MBI Publications

MBI Publications for Jonathan Rubin (9)

  • J. Best, A. Borisyuk, J. Rubin, D. Terman and M. Wechselberger
    The dynamic range of bursting in a network of synaptically coupled square-wave bursting respiratory pacemaker cells
    SIAM J. of Appl. Dyn. Syst.Vol. 4 (2005) pp. 1107-1139

    Abstract

  • J. Best, A. Borisyuk, J. Rubin, D. Terman and M. Wechselberger
    The dynamic range of bursting in a model respiratory pacemaker network
    SIAM Journal of Applied Dynamical SystemsVol. 4 (2005) pp. 1107-1139

    Abstract

  • J. Best, A. Borisyuk, J. Rubin, D. Terman and M. Wechselberger
    The Dynamic range of bursting in a model respiratory pacemaker network
    SIAM Journal on Applied Dynamical SystemsVol. 4 (2005) pp. 1107-1139

    Abstract

  • Y. Guo, J. Rubin, C. McIntyre, J. Vitek and D. Terman
    Thalamocortical Relay Fidelity Varies Across Subthalamic Nucleus Deep Brain Stimulation Protocols in a Data-Driven Computational Model
    J. NeurophysiolVol. 99 (2008) pp. 1477-1492

    Abstract

  • J. Day, J. Rubin, Y. Vodovotz, C. Chow and G. Clermont
    Using nonlinear model predictive control to optimize inflammation-modulating therapy.
    (2008) (In Preparation)

    Abstract

  • J. Day, J. Rubin and C. Chow
    Competition between transients in the rate of approach to a fixed point
    SIAM J. Appl. Dyn. Syst.Vol. 8 No. 4 (2009) pp. 1523-1563

    Abstract

    The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.
  • J. Day, J. Rubin and G. Clermont
    Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation
    Math. Biosci. Eng.Vol. 7 No. 4 (2010) pp. 739-763

    Abstract

    Modulation of the inflammatory response has become a key focal point in the treatment of critically ill patients. Much of the computational work in this emerging field has been carried out with the goal of unraveling the primary drivers, interconnections, and dynamics of systemic inflammation. To translate these theoretical efforts into clinical approaches, the proper biological targets and specific manipulations must be identified. In this work, we pursue this goal by implementing a nonlinear model predictive control (NMPC) algorithm in the context of a reduced computational model of the acute inflammatory response to severe infection. In our simulations, NMPC successfully identifies patient-specific therapeutic strategies, based on simulated observations of clinically accessible inflammatory mediators, which outperform standardized therapies, even when the latter are derived using a general optimization routine. These results imply that a combination of computational modeling and NMPC may be of practical use in suggesting novel immuno-modulatory strategies for the treatment of intensive care patients.
  • Y. Guo and J. Rubin
    Multi-site Stimulation of Subthalamic Nucleus Diminishes Thalamocortical Relay Error in a Biophysical Network Model
    Special Issue: Neurocomputational Models of Brain DisordersVol. 26 No. 6 (2011) pp. 602-616

    Abstract

  • J. Day, J. Rubin and C. Chow
    Competition between transients in the rate of approach to a fixed point.
    SIAM J. Appl. Dyn. Syst.Vol. 8 No. 4 (2012) pp. 1523-1563

    Abstract

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