{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:49:28Z","timestamp":1787320168852,"version":"build-2736575974"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2007,11,13]],"date-time":"2007-11-13T00:00:00Z","timestamp":1194912000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Comput Neurosci"],"published-print":{"date-parts":[[2008,6]]},"DOI":"10.1007\/s10827-007-0060-8","type":"journal-article","created":{"date-parts":[[2007,11,12]],"date-time":"2007-11-12T14:57:24Z","timestamp":1194879444000},"page":"358-373","source":"Crossref","is-referenced-by-count":15,"title":["Parameter estimation for bursting neural models"],"prefix":"10.1007","volume":"24","author":[{"given":"Joseph H.","family":"Tien","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John","family":"Guckenheimer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2007,11,13]]},"reference":[{"issue":"6","key":"60_CR1","doi-asserted-by":"crossref","first-page":"1948","DOI":"10.1152\/jn.1993.69.6.1948","volume":"69","author":"U. Bhalla","year":"1993","unstructured":"Bhalla, U., & Bower, J. (1993). Exploring parameter space in detailed single neuron models: Simulations of the mitral and granule cells of the olfactory bulb. Journal of Neurophysiology 69(6), 1948\u20131965.","journal-title":"Journal of Neurophysiology"},{"key":"60_CR2","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1046\/j.1460-9568.2002.02072.x","volume":"16","author":"U. Bickmeyer","year":"2002","unstructured":"Bickmeyer, U., Heine, M., Manzke, T., & Richter, D. (2002). Differential modulation of I h by 5-HT receptors in mouse CA1 hippocampal neurons. European Journal of Neuroscience 16, 209\u2013218.","journal-title":"European Journal of Neuroscience"},{"key":"60_CR3","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1152\/jn.1999.82.1.382","volume":"81","author":"R.J. Butera","year":"1999","unstructured":"Butera, R. J., Rinzel, J., & Smith, J. C. (1999). Models of respiratory rhythm generation in the pre-B\u00f6tzinger complex. I. Bursting pacemaker neurons. Journal of Neurophysiology 81, 382\u2013397.","journal-title":"Journal of Neurophysiology"},{"key":"60_CR4","unstructured":"Casey, R. (2004). Periodic orbits in neural models: Sensitivity analysis and algorithms for parameter estimation. PhD Thesis, Cornell University."},{"key":"60_CR5","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1146\/annurev.ph.58.030196.002025","volume":"58","author":"W. Crill","year":"1996","unstructured":"Crill, W. (1996). Persistent sodium current in mammalian central neurons. Annual Review of Physiology 58, 349\u2013362.","journal-title":"Annual Review of Physiology"},{"key":"60_CR6","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1152\/jn.1991.65.2.371","volume":"65","author":"R. Deisz","year":"1991","unstructured":"Deisz, R., Fortin, G., & Zieglgansberger, W. (1991). Voltage dependence of excitatory postsynaptic potentials of rat neocortical neurons. Journal of Neurophysiology 65, 371\u2013382.","journal-title":"Journal of Neurophysiology"},{"key":"60_CR7","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1146\/annurev.neuro.26.041002.131103","volume":"26","author":"J.L. Feldman","year":"2003","unstructured":"Feldman, J. L., Mitchell, G. S., & Nattie, E. E. (2003). Breathing: rhythmicity, plasticity, chemosensitivity. Annual Review of Neuroscience 26, 239\u2013266.","journal-title":"Annual Review of Neuroscience"},{"key":"60_CR8","volume-title":"Practical methods of optimization","author":"R. Fletcher","year":"1987","unstructured":"Fletcher, R. (1987). Practical methods of optimization. Chichester: John Wiley and Sons."},{"issue":"6","key":"60_CR9","doi-asserted-by":"crossref","first-page":"2502","DOI":"10.1152\/jn.1993.70.6.2502","volume":"70","author":"W. Foster","year":"1993","unstructured":"Foster, W., Ungar, L., & Schwaber, J. (1993). Significance of conductances in Hodgkin\u2013Huxley models. Journal of Neurophysiology 70(6), 2502\u20132518.","journal-title":"Journal of Neurophysiology"},{"issue":"4","key":"60_CR10","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1137\/030602307","volume":"3","author":"R. Ghigliazza","year":"2004","unstructured":"Ghigliazza, R., & Holmes, P. (2004). Minimal models of bursting neurons: How multiple currents, conductances, and timescales affect bifurcation diagrams. SIAM Journal on Applied Dynamical Systems 3(4), 636\u2013670.","journal-title":"SIAM Journal on Applied Dynamical Systems"},{"key":"60_CR11","volume-title":"Evaluating derivatives: Principles and techniques of automatic differentiation","author":"A. Griewank","year":"2000","unstructured":"Griewank, A. (2000). Evaluating derivatives: Principles and techniques of automatic differentiation. Philadelphia: SIAM."},{"issue":"3","key":"60_CR12","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1137\/S1064827599359278","volume":"22","author":"J. Guckenheimer","year":"2000","unstructured":"Guckenheimer, J., & Meloon, B. (2000). Computing periodic orbits and their bifurcations with automatic differentiation. SIAM Journal on Scientific Computing 22(3), 951\u2013985.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"60_CR13","volume-title":"Bursting: the genesis of rhythm in the nervous system","author":"J. Guckenheimer","year":"2005","unstructured":"Guckenheimer, J., Tien, J. H., & Willms, A. (2005). Bifurcations in the fast dynamics of neurons: implications for bursting. In S. Coombes & P. C. Bresloff (Eds.), Bursting: the genesis of rhythm in the nervous system. New Jersey: World Scientific Publishing Co."},{"issue":"1","key":"60_CR14","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1111\/j.1469-7793.2001.0069k.x","volume":"537","author":"M. Haller","year":"2001","unstructured":"Haller, M., Mironov, S., Karschin, A., & Richter, D. (2001). Dynamic activation of K ATP channels in rhythmically active neurons. Journal of Physiology 537(1), 69\u201381.","journal-title":"Journal of Physiology"},{"key":"60_CR15","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/j.neucom.2004.10.039","volume":"65","author":"R. Hayes","year":"2005","unstructured":"Hayes, R., Byrne, J., Cox, S., & Baxter, D. (2005). Estimation of single-neuron model parameters from spike train data. Neurocomputing 65, 517\u2013529.","journal-title":"Neurocomputing"},{"key":"60_CR16","volume-title":"Ion channels of excitable membranes","author":"B. Hille","year":"2001","unstructured":"Hille, B. (2001). Ion channels of excitable membranes., (3rd ed.). Sunderland, MA: Sinauer.","edition":"3"},{"issue":"1222","key":"60_CR17","first-page":"87","volume":"221","author":"J. Hindmarsh","year":"1984","unstructured":"Hindmarsh, J., & Rose, R. (1984). A model of neuronal bursting using 3 coupled 1st order differential equations. Proceedings of the Royal Society of London Series B 221(1222), 87\u2013102.","journal-title":"Proceedings of the Royal Society of London Series B"},{"key":"60_CR18","doi-asserted-by":"crossref","first-page":"2598","DOI":"10.1152\/jn.1994.72.6.2598","volume":"72","author":"S. Johnson","year":"1994","unstructured":"Johnson, S., Smith, J., Funk, G., & Feldman, J. (1994). Pacemaker behavior of respiratory neurons in medullary slices from neonatal rat. Journal of Neurophysiology 72, 2598\u20132608.","journal-title":"Journal of Neurophysiology"},{"key":"60_CR19","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/BFb0095239","volume":"1609","author":"C. K. R. T. Jones","year":"1995","unstructured":"Jones, C. K. R. T. (1995). Geometric singular perturbation theory. Lecture Notes in Mathematics 1609, 44\u2013118.","journal-title":"Lecture Notes in Mathematics"},{"key":"60_CR20","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S1095-6433(01)00393-2","volume":"130","author":"R. Kinkead","year":"2001","unstructured":"Kinkead, R., Bach, K., Johnson, S., Hodgeman, B., & Mitchell, G. (2001). Plasticity in respiratory motor control: Intermittent hypoxia and hypercapnia activate opposing serotonergic and noradrenergic modulatory systems. Comparative Biochemistry and Physiology A. Molecular and Integrative Physiology 130, 207\u2013218.","journal-title":"Comparative Biochemistry and Physiology A. Molecular and Integrative Physiology"},{"key":"60_CR21","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1038\/22540","volume":"400","author":"N. Koshiya","year":"1999","unstructured":"Koshiya, N., & Smith, J. C. (1999). Neuronal pacemaker for breathing visualized in vitro. Nature 400, 360\u2013363.","journal-title":"Nature"},{"key":"60_CR22","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1085\/jgp.114.4.491","volume":"114","author":"J. Magistretti","year":"1999","unstructured":"Magistretti, J., & Alonso, A. (1999). Biophysical properties and slow voltage-dependent inactivation of a sustained sodium current in entorhinal cortex layer-II principal neurons. Journal of General Physiology 114, 491\u2013509.","journal-title":"Journal of General Physiology"},{"key":"60_CR23","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.brainres.2004.11.011","volume":"1033","author":"S. Mironov","year":"2005","unstructured":"Mironov, S., Hartelt, N., & Ivannikov, M. (2005). Mitochondrial K ATP channels in respiratory neurons and their role in hypoxic facilitation of rhythmic activity. Brain Research 1033, 20\u201327.","journal-title":"Brain Research"},{"key":"60_CR24","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1007\/BF00248909","volume":"76","author":"H. Onimaru","year":"1989","unstructured":"Onimaru, H., Arata, A., & Homma, I. (1989). Firing properties of respiratory rhythm generating neurons in the absence of synaptic transmission in rat medulla in vitro. Experimental Brain Research 76, 530\u2013536.","journal-title":"Experimental Brain Research"},{"key":"60_CR25","unstructured":"Phipps, E. T. (2003). Taylor series integration of differential-algebraic equations: Automatic differentiation as a tool for simulating rigid body mechanical systems. Ph.D. Thesis, Cornell University."},{"key":"60_CR26","doi-asserted-by":"crossref","first-page":"3998","DOI":"10.1152\/jn.00641.2003","volume":"90","author":"A. A. Prinz","year":"2003","unstructured":"Prinz, A. A., Billimoria, C. P., & Marder, E. (2003). Alternative to hand-tuning conductance-based models: Construction and analysis of databases of model neurons. Journal of Neurophysiology 90, 3998\u20134015.","journal-title":"Journal of Neurophysiology"},{"issue":"12","key":"60_CR27","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1016\/j.molmed.2003.10.010","volume":"9","author":"D. Richter","year":"2003","unstructured":"Richter, D., Manzke, T., Wiklen, B., & Ponimaskin, E. (2003). Serotonin receptors: Guardians of stable breathing. Trends in Molecular Medicine 9(12), 542\u2013548.","journal-title":"Trends in Molecular Medicine"},{"key":"60_CR28","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1007\/BF00275501","volume":"25","author":"J. Rinzel","year":"1987","unstructured":"Rinzel, J., & Lee, Y. S. (1987). Dissection of a model for neuronal parabolic bursting. Journal of Mathematical Biology 25, 653\u2013675.","journal-title":"Journal of Mathematical Biology"},{"key":"60_CR29","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s00422-003-0447-1","volume":"90","author":"I.A. Rybak","year":"2004","unstructured":"Rybak, I. A., Shevtsova, N. A., Ptak, K., & McCrimmon, D. R. (2004). Intrinsic bursting activity in the pre-B\u00f6tzinger complex: Role of persistent sodium and potassium currents. Biological Cybernetics 90, 59\u201374.","journal-title":"Biological Cybernetics"},{"key":"60_CR30","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/S0006-3495(88)82975-8","volume":"54","author":"A. Sherman","year":"1988","unstructured":"Sherman, A., Rinzel, J., & Keizer, J. (1988). Emergence of organized bursting in clusters of pancreatic beta cells by channel sharing. Biophysical Journal 54, 411\u2013425.","journal-title":"Biophysical Journal"},{"key":"60_CR31","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1126\/science.1683005","volume":"254","author":"J. Smith","year":"1991","unstructured":"Smith, J., Ellenberger, H., Ballanyi, K., Richter, D., & Feldman, J. (1991). Pre-B\u00f6tzinger complex: A brainstem region that may generate respiratory rhythm in mammals. Science 254, 726\u2013729.","journal-title":"Science"},{"issue":"3","key":"60_CR32","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1023\/A:1026531603628","volume":"9","author":"J. Tabak","year":"2000","unstructured":"Tabak, J., Murphey, C., & Moore, L. (2000). Parameter estimation methods for single neuron models. Journal of Computational Neuroscience 9(3), 215\u2013236.","journal-title":"Journal of Computational Neuroscience"},{"issue":"5","key":"60_CR33","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1137\/0151071","volume":"51","author":"D. Terman","year":"1991","unstructured":"Terman, D. (1991). Chaotic spikes arising from a model of bursting in excitable membranes. SIAM Journal on Applied Mathematics 51(5), 1418\u20131450.","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"20","key":"60_CR34","doi-asserted-by":"crossref","first-page":"7685","DOI":"10.1523\/JNEUROSCI.23-20-07685.2003","volume":"23","author":"M. Thoby-Brisson","year":"2003","unstructured":"Thoby-Brisson, M., Cauli, B., Champagnat, J., Fortin, G., & Katz, D. (2003). Expression of functional tyrosine kinase B receptors by rhythmically active respiratory neurons in the preBotzinger complex of neonatal mice. Journal of Neuroscience 23(20), 7685\u20137689.","journal-title":"Journal of Neuroscience"},{"key":"60_CR35","unstructured":"Tien, J. H. (2007). Optimization for bursting neural models. Ph.D. Thesis, Cornell University."},{"key":"60_CR36","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1023\/A:1008972005316","volume":"7","author":"M. C. Vanier","year":"1999","unstructured":"Vanier, M. C., & Bower, J. M. (1999). A comparative survey of automated parameter-search methods for compartmental neural models. Journal of Computational Neuroscience 7, 149\u2013171.","journal-title":"Journal of Computational Neuroscience"},{"issue":"4","key":"60_CR37","doi-asserted-by":"crossref","first-page":"2070","DOI":"10.1152\/jn.01308.2005","volume":"95","author":"J. Viemari","year":"2006","unstructured":"Viemari, J., & Ramirez, J. (2006). Norepinephrine differentially modulates different types of respiratory pacemaker and nonpacemaker neurons. Journal of Neurophysiology 95(4), 2070\u20132082.","journal-title":"Journal of Neurophysiology"},{"key":"60_CR38","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S1569-9048(03)00185-X","volume":"138","author":"C. Washburn","year":"2003","unstructured":"Washburn, C., Bayliss, D., & Guyenet, P. (2003). Cardiorespiratory neurons of the rat ventrolateral medulla contain TASK-1 and TASK-3 channel mRNA. Respiratory Physiology and Neurobiology 138, 19\u201335.","journal-title":"Respiratory Physiology and Neurobiology"},{"issue":"4","key":"60_CR39","doi-asserted-by":"crossref","first-page":"1256","DOI":"10.1523\/JNEUROSCI.22-04-01256.2002","volume":"22","author":"C. Washburn","year":"2002","unstructured":"Washburn, C., Sirois, J., Talley, E., Guyenet, P., & Bayliss, D. (2002). Serotonergic raphe neurons express TASK channel transcripts and a TASK-like pH-and halothane-sensitive K\u2009+\u2009 conductance. Journal of Neuroscience 22(4), 1256\u20131265.","journal-title":"Journal of Neuroscience"}],"container-title":["Journal of Computational Neuroscience"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10827-007-0060-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10827-007-0060-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10827-007-0060-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T21:37:12Z","timestamp":1559252232000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10827-007-0060-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,13]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["60"],"URL":"https:\/\/doi.org\/10.1007\/s10827-007-0060-8","relation":{},"ISSN":["0929-5313","1573-6873"],"issn-type":[{"value":"0929-5313","type":"print"},{"value":"1573-6873","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11,13]]}}}