{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T09:53:06Z","timestamp":1763632386312,"version":"3.45.0"},"reference-count":68,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T00:00:00Z","timestamp":1763596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12231004","12071190"],"award-info":[{"award-number":["12231004","12071190"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Effective metabolic waste clearance and maintaining ionic homeostasis are essential for the health and normal function of the central nervous system (CNS). To understand its mechanism and the role of fluid flow, we develop a multidomain electro-osmotic model of optic-nerve microcirculation (as a part of the CNS) that couples hydrostatic and osmotic fluid transport with electro-diffusive solute movement across axons, glia, the extracellular space (ECS), and arterial\/venous\/capillary perivascular spaces (PVS). Cerebrospinal fluid enters the optic nerve via the arterial parivascular space (PVS-A) and passes both the glial and ECS before exiting through the venous parivascular space (PVS-V). Exchanges across astrocytic endfeet are essential and they occur in two distinct and coupled paths: through AQP4 on glial membranes and gaps between glial endfeet, thus establishing a mechanistic substrate for two modes of glymphatic transport, at rest and during stimulus-evoked perturbations. Parameter sweeps show that lowering AQP4-mediated fluid permeability or PVS permeability elevates pressure, suppresses radial exchange (due mainly to hydrostatic pressure difference at the lateral surface and the center of the optic nerve), and slows clearance, effects most pronounced for solutes reliant on PVS\u2013V export. The model reproduces baseline and stimulus-evoked flow and demonstrates that PVS-mediated export is the primary clearance route for both small and moderate solutes. Small molecules (e.g., A\u03b2) clear faster because rapid ECS diffusion broadens their distribution and enhances ECS\u2013PVS exchange, whereas moderate species (e.g., tau monomers\/oligomers) have low ECS diffusivity, depend on trans-endfoot transfer, and clear more slowly via PVS\u2013V convection. Our framework can also be used to explain the sleep\u2013wake effect mechanistically: enlarging ECS volume (as occurs in sleep) or permeability increases trans-interface flux and accelerates waste removal. Together, these results provide a unified physical picture of glymphatic transport in the optic nerve, yield testable predictions for how AQP4 function, PVS patency, and sleep modulate size-dependent clearance, and offer guidance for targeting impaired waste removal in neurological disease.<\/jats:p>","DOI":"10.3390\/e27111174","type":"journal-article","created":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T09:44:53Z","timestamp":1763631893000},"page":"1174","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Glymphatic Clearance in the Optic Nerve: A Multidomain Electro-Osmostic Model"],"prefix":"10.3390","volume":"27","author":[{"given":"Shanfeng","family":"Xiao","sequence":"first","affiliation":[{"name":"The Department of Mathematics, Changzhi University, 73 Baoningmen East Street, Changzhi 046011, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1266-9428","authenticated-orcid":false,"given":"Huaxiong","family":"Huang","sequence":"additional","affiliation":[{"name":"Zu Chongzhi Center, Duke Kunshan University, 8 Duke Ave, Kunshan 215316, China"},{"name":"Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875, China"},{"name":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4860-5434","authenticated-orcid":false,"given":"Robert","family":"Eisenberg","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2823-199X","authenticated-orcid":false,"given":"Zilong","family":"Song","sequence":"additional","affiliation":[{"name":"Math and Statistics Department, Utah State University, Old Main Hill, Logan, UT 84322, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8207-7313","authenticated-orcid":false,"given":"Shixin","family":"Xu","sequence":"additional","affiliation":[{"name":"Zu Chongzhi Center, Duke Kunshan University, 8 Duke Ave, Kunshan 215316, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1126\/scitranslmed.3003748","article-title":"A Paravascular Pathway Facilitates CSF Flow Through the Brain Parenchyma and the Clearance of Interstitial Solutes, Including Amyloid beta","volume":"4","author":"Iliff","year":"2012","journal-title":"Sci. Transl. Med."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2583","DOI":"10.1007\/s11064-015-1581-6","article-title":"The Glymphatic System: A Beginner\u2019s Guide","volume":"40","author":"Jessen","year":"2015","journal-title":"Neurochem. Res."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Asgari, M., de Z\u00e9licourt, D., and Kurtcuoglu, V. (2016). Glymphatic solute transport does not require bulk flow. Sci. Rep., 6.","DOI":"10.1038\/srep38635"},{"key":"ref_4","first-page":"1326","article-title":"Impairment of the glymphatic system after diabetes","volume":"37","author":"Jiang","year":"2017","journal-title":"SAGE Publ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1126\/science.abb8739","article-title":"Glymphatic failure as a final common pathway to dementia","volume":"370","author":"Nedergaard","year":"2020","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1186\/s12987-024-00582-0","article-title":"Modeling CSF circulation and the glymphatic system during infusion using subject specific intracranial pressures and brain geometries","volume":"21","author":"Dreyer","year":"2024","journal-title":"Fluids Barriers CNS"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4878","DOI":"10.1038\/s41467-018-07318-3","article-title":"Flow of cerebrospinal fluid is driven by arterial pulsations and is reduced in hypertension","volume":"9","author":"Mestre","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3566","DOI":"10.1016\/j.neuron.2022.10.024","article-title":"Perivascular spaces and their role in neuroinflammation","volume":"110","author":"Ineichen","year":"2022","journal-title":"Neuron"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1126\/science.1566067","article-title":"Alzheimer\u2019s disease: The amyloid cascade hypothesis","volume":"256","author":"Hardy","year":"1992","journal-title":"Science"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"595","DOI":"10.15252\/emmm.201606210","article-title":"The amyloid hypothesis of Alzheimer\u2019s disease at 25 years","volume":"8","author":"Selkoe","year":"2016","journal-title":"Embo Mol. Med."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1126\/science.1241224","article-title":"Sleep drives metabolite clearance from the adult brain","volume":"342","author":"Xie","year":"2013","journal-title":"Science"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1126\/science.aax5440","article-title":"Coupled electrophysiological, hemodynamic, and cerebrospinal fluid oscillations in human sleep","volume":"366","author":"Fultz","year":"2019","journal-title":"Science"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1038\/s41586-024-07108-6","article-title":"Neuronal dynamics direct cerebrospinal fluid perfusion and brain clearance","volume":"627","author":"Drieu","year":"2024","journal-title":"Nature"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/10255840310001606116","article-title":"Arterial Pulsation-driven Cerebrospinal Fluid Flow in the Perivascular Space: A Computational Model","volume":"6","author":"Bilston","year":"2003","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"e2217744120","DOI":"10.1073\/pnas.2217744120","article-title":"Artificial intelligence velocimetry reveals in vivo flow rates, pressure gradients, and shear stresses in murine perivascular flows","volume":"120","author":"Boster","year":"2023","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114334","DOI":"10.1016\/j.chaos.2023.114334","article-title":"A machine learning method to explore the glymphatic system via poroelastodynamics","volume":"178","author":"Chou","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bohr, T., Hjorth, P.G., Holst, S.C., Hrab\u011btov\u00e1, S., Kiviniemi, V., Lilius, T., Lundgaard, I., Mardal, K.A., Martens, E.A., and Mori, Y. (2022). The glymphatic system: Current understanding and modeling. iScience, 25.","DOI":"10.1016\/j.isci.2022.104987"},{"key":"ref_18","unstructured":"Feher, J.J. (2012). Quantitative Human Physiology, Academic Press."},{"key":"ref_19","unstructured":"Silverthorn, D.U., Johnson, B.R., Ober, W.C., Ober, C., Impagliazzo, A., and Silverthorn, A. (2019). Human Physiology: An Integrated Approach, Pearson."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3008","DOI":"10.1016\/j.bpj.2021.06.020","article-title":"A tridomain model for potassium clearance in optic nerve of Necturus","volume":"120","author":"Zhu","year":"2021","journal-title":"Biophys. J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Eisenberg, R. (2023). Structural analysis of fluid flow in complex biological systems. Model. Artif. Intell. Ophthalmol.","DOI":"10.14293\/S2199-1006.1.SOR-.PPLLJDK.v1"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1016\/S0006-3495(85)83986-2","article-title":"Epithelial water transport in a balanced gradient system","volume":"47","author":"Mathias","year":"1985","journal-title":"Biophys. J."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1152\/physrev.1997.77.1.21","article-title":"Physiological properties of the normal lens","volume":"77","author":"Mathias","year":"1997","journal-title":"Physiol. Rev."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1016\/j.bpj.2019.02.007","article-title":"A Bidomain Model for Lens Microcirculation","volume":"116","author":"Zhu","year":"2019","journal-title":"Biophys. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1085\/jgp.201010538","article-title":"Lens intracellular hydrostatic pressure is generated by the circulation of sodium and modulated by gap junction coupling","volume":"137","author":"Gao","year":"2011","journal-title":"J. Gen. Physiol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.21037\/qims.2019.11.18","article-title":"Quantitative imaging of the clearance systems in the eye and the brain","volume":"10","author":"Deng","year":"2020","journal-title":"Quant. Imaging Med. Surg."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.preteyeres.2008.11.002","article-title":"Ischemic optic neuropathy","volume":"28","author":"Hayreh","year":"2009","journal-title":"Prog. Retin. Eye Res."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4784","DOI":"10.1167\/iovs.17-22290","article-title":"Evidence for Cerebrospinal Fluid Entry Into the Optic Nerve via a Glymphatic Pathway","volume":"58","author":"Mathieu","year":"2017","journal-title":"Investig. Ophthalmol. Vis. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1152\/jn.1966.29.4.768","article-title":"Physiological properties of glial cells in the central nervous system of amphibia","volume":"29","author":"Kuffler","year":"1966","journal-title":"J. Neurophysiol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1152\/jn.1966.29.4.788","article-title":"Effect of nerve impulses on the membrane potential of glial cells in the central nervous system of amphibia","volume":"29","author":"Orkand","year":"1966","journal-title":"J. Neurophysiol."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Nakada, T., Kwee, I.L., Igarashi, H., and Suzuki, Y. (2017). Aquaporin-4 Functionality and Virchow-Robin Space Water Dynamics: Physiological Model for Neurovascular Coupling and Glymphatic Flow. J. Turbul., 18.","DOI":"10.3390\/ijms18081798"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.neubiorev.2017.03.002","article-title":"Astrocytic modulation of neuronal excitability through K+ spatial buffering","volume":"77","author":"Kekesi","year":"2017","journal-title":"Neurosci. Biobehav. Rev."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5438","DOI":"10.1523\/JNEUROSCI.0037-06.2006","article-title":"The impact of astrocytic gap junctional coupling on potassium buffering in the hippocampus","volume":"26","author":"Wallraff","year":"2006","journal-title":"J. Neurosci. Off. J. Soc. Neurosci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2563","DOI":"10.1073\/pnas.1012867108","article-title":"An aquaporin-4\/transient receptor potential vanilloid 4 (AQP4\/TRPV4) complex is essential for cell-volume control in astrocytes","volume":"108","author":"Benfenati","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.preteyeres.2017.10.006","article-title":"Mechanisms of macular edema: Beyond the surface","volume":"63","author":"Daruich","year":"2017","journal-title":"Prog. Retin. Eye Res."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Xiao, S., Huang, H., Eisenberg, R., Song, Z., and Xu, S. (2025). Potassium Clearance in Optic Nerve: A Multidomain Model. Front. Biosci. (Landmark Ed.), 30.","DOI":"10.31083\/FBL39722"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1159\/000309386","article-title":"The sheath of the optic nerve","volume":"189","author":"Hayreh","year":"1984","journal-title":"Ophthalmologica"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5189","DOI":"10.1167\/iovs.03-0174","article-title":"Anatomic relationship between lamina cribrosa, intraocular space, and cerebrospinal fluid space","volume":"44","author":"Jonas","year":"2003","journal-title":"Investig. Ophthalmol. Vis. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1023\/A:1006561408186","article-title":"Transport of Multi-Electrolytes in Charged Hydrated Biological Soft Tissues","volume":"34","author":"Lai","year":"1999","journal-title":"Transp. Porous Media"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Sibille, J., Dao Duc, K., Holcman, D., Rouach, N., and Jolivet, R. (2015). The Neuroglial Potassium Cycle during Neurotransmission: Role of Kir4.1 Channels. PLoS Comput. Biol., 11.","DOI":"10.1371\/journal.pcbi.1004137"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Subileau, M., and Vittet, D. (2021). Lymphatics in Eye Fluid Homeostasis: Minor Contributors or Significant Actors?. Multidiscip. Digit. Publ. Inst., 10.","DOI":"10.3390\/biology10070582"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Uddin, N., and Rutar, M. (2022). Ocular lymphatic and glymphatic systems: Implications for retinal health and disease. Int. J. Mol. Sci., 23.","DOI":"10.3390\/ijms231710139"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1186\/s12987-022-00326-y","article-title":"Arterial vasodilation drives convective fluid flow in the brain: A poroelastic model","volume":"19","author":"Kedarasetti","year":"2022","journal-title":"Fluids Barriers CNS"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1016","DOI":"10.1016\/S1474-4422(18)30318-1","article-title":"The glymphatic pathway in neurological disorders","volume":"17","author":"Rasmussen","year":"2018","journal-title":"Lancet Neurol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"17268","DOI":"10.1074\/jbc.270.29.17268","article-title":"Generation of Amyloidogenic C-terminal Fragments during Rapid Axonal Transport in Vivo of \u03b2-Amyloid Precursor Protein in the Optic Nerve","volume":"270","author":"Amaratunga","year":"1995","journal-title":"J. Biol. Chem."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1111\/j.1471-4159.1993.tb02147.x","article-title":"Amyloid Precursor Protein Is Synthesized by Retinal Ganglion Cells, Rapidly Transported to the Optic Nerve Plasma Membrane and Nerve Terminals, and Metabolized","volume":"61","author":"Morin","year":"1993","journal-title":"J. Neurochem."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1581","DOI":"10.1007\/s00234-021-02718-7","article-title":"Perivascular spaces and brain waste clearance systems: Relevance for neurodegenerative and cerebrovascular pathology","volume":"63","author":"Freitas","year":"2021","journal-title":"Neuroradiology"},{"key":"ref_48","first-page":"789","article-title":"Electrostatic properties of amyloid \u03b2-protein and their impact on aggregation","volume":"432","author":"Smith","year":"2022","journal-title":"J. Mol. Biol."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"041906","DOI":"10.1063\/5.0046323","article-title":"Optic Nerve Microcirculation: Fluid Flow and Electro-Diffusion","volume":"33","author":"Zhu","year":"2021","journal-title":"Phys. Fluids"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1186\/s12987-021-00282-z","article-title":"The glymphatic hypothesis: The theory and the evidence","volume":"19","author":"Hladky","year":"2022","journal-title":"Fluids Barriers CNS"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"4411","DOI":"10.1038\/s41467-020-18115-2","article-title":"Circadian control of brain glymphatic and lymphatic fluid flow","volume":"11","author":"Hablitz","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"20240369","DOI":"10.1098\/rsif.2024.0369","article-title":"A brain-wide solute transport model of the glymphatic system","volume":"21","author":"Quirk","year":"2024","journal-title":"J. R. Soc. Interface"},{"key":"ref_53","unstructured":"Xu, S., Eisenberg, B., Song, Z., and Huang, H. (2018). Osmosis through a Semi-permeable Membrane: A Consistent Approach to Interactions. arXiv."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.physd.2015.06.008","article-title":"A Multidomain Model for Ionic Electrodiffusion and Osmosis with an Application to Cortical Spreading Depression","volume":"308","author":"Yoichiro","year":"2015","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/S0006-3495(85)83799-1","article-title":"Steady-state voltages, ion fluxes, and volume regulation in syncytial tissues","volume":"48","author":"Mathias","year":"1985","journal-title":"Biophys. J."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0006-3495(79)85284-4","article-title":"Electrical Properties of Structural Components of the Crystalline Lens","volume":"25","author":"Mathias","year":"1979","journal-title":"Biophys. J."},{"key":"ref_57","first-page":"011042","article-title":"Self-consistent approach to global charge neutrality in electrokinetics: A surface potential trap model","volume":"4","author":"Wan","year":"2014","journal-title":"Phys. Rev. X"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Vaghefi, E., Malcolm, D.T.K., Jacobs, M.D., and Donaldson, P.J. (2012). Development of a 3D finite element model of lens microcirculation. BioMed. Eng. OnLine, 11.","DOI":"10.1186\/1475-925X-11-69"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0006-3495(83)84368-9","article-title":"Effect of tortuous extracellular pathways on resistance measurements","volume":"42","author":"Mathias","year":"1983","journal-title":"Biophys. J."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1088\/0034-4885\/64\/7\/202","article-title":"Diffusion and related transport mechanisms in brain tissue","volume":"64","author":"Nicholson","year":"2001","journal-title":"Rep. Prog. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1152\/jn.1995.74.2.565","article-title":"Extracellular potassium, volume fraction, and tortuosity in rat hippocampal ca1, ca3, and cortical slices during ischemia","volume":"74","author":"Tao","year":"1995","journal-title":"J. Neurophysiol."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/S0006-3495(77)85627-0","article-title":"Electrical properties of frog skeletal muscle fibers interpreted with a mesh model of the tubular system","volume":"17","author":"Mathias","year":"1977","journal-title":"Biophys. J."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1085\/jgp.85.5.699","article-title":"Electro-osmosis and the reabsorption of fluid in renal proximal tubules","volume":"85","author":"McLAUGHLIN","year":"1985","journal-title":"J. Gen. Physiol."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"3750","DOI":"10.1167\/iovs.08-2396","article-title":"Intracellular Flow in Optic Nerve Axons: A Mechanism for Cell Death in Glaucoma","volume":"50","author":"Band","year":"2009","journal-title":"Investig. Opthalmol. Vis. Sci."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1186\/s12987-021-00290-z","article-title":"Quantitative analysis of macroscopic solute transport in the murine brain","volume":"18","author":"Ray","year":"2021","journal-title":"Fluids Barriers CNS"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1085\/jgp.43.5.867","article-title":"Thresholds and plateaus in the hodgkin-huxley nerve equations","volume":"43","author":"Fitzhugh","year":"1960","journal-title":"J. Gen. Physiol."},{"key":"ref_67","unstructured":"Gabbiani, F., and Cox, S.J. (2017). Mathematics for Neuroscientists, Academic Press."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s002320010017","article-title":"Isoform-specific function and distribution of na\/k pumps in the frog lens epithelium","volume":"178","author":"Gao","year":"2000","journal-title":"J. Membr. Biol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/11\/1174\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T09:50:35Z","timestamp":1763632235000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/11\/1174"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,20]]},"references-count":68,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["e27111174"],"URL":"https:\/\/doi.org\/10.3390\/e27111174","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,20]]}}}