier-Stokes equations, adds non-Newtonian blood rheology, and represents the coil as an inhomogeneous porous medium inside patient-specific aneurysm geometries. The workflow aims at predicting flow changes after coiling, which is a real clinical need in aneurysm treatment planning. That specific combination in this setting is what is new; prior LBM work on blood flow exists, but the inhomogeneous porous treatment tied to a full patient workflow is the extension here. The setup is clearly described and the clinical motivation is direct, so readers working on biomedical CFD will see a practical way to handle the coil without resolving every wire. The comparison to fully-resolved simulations is mentioned as support for the model, which is the right kind of check to attempt. The soft spot is exactly the one in the stress-test note: the abstract states that the comparison indicates validity but supplies no error metrics, L2 norms, flow-rate differences, or sensitivity results on the permeability parameters. Without those numbers it is difficult to judge whether the porous approximation captures the flow diversion and stasis changes at the level needed for treatment decisions. The assumption that the volume-averaged model plus chosen permeability is sufficient is invoked but not yet demonstrated quantitatively in what is shown. This work is for numerical analysts and biomedical engineers who already use LBM or porous-medium models and want to see the aneurysm application. A reader looking for a ready-to-use clinical tool will find the idea but will need the missing metrics before relying on the predictions. The paper deserves peer review because the problem is relevant, the method is formally grounded in existing equations, and the gaps are fixable with added data rather than fundamental flaws in the approach.

Referee Report

2 major / 1 minor

Summary. The paper presents a lattice Boltzmann discretization of the volume-averaged Navier-Stokes equations with a non-Newtonian blood rheology for patient-specific intracranial aneurysm geometries. Coils are represented as an inhomogeneous porous medium whose permeability parameters are chosen to match a fully-resolved coil geometry; the authors perform a comparison between the fully-resolved and volume-averaged simulations and conclude that the results indicate model validity, thereby enabling patient-specific post-treatment flow assessment.

Significance. If the porous-medium approximation is shown to reproduce the essential flow diversion and intra-aneurysmal stasis with quantifiable accuracy, the method would offer a computationally tractable route to treatment planning that avoids explicit resolution of individual coil wires. The use of a problem-adapted LBM and non-Newtonian rheology are standard strengths in this domain.

major comments (2)

[Abstract] Abstract: the statement that 'the results indicate the validity of the model' is unsupported because the manuscript reports no quantitative comparison metrics (relative L2 errors on velocity or wall-shear-stress fields, integrated flow-rate differences, or sensitivity of results to the chosen permeability values) between the fully-resolved and volume-averaged simulations.
[Model description / Results] Model description and results sections: the central claim that the inhomogeneous porous-medium representation 'sufficiently captures the essential flow changes for treatment prediction' rests on an unquantified agreement; without reported error thresholds or parameter-selection procedure, it is impossible to judge whether the approximation meets the accuracy needed for the stated clinical workflow.

minor comments (1)

The permeability tensor is described as 'inhomogeneous' but the precise spatial variation and the fitting procedure used to obtain its components from the fully-resolved geometry are not stated explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments correctly identify that the comparison between fully-resolved and volume-averaged simulations is presented primarily through qualitative figures without accompanying quantitative error metrics. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Abstract] Abstract: the statement that 'the results indicate the validity of the model' is unsupported because the manuscript reports no quantitative comparison metrics (relative L2 errors on velocity or wall-shear-stress fields, integrated flow-rate differences, or sensitivity of results to the chosen permeability values) between the fully-resolved and volume-averaged simulations.

Authors: We agree that the abstract claim would be strengthened by quantitative support. The current manuscript presents the comparison via side-by-side visualizations of velocity and flow patterns that demonstrate agreement in flow diversion and stasis, but does not include the listed numerical metrics. In revision we will add relative L2 errors on velocity, wall-shear-stress differences, integrated flow-rate discrepancies, and a brief sensitivity study with respect to permeability values, then update the abstract to reflect these results. revision: yes
Referee: [Model description / Results] Model description and results sections: the central claim that the inhomogeneous porous-medium representation 'sufficiently captures the essential flow changes for treatment prediction' rests on an unquantified agreement; without reported error thresholds or parameter-selection procedure, it is impossible to judge whether the approximation meets the accuracy needed for the stated clinical workflow.

Authors: The model description section explains the permeability calibration by matching the effective hydraulic resistance of the fully-resolved coil geometry via separate simulations on the same domain. The results section then shows that the volume-averaged model reproduces the main flow features. We acknowledge, however, that no explicit error thresholds or quantitative assessment of clinical relevance are supplied. We will therefore include error thresholds, report the parameter-selection procedure more explicitly, and discuss the observed accuracy level relative to the requirements of post-treatment flow assessment. revision: yes

Circularity Check

0 steps flagged

No circularity; validity rests on independent fully-resolved comparison

full rationale

The paper sets up volume-averaged Navier-Stokes with non-Newtonian rheology and an inhomogeneous porous-medium coil representation, then solves via adapted LBM. The central validity claim is explicitly tied to a comparison against separate fully-resolved simulations rather than any fitted parameter, self-citation chain, or definitional equivalence. No step reduces a prediction to its own inputs by construction, and the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based solely on abstract: the central claim rests on the domain assumption that volume-averaged equations plus porous-medium coil model are adequate, plus unspecified parameters for the porous representation.

free parameters (1)

porous medium permeability parameters
Inhomogeneous porous medium representation for coils requires location-dependent permeability values that must be chosen or fitted to coil geometry and packing density.

axioms (1)

domain assumption Volume-averaged Navier-Stokes equations with non-Newtonian rheology accurately represent flow inside and around the coiled region when coils are treated as porous medium
Invoked when defining the model and stating that comparison indicates validity.

pith-pipeline@v0.9.0 · 5669 in / 1353 out tokens · 39174 ms · 2026-05-24T03:14:25.081163+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

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Eddleman, C.S., Welch, B.G., Vance, A.Z., Rickert, K.L., White, J.A., Pride, G.L., Purdy, P.D.: Endovascular coils: properties, technical complications and salvage techniques. J. Neurointerv. Surg. 5(2), 104–109 (2013). DOI 10.1136/neurintsurg-2012-010263

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Ergun, S.: Fluid flow through packed columns. Chem. Eng. Prog. 48, 89–94 (1952) 10 M. Horvat, S. B. Lunowa, D. Sytnyk, and B. Wohlmuth

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He, Y.L., Liu, Q., Li, Q., Tao, W.Q.: Lattice Boltzmann methods for single-phase and solid- liquid phase-change heat transfer in porous media: A review. Int. J. Heat Mass Tran. 129, 160–197 (2019). DOI j.ijheatmasstransfer.2018.08.135

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Hosseini, S.A., Huang, F., Th ´evenin, D.: Lattice Boltzmann model for simulation of flow in intracranial aneurysms considering non-Newtonian effects. Phys. Fluids34(7), 073105 (2022). DOI 10.1063/5.0098383

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work page doi:10.1007/s11517-016- 2017
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Ouared, R., Chopard, B.: Lattice Boltzmann simulations of blood flow: Non-Newtonian rhe- ology and clotting processes. J. Stat. Phys. 121, 209–221 (2005). DOI 10.1007/s10955-005- 8415-x

work page doi:10.1007/s10955-005- 2005
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Stroke 44, 2046–2054 (2013)

Pierot, L., Wakhloo, A.K.: Endovascular treatment of intracranial aneurysms. Stroke 44, 2046–2054 (2013). DOI 10.1161/STROKEAHA.113.000733

work page doi:10.1161/strokeaha.113.000733 2046
[20]

Cardiovasc

Romero Bhathal, J., Chassagne, F., Marsh, L., Levitt, M.R., Geindreau, C., Aliseda, A.: Mod- eling flow in cerebral aneurysm after coils embolization treatment: a realistic patient-specific porous model approach. Cardiovasc. Eng. Tech.14(1), 115–128 (2023). DOI 10.1007/s13239- 022-00639-x

work page doi:10.1007/s13239- 2023
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Sequeira, A.: Hemorheology: Non-Newtonian Constitutive Models for Blood Flow Simula- tions, pp. 1–44. Springer (2018). DOI 10.1007/978-3-319-74796-5 1

work page doi:10.1007/978-3-319-74796-5 2018
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Liesen, Z

Succi, S.: The Lattice Boltzmann Equation: For Complex States of Flowing Matter. Oxford University Press (2018). DOI 10.1093/oso/9780199592357.001.0001

work page doi:10.1093/oso/9780199592357.001.0001 2018
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Cardiovasc

Yadollahi-Farsani, H., Herrmann, M., Frakes, D., Chong, B.: A new method for simulating embolic coils as heterogeneous porous media. Cardiovasc. Eng. Techn. 10, 32–45 (2019). DOI 10.1007/s13239-018-00383-1

work page doi:10.1007/s13239-018-00383-1 2019
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Angiology 69(1), 17–30 (2018)

Zhao, J., Lin, H., Summers, R., Yang, M., Cousins, B.G., Tsui, J.: Current treatment strate- gies for intracranial aneurysms: an overview. Angiology 69(1), 17–30 (2018). DOI 10.1177/0003319717700503

work page doi:10.1177/0003319717700503 2018
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Zou, Q., He, X.: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 9(6), 1591–1598 (1997). DOI 10.1063/1.869307

work page doi:10.1063/1.869307 1997

[1] [1]

Ashrafizaadeh, M., Bakhshaei, H.: A comparison of non-Newtonian models for lattice Boltz- mann blood flow simulations. Comput. Math. Appl. 58(5), 1045–1054 (2009). DOI 10.1016/j.camwa.2009.02.021

work page doi:10.1016/j.camwa.2009.02.021 2009

[2] [2]

Ataei, M., Salehipour, H.: XLB: A differentiable massively parallel lattice Boltzmann library in Python. Comput. Phys. Commun. 300, 109187 (2024). DOI 10.1016/j.cpc.2024.109187

work page doi:10.1016/j.cpc.2024.109187 2024

[3] [3]

Boyd, J., Buick, J.M., Green, S.: Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method. Phys. Fluids 19(9), 093103 (2007). DOI 10.1063/1.2772250

work page doi:10.1063/1.2772250 2007

[4] [4]

Eddleman, C.S., Welch, B.G., Vance, A.Z., Rickert, K.L., White, J.A., Pride, G.L., Purdy, P.D.: Endovascular coils: properties, technical complications and salvage techniques. J. Neurointerv. Surg. 5(2), 104–109 (2013). DOI 10.1136/neurintsurg-2012-010263

work page doi:10.1136/neurintsurg-2012-010263 2013

[5] [5]

Ergun, S.: Fluid flow through packed columns. Chem. Eng. Prog. 48, 89–94 (1952) 10 M. Horvat, S. B. Lunowa, D. Sytnyk, and B. Wohlmuth

work page 1952

[6] [6]

Fritz, M., K ¨oppl, T., Oden, J.T., Wagner, A., Wohlmuth, B., Wu, C.: A 1D–0D–3D coupled model for simulating blood flow and transport processes in breast tissue. Int. J. Numer. Meth. Bio. 38(7), e3612 (2022). DOI 10.1002/cnm.3612

work page doi:10.1002/cnm.3612 2022

[7] [7]

Geier, M., Sch ¨onherr, M., Pasquali, A., Krafczyk, M.: The cumulant lattice Boltzmann equation in three dimensions: Theory and validation. Comput. Math. Appl.70(4), 507–547 (2015). DOI 10.1016/j.camwa.2015.05.001

work page doi:10.1016/j.camwa.2015.05.001 2015

[8] [8]

Guo, Z., Zheng, C., Shi, B.: Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 65(4), 046308 (2002). DOI 10.1103/physreve.65.046308

work page doi:10.1103/physreve.65.046308 2002

[9] [9]

He, Y.L., Liu, Q., Li, Q., Tao, W.Q.: Lattice Boltzmann methods for single-phase and solid- liquid phase-change heat transfer in porous media: A review. Int. J. Heat Mass Tran. 129, 160–197 (2019). DOI j.ijheatmasstransfer.2018.08.135

work page 2019

[10] [10]

H ¨ocker, S.B., Trunk, R., D¨orfler, W., Krause, M.J.: Towards the simulations of inertial dense particulate flows with a volume-averaged lattice Boltzmann method. Comput. Fluids 166, 152–162 (2018). DOI 10.1016/j.compfluid.2018.02.011

work page doi:10.1016/j.compfluid.2018.02.011 2018

[11] [11]

ArXiv:2402.02798

Holzberger, F., Muhr, M., Wohlmuth, B.: A comprehensive numerical approach to coil place- ment in cerebral aneurysms: Mathematical modeling and in silico occlusion classification (2024). ArXiv:2402.02798. To appear in Biomech. Model. Mechan

work page arXiv 2024

[12] [12]

Hosseini, S.A., Huang, F., Th ´evenin, D.: Lattice Boltzmann model for simulation of flow in intracranial aneurysms considering non-Newtonian effects. Phys. Fluids34(7), 073105 (2022). DOI 10.1063/5.0098383

work page doi:10.1063/5.0098383 2022

[13] [13]

Springer (2017)

Kr¨ uger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., Viggen, E.M.: The Lattice Boltzmann Method. Springer (2017). DOI 10.1007/978-3-319-44649-3

work page doi:10.1007/978-3-319-44649-3 2017

[14] [14]

Maier, M.L.: Coupled lattice Boltzmann and discrete element method for reactive particle fluid flows with applications in process engineering. Ph.D. thesis, Karlsruher Institut f¨ ur Technologie (KIT) (2021). DOI 10.5445/IR/1000132643

work page doi:10.5445/ir/1000132643 2021

[15] [15]

Matyka, M., Koza, Z., Lukasz Miros law: Wall orientation and shear stress in the lattice Boltzmann model. Comput. Fluids73, 115–123 (2013). DOI 10.1016/j.compfluid.2012.12.018

work page doi:10.1016/j.compfluid.2012.12.018 2013

[16] [16]

https://doi.org/10.1007/978-1- 4684-3384-5_11

Nield, D.A., Bejan, A.: Convection in Porous Media. Springer (2013). DOI 10.1007/978-1- 4614-5541-7

work page doi:10.1007/978-1- 2013

[17] [17]

Otani, T., Ii, S., Shigematsu, T., Fujinaka, T., Hirata, M., Ozaki, T., Wada, S.: Computational study for the effects of coil configuration on blood flow characteristics in coil-embolized cerebral aneurysm. Med. Biol. Eng. Comput. 55, 697–710 (2017). DOI 10.1007/s11517-016- 1541-6

work page doi:10.1007/s11517-016- 2017

[18] [18]

Ouared, R., Chopard, B.: Lattice Boltzmann simulations of blood flow: Non-Newtonian rhe- ology and clotting processes. J. Stat. Phys. 121, 209–221 (2005). DOI 10.1007/s10955-005- 8415-x

work page doi:10.1007/s10955-005- 2005

[19] [19]

Stroke 44, 2046–2054 (2013)

Pierot, L., Wakhloo, A.K.: Endovascular treatment of intracranial aneurysms. Stroke 44, 2046–2054 (2013). DOI 10.1161/STROKEAHA.113.000733

work page doi:10.1161/strokeaha.113.000733 2046

[20] [20]

Cardiovasc

Romero Bhathal, J., Chassagne, F., Marsh, L., Levitt, M.R., Geindreau, C., Aliseda, A.: Mod- eling flow in cerebral aneurysm after coils embolization treatment: a realistic patient-specific porous model approach. Cardiovasc. Eng. Tech.14(1), 115–128 (2023). DOI 10.1007/s13239- 022-00639-x

work page doi:10.1007/s13239- 2023

[21] [21]

Sequeira, A.: Hemorheology: Non-Newtonian Constitutive Models for Blood Flow Simula- tions, pp. 1–44. Springer (2018). DOI 10.1007/978-3-319-74796-5 1

work page doi:10.1007/978-3-319-74796-5 2018

[22] [22]

Liesen, Z

Succi, S.: The Lattice Boltzmann Equation: For Complex States of Flowing Matter. Oxford University Press (2018). DOI 10.1093/oso/9780199592357.001.0001

work page doi:10.1093/oso/9780199592357.001.0001 2018

[23] [23]

Cardiovasc

Yadollahi-Farsani, H., Herrmann, M., Frakes, D., Chong, B.: A new method for simulating embolic coils as heterogeneous porous media. Cardiovasc. Eng. Techn. 10, 32–45 (2019). DOI 10.1007/s13239-018-00383-1

work page doi:10.1007/s13239-018-00383-1 2019

[24] [24]

Angiology 69(1), 17–30 (2018)

Zhao, J., Lin, H., Summers, R., Yang, M., Cousins, B.G., Tsui, J.: Current treatment strate- gies for intracranial aneurysms: an overview. Angiology 69(1), 17–30 (2018). DOI 10.1177/0003319717700503

work page doi:10.1177/0003319717700503 2018

[25] [25]

Zou, Q., He, X.: On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 9(6), 1591–1598 (1997). DOI 10.1063/1.869307

work page doi:10.1063/1.869307 1997