Digestion in the small intestine Chris Budd, Andre Leger, Alastair Spence EPSRC CASE Award with Unilever - PowerPoint PPT Presentation

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Digestion in the small intestine Chris Budd, Andre Leger, Alastair Spence EPSRC CASE Award with Unilever PowerPoint Presentation
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Digestion in the small intestine Chris Budd, Andre Leger, Alastair Spence EPSRC CASE Award with Unilever

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  1. Digestion in the small intestine Chris Budd, Andre Leger, Alastair Spence EPSRC CASE Award with Unilever

  2. What happens when we eat? Stomach Small intestine: 7m x 1.25cm Intestinal wall: Villi and Microvilli

  3. Process: • Food enters stomach and leaves as Chyme • Nutrients are absorbed through the intestinal wall • Chyme passes through small intestine in 4.5hrs Intestinal wall Stomach Colon, illeocecal sphincter Peristaltic wave Mixing process

  4. Objectives • Model the process of food moving through the intestine • Model the process of nutrient mixing and absorption • Conclusions … • Peristalsis is effective at mixing the nutrients • It also acts to retard the mean flow of nutrient, allowing for greater nutrient absorption in the first part of the gut

  5. Basic model: axisymmetric flow pumped by a peristaltic wave and a pressure gradient • Chyne moves at velocity: u(x,r,t) • Nutrient concentration: c(x,r,t) • Peristaltic wave: r = f(x,t) r h = 1.25cm x r=f(x,t) Wavelength:8cm

  6. Decouple the system: • Calculate the flow u of the Chyme assuming Stokes flow and long wavelength • Calculate the Nutrient transport and absorption

  7. 7 Compartmental and Transit(CAT) Model Approximations to the flow: I Degradation D1 Degradation D7 cn Inflow Outflow INTESTINE Absorption K1 Absorption K7 Stomach Outflow Degradation Inflow Absorption

  8. Approximations to the flow: II Macro-transport • Stoll et al (Chem Eng Sci 2000)‘A Theory of Molecular Absorption from the Small Intestine’ • Approximate flow u by 2D Poiseuille flow and consider a 1D equation for the average concentration C (Taylor,Moffatt) • Consider peristalsis as enhanced diffusion 2D: 1D:

  9. Good news: Models are easy to use Bad news: results are poor fits to the numerically computed concentration profiles for complex peristaltic flow • Better approach: • Use an asymptotic approach to give a good approximation to the peristaltic flow velocity u in the case of a small wave number • Identify different flow regimes • Use this in a numerical calculation of the concentration c

  10. Navier Stokes • Slow viscous Axisymmetric flow • Velocity & Stokes Streamfunction

  11. No slip on boundary WAVE FRAME FIXED FRAME Change from Impose periodicity

  12. Amplitude: • Wave Number: Small parameters Axisymmetry

  13. Flow depends on: Proportional to pressure drop Flow rate gives Poiseuille flow Amplitude Wave number Develop asymptotic series in powers of

  14. Distinct flow types • Reflux Pressure Rise Particles undergo net retrograde motion • Trapping Regions of Pressure Rise & Pressure Drop Streamlines encompass a bolus of fluid particles Trapped Fluid recirculates

  15. Flow regions A: Copumping, Detached Trapping B: Copumping, Centreline Trapping C: Copumping, No Trapping Illeocecal sphincter open D: Pumping, No Trapping E: Pumping, Centreline Trapping Illeocecal sphincter closed A B E C D F G Poiseuille

  16. Case A: Copumping, Detached Trapping Recirculation Particle paths

  17. Case B: Copumping, Centreline Trapping Recirculation Particle paths x

  18. Case C: Copumping, No Trapping Particle paths Poiseuille Flow x

  19. Case D: Pumping, No Trapping Particle paths Poiseuille Flow x Reflux

  20. Case E: Pumping, Centreline Trapping Particle paths Recirculation x Reflux

  21. Calculate the concentration c(x,r,t) 1. Substitute asymptotic solution for u into 2. Solve for c(x,r,t) numerically using an upwind scheme on a domain transformed into a computational rectangle. 3. Calculate rate of absorption

  22. Type C flow: no trapping Poiseuille flowPeristaltic flow

  23. Type E flow: trapping and reflux Poiseuille flowPeristaltic flow

  24. Cross sectional average of nutrient x x x Location of absorped mass at final time Nutrient absorped Peristaltic flow x t

  25. Conclusions • Peristalsis helps both pumping and mixing • Significantly greater absorption with Peristaltic flow than with Poiseuille flow • Next steps • Improve the absorption model • Improve the fluid model (Non-Newtonian flow) • More accurate representation of the intestine geometry • Experiments