Mathematical Modelling of Gastric Electrophysiology

Abstract

This thesis investigates the electrophysiology of the stomach, using a joint experimental and mathematical modelling approach. Normal gastrointestinal (GI) motility is coordinated by multiple cooperating mechanisms, both intrinsic and extrinsic to the GI tract. A fundamental component of the GI motility is an omnipresent electrical activity termed slow waves, which are initiated and propagated by the interstitial cells of Cajal (ICCs) and smooth muscle cells (SMCs). The role of ICC and/or SMC pathophysiology in GI motility disorders is an area of on-going research. This thesis begins with an overview of the functions of the GI tract and slow wave electrophysiology. High-resolution electrode arrays were designed and manufactured using the printed-circuit-board (PCB) technology. The performance of the PCB electrodes were validated against the performance of epoxy-embedded electrodes in porcine subjects, in terms of amplitudes (0.17 vs 0.52 mV), velocity (15.9 vs 13.8 mms-1), and signal-to-noise ratio (9.7 vs 18.7 dB). The PCB electrodes were then used to record gastric slow waves from a number of human subjects. Automatic slow wave activation times identification and velocity calculation techniques were applied to analyse the recorded slow wave data. Analysis of the human data revealed that the gastric slow wave activity originates from a pacemaker region (average amplitude: 0.57 mV ; average velocity: 8.0 mms-1) in the stomach, and continues into the corpus (average amplitude: 0.25 mV ; average velocity: 3.0 mms-1), and then the antrum (average amplitude: 0.52 mV ; average velocity: 5.7 mms-1). The focus of this thesis then shifts to mathematical models of slow wave activity. An existing SMC model was adapted to investigate the effects of gastric electrical stimulation (GES) protocols, in conjunction with experimental recordings in rat antral SMCs. The simulations using the adapted SMC model showed that effective GES protocols could be adapted to include frequency-trains (40 Hz) of short pulse- width (3-6 ms); In a separate study, an existing ICC model was adapted to include a voltage-sensitive inositol 1,4,5-trisphosphate receptor model, which modelled entrainment of slow waves in a network of ICCs; Two coupling mechanisms were also proposed to link the slow waves in the ICC and SMC models. A continuum approach was used to model slow waves in tissue and whole-organ models. The monodomain equation was used to simulate slow wave propagation in a grid of SMCs coupled to a cell automata model, which was used to quantify the entrainment of normal slow wave activity and entrainment of slow waves by a 3.5 cpm GES protocol. The simulation results demonstrated the highest 'zone of entrainment' that could be achieved by the GES protocol was 78% of the modelled tissue area; Next, the bidomain equations were applied to simulate entrainment of slow waves in a wild-type (normal) and a degraded (serotonin receptor knockout) ICC networks obtained from mouse tissue. The ICC network models demonstrated that slow wave propagation was influenced by ICC loss. In addition, compared to the degraded ICC network, the normal ICC network model demonstrated a higher peak current density (1.94 vs 1.45 μAmm-2) as well as [Ca2+]i density (0.67 vs 0.41 mM mm-2), which could help to explain functional impairments that arise when ICC populations are depleted; The human recordings were used to create slow wave activation in a whole organ stomach model. The whole organ model was used as a platform to simulate gastric slow wave propagation, as well as to incorporate physiological characteristics that could not directly measured using the HR technique, such as the variation in the resting membrane potentials of gastric tissues. The final set of modelling studies employed the forward modelling technique to simulate the resultant body surface potential, i.e., electrogastrogram (EGG) of gastric slow waves. A virtual EGG analysis showed that the frequency of EGG matched the underlying slow waves (3 cpm) and the peak potential (-0.63 mV ) in the EGG signal could be correlated to the timing of the full antral activation. This thesis concludes with a discussion on the results and potential future research directions in this field.