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

2. Motivation of Project n The living state physics group have state of the art equipment to measure the magnetic field of the intestine. n The magnetic field can be used to estimate the electric field: trans-membrane potential and slow currents. n Thus, the need arose for a mathematical model of electrical activity in the GI.

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

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

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

6. Project Specifications User Wishes n If possible, the simulation toolbox should: n 1. Have a user-friendly interface n 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.

7. Wishes Continued n 3. Provide the user with “on the spot” graphics that represent the response of the model to the parameters supplied to the toolbox n 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.

8. Background n 1960 Nelson and Becker suggest that a chain of relaxation oscillators (RO) could simulate GI electrical activity. n 1971 Sarna et al. Used a modified version of the Van der Pol oscillator to simulate GI electrical activity n Danial at al. 1994 gives pros and cons of both models. n The name “relaxation oscillators” comes into place because the “stress” accumulated during the slow buildup is “relaxed” during the sudden discharge.

9. Core conductor models n The parameters of relaxation oscillators can not be directly related to physiologic parameters (i.e. ion channels and cell coupling). n Models based on ionic mechanisms of membrane activity and on symmetric electrical coupling of cells are called core conduction models.

10. Our model n We proposed a simple model that attempts to combine the mathematical utility and simplicity of relaxation oscillators and the physiologic intuition of core-conductor models. n Two muscle layers: longitudinal muscle (LM) and interstitial cells of Cajal (ICC) n The model consists of 4 (2 for each muscle layer) nonlinear coupled partial differential equations in time and space.

11. Equations of the model n LM muscle layer du LM /dt = K u LM (u LM -a)(1-u LM ) - v LM - D k^2 u LM + Dil(u LM -u ICC ) dv LM /dt = e(gamma (u LM -b) -v LM ) n ICC muscle layer du ICC /dt = K u ICC (u ICC -a)(1-u ICC ) - v ICC - D k^2 u ICC - Dil (u LM -u ICC ) dv ICC /dt = e(gamma (u ICC -b) -v ICC )

12. Mathematical model cont. n parameters for the LM layer and ICC layer are chosen to give rise to the desired output. n The parameter Dil determines the coupling between the two layers. The system has 4 state variables n x(1) = u LM, x(2) = v LM n x(3) = u ICC, x(4) = v ICC

13. Current status of project n 1. An initial prototype is up and running. n 2. I am currently working on implementing a hypothesis testing module to do curve fitting.

14. Demo n Matlab