A model of gallbladder motility

Impaired gallbladder motility leads to some clinical manifestations associated with its muscle contraction and/or the rate of filling with bile. To gain a better understanding of the possible reasons for different filling/emptying patterns we developed a mathematical model of the gallbladder that takes into account the kinetics of its filling and emptying and changes in the concentration of the accumulated bile. The model is based on four parameters responsible for the maximum speed of bile evacuation (M_g), pulsation of contractions (ω), the kinetic filling rate (k_g) and the maximum bile mass accumulated in the gallbladder (m_total). The model results were fitted to different clinical results describing gallbladder motility depending on the meal composition, patient's age and health condition (obesity and gallstones). Compatibility of the model results with the experimental data allows us to draw physiological conclusions. We found that different gallbladder emptying patterns may result from differences in the amplitude of contraction of gallbladder muscles (e.g. for various meal composition), differences in the rate of bile inflow (e.g. for obese patients during filling), and differences in gallbladder muscle pulsations (e.g. for lean patients during early gallbladder emptying). The model of gallbladder motility can facilitate identification of causes of disorders, help to explore complicated physiological pathways, and can be applied in etiology analysis or studies of observable clinical indicators.