A myofibre model for the study of uterine excitation-contraction dynamics

Abstract

As the uterus remodels in preparation for delivery, the excitability and contractility of the uterine smooth muscle layer, the myometrium, increase drastically. But when remodelling proceeds abnormally it can contribute to preterm birth, slow progress of labour, and failure to initiate labour. Remodelling increases intercellular coupling and cellular excitability, which are the main targets of pharmaceutical treatments for uterine contraction disorders. However, the way in which electrical propagation and force development depend on intercellular coupling and cellular excitability is not fully understood. Using a computational myofibre model we study the dependency of electrical propagation and force development on intercellular coupling and cellular excitability. This model reveals that intercellular coupling determines the conduction velocity. Moreover, our model shows that intercellular coupling alone does not regulate force development. Further, cellular excitability controls whether conduction across the cells is blocked. Lastly, our model describes how cellular excitability regulates force development. Our results bridge cellular factors, targeted by drugs to regulate uterine contractions, and tissue level electromechanical properties, which are responsible for delivery. They are a step forward towards understanding uterine excitation-contraction dynamics and developing safer and more efficient pharmaceutical treatments for uterine contraction disorders.

Figure 1

Myofibre model overview and validation. (a) A graphic representation of the model. The myofibre model (upper) consists of 70 serially connected cells (bottom). The detailed ionic current model, calcium handling dynamics, and force-producing mechanism are schematically represented. The upper and lower waveforms are schematic representations of the traveling depolarization and contraction waves, respectively. (b) The action potentials (AP) obtained at various cells along the myofibre. Downstream cells activate later in time. The AP amplitude decays slightly as it travels along the first cells and then stabilizes. (c) The intracellular calcium traces for the same cells as in (a). These traces present rapid upstrokes and slow decay rates. (d) The cellular length over time for the same cells as in (a). Cells with higher concentrations of myosin in force-producing states contract, while their relaxed neighbours dilate to satisfy the isometric condition. (e) The force developed by the myofibre in response to the depolarizing stimulus. The cellular response to a depolarization stimulus is long lasting and decays monotonically until it returns to its base value after 12 s (Supplementary Fig. S1).

Figure 2

Electrical conduction characteristics with respect to intercellular resistivity (IR). (a) Conduction velocity (CV) with respect to IR. CV decreases with increasing IR until block occurs at 200 $\mathrm{\Omega }$ cm. (b) The maximal slope of the depolarization upstroke (${max}_t\frac{\partial v_{\mathrm{m}}}{\partial t}$) with respect to IR. It’s behavior is similar to that of CV. (c) The upstroke duration with respect to IR. Upstroke duration increases with increasing IR. (a)–(c) The black lines identify the high intercellular coupling domain, and the blue lines identify the low intercellular coupling domain. Data points are shown at IR = 1, 5, 10, 25, 50, 100, and 150 $\mathrm{\Omega }$ cm.

Figure 3

Force development with respect to intercellular resistivity (IR). (a) The normalized cumulative force developed by the myofibre is stable at low IR values, but it drops sharply as the IR approaches 200 $\mathrm{\Omega }$ cm, where conduction block occurs. Then it remains at unity, reflecting that no force is generated besides passive tension. The normalized cumulative force value is defined as the integral of the force over 14 s after the initial stimulus, normalized by the passive force (i.e., without stimulation) developed by the myofibre over the same time period. (b) The amplitude of the force generated follows a similar pattern as the normalized force. (a,b) The blue lines mark the buffered domain, and the red lines mark the conduction block domain. Data points are shown are at IR = 1, 5, 10, 25, 50, 100, 150, 200, 250, 300, and 400 $\mathrm{\Omega }$ cm.

Figure 4

Mechanism for force robustness against intercellular resistivity (IR). (a) Simulated action potential (AP) traces for various IR values (see figure’s legend) at the 30th cell in a 70 cell long myofibre. (b) The action potential duration at 90% repolarization (${\mathrm{APD}}_{90}$) and the AP amplitude of the traces in (a). (c) The intracellular calcium levels for the same conditions as in (a). (d) The calcium load over 14 s of simulation, calculated as the area under the curve of the traces in (c). (e) The fraction of myosin bound to actin over time. (f) The tensile force developed by the myofibre over time.

Figure 5

Electrical conduction and force development dependency on cellular excitability. (a–c) Conduction velocity (CV) as a function of I_CaL, I_CaT, and I_Na conductivity modulation, respectively. A zero CV indicates conduction block. Ionic channel current modulation is implemented as a multiplicative factor of the ionic channel conductivity: a modulation of 1.0 represents normal conductivity. The simulations were run under varying coupling levels, IR = 10, 100, 300, and 1000 $\mathrm{\Omega }$ cm. (d–f) Normalized cumulative force developed by the myofibre under varying intercellular coupling levels and conductivity modulation of I_CaL, I_CaT, and I_Na, respectively. Data points are shown at modulation = 0.3, 0.5, 0.8, 0.9, 1, 1.1, 1.2, 1.5, and 2.