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Farr H, David T (2011) Models of neurovascular coupling via potassium and EET signalling. J Theor Biol 286:13-23 [PubMed]

   A mathematical model of a neurovascular unit (Dormanns et al 2015, 2016) (Farrs & David 2011)

   A model of neurovascular coupling and the BOLD response (Mathias et al 2017, Kenny et al 2018)

References and models cited by this paper

References and models that cite this paper

Attwell D, Buchan AM, Charpak S, Lauritzen M, Macvicar BA, Newman EA (2010) Glial and neuronal control of brain blood flow. Nature 468:232-43 [Journal] [PubMed]

Bennett MR, Farnell L, Gibson WG (2008) Origins of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells. J Theor Biol 250:172-85 [Journal] [PubMed]

Bogacki P,Shampine LF (1996) An efficient Runge-Kutta (4,5) pair Comput. Math. Appl. 32(6):15-28

Borisova L, Wray S, Eisner DA, Burdyga T (2009) How structure, Ca signals, and cellular communications underlie function in precapillary arterioles. Circ Res 105:803-10 [Journal] [PubMed]

Buerk DG (2001) Can we model nitric oxide biotransport? A survey of mathematical models for a simple diatomic molecule with surprisingly complex biological activities. Annu Rev Biomed Eng 3:109-43 [Journal] [PubMed]

Cameron IR, Caronna J (1976) The effect of local changes in potassium and bicarbonate concentration on hypothalamic blood flow in the rabbit. J Physiol 262:415-30 [PubMed]

Carmignoto G, Pasti L, Pozzan T (1998) On the role of voltage-dependent calcium channels in calcium signaling of astrocytes in situ. J Neurosci 18:4637-45 [PubMed]

Chen KC, Nicholson C (2000) Spatial buffering of potassium ions in brain extracellular space. Biophys J 78:2776-97 [Journal] [PubMed]

Chrissobolis S, Ziogas J, Chu Y, Faraci FM, Sobey CG (2000) Role of inwardly rectifying K(+) channels in K(+)-induced cerebral vasodilatation in vivo. Am J Physiol Heart Circ Physiol 279:H2704-12 [Journal] [PubMed]

Edwards FR, Hirst GD, Silverberg GD (1988) Inward rectification in rat cerebral arterioles; involvement of potassium ions in autoregulation. J Physiol 404:455-66 [PubMed]

Ehrenstein G, Lecar H (1977) Electrically gated ionic channels in lipid bilayers. Q Rev Biophys 10:1-34 [PubMed]

Filosa JA, Blanco VM (2007) Neurovascular coupling in the mammalian brain. Exp Physiol 92:641-6 [Journal] [PubMed]

Filosa JA, Bonev AD, Straub SV, Meredith AL, Wilkerson MK, Aldrich RW, Nelson MT (2006) Local potassium signaling couples neuronal activity to vasodilation in the brain. Nat Neurosci 9:1397-1403 [Journal] [PubMed]

Girouard H, Bonev AD, Hannah RM, Meredith A, Aldrich RW, Nelson MT (2010) Astrocytic endfoot Ca2+ and BK channels determine both arteriolar dilation and constriction. Proc Natl Acad Sci U S A 107:3811-6 [Journal] [PubMed]

Girouard H, Iadecola C (2006) Neurovascular coupling in the normal brain and in hypertension, stroke, and Alzheimer disease. J Appl Physiol (1985) 100:328-35 [Journal] [PubMed]

Golding EM, Steenberg ML, Johnson TD, Bryan RM (2000) The effects of potassium on the rat middle cerebral artery. Brain Res 880:159-66 [PubMed]

Gonzalez-Fernandez JM, Ermentrout B (1994) On the origin and dynamics of the vasomotion of small arteries. Math Biosci 119:127-67 [PubMed]

Gore RW, Davis MJ (1984) Mechanics of smooth muscle in isolated single microvessels. Ann Biomed Eng 12:511-20 [PubMed]

Hai CM, Murphy RA (1988) Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am J Physiol 254:C99-106 [Journal] [PubMed]

Higashi K, Fujita A, Inanobe A, Tanemoto M, Doi K, Kubo T, Kurachi Y (2001) An inwardly rectifying K(+) channel, Kir4.1, expressed in astrocytes surrounds synapses and blood vessels in brain. Am J Physiol Cell Physiol 281:C922-31 [Journal] [PubMed]

Higashimori H, Blanco VM, Tuniki VR, Falck JR, Filosa JA (2010) Role of epoxyeicosatrienoic acids as autocrine metabolites in glutamate-mediated K+ signaling in perivascular astrocytes. Am J Physiol Cell Physiol 299:C1068-78 [Journal] [PubMed]

Horiuchi T, Dietrich HH, Hongo K, Dacey RG (2002) Mechanism of extracellular K+-induced local and conducted responses in cerebral penetrating arterioles. Stroke 33:2692-9 [PubMed]

Iadecola C (2004) Neurovascular regulation in the normal brain and in Alzheimer's disease. Nat Rev Neurosci 5:347-60 [Journal] [PubMed]

Jiang ZG, Si JQ, Lasarev MR, Nuttall AL (2001) Two resting potential levels regulated by the inward-rectifier potassium channel in the guinea-pig spiral modiolar artery. J Physiol 537:829-42 [PubMed]

Johnson TD, Marrelli SP, Steenberg ML, Childres WF, Bryan RM (1998) Inward rectifier potassium channels in the rat middle cerebral artery. Am J Physiol 274:R541-7 [PubMed]

Knot HJ, Zimmermann PA, Nelson MT (1996) Extracellular K(+)-induced hyperpolarizations and dilatations of rat coronary and cerebral arteries involve inward rectifier K(+) channels. J Physiol 492 ( Pt 2):419-30 [PubMed]

Koenigsberger M, Sauser R, Bény JL, Meister JJ (2006) Effects of arterial wall stress on vasomotion. Biophys J 91:1663-74 [Journal] [PubMed]

Kofuji P, Newman EA (2004) Potassium buffering in the central nervous system. Neuroscience 129:1045-56 [Journal] [PubMed]

Kudryashov N,Chernyavskii I (2008) Numerical simulation of the process of autoregulation of the arterial blood flow Fluid Dyn. 43(1):32-48 [Journal]

Kurachi Y (1985) Voltage-dependent activation of the inward-rectifier potassium channel in the ventricular cell membrane of guinea-pig heart. J Physiol 366:365-85 [PubMed]

Kuschinsky W, Wahl M, Bosse O, Thurau K (1972) Perivascular potassium and pH as determinants of local pial arterial diameter in cats. A microapplication study. Circ Res 31:240-7 [PubMed]

Lauwers F, Cassot F, Lauwers-Cances V, Puwanarajah P, Duvernoy H (2008) Morphometry of the human cerebral cortex microcirculation: general characteristics and space-related profiles. Neuroimage 39:936-48 [Journal] [PubMed]

Lemon G, Gibson WG, Bennett MR (2003) Metabotropic receptor activation, desensitization and sequestration-I: modelling calcium and inositol 1,4,5-trisphosphate dynamics following receptor activation. J Theor Biol 223:93-111 [PubMed]

Lu T, Katakam PV, VanRollins M, Weintraub NL, Spector AA, Lee HC (2001) Dihydroxyeicosatrienoic acids are potent activators of Ca(2+)-activated K(+) channels in isolated rat coronary arterial myocytes. J Physiol 534:651-67 [PubMed]

Matyash V, Kettenmann H (2010) Heterogeneity in astrocyte morphology and physiology. Brain Res Rev 63:2-10 [Journal] [PubMed]

McCarron JG, Halpern W (1990) Potassium dilates rat cerebral arteries by two independent mechanisms. Am J Physiol 259:H902-8 [Journal] [PubMed]

Metea MR, Kofuji P, Newman EA (2007) Neurovascular coupling is not mediated by potassium siphoning from glial cells. J Neurosci 27:2468-71 [PubMed]

Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193-213 [Journal] [PubMed]

   Morris-Lecar model of the barnacle giant muscle fiber (Morris, Lecar 1981) [Model]

Nakahata K, Kinoshita H, Tokinaga Y, Ishida Y, Kimoto Y, Dojo M, Mizumoto K, Ogawa K, Hatano Y (2006) Vasodilation mediated by inward rectifier K+ channels in cerebral microvessels of hypertensive and normotensive rats. Anesth Analg 102:571-6 [Journal] [PubMed]

Nystoriak MA, O'Connor KP, Sonkusare SK, Brayden JE, Nelson MT, Wellman GC (2011) Fundamental increase in pressure-dependent constriction of brain parenchymal arterioles from subarachnoid hemorrhage model rats due to membrane depolarization. Am J Physiol Heart Circ Physiol 300:H803-12 [Journal] [PubMed]

Østby I, Øyehaug L, Einevoll GT, Nagelhus EA, Plahte E, Zeuthen T, Lloyd CM, Ottersen OP, Omholt SW (2009) Astrocytic mechanisms explaining neural-activity-induced shrinkage of extraneuronal space. PLoS Comput Biol 5:e1000272 [Journal] [PubMed]

   Mechanisms of extraneuronal space shrinkage (Ostby et al 2009) [Model]

Paulson OB, Newman EA (1987) Does the release of potassium from astrocyte endfeet regulate cerebral blood flow? Science 237:896-8 [PubMed]

Price DL, Ludwig JW, Mi H, Schwarz TL, Ellisman MH (2002) Distribution of rSlo Ca2+-activated K+ channels in rat astrocyte perivascular endfeet. Brain Res 956:183-93 [PubMed]

Quayle JM, Dart C, Standen NB (1996) The properties and distribution of inward rectifier potassium currents in pig coronary arterial smooth muscle. J Physiol 494 ( Pt 3):715-26 [PubMed]

Quayle JM, Nelson MT, Standen NB (1997) ATP-sensitive and inwardly rectifying potassium channels in smooth muscle. Physiol Rev 77:1165-232 [Journal] [PubMed]

Quinn K, Guibert C, Beech DJ (2000) Sodium-potassium-ATPase electrogenicity in cerebral precapillary arterioles. Am J Physiol Heart Circ Physiol 279:H351-60 [Journal] [PubMed]

Setoguchi M, Ohya Y, Abe I, Fujishima M (1997) Stretch-activated whole-cell currents in smooth muscle cells from mesenteric resistance artery of guinea-pig. J Physiol 501 ( Pt 2):343-53 [PubMed]

Shi Y, Liu X, Gebremedhin D, Falck JR, Harder DR, Koehler RC (2008) Interaction of mechanisms involving epoxyeicosatrienoic acids, adenosine receptors, and metabotropic glutamate receptors in neurovascular coupling in rat whisker barrel cortex. J Cereb Blood Flow Metab 28:111-25 [Journal] [PubMed]

Siegl D, Koeppen M, Wölfle SE, Pohl U, de Wit C (2005) Myoendothelial coupling is not prominent in arterioles within the mouse cremaster microcirculation in vivo. Circ Res 97:781-8 [Journal] [PubMed]

Smeda JS, Payne GW (2003) Alterations in autoregulatory and myogenic function in the cerebrovasculature of Dahl salt-sensitive rats. Stroke 34:1484-90 [Journal] [PubMed]

Stensaas LJ (1975) Pericytes and perivascular microglial cells in the basal forebrain of the neonatal rabbit. Cell Tissue Res 158:517-41 [PubMed]

Ullah G, Jung P, Cornell-Bell AH (2006) Anti-phase calcium oscillations in astrocytes via inositol (1, 4, 5)-trisphosphate regeneration. Cell Calcium 39:197-208 [Journal] [PubMed]

Xu G, Antuono PG, Jones J, Xu Y, Wu G, Ward D, Li SJ (2007) Perfusion fMRI detects deficits in regional CBF during memory-encoding tasks in MCI subjects. Neurology 69:1650-6 [Journal] [PubMed]

Zhou M, Kimelberg HK (2000) Freshly isolated astrocytes from rat hippocampus show two distinct current patterns and different [K(+)](o) uptake capabilities. J Neurophysiol 84:2746-57 [Journal] [PubMed]

Dormanns K, Brown RG, David T (2016) The role of nitric oxide in neurovascular coupling. J Theor Biol 394:1-17 [Journal] [PubMed]

   A mathematical model of a neurovascular unit (Dormanns et al 2015, 2016) (Farrs & David 2011) [Model]
   A model of neurovascular coupling and the BOLD response (Mathias et al 2017, Kenny et al 2018) [Model]

Dormanns K, van Disseldorp EM, Brown RG, David T (2015) Neurovascular coupling and the influence of luminal agonists via the endothelium. J Theor Biol 364:49-70 [Journal] [PubMed]

   A mathematical model of a neurovascular unit (Dormanns et al 2015, 2016) (Farrs & David 2011) [Model]
   A model of neurovascular coupling and the BOLD response (Mathias et al 2017, Kenny et al 2018) [Model]

Mathias EJ, Plank MJ, David T (2017) A model of neurovascular coupling and the BOLD response: PART I. Comput Methods Biomech Biomed Engin 20:508-518 [Journal] [PubMed]

   A model of neurovascular coupling and the BOLD response (Mathias et al 2017, Kenny et al 2018) [Model]

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