Ardo Illaste edited res_fitting.md  about 10 years ago

Commit id: 4dce4c6e05fb2c56d1404b4f64755017dcdd9376

deletions | additions      

       

### Signal fitting  The function used for fitting Ca2+ release events is shown on Figure \ref{fig:f2}. The shape of the function is described by 4 parameters: amplitude (\(A\)), rise and decay time constants (\(\tau_{rise},\tau_{decay}\)) and plateau duration (\(d\)). An additional parameter (\(t_{max}\)) (\(\mu\))  determines the time when the maximum is reached. For the optimizer to obtain good performance when fitting the function used for fitting should be continously differentiable. The original fitting function:  \[  g(A, d, \tau_{d}, \tau_{r}, \mu) =   \left\{   \begin{array}{l l}  n/2 & \quad \text{if $n$ is even}\\  -(n+1)/2 & \quad \text{if $n$ is odd}  \end{array} \right.  \]  Because it is not know which part of the signal is the event and which is the baseline the first fit also has to estimate the baseline properties.  Signal in the candidate region is fitted with an extended fit function (Figure \ref{fig:fig2}) that also depends on relaxation baseline \(B\) and baseline offset \(C\). The \(C\) parameter allows for the possibility of an elevated background before the release event.