Digestion in the small intestine

Overview

This numerical program computes degradation and transit of a bolus in the small intestine. This bolus is composed of one kind of feedstuffs. The model is based on a system of ordinary differential equations.

Variables of the model 4

• The time t in hours represents the time after the entry of the bolus in the small intestine.
• The position x(t) at time t of the bolus, in meters, from the begining of the duodenum.
• The instantaneous velocity of the bolus, measured in meter per hour.
• A_s is the solubilized part of the substrate.
• A_ns is the non solubilized part of the substrate.
• Quantity (expressed in grammes) of gastric and pancreatic enzymes inside the bolus ; the brush-border enzymes are assumed to be in excess.
• B_int the substrat in intermediary form, partially hydrolized but non absorbable
• B_abs absorbable substrate in the intestinal lumen.
• [W] is the proportion of water inside the bolus.

Input parameters

They are of four types

• Control of the transit : In model 4, the equation for transit is
  
  where the parameters c₀ and c₁ describe the linear dependance of velocity to the volume of the bolus. K/[W] is the coefficient of friction (viscosity) of the bolus by the wall ; a=2.72 and b=1.2346 are fixed corresponding to the attenuation of the migrating myoelectric complex (MMC), ã represents the mean effect of the periodic pulses.
• Control of the degradation and water proportion : The solubilized part A_s is hydrolised to B which is composed of B_int (intermediary product transformed by the brush-borders enzymes) and B_abs absorbable following the scheme
  
  The coefficients are
  • Cv₁ : transformation of A to B_int
  • Cv₂ : transformation from A to B_abs
  • Cbv₂ : transformation from B_int to B_abs
  • k_t: absorbtion rate by intestinal wall
  • k_b : degradation of the enzymes vs time
  • k₁ : return to equilibrium for water
• Characteristics of the bolus : the constant length l and the density rho.
• Initial conditions :
  • Initial velocity v₀ (meter per hour) of the bolus entering the small intestine.
  • Quantity of enzymes z₀ in the bolus.
  • Quantity B₁₀ of B_int in the bolus.
  • Quantity B₂₀ of B_abs in the bolus.
  • Initial radius r₀.

Instructions

You can edit the default values of the parameters, if you want. Clicking on the button 'Go !!!' begins the computation.

Then you can save the data in a file for a future exploitation in a spreadsheet. Data are in CVS format with two possibilities

• decimal separator set to the point and data separator set to blank space,
• decimal separator set to the comma and data separator set to tabulation.

No problem with OpenOffice. With Excel 2003 you have to save the file, open Excel, read the file, go to the menu "Data" and choose "Convert".

You can have a graphical output, choosing the output datas to display.
Finally you can return to the graphical for changing the displayed curves or their size. You can also return and change the value of the parameters.

Inputs

Transit

c0 : Amplification MMC/volume		c1 : Amplification MMC/volume		K : Friction (viscosity) coefficient
tau : Pulses frequency

Degradation

Cv1 : Transformation Bint		Cv2 : Transformation Babs		k1 : Water balance
Cbv2 : Transformation Babs		kt : Absorbtion rate by coat		kb : Diminution rate of enzymes

Bolus and Impulsions

l : Length bolus

rho : Density bolus

Initial Conditions

v0 : Initial velocity of the bolus		z0 : Initial enzymes		B10 : Initial Bint
B20 : Initial Babs		r0 : Initial radius of the bolus