{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T10:47:26Z","timestamp":1753181246377},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,4,28]],"date-time":"2016-04-28T00:00:00Z","timestamp":1461801600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comput Neurosci"],"published-print":{"date-parts":[[2016,8]]},"DOI":"10.1007\/s10827-016-0604-x","type":"journal-article","created":{"date-parts":[[2016,4,28]],"date-time":"2016-04-28T16:31:32Z","timestamp":1461861092000},"page":"45-63","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Efficient simulations of tubulin-driven axonal growth"],"prefix":"10.1007","volume":"41","author":[{"given":"Stefan","family":"Diehl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erik","family":"Henningsson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anders","family":"Heyden","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,4,28]]},"reference":[{"key":"604_CR1","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.jtbi.2014.06.019","volume":"358","author":"S Diehl","year":"2014","unstructured":"Diehl, S., Henningsson, E., Heyden, A., & Perna, S. (2014). A one-dimensional moving-boundary model for tubulin-driven axonal growth. Journal of Theoretical Biology, 358, 194\u2013207.","journal-title":"Journal of Theoretical Biology"},{"issue":"1","key":"604_CR2","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1137\/0103004","volume":"3","author":"J Douglas","year":"1955","unstructured":"Douglas, J. (1955). On the numerical integration of \u2202 2 u \u2202 x 2 + \u2202 2 u \u2202 y 2 = \u2202u \u2202t $\\frac {\\partial ^{2} u} {\\partial x^{2}} + \\frac {\\partial ^{2} u}{\\partial y^{2}} = \\frac {\\partial u} {\\partial t}$ by implicit methods. Journal of the Society for Industrial and Applied Mathematics, 3(1), 42\u201365.","journal-title":"Journal of the Society for Industrial and Applied Mathematics"},{"issue":"5","key":"604_CR3","first-page":"411","volume":"87","author":"JA Garc\u00eda","year":"2012","unstructured":"Garc\u00eda, J.A., Pe\u00f1a, J.M., McHugh, S., & J\u00e9rusalem, A. (2012). A model of the spatially dependent mechanical properties of the axon during its growth. CMES \u2013 Computer Modeling in Engineering and Sciences, 87 (5), 411\u2013432.","journal-title":"CMES \u2013 Computer Modeling in Engineering and Sciences"},{"key":"604_CR4","doi-asserted-by":"crossref","unstructured":"Graham, B.P., & van Ooyen, A. (2006). Mathematical modelling and numerical simulation of the morphological development of neurons. BMC Neuroscience, 7(Suppl. 1).","DOI":"10.1186\/1471-2202-7-S1-S9"},{"issue":"1","key":"604_CR5","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s10827-006-5330-3","volume":"20","author":"BP Graham","year":"2006","unstructured":"Graham, B.P., Lauchlan, K., & McLean, D.R. (2006). Dynamics of outgrowth in a continuum model of neurite elongation. Journal of Computational Neuroscience, 20(1), 43\u201360.","journal-title":"Journal of Computational Neuroscience"},{"issue":"4","key":"604_CR6","doi-asserted-by":"crossref","first-page":"1900","DOI":"10.1137\/120890570","volume":"51","author":"E Hansen","year":"2013","unstructured":"Hansen, E., & Henningsson, E. (2013). A convergence analysis of the Peaceman\u2013Rachford scheme for semilinear evolution equations. SIAM Journal on Numerical Analysis, 51(4), 1900\u2013 1910.","journal-title":"SIAM Journal on Numerical Analysis"},{"key":"604_CR7","doi-asserted-by":"crossref","unstructured":"Hundsdorfer, W., & Verwer, J. (2003). Numerical solution of time-dependent advection-diffusion-reaction equations, Springer series in computational mathematics Vol. 33. New York: Springer.","DOI":"10.1007\/978-3-662-09017-6"},{"key":"604_CR8","doi-asserted-by":"crossref","unstructured":"Kiddie, G., McLean, D., Ooyen, A.V., & Graham, B. (2005). Biologically plausible models of neurite outgrowth. In van Pelt, J, Kamermans, M, Levelt, C N, van Ooyen, A, Ramakers, G J A, & Roelfsema, P R (Eds.), Development, dynamics and pathiology of neuronal networks: from molecules to functional circuits, progress in brain research, (Vol. 147 pp. 67\u201380): Elsevier.","DOI":"10.1016\/S0079-6123(04)47006-X"},{"issue":"2048","key":"604_CR9","doi-asserted-by":"crossref","first-page":"2437","DOI":"10.1098\/rspa.2004.1288","volume":"460","author":"DR McLean","year":"2004","unstructured":"McLean, D.R., & Graham, B.P. (2004). Mathematical formulation and analysis of a continuum model for tubulin-driven neurite elongation. Proceedings Royal Society A: Mathematical, Physical and Engineering Sciences, 460(2048), 2437\u20132456.","journal-title":"Proceedings Royal Society A: Mathematical, Physical and Engineering Sciences"},{"issue":"2","key":"604_CR10","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1093\/imammb\/dql010","volume":"23","author":"DR McLean","year":"2006","unstructured":"McLean, D.R., & Graham, B.P. (2006). Stability in a mathematical model of neurite elongation. Mathematical Medicine and Biology \u2013 A Journal of the IMA, 23(2), 101\u2013117.","journal-title":"Mathematical Medicine and Biology \u2013 A Journal of the IMA"},{"key":"604_CR11","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/j.neucom.2004.01.088","volume":"58\u201360","author":"DR McLean","year":"2004","unstructured":"McLean, D.R., van Ooyen, A., & Graham, B.P. (2004). Continuum model for tubulin-driven neurite elongation. Neurocomputing, 58\u201360, 511\u2013516.","journal-title":"Neurocomputing"},{"issue":"10","key":"604_CR12","doi-asserted-by":"crossref","first-page":"1981","DOI":"10.1016\/j.yexcr.2008.03.004","volume":"314","author":"KE Miller","year":"2008","unstructured":"Miller, K.E., & Heidemann, S.R. (2008). What is slow axonal transport? Experimental Cell Research, 314 (10), 1981\u20131990.","journal-title":"Experimental Cell Research"},{"issue":"1","key":"604_CR13","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1137\/0103003","volume":"3","author":"DW Peaceman","year":"1955","unstructured":"Peaceman, D.W., & Rachford, H.H. (1955). The numerical solution of parabolic and elliptic differential equations. Journal of the Society for Industrial and Applied Mathematics, 3(1), 28\u201341.","journal-title":"Journal of the Society for Industrial and Applied Mathematics"},{"issue":"3","key":"604_CR14","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1007\/s10827-010-0232-9","volume":"28","author":"K Sadegh Zadeh","year":"2010","unstructured":"Sadegh Zadeh, K., & Shah, S.B. (2010). Mathematical modeling and parameter estimation of axonal cargo transport. Journal of Computational Neuroscience, 28(3), 495\u2013507.","journal-title":"Journal of Computational Neuroscience"},{"issue":"1","key":"604_CR15","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0006-3495(01)75994-2","volume":"80","author":"DA Smith","year":"2001","unstructured":"Smith, D.A., & Simmons, R.M. (2001). Models of motor-assisted transport of intracellular particles. Biophysical Journal, 80(1), 45\u201368.","journal-title":"Biophysical Journal"},{"issue":"2","key":"604_CR16","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.pneurobio.2011.04.002","volume":"94","author":"DM Suter","year":"2011","unstructured":"Suter, D.M., & Miller, K.E. (2011). The emerging role of forces in axonal elongation. Progress in Neurobiology, 94(2), 91\u2013101.","journal-title":"Progress in Neurobiology"},{"issue":"6","key":"604_CR17","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1038\/nrn3031","volume":"12","author":"A van Ooyen","year":"2011","unstructured":"van Ooyen, A. (2011). Using theoretical models to analyse neural development. Nature Reviews Neuroscience, 12(6), 311\u2013 326.","journal-title":"Nature Reviews Neuroscience"},{"key":"604_CR18","doi-asserted-by":"crossref","unstructured":"Walker, R.A., O\u2019Brien, E.T., Pryer, N.K., Soboeiro, M.F., Voter, W.A., Erickson, H.P., & Salmon, E.D. (1988). Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies. Journal of Cell Biology, 107(4), 1437\u20131448.","DOI":"10.1083\/jcb.107.4.1437"}],"container-title":["Journal of Computational Neuroscience"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10827-016-0604-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10827-016-0604-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10827-016-0604-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T01:37:26Z","timestamp":1559266646000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10827-016-0604-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,28]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["604"],"URL":"https:\/\/doi.org\/10.1007\/s10827-016-0604-x","relation":{},"ISSN":["0929-5313","1573-6873"],"issn-type":[{"value":"0929-5313","type":"print"},{"value":"1573-6873","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,28]]}}}