Thesis - Instituto de Telecomunicações

4.2. ELECTRODERMAL ACTIVITY 73model (eq. 4.25) for the EDA, based on the assumption that the EDA signal can be computedfrom the sudomotor nerve signal [172]. The authors consider a differential equationmodeling the skin conductance time series, with a driving signal corresponding to sudomotornerve impulses. Data fitting this model is used to identify the driving signal and theSCR’s timing parameters.f(t) =C(e −t/τ 0− e −t/τ 1)u(t). (4.25)In the work by Alexander et al. [6], the constants τ 0 and τ 1 , in the base equation (4.25)of the model for the SCR event, have been found to be constant over the study population.While it is possible to search for mean values in a population, the work in [149] shows theexistence of considerable differences in the individual parameters, questioning the validityof using a set of common parameters. Additionally, the model oversimplifies the shape ofthe SCR signal since the bi-exponential function is not differentiable for all time instants.This bi-exponential model is also used in an EDA model with distinct computationalsteps [125], based on a multi-compartment structure for the behavior of the electrodermalsystem. The algorithm is based on an optimization routine where the authors express thatthe results are improved if the searching for the SCR is manually guided (the user identifiesthe region where the event occurs, in order to guarantee a better convergence and removeerroneous SCR event detection).4.2.3 Proposed ModelMotivation and Morphological StudyThe proposed model is primarily based on a morphological study of the electrodermalactivity signal.The morphology of the signal is emphasized in the synthetic representation in figure4.4. For simplicity we assume that the SCR event is isolated, with null SCL, and the signalis referred as SC. First and second order derivatives of the signal are also represented inthis figure as SC ′ and SC ′′ , respectively. The first modification of the signal is the rise ofthe wave at the time instant t 0 (first instant where SC ′ = 0). The signal continues to rise,reaching a maximum speed at t 1 (the first instant where SC ′′ = 0) and starts to slow the