An application of higher order multivariate cumulants in modelling of myoelectrical activity of porcine uterus during early pregnancy
Introduction
The analysis of the uterine contraction have become a general practice in an effort to improve the clinical management of uterine contractions during pregnancy and labour (Figueroa et al., 1987; Gajewski and Faundez, 1992; Maul et al., 2003; Rabotti et al., 2008; Jacod et al., 2010; Lammers, 2013; Rooijakkers et al., 2014; Pawlinski et al., 2017). In healthy, no pregnant uteri specific contractile patterns evolve during the estrus cycle both in humans and animals (Fanchin and Ayoubi, 2009; Kuijsters et al., 2017; Domino et al., 2018a). Significant attention has been dedicated to evolving patterns being in line with the hypothesis of a functional role of uterine activity in promotion of fertilization (Pusey et al., 1980; Sammali et al., 2018). Uterine contractility is known to affect embryo implantation (Rogers et al., 1983; Ziecik et al., 2011; Lammers, 2013). Furthermore, the quiescence of the uterus during pregnancy is required to maintain pregnancy and allow adequate nourishment and development of the foetus (Gajewski and Faundez, 1992; Rabotti and Mischi, 2015; Markiewicz et al., 2016). During early pregnancy, some fluctuations in uterine activity can always be present without affecting progress of gestation, however the painful uterine contractions occurring in a coordinated and forceful fashion may be the first threat of a preterm delivery (Norwitz and Robinson, 2001).
The animal and in vitro experiments have been found to provide valuable methods and results for parameter estimation, undertaking up to humans clinical studies (Devedeux et al., 1993; Rabotti et al., 2010). While pigs are considered as an ideal preclinical model due to many anatomical and functional similarities with humans, the investigations carried out on the porcine reproductive tract may be treated as a referential (Ziecik et al., 1993; Gajewski et al., 2001; Kobayashi et al., 2012). The electrical activity of the porcine uterus as the primary cause of contractions, was established both during estrus cycle (Gajewski et al., 2001; Domino et al., 2018a) and early pregnancy (Maner et al., 2003; Markiewicz et al., 2016; Pawlinski et al., 2017). In those cases smooth muscle cells (SMCs) contract, action potentials reach a depolarization threshold and generate an electromagnetic field (Eswaran et al., 2004). The billions of SMCs are coupled electrically by the gap junctions into the complex biological system (Garfield et al., 1977) within numerous electrochemical events generate electric currents as a sum of action potential differences between SMCs (Alkan and Günay, 2012). Those myometrial electromagnetic field is possible to be measured as voltage and quantified with different sensitivity by electromyography (EMG) (Gajewski et al., 2001; Wolinski et al., 2003; Eswaran et al., 2004) and electrohysterography (EHG) (Rabotti et al., 2008; Jacod et al., 2010; Rabotti et al., 2010; Sammali et al., 2018). The EHG was reported as a feasible option to evaluate noninvasively and objectively the myometrial activity in humans, both of the non-pregnant uterus (Sammali et al., 2018) as well as during late gestation and labour (Jacod et al., 2010; Rabotti et al., 2010). In early gestation in humans, EHG method is insufficient to register the subtle changes in spectral content of uterine EMG signal, whereas invasive EMG method is unacceptable for obvious, ethical reasons (Rabotti et al., 2010). The needle EMG gathered the bioelectrical signal directly associated with the contractile activity of myometrium, while EHG collected signal abundant in noise generated between uterus and implanted superficial electrodes positioned on the surface of abdomen (Devedeux et al.,1993; Jacod et al., 2010). Therefore, the electrical activity recorded more invasively, directly from myometrium, may provide crucial information about uterine activity. For this reason the animal models are essential for understanding the sophisticated mechanisms behind the phenomena of contribution of uterine activity into the fertilization and early pregnancy maintenance.
In the case of all electroencephalograms (EEG) (Singh et al., 2015; Chen et al., 2016), EMG (Domino et al., 2016, 2017a; 2018a) and EHG (Farina and Negro, 2007; Garfield and Maner, 2007a; Domino et al., 2017a), considering spectral content in addition to studying changes in its time domain features is widely used. Moreover a variety of features have been extracted by different feature selection methods in the time and frequency domains. The time domain features of EMG include duration (D), amplitude (A) and root mean square (RMS) of bursts as well as duration of pauses between bursts (P) (Devedeux et al.,1993; Gajewski et al., 2004; Garfield and Maner, 2007a; Pawlinski et al., 2016). It has been established that the uterine EMG signals can be quantified sufficiently with mathematical functions and transforms such as power spectral analysis (Maner et al., 2003; Garfield and Maner, 2007b). In frequency domain we receive features corresponding to each frequency bands. However in our work for simplicity and informative significance we concentrate on: dominant frequency (DF), maximum power (Max P) and the minimum power (Min P) which can be estimated by Fast Fourier transform (FFT) method (Oczeretko et al., 2007; Domino et al., 2016, 2017a; 2018a). Recent methods used in a detailed analysis of myoelectrical signals are divided in four major categories: cross-coherence function (Farina and Merletti, 2004; Domino et al., 2016), phase difference (Hunter et al., 1987), maximum likelihood (Farina et al., 2001; Rabotti et al., 2010) and the detection of spectral relations (Farina and Negro, 2007; Domino et al., 2017a, b; Garfield and Maner, 2007b). Garfield and Maner (2007b) suggested the features of power density spectrum as a more effective than the conventional time dependent features in reflecting the actual function of the uterus. The decomposition of myoelectrical signals into their individual frequency or ‘scale’ subcomponents provided much more advantageous data, that can be used as indicators of changes in uterine status such as pre-term delivery (Maner et al., 2003; Garfield and Maner, 2007b). In our research we have acquired both recent features (D, A, RMS, P) and following frequency domain subcomponents (DF, Max P, Min P) of EMG signal, from porcine uterus in relation to early pregnancy phenomena. Further we speculate that those features are non-Gaussian distributed due to complex biochemical processes that take place in myometrium, which represents contractile element of the uterine wall composing of SMCs (Rabotti and Mischi, 2015). Observe that higher order multivariate cumulants can be used to analyse non-Gaussian distributed multivariate data (Domino et al., 2018b) such as considering together time and frequency features in our case. Observe as well, that higher order cumulants approach was successfully applied in EEG (Becker et al., 2014) and superficial EMG (Ju and Liu, 2011) data analysis. However, none of recent researchers has introduced the computational modelling of spontaneous myoelectrical activity of complex SMCs systems in peri-fertilization period.
Section snippets
Experimental design
The spontaneous myoelectrical activity of uterus has been recorded from 8 Polish Landrace sows according to protocol approved by the III Local Ethical Committee on Animal Testing in Warsaw (Permit Number: 71/2009, from 19.11.2009) on behalf of the National Ethical Committees on Animal Testing. The study was conducted on sexually mature sows at the age of 6 months and 95–110 kg body weight. All sows were selected from pig producing units after experiencing a single estrous cycle and had not been
Results and discussion
The clear, free of artefacts EMG signal was recorded from all electrodes positioned along one side of uterus from day -6 to day 12 in respect to AI. We used the Frobenius norm on the higher order multivariate cumulant and found that considering together time and frequency features of EMG signal was extremely non-Gaussian distributed as following and in all points of designed time-line.
Beginning with the standard cumulants the Frobenious norm of the mean vector (for ) and the
Conclusions
An additional novelty of this paper resides in the porcine EMG signal analyzing methodology based on the use of higher order multivariate cumulants. We have applied those cumulants to study the dependence structure of EMG patterns with an effective EMG feature, and then have built up the myoelectrical activity templates for recognizing complex uterine contraction according to crucial stages for successful fertilization and early pregnancy maintenance.
Based on our results, we may conclude that
Conflict of interest
None.
Acknowledgements
This work was conducted in the Veterinary Research Centre WULS (WCB) and the Center for Biomedical Research (CBB) supported by EFRR RPO WM 2007-2013. Additionally, KD acknowledge the support of the National Science Centre, Poland under project number 2014/15/B/ST6/05204.
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