Biomathematical pattern of EMG signal propagation in smooth muscle of the non-pregnant porcine uterus

Uterine contractions are generated by myometrial smooth muscle cells (SMCs) comprising most of the myometrial layer of the uterine wall. Synchronous contractions of SMCs are responsible for normal gamete transport in the female reproductive tract and contribute to the expulsion of uterine debris [ 1 ]. The occurrence of uterine contractions must be strictly controlled and coordinated to sustain these reproductive functions [ 1 , 2 ]. Abnormal patterns of uterine motility such as hypoactive, hyperactive or asynchronous contractions have been implicated in the pathogenesis of infertility, implantation failure, endometriosis and abnormal estrous cycles [ 3 ]. However, the specific mechanism by which the non-pregnant uterus autonomously initiates myometrial contractions remains poorly described. In spite of their clinical significance, contractile properties of the uterus during the entire estrous cycle have not been examined [ 4 ]. A better understanding of the complex myometrial activity would help to develop effective therapies for an array of reproductive disorders associated with the flawed rhythmicity of uterine contractions. A single impulse can initiate a myometrial contraction but multiple, coordinated impulses are needed for forceful and sustained contractions [ 5 ]. Moreover, individual impulses within the myometrial tissue may differ in speed and direction, and such intrinsic variations in conduction velocities are essential for sustaining forceful and coordinated muscular contractions [ 6 , 7 ]. Uterine SMCs themselves trigger cellular processes resulting in uterine contractions. The typical sequence of these interrelated processes is referred to as the excitation-contraction (EC) coupling [ 8 ] and entails three stages: Ca 2+ entry into the cell; Ca 2+ expulsion from the cell; and SMC contraction. Calcium influx occurs through the voltage-dependent calcium channels in response to depolarization of the cell membrane and results in a transient increase in intracellular concentrations of Ca 2+ ions [ 1 , 2 ]. The voltage- and time-dependent changes in the membrane ionic permeability initiate an action potential (AP) or myoelectrical activity [ 5 ]. Cell membrane stimulated by external impulses responds with a change in the transmembrane electrical potential, which leads to opening of membrane channels to let ions enter or leave the cell [ 8 ]. Calcium ions constitute the main component of depolarizing current during the propagation of AP as well as the most important factor determining contractile force of myometrial myocytes [ 1 ]. Elevated level of intracellular Ca 2+ ions allows for binding of Ca 2+ by calmodulin, which ultimately results in activation of the light-chain myosin kinase and phosphorylation. Subsequently, the cross-bridges between actin and myosin filaments are formed and SMCs contract [ 1 , 2 ]. There is a paucity of studies on the generation of EC processes by the uterine SMCs in situ . Such investigations are confined to the determination of intrauterine pressure and uterine electrical activity during simulated uterine contractions [ 8 , 9 ]. For example, Cochran and Gao [ 9 ] designed the electromechanical model to simulate intrauterine pressure and to assess uterine contractions during parturition. Sharifimajd et al. [ 8 ] developed an electro-chemo-mechanical model to replicate excitation, activation, and contraction of uterine smooth muscle cells. In both cases, uterine contractions were induced “from cellular level to the organ level” due to electrophysiological properties of the pacemaker cells and ensuing propagation of electrical discharges via gap junctions within the myometrium. Most of earlier studies on uterine activity deal primarily with the electrophysiology of the SMC membrane [ 4 , 10 ]. In all in vitro investigations, at the level of single myometrial myocyte, equations describing various ionic membrane currents were established from their respective activation curves. Parameters were determined using the voltage-clamp technique and measurements performed on isolated cells [ 11 ]. This particular approach is excellent for describing contribution of cellular phenomena in muscular contractions but provides inadequate information on contractile activity of the tissue or organ [ 8 , 12 ]. Alternatively, in vivo models of uterine contractility utilize the “top-down approach” in which function in the entire organ or tissue following activation of SMCs is monitored. Changes in electrical activity of smooth muscle fibers during contraction or relaxation can be detected on surface of skin (surface EMG) or directly within the myometrium (needle EMG) as an electromyography (EMG) signal. The EMG is the sum of bioelectrical signals or electric currents produced by differences in bioelectrical potentials along a specialized tissue and is associated with electrochemical events occurring during the propagation of action potential [ 13 ]. Two distinctive forms of action potential have been recorded in myometrium of various species, namely a single action potentials and multiple action potentials. The single action potential, called the "single spike", consists of rapid depolarization followed by immediate repolarization of cell membranes. These spikes often occur in sequels called "bursts", number and frequency of spikes within burst predetermine strength and rapidness of smooth muscle contraction. Multiple spontaneous action potentials (bursts) seem to arise simultaneously in different regions of the uterine wall [ 1 , 12 ]. The frequency and duration of the bursts as well as the frequency of spikes within a burst shows considerable individual variations and vary with the stage of parturition [ 7 ]. The propagation of electrical activity in the myometrium mainly depends on arrangement of myometrial bundle fibers [ 6 ], population of gap junctions formed between adjacent cells during each contraction [ 14 , 15 ], and waves of calcium transport [ 16 ]. In contrast to skeletal muscle, in which the propagation of action potentials that progresses in muscle fibers is highly predictable, the direction and speed of electrical activation in myometrial cells remain to be elucidated [ 17 ]. Most of previously published studies were devoted to the analysis of entire bursts or single spikes in pregnant uterus [ 8 , 18 , 19 , 20 ], and only few studies dealt with non-pregnant state [ 4 , 21 ]. Hence, the main goal of the present study was to determine the biomathematical pattern describing EMG signal propagation in the non-gravid porcine uterus in vivo .

Successful EMG recordings were obtained from each electrode site. Over 240 bursts were extracted from each animal during long time measurement (>24 hours of continuous recording). From all registered bursts only those with high similarity were used as a “fingerprint” to establish the direction of propagation and propagation speed. The characteristic for porcine uterus myoelectrical activity pattern was established based on burst parameters ( Table 1 ). There were no significant differences in the mean amplitude, RMS and duration between different topographic regions (P>0.05). a A—amplitude, b RMS—root mean square, c T—time—duration of burst. There were no significant differences in the mean |R| (P = 0.42) and |r| (P = 0.30) values between the right (x(n) and y(n) discrete data series) and left uterine horn (y(n) and z(n) discrete data series. The mean (±SEM) values of similarity measures were (|r| = 0.22±0.02; {0.08 |r| Є R: 0.50 ≤ |r| ≤ 1}) and (|R| = 0.23±0.02; {0.17 |R| Є R: 0.50 ≤ |R| ≤ 1}) for the cross-correlation and cross-coherence, respectively. The cross-coherence function demonstrated a significantly higher similarity rate and was used to determine the direction and speed of signal propagation in the complex biological system of uterine myometrium. Figs 2 and 3 demonstrate Fourier analysis of highly synchronized uterine contraction signals in different topographic regions: RUH and CU ( Fig 2 ) as well as CU and LUH ( Fig 3 ). Values of DFs, which are marked by black dots, are very similar for these two signal pairs. Highly synchronized time series (empirically considered |R|>0.50) are built and details components shown in Fig 1 . They were used to determinate the direction and speed of signal propagation. EMG signals from the right uterine horn (A, B) and corpus uteri (C, D) in time (A, C) and frequency (B, D) domains. EMG signals from the corpus uteri (A, B) and left uterine horn (C, D) in time (A, C) and frequency (B, D) domains. The EMG signals were propagated along the uterine horn in both cervico-tubal (from CU to UH) and tubo-cervical (from UH to CU) directions. There were no significant differences (P = 0.20) between the percentages (mean % ± the standard error of mean (SEM)) of bursts propagated in both directions, from CU to UH (45.30% ± 3.27) and from UH to CU (4.73% ± 3.25) in relation to the total number of highly synchronized uterine contraction signals. There were also no significant differences (P = 0.20 and P = 0.60, respectively) between bursts propagation in the right and left uterine horns ( Table 2 ). a RUH-CU—tubo-cervical direction in the right uterine horn, b CU-RUH—cervico-tubal direction in the right uterine horn, c LUH-CU—tubo-cervical direction in the left uterine horn, d CU-LUH—cervico-tubal direction in the left uterine horn. Mann-Whitney test (P<0.01) EMG signals were propagated along the uterine horn with three significantly different (P<0.0001), independent speeds: SBMR (slow basic migration rhythm), RBMR (rapid basic migration rhythm) and RAMR (rapid accessory migration rhythm). Bursts propagation speed was determined experimentally and tested for homogeneity inside the population for: SBMR, RBMR and RAMR. All propagation speeds were considered to be homogeneous (P>0.05). The SBMR, RBMR and RAMR values (mean ± SEM) as well as the percentage (mean %) of bursts propagation speed in relation to total number of highly synchronized uterine contraction signals are presented in Table 3 . a SBMR—slow basic migration rhythm, b RBMR—rapid basic migration rhythm, c RAMR—rapid accessory migration rhythm. For independence: Kruskal-Wallis test with Dunn's multiple comparisons test (P<0.05). For homogeneity: one-way ANOVA test with Tukey's multiple comparisons test (P<0.05).

In conclusion, the EMG signal propagation in smooth uterine muscles could be determined using linear synchronization measures. We described for the first time the successful cross-correlation function the EMG signal propagation in a long term in vivo experiment in the non-gravid porcine uterus. The pattern of the EMG signal propagation is not random but it occurs in an orderly, bidirectional fashion and at distinctive speed. The spontaneous potentials are propagated equally in both directions between both horns and the uterus. Since other studies have shown that the presence of intercellular contacts appears to be controlled by changing estrogen and progesterone levels, further information is needed to elucidate the coordination of contractility during different stages of the estrous cycle. Nevertheless, the analysis of electrical signal propagation in the uterus offers a unique opportunity to understand the mechanisms underlying uterine contractility both in animals and human beings.

The experiment has been conducted on 10 mature Polish Landrace sows (n = 10). The experiment has been conducted according to applicable national and international ethical guidelines and all efforts were made to minimize animals suffering. The protocol was 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. Sows had been adapted to the animal facilities for 7 days before studies. During the entire experiment animals were housed in metabolic cages, fed and watered ad libitum . In order to maintain animal welfare surgery was carried out under general anesthesia and the telemetry EMG recording method was applied. Telemetry method [ 22 ] allows to reduce the number of animals used in the experiment and provide long-term registration without stress connected with immobilization. Spontaneous uterine activity in non-pregnant state during diestrus was recorded by the combination of three electrodes connected to 3-channel transmitter used in large animals. The telemetry transmitter TL10M3-D70-EEE (DSI, St. Paul, Minnesota, USA) was surgically positioned between abdominal muscles and three silver bipolar needle electrodes were sutured onto different topographic regions of uterus: right uterine horn (RUH—channel 1), corpus uteri (CU—channel 2) and the left uterine horn (LUH—channel 3) surfaces ( Fig 1 ). The distance between electrodes (channel 1 to channel 2 and channel 2 to channel 3) was constant and fixed at 17 cm. Animals were premedicated with an intramuscular injection of azaperone (Stresnil, 3 [mg/kg b.wt.], i.m., Janssen Pharmaceutica) and then catheter was inserted into the auricular vein. Surgery was carried out under general anesthesia, consisting of combined administration of medetomidyne (Cepetor, 1 [mg/kg b.wt.], i.v., CP- Pharma Handelsges), butorphanol (Butomidor, 0,2 [mg/kgb.wt.], i.v., Ricgter Pharma AG), ketamine (Bioketan, 3 [mg/kg b.wt.], i.v., Vetoquinol Biowet) and propofol (Propofol, 2–4 [mg/kg b.wt.], i.v., Pfizer). Then pigs recovered from surgery analgesic—meloxicam (Metacam 0.4 [mg/kg b.wt.], i.m., Boehringer Ingelheim) and anti-microbial—cefquinom (Cobactan, 2.0 [mg/kg b.wt.], i.m., Intervet) had been administered for 5 days. Obtained analog signal was digitalized and sent by radio waves to the telemetric receiver (DL10 analog output (DSI)). The signal was acquired with a 3-channel transmitter (PowerLab (ADInstruments, Melbourne, Australia) and analyzed. Sampling frequency was 100 Hz. Pigs were euthanized at the end of the experiment by—Sodium Pentobarbital (Morbital 100.0 or [mg/kg b.wt.], i.v., Biowet Pulawy). Electrodes were arranged in the porcine reproductive tract (A) and the EMG signals (B) were sampled from: channel 1, right uterine horn, RUH; channel 2, corpus uteri, CU; and channel 3, left uterine horn, LUH. The EMG signals were digitally filtered with a band-pass filter [5–50 Hz], then power line interference was lowered from the EMG recordings with a notch filter. Mean and linear trends were removed [ 23 ]. Uterine contractions were defined as series of electrical potentials with amplitude above 5 μV and a duration of more than 3 s, separated from each of next series by a time period not less than 5 s. Any new electrical activity after this period (5 s) was interpreted as a subsequent contraction (8). Each contraction was described using spike and burst parameters. The spike represented single action potentials while the burst comprised multiple action potentials. Mean amplitude [mV], mean RMS (root mean square) [mV], duration of electrical activity [s], duration of pauses [s], and number of spikes forming a burst were analyzed relative to bursts and spikes, respectively. The EMG signal spectral content was analyzed in addition to studying changes in its time domain features. The spectrum analysis gave amplitudes of each of pure tones of different frequencies and phases, summed in single EMG signal. The amplitude spectrum of investigated signals was defined as the distribution of amplitudes over different frequencies. By means of Fourier analysis (FFT—Fast Fourier transform), dominant frequency (DF) [Hz] (the frequency at which most signal energy was transmitted) was assessed for each data series. We used the Hamming window only for the Fourier analysis [ 21 , 24 ]. The uterus is indubitably a complex system in which billions of cells comprising myometrium interact in a complex manner. Our understanding of the co-ordination of uterine contractions is incomplete. In physiological research, multivariate data sets containing two or more simultaneously recorded time series are usually examined to establish signals similarity [ 24 ]. We used similarity measures based on the concept of time series data synchronization. In order to describe similarities between EMG signals, we used two-dimensional functions analysis. Degree of synchronization between three simultaneously recorded data series (channels 1(x), 2(y), 3(z)) was estimated for two signal pairs (xy and yz) using linear measures: the cross-correlation function (ƒ x,y (l), ƒ y,z (l)) and the cross-coherence function (C xy (ƒ), C yz (ƒ)). The coherence function in frequency domain was equivalent to the correlation function in time domain. C xy was estimated after Fourier analysis (FFT) [ 21 ]. Cross-correlation function gives the correlation degree between the two signals—amplitude data series (pair xy—channel 1 and channel 2 / pair yz—channel 2 and channel 3) [ 25 ]. The cross-correlation function of two discrete data series x(n) and y(n) is a statistical quantity defined as follows: ƒ x , y ( l )   = c o v ( x , y ) S d x x   S d y (1) Signals x(n), y(n) and z(n) are collected from the right uterine horn, corpus uteri and left uterine horn electrodes, respectively. After normalization, the value of cross-correlation parameters will be between -1 and 1. The result is 1 if x(n) = y(n) or y(n) = z(n) and l = 0; ƒx , y(l) = 0 if x,y are statistically independent and it is -1 if x(n) = —y(n) or y(n) = —z(n) and l = 0. Synchronization is high if | ƒx , y(l) | = 1 and absent if ƒx , y(l) = 0. The cross-coherence function gives the coherence degree between two signals—dominant frequencies data series (pair xy—channel 1 and channel 2 / pair yz—channel 2 and channel 3) [ 25 ]. The cross-coherence function of two discrete data series x(n) and y(n) is a statistical quantity defined as follows: C x y ( ƒ ) = | P x y ( ƒ ) | 2 P x x ( ƒ )   x   P y y ( ƒ ) (2) It is real-valued, positive and normalized to vary between 0 (no coherence) and 1 (complete coherence). In the same way, high synchronization corresponds to a value of 1, whereas a value of 0 indicates lack of synchronization. Values for the cross-correlation coefficient |r| and cross-coherence coefficient |R| were estimated separately for two pairs of discrete time series x(n) and y(n) as well as y(n) and z(n). Synchronization between the right uterine horn (x(n)) and corpus uteri (y(n)) as well as the corpus uteri (y(n)) and left uterine horn (z(n)) was observed. The threshold at which the values of |r| and |R| were considered significant was determined empirically, and was always over > 0.50 with significant strength from middle to very high. The burst pairs with an empirical value of |R| over threshold were considered as synchronized. Results of linear synchronization measures application to pairs of EMG signals demonstrated that the cross-coherence function is effective in determining bursts similarity. Similarity measures based on the concept of synchronization allow detection of bursts propagation in different topographic regions. They were used to "identify" the frequency fingerprint of the spatial burst and determined when the burst reached the other location during propagation. Locations of the first and second electrodes (on the x/y or y/z axis) were used to measure highly synchronized signals, and the direction of bursts propagation was evaluated. The second signal location (on the x/y or y/z axis) in the time function pointed towards cervico-tubal and tubo-cervical directions. The speed of bursts propagation was evaluated based on the time elapsed for highly synchronized signals to move from the first electrode to the second one (measuring points on the x/y or y/z axis). To assess statistical differences among three channel data series, a one-way ANOVA and the Kruskal-Wallis test (the level of statistical significance was set to P<0.05) were performed. To evaluate the percentage of signal propagation (direction and speed) in relation to the total number of synchronizations examined, non-parametric, two-tailed Mann-Whitney test was applied (P<0.01). The independence of speed was tested using a non-parametric Kruskal-Wallis test with Dunn's multiple comparisons test (P<0.05) afterwards, while the homogeneity of speed populations was defined using a one-way ANOVA test followed by Tukey's multiple comparisons test (P<0.05) using GraphPad Prism 6 (GraphPad Software Inc., San Diego, CA, USA).