CEPS: Units for cardiac applications

In the currently implemented cardiac models, we solve for the following equation (or a variant)

$\sisetup{math-micro=\text{µ},text-micro=µ} A_\mathrm{m}(C_\mathrm{m}\partial_t v + I_\mathrm{ion}) = \nabla\cdot(\sigma\nabla v).$

The following chart tells the unit of each variable involved in the equation.

Variable - Dimension	Description	CEPS Units
Time		$\mathrm{ms}$
Length		$\mathrm{cm}$
	Transmembrane voltage	$\mathrm{mV}$
$A_\mathrm{m}$	Membrane surface to volume ratio	$\si{\per\centi\metre}$
$C_\mathrm{m}$	Membrane surfacic capacitance	$\si{\micro\farad\per\centi\metre\squared}$
$I_\mathrm{ion}$	Ionic current	$\si{\micro\ampere\per\centi\metre\squared}$
$\sigma$	Electric conductivity	$\si{\milli\siemens\per\centi\metre}$

However, ionic models have often a different unit, and are sometimes expressed for $I_\mathrm{ion}/C_\mathrm{m}$ .

Ionic Model	Computed variable	Unit	Indicated value of $C_\mathrm{m}$
Beeler Reuter 1977	$I_\mathrm{ion}$	$\si{\micro\ampere\per\centi\metre\squared}$	$\SI{0.01}{\micro\farad\per\milli\metre\squared}$
TenTuscher Panfilov 2006	$I_\mathrm{ion}/C_\mathrm{m}$	$\si{\milli\volt\per\milli\second}$	$\SI{0.185}{\micro\farad}$
Courtemanche Ramirez Nattel 1998	$I_\mathrm{ion}$	$\si{\micro\ampere}$	$\SI{100}{\pico\farad}$
Mitchell Schaeffer 2003	$I_\mathrm{ion}/(C_\mathrm{m}\Delta V)$	$\si{\per\milli\second}$	-

The conversion from CEPS units to ionic model units is automatic. However, for models that require to change from absolute to surfacic currents, we considered a myocyte to have a cylinder shape of radius 10 µm and length 100 µm.