MBI Publications

MBI Publications for Casey Diekman (9)

  • C. Diekman, M. Belle, H. Piggins and D. Forger
    Modeling hyperexcitation in central clock neurons
    (In Preparation)

    Abstract

  • C. Diekman, K. Dasgupta, V. Nair and K. Unnikrishnan
    Detecting neuronal connectivity from serial patterns in spike train data
    (In Preparation)

    Abstract

  • P. Thomas, C. Wilson and C. Diekman
    Spontaneous autoresuscitation in a model of respiratory control
    Conf Proc IEEE Eng Med Biol Soc (2012) pp. 6669-6672

    Abstract

    We introduce a closed-loop model of respiratory control incorporating a conductance-based central pattern generator (CPG), low-pass filtering of CPG output by the respiratory musculature, gas exchange in the lung, metabolic oxygen demand, and chemosensation. The CPG incorporates Butera, Rinzel and Smith (BRS)??s (1999) conditional pacemaker model. BRS model cells can support quiescent, bursting, or beating activity depending on the level of excitatory drive; we identify these activity modes with apnea (cessation of breathing), eupnea (normal breathing), and tachypnea (excessively rapid breathing). We demonstrate the coexistence of two dynamically stable behaviors in the closed-loop model, corresponding respectively to eupnea and tachypnea. The latter state represents a novel failure mode within a respiratory control model. In addition, the closed-loop system exhibits a form of autoresuscitation: conductances intrinsic to the BRS model buffer the CPG against brief episodes of hypoxia, steering the system away from catastrophic collapse as can occur with tachypnea.
  • Y. Wang, T. McMillen, M. Golubitsky and C. Diekman
    Reduction and dynamics of a generalized rivalry network with two learned patterns
    SIAM Journal of Applied Dynamical SystemsVol. 11 (2012) pp. 1270-1309

    Abstract

    We use the theory of coupled cell systems to analyze a neuronal network model for generalized rivalry posed by H. Wilson. We focus on the case of rivalry between two patterns and identify conditions under which large networks of n attributes and m intensity levels can reduce to a model consisting of two or three cells depending on whether or not the patterns have any attribute levels in common. (The two-cell reduction is equivalent to certain recent models of binocular rivalry.) Notably, these reductions can lead to large recurrent excitation in the reduced network even though the individual cells in the original network may have none. We also show that symmetry-breaking Takens??Bogdanov (TB) bifurcations occur in the reduced networks, and this allows us to further reduce much of the dynamics to a planar system. We analyze the dynamics of the quotient systems near the TB singularity, discussing how variation of the input parameter I organizes the dynamics. This variation leads to a degenerate path through the unfolding of the TB point. We also discuss how the network structure affects recurrent excitation in the reduced networks, and the consequences for the dynamics.
  • C. Diekman, C. Wilson and P. Thomas
    Spontaneous autoresuscitation in a model of respiratory control.
    Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. ConferenceVol. 2012 (2012) pp. 6669-72

    Abstract

    We introduce a closed-loop model of respiratory control incorporating a conductance-based central pattern generator (CPG), low-pass filtering of CPG output by the respiratory musculature, gas exchange in the lung, metabolic oxygen demand, and chemosensation. The CPG incorporates Butera, Rinzel and Smith (BRS)'s (1999) conditional pacemaker model. BRS model cells can support quiescent, bursting, or beating activity depending on the level of excitatory drive; we identify these activity modes with apnea (cessation of breathing), eupnea (normal breathing), and tachypnea (excessively rapid breathing). We demonstrate the coexistence of two dynamically stable behaviors in the closed-loop model, corresponding respectively to eupnea and tachypnea. The latter state represents a novel failure mode within a respiratory control model. In addition, the closed-loop system exhibits a form of autoresuscitation: conductances intrinsic to the BRS model buffer the CPG against brief episodes of hypoxia, steering the system away from catastrophic collapse as can occur with tachypnea.
  • C. Diekman, C. Fall, J. Lechleiter and D. Terman
    Modeling the neuroprotective role of enhancing astrocyte mitochondrial metabolism during stroke
    Biophysical Journal (2013) (In Press)

    Abstract

    A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and ER Ca2+ handling, IP3 production and GTP-binding protein coupled receptor (GPCR) signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GPCR (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed in order to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yielded explicit formulas determining how changes in IP3-mediated Ca2+ release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting v
  • C. Diekman, C. Fall, J. Lechleiter and D. Terman
    Modeling the neuroprotective role of enhanced astrocyte mitochondrial metabolism during stroke.
    Biophysical journalVol. 104 No. 8 (2013) pp. 1752-63

    Abstract

    A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and endoplasmic reticulum Ca(2+) handling, IP3 production, and GTP-binding protein-coupled receptor signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GTP-binding protein-coupled receptor (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yielded explicit formulas determining how changes in IP3-mediated Ca(2+) release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting variables in P2Y1R-enhanced astrocyte protection after cerebral ischemic stroke.
  • C. Diekman, M. Golubitsky and Y. Wang
    Derived patterns in binocular rivalry networks.
    Journal of mathematical neuroscienceVol. 3 No. 1 (2013) pp. 6

    Abstract

    Binocular rivalry is the alternation in visual perception that can occur when the two eyes are presented with different images. Wilson proposed a class of neuronal network models that generalize rivalry to multiple competing patterns. The networks are assumed to have learned several patterns, and rivalry is identified with time periodic states that have periods of dominance of different patterns. Here, we show that these networks can also support patterns that were not learned, which we call derived. This is important because there is evidence for perception of derived patterns in the binocular rivalry experiments of Kovács, Papathomas, Yang, and Fehér. We construct modified Wilson networks for these experiments and use symmetry breaking to make predictions regarding states that a subject might perceive. Specifically, we modify the networks to include lateral coupling, which is inspired by the known structure of the primary visual cortex. The modified network models make expected the surprising outcomes observed in these experiments.
  • C. Diekman and M. Golubitsky
    Network symmetry and binocular rivalry experiments.
    Journal of mathematical neuroscienceVol. 4 (2014) pp. 12

    Abstract

    Hugh Wilson has proposed a class of models that treat higher-level decision making as a competition between patterns coded as levels of a set of attributes in an appropriately defined network (Cortical Mechanisms of Vision, pp. 399-417, 2009; The Constitution of Visual Consciousness: Lessons from Binocular Rivalry, pp. 281-304, 2013). In this paper, we propose that symmetry-breaking Hopf bifurcation from fusion states in suitably modified Wilson networks, which we call rivalry networks, can be used in an algorithmic way to explain the surprising percepts that have been observed in a number of binocular rivalry experiments. These rivalry networks modify and extend Wilson networks by permitting different kinds of attributes and different types of coupling. We apply this algorithm to psychophysics experiments discussed by Kovács et al. (Proc. Natl. Acad. Sci. USA 93:15508-15511, 1996), Shevell and Hong (Vis. Neurosci. 23:561-566, 2006; Vis. Neurosci. 25:355-360, 2008), and Suzuki and Grabowecky (Neuron 36:143-157, 2002). We also analyze an experiment with four colored dots (a simplified version of a 24-dot experiment performed by Kovács), and a three-dot analog of the four-dot experiment. Our algorithm predicts surprising differences between the three- and four-dot experiments.

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