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All issues Volume 58 / No 5 (September-October 2024) ESAIM: M2AN, 58 5 (2024) 1681-1724 References
Open Access
Issue
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
Page(s) 1681 - 1724
DOI https://doi.org/10.1051/m2an/2024060
Published online 23 September 2024
  1. N.J. Abbott, Evidence for bulk flow of brain interstitial fluid: significance for physiology and pathology. Neurochem. Int. 45 (2004) 545–552. [CrossRef] [Google Scholar]
  2. M. Alnæs, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M.E. Rognes and G.N. Wells, The FEniCS project version 1.5. Arch. Numer. Softw. 3 (2015) 9–23. [Google Scholar]
  3. A. Alphonse, C.M. Elliott and B. Stinner, An abstract framework for parabolic PDEs on evolving spaces. Port. Math. 72 (2015) 1–46. [CrossRef] [MathSciNet] [Google Scholar]
  4. W. Arendt, D. Dier and S. Fackler, JL Lions’ problem on maximal regularity. Arch. Math. 109 (2017) 59–72. [CrossRef] [MathSciNet] [Google Scholar]
  5. W.F. Boron and E.L. Boulpaep, Medical Physiology. Elsevier Health Sciences (2012). [Google Scholar]
  6. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, Vol. 3. Springer (2008). [Google Scholar]
  7. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Vol. 2. Springer (2010). [Google Scholar]
  8. T. Brinker, E. Stopa, J. Morrison and P. Klinge, A new look at cerebrospinal fluid circulation. Fluids Barriers CNS 11 (2014) 1–16. [Google Scholar]
  9. S. Čanić and E.H. Kim, Mathematical analysis of the quasilinear effects in a hyperbolic model blood flow through compliant axi-symmetric vessels. Math. Methods Appl. Sci. 26 (2003) 1161–1186. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Causemann, V. Vinje and M.E. Rognes, Human intracranial pulsatility during the cardiac cycle: a computational modelling framework. Fluids Barriers CNS 19 (2022) 1–17. [CrossRef] [PubMed] [Google Scholar]
  11. C. D’Angelo, Multiscale modelling of metabolism and transport phenomena in living tissues, Technical report, EPFL (2007). [Google Scholar]
  12. C. D’Angelo, Finite element approximation of elliptic problems with Dirac measure terms in weighted spaces: applications to one-and three-dimensional coupled problems. SIAM J. Numer. Anal. 50 (2012) 194–215. [Google Scholar]
  13. C. D’Angelo and A. Quarteroni, On the coupling of 1D and 3D diffusion-reaction equations: application to tissue perfusion problems. Math. Models Methods Appl. Sci. 18 (2008) 1481–1504. [CrossRef] [MathSciNet] [Google Scholar]
  14. C. Daversin-Catty, V. Vinje, K.-A. Mardal and M.E. Rognes, The mechanisms behind perivascular fluid flow. PLoS ONE 15 (2020) e0244442. [CrossRef] [PubMed] [Google Scholar]
  15. C. Daversin-Catty, I.G. Gjerde and M.E. Rognes, Geometrically reduced modelling of pulsatile flow in perivascular networks. Front. Phys. 10 (2022) 882260. [CrossRef] [Google Scholar]
  16. M.C. Delfour and J.-P. Zolésio, Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization. SIAM (2011). [Google Scholar]
  17. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  18. I. Drelichman, R.G. Durán and I. Ojea, A weighted setting for the numerical approximation of the Poisson problem with singular sources. SIAM J. Numer. Anal. 58 (2020) 590–606. [CrossRef] [MathSciNet] [Google Scholar]
  19. L.C. Evans, Partial Differential Equations, Vol. 19. American Mathematical Society (2010). [Google Scholar]
  20. G.J. Fleischman, T.W. Secomb and J.F. Gross, The interaction of extravascular pressure fields and fluid exchange in capillary networks. Math. Biosci. 82 (1986) 141–151. [Google Scholar]
  21. L. Formaggia, J.-F. Gerbeau, F. Nobile and A. Quarteroni, On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191 (2001) 561–582. [CrossRef] [Google Scholar]
  22. I.G. Gjerde, K. Kumar, J.M. Nordbotten and B. Wohlmuth, Splitting method for elliptic equations with line sources. ESAIM:M2AN 53 (2019) 1715–1739. [CrossRef] [EDP Sciences] [Google Scholar]
  23. I.G. Gjerde, K. Kumar and J.M. Nordbotten, A singularity removal method for coupled 1D–3D flow models. Comput. Geosci. 24 (2020) 443–457. [CrossRef] [MathSciNet] [Google Scholar]
  24. F. Goirand, T.L. Borgne and S. Lorthois, Network-driven anomalous transport is a fundamental component of brain microvascular dysfunction. Nat. Commun. 12 (2021) 7295. [CrossRef] [Google Scholar]
  25. W. Gong, G. Wang and N. Yan, Approximations of elliptic optimal control problems with controls acting on a lower dimensional manifold. SIAM J. Control Optim. 52 (2014) 2008–2035. [Google Scholar]
  26. J.-L. Guermond and A. Ern, Finite Elements I: Approximation and Interpolation. Springer (2021). [Google Scholar]
  27. M.-J. Hannocks, M.E. Pizzo, J. Huppert, T. Deshpande, N.J. Abbott, R.G. Thorne and L. Sorokin, Molecular characterization of perivascular drainage pathways in the murine brain. J. Cereb. Blood Flow Metab. 38 (2018) 669–686. [CrossRef] [PubMed] [Google Scholar]
  28. V. Hernandez, J.E. Roman and V. Vidal, SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31 (2005) 351–362. [CrossRef] [Google Scholar]
  29. S.B. Hladky and M.A. Barrand, The glymphatic hypothesis: the theory and the evidence. Fluids Barriers CNS 19 (2022) 1–33. [CrossRef] [PubMed] [Google Scholar]
  30. S. Hofmann, M. Mitrea and M. Taylor, Geometric and transformational properties of Lipschitz domains, Semmes–Kenig–Toro domains, and other classes of finite perimeter domains. J. Geom. Anal. 17 (2007) 593–647. [CrossRef] [MathSciNet] [Google Scholar]
  31. D.H. Kelley, T. Bohr, P.G. Hjorth, S.C. Holst, S. Hrabětová, V. Kiviniemi, T. Lilius, I. Lundgaard, K.-A. Mardal, E.A. Martens, Y. Mori and U.V. N¨agerl, The glymphatic system: current understanding and modeling. iScience 25 (2022) 104987. [CrossRef] [PubMed] [Google Scholar]
  32. T. Koch, K. Heck, N. Schröder, H. Class and R. Helmig, A new simulation framework for soil–root interaction, evaporation, root growth, and solute transport. Vadose Zone J. 17 (2018) 1–21. [CrossRef] [Google Scholar]
  33. T. Koch, M. Schneider, R. Helmig and P. Jenny, Modeling tissue perfusion in terms of 1D–3D embedded mixed-dimension coupled problems with distributed sources. J. Comput. Phys. 410 (2020) 109370. [CrossRef] [MathSciNet] [Google Scholar]
  34. T. Koch, H. Wu and M. Schneider, Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake. J. Comput. Phys. 450 (2022) 110823. [CrossRef] [Google Scholar]
  35. T. Köppl, E. Vidotto, B. Wohlmuth and P. Zunino, Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions. Math. Models Methods Appl. Sci. 28 (2018) 953–978. [Google Scholar]
  36. T. Köppl, E. Vidotto and B. Wohlmuth, A 3D–1D coupled blood flow and oxygen transport model to generate microvascular networks. Int. J. Numer. Methods Biomed. Eng. 36 (2020) e3386. [CrossRef] [PubMed] [Google Scholar]
  37. M. Kuchta, Assembly of multiscale linear PDE operators. In: Numerical Mathematics and Advanced Applications ENUMATH 2019: European Conference, Egmond aan Zee, The Netherlands, September 30–October 4. Springer (2020) 641–650. [Google Scholar]
  38. M. Kuchta, K.-A. Mardal and M. Mortensen, Preconditioning trace coupled 3D–1D systems using fractional Laplacian. Numer. Methods Partial Differ. Equ. 35 (2019) 375–393. [CrossRef] [Google Scholar]
  39. M. Kuchta, F. Laurino, K.-A. Mardal and P. Zunino, Analysis and approximation of mixed-dimensional PDEs on 3D–1D domains coupled with Lagrange multipliers. SIAM J. Numer. Anal. 59 (2021) 558–582. [CrossRef] [MathSciNet] [Google Scholar]
  40. J.R. Kuttler and V.G. Sigillito, An inequality for a Stekloff eigenvalue by the method of defect. Proc. Am. Math. Soc. 20 (1969) 357–360. [Google Scholar]
  41. E. LaMontagne, A.R. Muotri and A.J. Engler, Recent advancements and future requirements in vascularization of cortical organoids. Front. Bioeng. Biotechnol. 10 (2022) 2059. [CrossRef] [Google Scholar]
  42. F. Laurino and P. Zunino, Derivation and analysis of coupled PDEs on manifolds with high dimensionality gap arising from topological model reduction. ESAIM:M2AN 53 (2019) 2047–2080. [CrossRef] [EDP Sciences] [Google Scholar]
  43. A. Logg, K.-A. Mardal and G. Wells, Automated Solution of Differential Equations by the Finite Element Method: The Fenics Book, Vol. 8. Springer Science & Business Media (2012). [CrossRef] [Google Scholar]
  44. T.J. Lohela, T.O. Lilius and M. Nedergaard, The glymphatic system: implications for drugs for central nervous system diseases. Nat. Rev. Drug Discov. 21 (2022) 763–779. [CrossRef] [PubMed] [Google Scholar]
  45. L. Malenica, H. Gotovac, G. Kamber, S. Simunovic, S. Allu and V. Divic, Groundwater flow modeling in karst aquifers: coupling 3D matrix and 1D conduit flow via control volume isogeometric analysis-experimental verification with a 3D physical model. Water 10 (2018) 1787. [CrossRef] [Google Scholar]
  46. H. Mestre, J. Tithof, T. Du, W. Song, W. Peng, A.M. Sweeney, G. Olveda, J.H. Thomas, M. Nedergaard and D.H. Kelley, Flow of cerebrospinal fluid is driven by arterial pulsations and is reduced in hypertension. Nat. Commun. 9 (2018) 1–9. [NASA ADS] [CrossRef] [Google Scholar]
  47. E. Nance, S.H. Pun, R. Saigal and D.L. Sellers, Drug delivery to the central nervous system. Nat. Rev. Mater. 7 (2022) 314–331. [Google Scholar]
  48. C. Nicholson, Diffusion and related transport mechanisms in brain tissue. Rep. Progress Phys. 64 (2001) 815. [CrossRef] [Google Scholar]
  49. F. Nobile, Numerical approximation of fluid–structure interaction problems with application to haemodynamics, Technical report, EPFL (2001). [Google Scholar]
  50. J.M. Nordbotten, D. Kavetski, M.A. Celia and S. Bachu, Model for CO2 leakage including multiple geological layers and multiple leaky wells. Environ. Sci. Technol. 43 (2009) 743–749. [CrossRef] [PubMed] [Google Scholar]
  51. D. Notaro, L. Cattaneo, L. Formaggia, A. Scotti and P. Zunino, A mixed finite element method for modeling the fluid exchange between microcirculation and tissue interstitium. In: Advances in Discretization Methods: Discontinuities, Virtual Elements, Fictitious Domain Methods (2016) 3–25. [CrossRef] [Google Scholar]
  52. L. Possenti, G. Casagrande, S. Di Gregorio, P. Zunino and M.L. Costantino, Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system. Microvasc. Res. 122 (2019) 101–110. [Google Scholar]
  53. L. Possenti, A. Cicchetti, R. Rosati, D. Cerroni, M.L. Costantino, T. Rancati and P. Zunino, A mesoscale computational model for microvascular oxygen transfer. Ann. Biomed. Eng. 49 (2021) 3356–3373. [CrossRef] [PubMed] [Google Scholar]
  54. E. Rohan, V. Lukeš and A. Jonášová, Modeling of the contrast-enhanced perfusion test in liver based on the multi-compartment flow in porous media. J. Math. Biol. 77 (2018) 421–454. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  55. S.A. Sauter and R. Warnke, Extension operators and approximation on domains containing small geometric details. East West J. Numer. Math. 7 (1999) 61–77. [MathSciNet] [Google Scholar]
  56. J.J. Sloots, G.J. Biessels and J.J. Zwanenburg, Cardiac and respiration-induced brain deformations in humans quantified with high-field MRI. Neuroimage 210 (2020) 116581. [CrossRef] [PubMed] [Google Scholar]
  57. W. Stekloff, Sur les problémes fondamentaux de la physique mathématique. Ann. Sci. de l’ École Norm. Supérieure 19 (1902) 191–259. [CrossRef] [Google Scholar]
  58. J.M. Tarasoff-Conway, R.O. Carare, R.S. Osorio, L. Glodzik, T. Butler, E. Fieremans, L. Axel, H. Rusinek, C. Nicholson, B.V. Zlokovic and B. Frangione, Clearance systems in the brain–implications for Alzheimer disease. Nat. Rev. Neurol. 11 (2015) 457–470. [CrossRef] [PubMed] [Google Scholar]
  59. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, Vol. 25. Springer Science & Business Media (2007). [Google Scholar]
  60. V. Vinje, E.N. Bakker and M.E. Rognes, Brain solute transport is more rapid in periarterial than perivenous spaces. Sci. Rep. 11 (2021) 1–11. [NASA ADS] [CrossRef] [Google Scholar]
  61. V. Vinje, B. Zapf, G. Ringstad, P.K. Eide, M.E. Rognes and K. Mardal, Human brain solute transport quantified by glymphatic MRI-informed biophysics during sleep and sleep deprivation. Fluids Barriers CNS 20 (2023) 62. [CrossRef] [PubMed] [Google Scholar]
  62. J.M. Wardlaw, H. Benveniste, M. Nedergaard, B.V. Zlokovic, H. Mestre, H. Lee, F.N. Doubal, R. Brown, J. Ramirez, B.J. MacIntosh and A. Tannenbaum, Perivascular spaces in the brain: anatomy, physiology and pathology. Nat. Rev. Neurol. 16 (2020) 137–153. [CrossRef] [PubMed] [Google Scholar]
  63. M.L. Wheeler and M.L. Oyen, Bioengineering approaches for placental research. Ann. Biomed. Eng. 49 (2021) 1–14. [Google Scholar]
  64. L. Zhao, A. Tannenbaum, E.N. Bakker and H. Benveniste, Physiology of glymphatic solute transport and waste clearance from the brain. Physiology 37 (2022) 349–362. [CrossRef] [Google Scholar]

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