The effect of changed dt and steps_per_ms

Managing anatomically complex model cells with the CellBuilder. Importing morphometric data with NEURON's Import3D tool or Robert Cannon's CVAPP. Where to find detailed morphometric data.
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Christine Chung
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Joined: Fri May 03, 2019 2:41 am

The effect of changed dt and steps_per_ms

Post by Christine Chung »

Hello,
I'm a graduate student who studied with NEURON.
I conducted extracellular stimulation to anatomically realistic models via the code written by Ted, and investigated electric field thresholds (through apc.n, I checked somatic membrane polarized over 0 or not).
However, there was difference in threshold value according to dt and steps_per_ms.
1) dt=0.1ms and steps_per_ms=10.
2) dt=0.025ms and steps_per_ms=40.
The gap of threshold value between the two cases was 4-5 mV/mm.

I wondered what causes this difference of thresholds.
If you explain to me the reason, it would be really appreciated.

Thank you in advance.
ted
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Re: The effect of changed dt and steps_per_ms

Post by ted »

Electrical and chemical signaling in cells are described by ordinary and partial differential equations in which time and space are continuous variables. The equations that describe real cells do not have analytical solutions. Instead, it is necessary to solve them by numerical integration, a process that involves two steps
1. Discretization, in which the differential equations are replaced by a set of algebraic formulas that approximate the differential equations. Both space and time are discretized.
2. Use of an algorithm (integration method) in which the algebraic formulas are evaluated repeatedly to calculate an approximate solution, over a sequence of specific times, for each state variable (membrane potential, channel gating state, ionic concentration etc.) at particular locations in space.

The original differential equations are never solved. Instead, only the discretized approximate algebraic formulas are evaluated, so numerical integration can only produce approximate results. The error of of the approximate solution is generally reduced if time and space are chopped into smaller pieces. However, using a finer spatial or temporal discretization increases the computational burden (generates more equations that have to be evaluated, and forces evalutation at more points in time). Also, since numerical calculations in a digital computer have finite precision, each calculation introduces some roundoff error. If the spatial or temporal discretization is too fine, roundoff error can accumulate and corrupt the approximate solution.

For more about this, you might read chapter 4 in The NEURON Book, or see the chapter Numerical Integration Methods by Hines and Carnevale in the Encyclopedia of Computational Neuroscience.
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