Name
Title | ||
|---|---|---|
Continuation-based numerical detection of after-depolarization and spike-adding thresholds. |
Abstract | ||
|---|---|---|
The changes in neuronal firing pattern are signatures of brain function, and it is of interest to understand how such changes evolve as a function of neuronal biophysical properties. We address this important problem by the analysis and numerical investigation of a class of mechanistic mathematical models. We focus on a hippocampal pyramidal neuron model and study the occurrence of bursting related to the after-depolarization (ADP) that follows a brief current injection. This type of burst is a transient phenomenon that is not amenable to the classical bifurcation analysis done, for example, for periodic bursting oscillators. In this letter, we show how to formulate such transient behavior as a two-point boundary value problem (2PBVP), which can be solved using well-known continuation methods. The 2PBVP is formulated such that the transient response is represented by a finite orbit segment for which onsets of ADP and additional spikes in a burst can be detected as bifurcations during a one-parameter continuation. This in turn provides us with a direct method to approximate the boundaries of regions in a two-parameter plane where certain model behavior of interest occurs. More precisely, we use two-parameter continuation of the detected onset points to identify the boundaries between regions with and without ADP and bursts with different numbers of spikes. Our 2PBVP formulation is a novel approach to parameter sensitivity analysis that can be applied to a wide range of problems. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1162/NECO_a_00425 | Neural Computation |
Keywords | Field | DocType |
one-parameter continuation,continuation-based numerical detection,brain function,after-depolarization adp,spike-adding threshold,classical bifurcation analysis,well-known continuation method,transient response,transient behavior,transient phenomenon,two-parameter continuation,sensitivity analysis | Statistical physics,Transient response,Boundary value problem,Direct method,Bursting,Mathematical optimization,Oscillation,Continuation,Mathematical model,Periodic graph (geometry),Calculus,Mathematics | Journal |
Volume | Issue | ISSN |
25 | 4 | 1530-888X |
Citations | PageRank | References |
1 | 0.39 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jakub Nowacki | 1 | 1 | 0.39 |
| Hinke M. Osinga | 2 | 160 | 20.82 |
| Krasimira T Tsaneva-Atanasova | 3 | 1 | 0.39 |