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# Feasibility of Estimating Maximum Ion Conductance Parameters from the Shape
of the Action Potential. A Simulation Study

### Alexandru Dan Corlan,
Bogdan Amuzescu,
Ivan Milicin,
Gheorghe Nistor,
Marin Popescu,
Adelina Georgescu,
Marcel Ovidiu Vlad,

### Biophysical Journal 96:664a-664a, 2009

## ABSTRACT

We verified whether the Vm(t) of a myocardial action potential
provides sufficient information to characterise the cell regarding
ion currents densities. We built a database of 45000 simulated action potentials by
running the Luo-Rudy dynamic model with Monte-Carlo
generated parameter sets comprising the maximum conductances for 12
major current components. Each parameter was generated
uniformly in the range of 0.5-2.0 times the default.
We then simulated experiments in which a 'data' action potential
(V_d(t)) was generated randomly in the same parameter interval and
using the same pacing protocol and we tried to estimate its
parameters. Each AP in the database was assigned the same prior
probability. Then at each of 50 steps spaced at 5 ms a
posterior probability was computed that was used as the prior probabily for
the next step. We considered for each step t(j) the difference DV(ij)
between the i'th action potential in the database and the 'data' action
potential. Using a normal noise model we calculated the non-conditional
probability of DV(ij) assuming it has a normal distribution then
the post-probability for step j given the prior obtained in step j-1.
We took the parameters of the database element with the maximum
posterior probability after the last step as the best estimate of the
parameters for the 'data' action potential. The absolute difference
between estimated and data parameters was used to assess the quality
of estimation. RMSD the root mean square difference between the V(t)
reconstructed from the estimated parameters and V_d(t) was used to
measure the quality of fit. In 100 experiments as described above we found
a RMSD of 4.14 +/- 1.15 mV (mean +/- SD) corresponding to a very close
resemblance of the data to the estimated V(t). However the absolute differences
in parameters were large ranging from 0.30 +/- 0.31 for I_Kr to
0.9 +/- 0.5 for I_Na.
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