Modelling the effects of diffusive coupling on spatio-temporal excitation patterns in the gravid human uterus

University College London 2006 (2006) Proc Physiol Soc 3, PC210

Poster Communications: Modelling the effects of diffusive coupling on spatio-temporal excitation patterns in the gravid human uterus

Arun V Holden1, Pan Li1, Nigel AB Simpson2

1. Institute of Membrane and Systems Biology, University of Leeds, Leeds, United Kingdom. 2. Obstetrics and Gynaecology, University of Leeds, Leeds, United Kingdom.

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Effective labour requires synchronous uterine contractions. Synchronisation in the electrical excitation in the gravid uterus can be inferred by non-invasive electromyography (Simpson et al. 1998) or spatio-temporal magneto-myography (Ramon et al. 2005). We have constructed a 3-D model of the myometrial wall of the third trimester gravid human uterus, with geometry from magnetic resonance image data, with a simplified (FitzHugh-Nagumo) model for excitation. Propagation is modelled by a reaction diffusion equation, with a diffusion coefficient D, dimensions of distance2 time-1, that describes the diffusive spread of excitation in space (Winfree, 1991). An increase in D simulates the increased inter-cellular coupling produced by upregulation of connexin-43 (Cx-43) in phase 1 of parturition. The increase in Cx-43 can be modelled by a linearly scaled increase in D. A solitary excitation wave has a wavelength λ that is the product of its duration and velocity. The velocity is proportional to √D. An irregular spatial distribution in parameters allows spatiotemporal-irregularity in activity, which can produce near synchronous excitation. For a homogeneous myometrium, near synchronous excitation could be produced by a single, excitation wave, with a λ ~ size of the uterus (Fig. 1b), or by repeated excitation by re-entrant waves with λ less than uterine size (Fig. 1c). A pair of such re-entrant waves can be initiated by a localised perturbation occuring in the vulnerable window of a preceeding propagating wave. Smooth, spatial gradients in excitation or coupling parameters produce slow drift of re-entrant waves, which lead to self-termination of re-entrant waves by moving their cores to a boundary (Biktashev & Holden, 1999). Persistent re-entrant excitation can occur if drift leads to a single re-entrant wave pinned at the cervix (Fig. 1d). Wave effects – long wavelength, re-entry, or spatio-temporal irregularity – can all contribute to the spatio-temporal synchronisation of excitation necessary for uterine contractions.


Figure 1. Anterior view of computed excitation wave patterns on gravid uterus white is excitation. a (D= 0.03) b (D=0.16) solitary circular waves initiated at the fundus; c pair of re-entrant spiral waves (0.01) and d (D=0.05) solitary broken wave pinned to the cervix.


Where applicable, experiments conform with Society ethical requirements.

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