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[cellml-discussion] Dimensional consistency and unitsconversions (was [Fwd: Re: ten Tusscher model])


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  • From: david.nickerson at nus.edu.sg (David Nickerson)
  • Subject: [cellml-discussion] Dimensional consistency and unitsconversions (was [Fwd: Re: ten Tusscher model])
  • Date: Mon, 23 Apr 2007 11:19:46 +0800
> Is there not a confusion between 'dimensionless' and 'unitless' ?? They
> mean different things, and the sample equation is invalid because the
> bracketed qualities are a mix of unit specification and dimension
> specification.

yep - I think this is the crux of the issue.

> The 10^-6 is dimensionless (being [length^3]/[length^3]) but has units
> of L/uL.
>
> In terms of dimensions we have:
>
> amount_Na [amount_of_substance] = 10^-6 [dimensionless] * conc_Na
> [amount_of_substance / length^3] * vol [length^3]
>
> With units:
>
> amount_Na [nmol] = 10^-6 [L / uL] * conc_Na [nmol / L] * vol [uL]
>
> Combining both units and dimensions:
>
> amount_Na [amount_of_substance (nmol)]
> = 10^-6 [dimensionless (L/uL)] * conc_Na [amount_of_substance
> (nmol) / length^3 (L)] * vol [length^3 (ul)]

That looks good to me, and since CellML requires the specification of
units it should be all the units included in the CellML model rather
than the mix of dimensions and units.


Andre.


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