Abstract
The uterine electrical activity is an efficient parameter to study the uterine contractility. In order to understand the ionic mechanisms responsible for its generation, we aimed at building a mathematical model of the uterine cell electrical activity based upon the physiological mechanisms. First, based on the voltage clamp experiments found in the literature, we focus on the principal ionic channels and their cognate currents involved in the generation of this electrical activity. Second, we provide the methodology of formulations of uterine ionic currents derived from a wide range of electrophysiological data. The model is validated step by step by comparing simulated voltage-clamp results with the experimental ones. The model reproduces successfully the generation of single spikes or trains of action potentials that fit with the experimental data. It allows analyzing ionic channels implications. Likewise, the calcium-dependent conductance influences significantly the cellular oscillatory behavior.
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References
Andersen HF, Barclay ML (1995) A computer model of uterine contractions based on discrete contractile elements. Obstet Gynecol 86(1):108–111. doi:10.1016/0029-7844(95)00111-4
Anwer K et al (1993) Calcium-activated K+channels as modulators of human myometrial contractile activity. Am J Physiol 265(4 Pt 1):C976–C985
Arnaudeau S, Lepretre N, Mironneau J (1994) Chloride and monovalent ion-selective cation currents activated by oxytocin in pregnant rat myometrial cells. Am J Obstet Gynecol 171(2):491–501
Buhimschi C et al (1998) Uterine activity during pregnancy and labor assessed by simultaneous recordings from the myometrium and abdominal surface in the rat. Am J Obstet Gynecol 178:811–822. doi:10.1016/S0002-9378(98)70498-3
Bursztyn L et al (2007) Mathematical model of excitation–contraction in a uterine smooth muscle cell. Am J Physiol Cell Physiol 292(5):C1816–C1829. doi:10.1152/ajpcell.00478.2006
Chay TR, Keizer J (1983) Minimal model for membrane oscillations in the pancreatic beta-cell. Biophys J 42(2):181–190
Coleman HA, Parkington HC (1987) Single channel Cl−and K+currents from cells of uterus not treated with enzymes. Pflugers Arch 410(4–5):560–562. doi:10.1007/BF00586540
Coleman HA, Parkington HC (1990) Hyperpolarization-activated channels in myometrium: a patch clamp study. Prog Clin Biol Res 327:665–672
Fele-Zorz G et al (2008) A comparison of various linear and non-linear signal processing techniques to separate uterine EMG records of term and pre-term delivery groups. Med Biol Eng Comput 46:911–922
Garfield RE (1994) Role of cell-to-cell coupling in control of myometrial contractility and labor. In: Garfield RE, Tabb TN (eds) Control of uterine contractility. C.P.I. Llc., Florida
Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544
Inoue Y et al (1990) Some electrical properties of human pregnant myometrium. Am J Obstet Gynecol 162(4):1090–1098
Kao CY, McCullough JR (1975) Ionic currents in the uterine smooth muscle. J Physiol 246(1):1–36
Khan RN et al (2001) Potassium channels in the human myometrium. Exp Physiol 86(2):255–264. doi:10.1113/eph8602181
Knock G, Smirnov S, Aaronson P (1999) Voltage gated K+ currents in freshly isolated myocytes of the pregnant human myometrium. J Physiol 518:769–781. doi:10.1111/j.1469-7793.1999.0769p.x
Kuriyama H, Suzuki H (1976) Changes in electrical properties of rat myometrium during gestation and following hormonal treatments. J Physiol 260:315–333
Marshall J (1990) Relation between membrane potential and spontaneous contraction of the uterus, in uterine contractility: mechanisms of control. In: Garfield R, Norwell M (eds) Sereno symposia, pp 3–7
Marque C, Duchene J (1989) Human abdominal EHG processing for uterine contraction monitoring. Biotechnology 11:187–226
Marque C et al (1986) Uterine EHG processing for obstetrical monitoring. IEEE Trans Biomed Eng 33(12):1182–1187. doi:10.1109/TBME.1986.325698
Miller SM, Garfield RE, Daniel EE (1989) Improved propagation in myometrium associated with gap junctions during parturition. Am J Physiol 256(1 Pt 1):C130–C141
Miyoshi H, Urabe T, Fujiwara A (1991) Electrophysiological properties of membrane currents in single myometrial cells isolated from pregnant rats. Pflugers Arch 419(3–4):386–393. doi:10.1007/BF00371121
Moore JW, Ramon F (1974) On numerical integration of the Hodgkin and Huxley equations for a membrane action potential. J Theor Biol 45(1):249–273. doi:10.1016/0022-5193(74)90054-X
Noble D (1962) A modification of the Hodgkin–Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J Physiol 160:317–352
Ohya Y, Sperelakis N (1989) Fast Na+and slow Ca2+channels in single uterine muscle cells from pregnant rats. Am J Physiol 257(2 Pt 1):C408–C412
Parkington HC, Coleman HA (1988) Ionic mechanisms underlying action potentials in myometrium. Clin Exp Pharmacol Physiol 15(9):657–665. doi:10.1111/j.1440-1681.1988.tb01125.x
Ramon F et al (1976) A model of propagation of action potentials in smooth muscle. J Theor Biol 59:381–408. doi:10.1016/0022-5193(76)90178-8
Sanborn BM (1995) Ion channels and the control of myometrial electrical activity. Semin Perinatol 19(1):31–40. doi:10.1016/S0146-0005(95)80045-X
Sanborn BM (2000) Relationship of ion channel activity to control of myometrial calcium. J Soc Gynecol Investig 7(1):4–11. doi:10.1016/S1071-5576(99)00051-9
Shmigol A, Eisner D, Wray S (1998) Properties of voltage-activated [Ca2+]i transients in single smooth muscle cells isolated from pregnant rat uterus. J Physiol 511(3):803–811. doi:10.1111/j.1469-7793.1998.803bg.x
Sperelakis N, Inoue Y, Ohya Y (1992) Fast Na+channels and slow Ca2+ current in smooth muscle from pregnant rat uterus. Mol Cell Biochem 114(1–2):79–89. doi:10.1007/BF00240301
Wang R, Karpinski E, Pang PK (1989) Two types of calcium channels in isolated smooth muscle cells from rat tail artery. Am J Physiol 256(5 Pt 2):H1361–H1368
Wang SY et al (1998) Potassium currents in freshly dissociated uterine myocytes from nonpregnant and late-pregnant rats. J Gen Physiol 112(6):737–756. doi:10.1085/jgp.112.6.737
Yoshino M, Wang SY, Kao CY (1997) Sodium and calcium inward currents in freshly dissociated smooth myocytes of rat uterus. J Gen Physiol 110(5):565–577. doi:10.1085/jgp.110.5.565
Young RC (1997) A computer model of uterine contractions based on action potential propagation and intercellular calcium waves. Obstet Gynecol 89(4):604–608. doi:10.1016/S0029-7844(96)00502-9
Young RC, Herndon-Smith L (1991) Characterization of sodium channels in cultured human uterine smooth muscle cells. Am J Obstet Gynecol 164(1 Pt 1):175–181
Young RC, Smith LH, McLaren MD (1993) T-type and L-type calcium currents in freshly dispersed human uterine smooth muscle cells. Am J Obstet Gynecol 169(4):785–792
Acknowledgments
This work was supported by a grant “Pôle GBM Périnatalité-Enfance” of the Picardy Region, France. It has been communicated and poster presented in proceedings of the third European Medical and Biological Engineering Conference, EMBC, held in Prague in November 2005.
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Rihana, S., Terrien, J., Germain, G. et al. Mathematical modeling of electrical activity of uterine muscle cells. Med Biol Eng Comput 47, 665–675 (2009). https://doi.org/10.1007/s11517-009-0433-4
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DOI: https://doi.org/10.1007/s11517-009-0433-4