Design of a Simulation Toolbox for Gastrointestinal Electrical Activity BME 273: Senior Design Projects John F Gouda Advisor: Dr. Alan Bradshaw, Ph.D. Assistant Professor of Physics, Living State Physics, Vanderbilt University

Motivation of Project The living state physics group have state of the art equipment to measure the magnetic field of the intestine. The magnetic field can be used to estimate the electric field: trans-membrane potential and slow currents. Thus, the need arose for an educational tool to help the investigators understand the quantitative features of electrical activity in the GI.

Further motivation After a discussion with Dr. King. The project was reorganized to serve as an educational tool for BME 251-252.

Squid

Experiment The data was collected from rabbit small intestine using platinum monopolar electrodes. 20 electrodes placed at 20 different location along the intestine 1 cm apart. Data was sampled for 5 minutes per study at a rate of 20-30 Hz. Data was sampled at the three section of the small intestine (duodenum, jejunum, ileum) and during induced ischemic conditions.

Clinical goals Study the difference between healthy electrical activity and pathologies: diabetic , ischemic electrical activity.

Design Specifications User Demands The simulation toolbox should: 1. Give the user an intuitive grasp of GI electrical activity 2. Rely on an accurate model of GI electrical activity 3. Rely on an intuitive model of GI electrical activity 4. Relate model simulations with experimental data

Project Specifications User Wishes If possible, the simulation toolbox should: 1. Have a user-friendly interface 2. Provide the user with “on the spot” calculations and metrics that represent the response of the model to the parameters supplied to the toolbox. Provide the user with a measure of goodness of fit with experimental data.

Wishes Continued 3. Provide the user with “on the spot” graphics that represent the response of the model to the parameters supplied to the toolbox 4. Provide the user with analysis modules that can analyze the complexity of GI activity and provide intuition into the physiologic function of GI tract.

Background 1960 Nelson and Becker suggest that a chain of relaxation oscillators (RO) could simulate GI electrical activity. 1971 Sarna et al. Used a modified version of the Van der Pol oscillator to simulate GI electrical activity. We used the widly acclaimed model developed by Sarna (1971).

Relaxation Oscillators The name “relaxation oscillators” comes into place because the “stress” accumulated during the slow buildup is “relaxed” during the sudden discharge.

Our model We used the widely acclaimed simple model developed by Sarna (1971). The model consists of 16 coupled nonlinear oscillators. The oscillators are lined along a straight line in the intestine.

Equations of the model 16 coupled oscillators, each oscillator has the form dxn/dt = alpha (e yn + f xn + g xn^2 + h xn^3 + C1 xn-1 + C2 xn+1) dyn/dt = -1/alpha (b yn + w^2 xn + c xn^2 + d xn^3 - a) xn= trans membrane potential yn= slow currents w= intrinsic frequency of oscillation C1 = coupling constants with previous osc. C2= coupling constant with next oscillator

Schematic

Current status of project 1. An initial prototype is up and running. 2. I am currently working on user friendly additions.

Demo Matlab

References Sarna SK, Daniel EE, Kingma YJ (1971): Simulation of slow-wave electrical activity of small intestine. Am J Physiol, 221(1):165-75.