A survey on linear relations between main electrical components during action potential in ventricular cell
Introduction
In a ventricular cell, the action potential (AP) is generated as a result of microscopic interactions between several components. These interactions are nonlinear and complex, and hence it can be difficult to determine the relationships between the components. Linear relationship is the simplest kind of similarity. Linear dependency (independency) is a rough measure of the linear relationship between observations. If two observations are linearly dependent (LD); they carry common information and we may generate one from a coefficient of the other. If three observations are LD, we can generate each of them from a combination of others, and so on. In this research we have a macroscopic look at the ventricular cell, i.e. we look at it as a system from which we have made several observations and try to determine how many of these observations carry dependent (independent) information about cell (microscopic) activity i.e. we are looking for some possible linear relationships between observations. We have used COR (Cellular Open Resource) [1] and the Noble et al. [2] guinea-pig ventricular cell model for generating eleven main observations. These observations are: AP, some main ionic concentrations and currents and also contraction. Using a novel and interesting mathematical criteria we investigate the dependency (independency) of every two and every three combinations of observations, finding that {[Na]i and [K]i} are two highly dependent observations and {iCaL, ito, and [Ca]i} are three very dependent ones. We also find that {iKr and iNaCa} are two very independent observations while {AP, iKr and ito} are three highly independent ones. In this paper we have presented tables which can be used for dependency (independency) comparison of observations. This dependency analysis may be used for the prediction of the effects of a parameter, e.g. an ionic concentration, on the different observations.
Section snippets
Method
Singular value decomposition (SVD) is a powerful mathematical tool for independent component analysis of observations [3]. In this study we make an observation matrix using eleven important signals during an AP. We have used COR and the [2] guinea-pig ventricular cell model for generating the 1 s length observations (see Table 1). The signals are sampled in 1-ms intervals so each observation includes 1000 sample points and the observation matrix will be an 11 × 1000 rectangular matrix. The
Results
In this study we discover that [Na]i and [K]i are the most dependent pair of observations during an action potential. We also find that iNaCa and iKr are the most independent pair of observations i.e. they carry the least common information. This study also shows us that the AP voltage is the most independent observation in comparison to the other signals i.e. the AP carries most uncommon information in comparison to other observations.
In relation to triad observations in this investigation we
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