Ardo Illaste edited res_fitfunction.md  over 6 years ago

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#### Fitting function for transients  The function used for fitting Ca2+ release events is shown on Figure \ref{fig:fit}. The shape of the function is described by 4 parameters: amplitude (\(A\)), rise and decay time constants (\(\tau_{r},\tau_{d}\)) and plateau duration (\(d\)). An additional parameter (\(\mu\)) determines the time when the maximum is reached. The function describing a transient is:   \begin{equation}   g(A, d, \tau_{d}, \tau_{r}, \mu, t) = A\cdot\left\{ \begin{array}{l l} 1-\exp\left( -\frac{t-\mu}{\tau_r}\right)\cdot\exp\left(-2\right) 1-\exp \left(-\frac{t-\mu}{\tau_r} \right)\cdot\exp\left(-2\right)  & \quad \mu-2\tau_r\leq t<\mu\\\\ \mu -2\tau_r\leq t< \mu\\  1-\exp(-2) & \quad \mu\leq t< \mu+d\\\\ \mu+d\\  \exp\left( -\frac{t-\mu-d}{\tau_d}\right)\cdot\left(1-\exp(-2)\right)& \quad t\geq\mu+d\\\\ t\geq\mu+d\\  0 &\quad \mathrm{otherwise}  \end{array} \right. \end{equation}   The transient consists of four phases: zero level before the onset of the transient, an exponential increase with time constant \(\tau_r\) starging when \(t=\mu-2\tau_r\), a plateau phase of duration \(d\) starting at \(t=\mu\) and an exponential decay with time constant \(\tau_d\) starting at \(t=\mu+d\)