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Hi Alan!

[Apologies for breaking the thread, I had subscribed to the list in digest
form.]

Thank you for your example. Unfortunately, fixed time-stepping schemes where
events (threshold
crossings and membrane potential resets) can occur only on a fixed time grid
are one of the big
no-nos in neuronal network modeling, since they can lead to strong
synchronization artefacts.
Indeed, quite a lot of research in recent years has focused on algorithms to
determine the exact
time of threshold crossings efficiencly. I'd be happy to send you reference
if you are interested.

Thus, if we wanted to use CellML to represent neuron models in a general
form, we would need a
possibility to represent instantaneous events in continuous time. I believe
SBML events provide
this, don't they?

Best,
Hans



> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 1 Jun 2009 12:17:54 +0100
> From: "Alan Garny" <alan.garny at dpag.ox.ac.uk>
> Subject: Re: [cellml-discussion] Using CellML for simplified neuron
> models?
> To: "'CellML Discussion List'" <cellml-discussion at cellml.org>
> Message-ID: <001001c9e2aa$9beba840$d3c2f8c0$@garny at dpag.ox.ac.uk>
> Content-Type: text/plain; charset="us-ascii"
>
> Hi Hans,
>
>> We are looking for a good way to describe and share neuron models, and
>> CellML appears a good
>> candidate. The neuron models we are interested in consist mostly of a
>> single compartment,
>> possibly of a small number of compartments.
>>
>> As far as I can see, CellML appears well suited to describe the so-called
>> subthreshold dynamics
>> of model neurons. But I am wondering if CellML can also capture (or be
>> extended to capture) the
>> threshold operation present in most simplified neuron models. Briefly, the
>> model dynamics are
>> integrated according to a set of differential equations. When the membrane
>> potential of the
>> neuron crosses a certain threshold, the neuron is said to "fire": the
>> membrane potential is
>> reset to a certain value instantaneuously, and often clamped at that value
>> for a certain period
>> of time afterwards (refractory period); also, an output signal is
> generated.
>> In simple
>> pseudocode, this would look like:
>>
>> while ( simulation time not up )
>>
>> process input
>> update dynamics according to ODE
>>
>> if ( neuron is refractory )
>> V_m = V_reset
>> count down "refractoriness"
>>
>> if ( V_m > Threshold )
>> V_m = V_reset
>> emit output signal
>>
>> count up time
>
> I believe this could easily be done, as long as you are OK with the
> following:
> - this would require integrating the model using an integration technique
> that relies on a fixed time step. In my experience, anything will make your
> resetting of Vm difficult.
> - your output signal (Vm?) will always be generated.
>
> Attached is a very simple CellML file (based on the van der Pol model) that
> illustrates the kind of thing I think you are after. You want to plot the x
> and y parameters (see attached screenshot).
>
> Alan
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> End of cellml-discussion Digest, Vol 59, Issue 1
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--
Dr. Hans Ekkehard Plesser
Associate Professor

Dept. of Mathematical Sciences and Technology
Norwegian University of Life Sciences

Phone +47 6496 5467
Fax +47 6496 5401
Email hans.ekkehard.plesser at umb.no
Home http://arken.umb.no/~plesser

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• [cellml-discussion] Using CellML for simplified neuron models? (Alan Garny), Dr. Hans Ekkehard Plesser, 06/05/2009
  • [cellml-discussion] Using CellML for simplified neuron models? (Alan Garny), Alan Garny, 06/05/2009
  • [cellml-discussion] Using CellML for simplified neuron models? (Alan Garny), Poul Nielsen, 06/05/2009
    • [cellml-discussion] Using CellML for simplified neuron models? (Alan Garny), Dr. Hans Ekkehard Plesser, 06/05/2009

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