ACAT Model Equations
This section details the equations that define and support the Advanced Compartmental Absorption and Transit (ACAT) model developed by Simulations Plus, which extends the capabilities of the pre-cursor Compartmental Absorption and Transit (CAT) model to include in vivo drug behavior of first-pass metabolism and colonic absorption. See:
For details about the internal standards that were used to define the equations in this section, see Equation Standards.
Dynamic Fluid Volume Model Equations
Equation 1-1: Change in fluid volume versus time
where:
Variable | Definition |
We don't have a way to export this macro. | The volume of the fluid in the jth intestinal compartment. |
We don't have a way to export this macro. | The volume of the fluid in the previous intestinal compartment (i.e. j-1). |
We don't have a way to export this macro. | Time. |
We don't have a way to export this macro. | The water secretion rate(s) in the jth intestinal compartment. |
We don't have a way to export this macro. | The water absorption rate(s) in the jth intestinal compartment. |
We don't have a way to export this macro. | The transit rate of the jth intestinal compartment. |
We don't have a way to export this macro. | The transit rate of the previous intestinal compartment (i.e. j-1). |
Equation 1-2: Change in drug concentration due to fluid volume versus time
where:
Variable | Definition |
We don't have a way to export this macro. | Time. |
We don't have a way to export this macro. | The total concentration of the drug in the jth intestinal compartment at time t. |
We don't have a way to export this macro. | The volume of fluid in the jth intestinal compartment. |
We don't have a way to export this macro. | The mass of drug in the jth intestinal compartment. |
Equation 1-3: Secretion rate for a new Dynamic Fluid Volume model
where:
Variable | Definition |
We don't have a way to export this macro. | The volume of the fluid in the jth intestinal compartment. |
We don't have a way to export this macro. | The volume of the fluid in the previous intestinal compartment (i.e. j-1). |
We don't have a way to export this macro. | Time. |
We don't have a way to export this macro. | The new secretion rate in the jth intestinal compartment. |
We don't have a way to export this macro. | The gut compartment. |
We don't have a way to export this macro. | The water absorption rate(s) in the jth intestinal compartment. |
We don't have a way to export this macro. | The transit rate of the jth intestinal compartment. |
We don't have a way to export this macro. | The new fluid volume in the jth intestinal compartment. |
We don't have a way to export this macro. | The transit rate of the previous intestinal compartment (i.e. j-1). |
We don't have a way to export this macro. | The new fluid volume in the previous intestinal compartment (i.e. j-1). |
Fed State Physiologies Equations
Equation 1-4: Second-order polynomial for the prediction of bile salt concentration in the intestinal lumen based on % fat in a meal
Table 1-1: Polynomial coefficients for Equation 1-4
| Duodenum | Jejunum1 | Jenjunum2 | Ileum1 | Ileum2 | Ileum3 |
A2 | 2.131E-04 | -3.716E-04 | -1.237E-03 | -1.217E-03 | -2.631E-03 | -7.747E-05 |
A1 | 2.957E-01 | 2.746E-01 | 2.863E-01 | 2.177E-01 | 2.677E-01 | 1.934E-02 |
A0 | 5.379E+00 | 4.117E+00 | 2.985E+00 | 1.844E+00 | 3.265E-01 | 2.196E-01 |
Solubility and Dissolution Models Equations
Equation 1-5: Difference between aqueous and in vivo solubility caused by the presence of bile salts
where:
Variable | Definition |
We don't have a way to export this macro. | The aqueous solubility at a given pH. |
We don't have a way to export this macro. | The aqueous solubilization capacity calculated as the ratio of moles of drug to moles of water at a concentration that is equal to aqueous solubility. |
We don't have a way to export this macro. | The drug molecular weight. |
We don't have a way to export this macro. | The bile salts concentration. |
We don't have a way to export this macro. | The solubility in the presence of bile salts at concentration [bile] and at the same pH as Cs,aq. |
We don't have a way to export this macro. | The bile salt solubilization ratio, where two options are available for estimation of this value.
|
Equation 1-6: Theoretical prediction of SR based on logP
Equation 1-7: Apparent Solubility of Drug in Presence of Surfactant
Note that if
Equation 1-8: Cyclodextrin binding constant
where:
Variable | Definition |
We don't have a way to export this macro. | The concentration of cyclodextrin-drug complex. |
We don't have a way to export this macro. | The concentration of free, dissolved drug. |
We don't have a way to export this macro. | The concentration of free cyclodextrin. |
Equation 1-9: Default model equation for dissolution rate
Equation 1-10: Wang-Flanagan model equation for dissolution rate
Equation 1-11: Z-Factor model equation for dissolution rate
where:
Variable | Definition |
Note: All symbols in all three model equations represent the same properties or quantities. | |
We don't have a way to export this macro. | The amount of drug that is dissolved. |
We don't have a way to export this macro. | The effective diffusion coefficient. |
We don't have a way to export this macro. | The spherical particle radius at the current time. |
We don't have a way to export this macro. | The shape factor that accounts for non-spherical shape of the particles and is specified as the ratio of length and diameter of the particle. Note: For spherical particles, S =1. |
We don't have a way to export this macro. | The solubility at the pH of the corresponding jth intestinal compartment. |
We don't have a way to export this macro. | The total concentration of drug in the lumen of the jth intestinal compartment at time t. |
We don't have a way to export this macro. | The amount of drug that is undissolved at time = t. |
We don't have a way to export this macro. | The amount of drug that is undissolved at time =0. |
We don't have a way to export this macro. | The density of the drug. |
We don't have a way to export this macro. | The thickness of the diffusion layer. |
Equation 1-12: Term represented by the z factor
Equation 1-13: Effective diffusion coefficient calculation
where:
Variable | Definition |
We don't have a way to export this macro. | The aqueous diffusion coefficient of drug monomers (free dissolved drug). |
We don't have a way to export this macro. | The fraction of free, dissolved drug calculated as the ratio of aqueous solubility and solubility in the presence of bile salts. |
We don't have a way to export this macro. | The diffusion coefficient of the bile salt-phospholipid-drug aggregate. |
Equation 1-14: Probability density function for the Legacy Log-Normal distribution
where:
Variable | Definition |
We don't have a way to export this macro. | The mean radius (μ) in log units as calculated from the user-specified value for the radius in microns. We don't have a way to export this macro. |
We don't have a way to export this macro. | The mean standard deviation in log units as calculated from the user-specified value of standard deviation (σ) in microns. We don't have a way to export this macro. |
Equation 1-15: Lower radius limit, Legacy Log-Normal distribution
Equation 1-16: Upper radius limit, Legacy Log-Normal distribution
Equation 1-17: Probability density function for the Normal distribution
where:
Variable | Definition |
We don't have a way to export this macro. | The mean radius in microns. |
We don't have a way to export this macro. | The mean standard deviation in microns. |
Equation 1-18: Lower radius limit, Normal distribution
Equation 1-19: Upper radius limit, Normal distribution
Equation 1-20: Adjusting the particle radius to the remaining undissolved amount
where:
Variable | Definition |
We don't have a way to export this macro. | The particle radius of bin k at time t. |
We don't have a way to export this macro. | The particle radius of bin k at time 0. |
We don't have a way to export this macro. | The total undissolved amount in bin k (across all compartments) at time t. |
We don't have a way to export this macro. | The total undissolved amount in bin k (across all compartments) at time 0. |
Equation 1-21: Kelvin equation
where:
Variable | Definition |
We don't have a way to export this macro. | The solubility of drug particle of radius r at temperature T. |
We don't have a way to export this macro. | The solubility with no curvature at temperature T. |
We don't have a way to export this macro. | The interfacial surface tension. |
We don't have a way to export this macro. | The molar volume of drug calculated as the ratio of molecular weight and density. |
We don't have a way to export this macro. | The gas constant. |
We don't have a way to export this macro. | The drug particle radius. |
Equation 1-22: Solubility with no curvature at temperature T
Equation 1-23: Calculation of K in Equation 1-22
where:
Variable | Definition |
We don't have a way to export this macro. | The reference solubility measured at temperature Tref. |
We don't have a way to export this macro. | The melting point of the drug. |
We don't have a way to export this macro. | The currently specified temperature. |
We don't have a way to export this macro. | The molecular weight of the drug. |
Equation 1-24: Nanofactor Effect calculation
where:
Variable | Definition |
We don't have a way to export this macro. | The drug particle radius. |
We don't have a way to export this macro. | The NanoFactor, which is a user-defined, compound-specific parameter, with the same value being applicable across formulations with differing sizes of drug particles. |
Equation 1-25: Fraction of Unbound Drug in Solution
where Cu(t) is the unbound drug concentration at all times and C(t) the total drug concentration at all times. Equilibration is assumed to be instantaneous and so fu is anticipated to be constant. The affinity to surfactants kaff, is experimentally determined to apparent solubility vs surfactant concentration (Csurf) in each dissolution medium (See Effect of surfactants on drug solubility).
Equation 1-26: Dissolution Rate Calculation
Where A(t) (m2) is the surface area of the particle at time t, Du and Db the diffusion coefficient of the unbound drug and micelle-bound drug respectively (m2.s-1), hu and hb the UWL thickness of the unbound drug and micelle-bound drug respectively (m), CS,u is the unbound drug solubility at the surface of the drug crystal and Cu, the unbound drug concentration in the bulk (kg.m-3). This equation sums up the flux of drug dissolving from the crystal surface as free and micelle bound drug.
Equation 1-27: Dissolution Rate Expanded Equation
Equation 1-28: Characteristic Length Scale for Diffusion
Equation 1-29: Stokes-Einstein Equation for Diffusion Coefficient
Where k = 1.3806504 10-23 (J.K-1) is the Boltzmann constant, T is the absolute temperature in kelvin, η (Pa.s) is the dynamic viscosity of the solvent and rh (m) is the hydrodynamic radius of the diffusing solute. The hydrodynamic radius of the solute can be estimated, assuming that the molecular shape is a sphere and that the hydration of the solute is negligible, by the following equation:
Equation 1-30: Calculation of Diffusion Coefficient in Water
Where MW is the molecular weight of the drug (g.mol-1), NA = 6.02214179 1023 (mol-1) is the Avogadro number and ρS is the drug true density in (kg.m-3). The effect of temperature for dissolution is accounted for by a change in the water viscosity.
Equation 1-31: Solubility of Drug Particles as a Function of Particle Radius
Where Cr stands for the solubility of a drug particle of radius r (m). C∞ is the solubility of the same drug with no curvature (or an infinite radius of curvature) at temperature T. Units for C∞ and Cr are the same relevant concentration units. Rg = 8.314472 J.K-1.mol-1 is the ideal gas constant, T (K) is the absolute temperature,
Equation 1-32: Calculation of Number of Particles per bin
Where ρS (kg.m-3) is the material true density assuming a spherical particle size. At all times, the UWL thickness for the dissolving particles and the unbound drug is given by hu(t)= r(t) if r(t)<30 µm or hu(t)=30 µm if r(t) ≥ 30 µm. In each particle bin the mass of particles is reduced by integrating equation 9 over time.
Equation 1-33: Surface Area of Dissolving Particles
Equation 1-34: Rate of Change of Solid Mass During Dissolution and Precipitation
Equation 1-35: First-Order Drug Degradation Rate Equation
Precipitation Models Equations
Equation 1-36: First Order Precipitation model equation to predict precipitation rate in the jth intestinal compartment
where:
Variable | Definition |
We don't have a way to export this macro. | The volume of the lumen in the jth intestinal compartment. |
We don't have a way to export this macro. | The precipitation rate constant in the jth intestinal compartment. |
We don't have a way to export this macro. | The precipitation time in the jth intestinal compartment. Note: You can define compartment-specific precipitation times through a precipitation time versus pH profile. |
We don't have a way to export this macro. | The concentration of dissolved drug in the jth intestinal compartment. |
We don't have a way to export this macro. | The drug solubility in the jth intestinal compartment. |
Equation 1-37: Sugano’s CLNT model - Differential equation for nucleation
where:
Variable | Definition |
We don't have a way to export this macro. | A fitted lump constant of various factors as shown in Equation 1-38. |
We don't have a way to export this macro. | The diffusion coefficient of a free monomer drug. |
We don't have a way to export this macro. | Avogadro’s number. |
We don't have a way to export this macro. | The concentration of a free monomer drug in aqueous solution and not in bile micelles. |
We don't have a way to export this macro. | The solubility of the precipitant in water without bile micelles. |
We don't have a way to export this macro. | The interfacial surface tension. |
We don't have a way to export this macro. | The Boltzman constant. |
We don't have a way to export this macro. | The temperature. |
We don't have a way to export this macro. | The molecular volume. |
Equation 1-38: Sugano’s CLNT model - Particle radius calculation and fitted lump sum of various factors for the calculation of β
where:
Variable | Definition |
We don't have a way to export this macro. | The amount of particle growth (weight or mole) that is generated during a time period, with i representing a particle group that is generated at a different time point. |
We don't have a way to export this macro. | The particle radius at time t. |
We don't have a way to export this macro. | The density of the drug. |
We don't have a way to export this macro. | The effective diffusion coefficient in a bile micelle media. |
We don't have a way to export this macro. | The diffusion layer thickness. |
We don't have a way to export this macro. | The sum of the concentrations of free monomer and the bile micelle-bound molecule. |
We don't have a way to export this macro. | The solubility in the bile micelle media. |
Equation 1-39: Simulation Plus’s CLNT model
where:
Variable | Definition |
We don't have a way to export this macro. | Assuming spherical geometry, the critical radius of the growing cluster. See Equation 1-40. |
We don't have a way to export this macro. | The crystallization parameter, which is a correction factor to account for surface integration processes. |
Note: All other variables have been defined previously. See Equation 1-37 and Equation 1-38. | |
Equation 1-40: Critical radius calculation for use in Equation 1-39
Equation 1-41: Formation rate of new nuclei with the optimizable ECF
Equation 1-42: Fraczkiewicz-Model V2 equation
Absorption Models Equations
Equation 1-43: Effective permeability calculation
where:
Variable | Definition |
We don't have a way to export this macro. | The volumetric flow rate. |
We don't have a way to export this macro. | The total concentration of drug in the input port. |
We don't have a way to export this macro. | The total concentration of drug in the output port. |
We don't have a way to export this macro. | The radius of the perfused section.* |
We don't have a way to export this macro. | The length of the perfused section.* |
Note: *For the experiments described here, values are constant: r = 1.75 cm. L = 10 cm. | |
Equation 1-44: Absorption rate coefficient calculation
Equation 1-45: Absorption rate calculation for passive transcellular absorption
where:
Variable | Definition |
We don't have a way to export this macro. | Indicates a particular intestinal compartment. |
We don't have a way to export this macro. | The rate of absorption in the jth intestinal compartment. |
We don't have a way to export this macro. | The volume of the lumen in the jth intestinal compartment. |
We don't have a way to export this macro. | The absorption rate coefficient for the jth intestinal compartment. |
We don't have a way to export this macro. | The total concentration of drug in the lumen for the jth intestinal compartment. |
We don't have a way to export this macro. | The concentration of unbound drug in the enterocyte sub-compartment of the jth intestinal compartment. |
GastroPlus absorption models assume that only dissolved drug is subject to absorption.
Equation 1-46: ASF (small intestine), logD model
where:
Variable | Definition |
We don't have a way to export this macro. | The surface area to volume ratio, where A =1.2/r and where r = the compartment radius. |
We don't have a way to export this macro. | Fitting constants for the purposes of weighting the ASFs to account for aspects that are not considered in this derivation such as active transport and physiological changes in the small intestine, where: We don't have a way to export this macro. We don't have a way to export this macro. We don't have a way to export this macro. |
We don't have a way to export this macro. | Value = 6.25. A fitting constant that avoids the singular condition. |
We don't have a way to export this macro. | Peff at pH 6.5. |
We don't have a way to export this macro. | The intrinsic (neutral) Peff of the compound. |
Equation 1-47: ASF (colon), logD model
where:
Variable | Definition |
We don't have a way to export this macro. | The surface area to volume ratio, where A =4/r and where r = the compartment radius. Note: This calculation is also applicable for the caecum. |
We don't have a way to export this macro. | Fitting constants that regulate the degree to which logD can influence ASF. If C3 and C4 were both equal to 1.0, then when logD is positive, ASF would be greater than 1.0. Conversely, when logD is negative, then ASF would be less than 1.0, which accounts for the decreased colonic absorption of polar compounds as described in Ungell’s studies 7 . |
Equation 1-48: ASF (small intestine), Opt logD model
where:
Variable | Description |
We don't have a way to export this macro. | Value = 6.25. A fitting constant that avoids the singular condition. |
We don't have a way to export this macro. | A fitting constant that determines the rate of change, or steepness, of the ASF gradient. |
We don't have a way to export this macro. | A fitting constant that influences the baseline value of the ASFs. |
We don't have a way to export this macro. | The surface area to volume ratio, where We don't have a way to export this macro. =
and r = the compartment radius. |
The ASF calculation for the caecum and the colon using the Opt logD model is identical to that for the logD model. See Equation 1-35.
Equation 1-49: ASF calculation (small intestine), Opt logD SA/V 6.1 model
Equation 1-50: ASF calculation (caecum, colon), Opt logD SA/V 6.1 model
Equation 1-51: ASF calculation (all compartments), Theoretical model
Equation 1-52: ASF calculation (all compartments), Theoretical SA/V model
Equation 1-53: Paracellular absorption rate prediction
where:
Variable | Definition |
We don't have a way to export this macro. | Indicates a particular intestinal compartment. |
We don't have a way to export this macro. | The paracellular absorption rate coefficient for the jth intestinal compartment. |
We don't have a way to export this macro. | The volume of the lumen in jth intestinal compartment. |
We don't have a way to export this macro. | The total drug concentration in the lumen for the jth intestinal compartment. |
We don't have a way to export this macro. | The concentration of unbound drug in the portal vein. |
Equation 1-54: Paracellular absorption rate coefficient
where:
Variable | Definition |
We don't have a way to export this macro. | A physiological parameter calculated as 2/radius(j). |
We don't have a way to export this macro. | Estimated according to the published equation 8 from the drug properties of size and charge, and the physiological parameters of pore radius and porosity in each intestinal compartment as shown in Equation 1-55. |
Equation 1-55: Paracellular permeability calculation
where:
Variable | Definition |
We don't have a way to export this macro. | Dimensionless electrochemical energy function of the jth intestinal compartment. |
We don't have a way to export this macro. | The unit charge of an ion. |
We don't have a way to export this macro. | The charge of the drug molecule at the pH of the jth intestinal compartment. |
We don't have a way to export this macro. | The electrical potential gradient across the aqueous pore. |
We don't have a way to export this macro. | The Boltzman constant. |
We don't have a way to export this macro. | The temperature. |
We don't have a way to export this macro. | The porosity, or the volume fraction of aqueous pores, in the jth intestinal compartment. |
We don't have a way to export this macro. | The pore length. |
We don't have a way to export this macro. | The aqueous diffusion coefficient for the drug. |
We don't have a way to export this macro. | A Renkin function that characterizes the diffusion of solute in a micropore. See Renkin functions in paracellular absorption. |
Equation 1-56: Total rate of drug absorption
where:
Variable | Definition |
We don't have a way to export this macro. | The paracellular absorption scale factor of the jth intestinal compartment. |
We don't have a way to export this macro. | The paracellular permeability of the jth intestinal compartment. |
We don't have a way to export this macro. | The drug concentration in the lumen. |
We don't have a way to export this macro. | The unbound concentration of drug in the portal vein. |
We don't have a way to export this macro. | The lumen fluid volume of the jth intestinal compartment. |
We don't have a way to export this macro. | The unbound concentration of drug in the enterocyte subcompartment. |
We don't have a way to export this macro. | The transcellular absorption scale factor of the jth intestinal compartment. |
We don't have a way to export this macro. | The transcellular permeability of the jth intestinal compartment. |
All absorption models described in this chapter account for passive transcellular absorption and paracellular absorption; however, if your model also accounts for active transcellular absorption, then you must include up to two additional terms— one for influx and one for efflux—in Equation 1-44.
Equation 1-57: Renkin function (Adson)
Equation 1-58: Renkin function (Zhimin)
where:
Variable | Definition |
We don't have a way to export this macro. | The pore radius. |
We don't have a way to export this macro. | The effective molecular radius when the molecule is described by a single value of molecular radius. |
We don't have a way to export this macro. | The mean projected radius of solute molecule. |
We don't have a way to export this macro. | The hydrodynamically equivalent sphere radius. |
Equation 1-59: reff calculation
where MW is the molecular weight of the drug compound.
Equation 1-60: Influx and efflux calculations for saturable carrier-mediated transport
where:
Variable | Definition |
We don't have a way to export this macro. | The index for the ith influx/efflux transporter. |
We don't have a way to export this macro. | The index for the jth lumen compartment. |
We don't have a way to export this macro. | The total concentration of the drug in the lumen of the jth intestinal compartment. |
We don't have a way to export this macro. | The concentration of unbound drug in the enterocyte sub-compartment of the jth intestinal compartment. |
We don't have a way to export this macro. | The fraction of unbound drug in the enterocytes. |
We don't have a way to export this macro. | The maximum transport rate for the ith influx/efflux transporter. |
We don't have a way to export this macro. | The Michaelis-Menten constant (the concentration at 1/2 Vmax) for the ith transporter. |
We don't have a way to export this macro. | The distribution factor for the ith transporter to adjust Vmax in the jth intestinal compartment, which represents the relative amount of the transporter compared to its Vmax measurement environment. The default value is 1.0. |
We don't have a way to export this macro. | The scale factor for overall influx transport. The default value is 1.0. |
We don't have a way to export this macro. | The scale factor for overall efflux transport. The default value is 1.0. |
We don't have a way to export this macro. | The scale factor for overall Km for influx transporters. The default value is 1.0. |
We don't have a way to export this macro. | The scale factor for overall Km for efflux transporters. The default value is 1.0. |
Saturable Metabolism in the GI Tract and Liver Equations
Equation 1-61: Saturable GI tract metabolism rate
where:
Variable | Definition |
We don't have a way to export this macro. | The index for the ith gut metabolism enzyme. |
We don't have a way to export this macro. | The index for the jth enterocyte compartment. |
We don't have a way to export this macro. | The concentration of unbound drug in the enterocyte sub-compartment of the jth intestinal compartment. |
We don't have a way to export this macro. | The fraction of unbound drug in the enterocytes. |
We don't have a way to export this macro. | The maximum velocity of the ith enzyme. |
We don't have a way to export this macro. | The Michaelis-Menten constant of the ith enzyme. |
We don't have a way to export this macro. | The scale factor for the maximum velocity for the ith enzyme in the enterocyte sub-compartment of the jth intestinal compartment. |
We don't have a way to export this macro. | The scale factor for overall enzyme velocity. The default value is 1.0. |
We don't have a way to export this macro. | The scale factor for overall Km for gut enzymes. The default value is 1.0. |
Equation 1-62: GastroPlus® Hepatic Extraction model, differential equation
where:
Variable | Definition |
We don't have a way to export this macro. | The hepatic flow rate. |
We don't have a way to export this macro. | The whole blood to plasma drug concentration ratio. |
We don't have a way to export this macro. | The total drug concentration in the portal vein. |
We don't have a way to export this macro. | The total drug concentration in the liver. |
We don't have a way to export this macro. | The rate of metabolism, which is calculated separately for each liver enzyme at each time point, and then the total rate of metabolism is calculated as the sum of all the rates of metabolism for all the individual enzymes according to Equation 1-63. |
Equation 1-63: Sum total rate of metabolism for all liver enzymes
where:
Variable | Definition |
We don't have a way to export this macro. | The index for the ith enzyme. |
We don't have a way to export this macro. | The plasma concentration of the drug in the liver. |
We don't have a way to export this macro. | The fraction of unbound of the drug in plasma. |
We don't have a way to export this macro. | The maximum metabolism rate for the ith enzyme. |
We don't have a way to export this macro. | The Michael-Menten constant, which is the concentration at 1/2 Vmax, for the ith enzyme. |
We don't have a way to export this macro. | The scale factor for overall liver Vmax. This factor is the same for all enzymes and is set to a default value of 1.0. |
We don't have a way to export this macro. | The scale factor for overall liver Km. This factor is the same for all enzymes and is set to a default value of 1.0. |
ACATPlus™ Equations
Equation 1-64: The diffusion process from sublayer i to sublayer i+1
where:
Variable | Definition |
We don't have a way to export this macro. | The compound diffusivity in mucus. |
We don't have a way to export this macro. | The thickness of the mucus sublayer. |
We don't have a way to export this macro. | The surface area of each GI segment. |
We don't have a way to export this macro. | The unbound concentration in mucus sublayer i. |
Equation 1-65: Mucus regeneration rate incorporated in the calculation of mucus turn over time
Mucus regeneration will cause compound transit from sublayer i to sublayer i-1. The corresponding transit rate has been defined as MucusTurnOverRate. MucusTurnOverRate from the first sublayer represents the shedding off rate, which will transport the compound from mucus to lumen.
Equation 1-66: Mucus Turnover Rate in each Sublayer
where:
Variable | Definition |
We don't have a way to export this macro. | The total concentration in mucus sublayer i. |
We don't have a way to export this macro. | The mucus volume in each sublayer. |
Equation 1-67: The mass balance in each sublayer
Equation 1-68: Mass Transport Model in Mucosa, Sub-Mucosa, and Muscularis Propria
Where:
Variable | Definition |
We don't have a way to export this macro. | The blood flow in mucosa, sub-mucosa, and muscularis propria sub-compartments. |
We don't have a way to export this macro. | The unbound concentration in the mucosa sub-compartment. |
We don't have a way to export this macro. | The unbound concentration in the sub-mucosa sub-compartment. |
We don't have a way to export this macro. | The unbound concentration in the muscularis sub-compartment. |
We don't have a way to export this macro. | The transport between mucosa and sub-mucosa. |
We don't have a way to export this macro. | The transport between sub-mucosa and muscularis propria. |
We don't have a way to export this macro. and We don't have a way to export this macro. are governed by the permeability between their sub-compartments. | |
Equation 1-69: Transcellular and Paracellular Diffusion in Mucosa and Sub-Mucosa
Where P12 and P23 are the permeability coefficients. SA12 and SA23 are the surface area.