Pharmacokinetics Equations

This section details the equations that define and support the PBPKPlus™ module that Simulations Plus developed for the simulation of physiologically-based pharmacokinetics (PBPK) of drug candidates. See:

For details about the internal standards that were used to define the equations in this section, see Equation Standards.

PBPK Tissue Model Equations

Equation 2-1: Perfusion-limited tissue model, non-eliminating tissue

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Equation 2-2: Perfusion-limited tissue model, eliminating tissue with intrinsic clearance

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Equation 2-3: Unbound intrinsic clearance rate calculated from the sum of all tissue enzyme kinetics

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where C_tissue,u is the concentration of unbound drug in the current tissue.

Equation 2-4: Unbound intrinsic clearance converted to systemic clearance

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where:

Variable	Definition
We don't have a way to export this macro.	The plasma and blood clearance rates, respectively.
We don't have a way to export this macro.	The blood/plasma drug concentration ratio.
We don't have a way to export this macro.	The unbound intrinsic clearance rate for the current tissue.
We don't have a way to export this macro.	The local tissue blood flow rate.
We don't have a way to export this macro.	The fraction of drug unbound in the plasma.

Equation 2-5: Permeability-limited tissue model, rate calculations

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Equation 2-6: Permeability-limited tissue model (no lysosomes), partitioning calculations

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where:

Variable	Definition
We don't have a way to export this macro.	The saturable clearance rate of drug calculated using Michaelis-Menten kinetic.
We don't have a way to export this macro.	The saturable, carrier-mediated transport rate of drug into the tissue using Michaelis-Menten kinetics.
We don't have a way to export this macro.	The saturable, carrier-mediated transport rate of drug out of the tissue using Michaelis-Menten kinetics.
We don't have a way to export this macro.	The number of enzymes specified for the tissue of interest.
We don't have a way to export this macro.	The number of influx transporters between the extracellular space and the intracellular space in the tissue compartment.
We don't have a way to export this macro.	The number of efflux transporters between the extracellular space and the intracellular space in the tissue compartment.
We don't have a way to export this macro.	The maximum velocity of the i^th transporter/enzyme.
We don't have a way to export this macro.	The Michaelis-Menten constant of the i^th transporter/ enzyme.
We don't have a way to export this macro. We don't have a way to export this macro.	The total concentration of drug in the extracellular space in the tissue compartment and the concentration of unbound drug in the extracellular space in the tissue compartment, respectively.
We don't have a way to export this macro.	The exchange of drug between the extracellular space and the intracellular space via a combination of passive processes and transporter-mediated processes.
We don't have a way to export this macro.	The (permeability*surface area) product for the tissue.
We don't have a way to export this macro. We don't have a way to export this macro.	The total concentration of drug in the intracellular space in the tissue compartment and the concentration of unbound drug in the intracellular space in the tissue compartment, respectively.
We don't have a way to export this macro.	The rate of clearance of the unbound drug in the intracellular space in the tissue compartment.
Note: All other variables have been defined previously for Figure 2-2.

Equation 2-7: Permeability-limited tissue model (w/ lysosomes) partitioning calculations

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where:

Variable	Definition
We don't have a way to export this macro.	The concentration of neutral, unbound drug in the intracellular space in the tissue compartment.
We don't have a way to export this macro.	The concentration of neutral, unbound drug in the extracellular space in the tissue compartment.
We don't have a way to export this macro.	The concentration of neutral, unbound drug in the lysosomal compartment.
We don't have a way to export this macro.	The total volume of the lysosomal compartment.
We don't have a way to export this macro.	The volume fraction of lysosomes in tissue.
We don't have a way to export this macro.	The total concentration of drug in the lysosomal compartments.
Note: All other variables have been defined previously for Figure 2-2. and Equation 2-6.

PBPK Model Tissues Type Equations

Equation 2-8: Biliary clearance as a fraction of total liver clearance

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where:

Variable	Definition
We don't have a way to export this macro.	The biliary clearance.
We don't have a way to export this macro.	The total liver clearance.
We don't have a way to export this macro.	The biliary clearance fraction, which is the fraction of total liver clearance that is the result of the extraction of the drug to bile.

Equation 2-9: Biliary clearance as the linear transport of drug from hepatocytes to bile

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where PStc_apical is the permeability-surface area product for the apical membrane.

Equation 2-10: Biliary clearance as the non-linear transport of drug from hepatocytes to bile (perfusion-limited tissue model)

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Equation 2-11: Biliary clearance as the non-linear transport of drug from hepatocytes to bile (permeability-limited tissue)

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where:

Variable	Definition
We don't have a way to export this macro.	The biliary clearance.
We don't have a way to export this macro.	The total number of apical transporters that are involved in biliary clearance.
We don't have a way to export this macro.	The maximum velocity of the i^th transporter/enzyme.
We don't have a way to export this macro.	The Michaelis-Menten constant of the i^th transporter/enzyme.
We don't have a way to export this macro.	The concentration of unbound drug in the tissue.
We don't have a way to export this macro.	The concentration of unbound drug in the intracellular space in the tissue compartment.

Equation 2-12: Total amount of drug cleared by excretion (perfusion-limited tissue model)

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Equation 2-13: Total amount of drug cleared by excretion (permeability-limited tissue model)

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where:

Variable	Definition
We don't have a way to export this macro.	The total mass of the drug that is cleared by biliary excretion.
We don't have a way to export this macro.	The expression of the i^th transporter on the liver apical (canalicular) membrane.
We don't have a way to export this macro.	The maximum velocity of the i^th transporter/enzyme.
We don't have a way to export this macro.	The Michaelis-Menten constant of the i^th transporter/enzyme.
We don't have a way to export this macro.	The concentration of unbound drug in the tissue.
We don't have a way to export this macro.	The concentration of unbound drug in the intracellular space in the tissue compartment.
We don't have a way to export this macro.	The (permeability*surface area) product for the liver apical membrane.
We don't have a way to export this macro.	The total mass of the drug that is cleared by the liver.
We don't have a way to export this macro.	The biliary clearance fraction, which is the fraction of total liver clearance that is the result of the extraction of the drug to bile.

Equation 2-14: General calculation for kidney clearance

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where:

Variable	Definition
We don't have a way to export this macro.	Kidney filtration clearance.
We don't have a way to export this macro.	Clearance due to active and passive secretion.
We don't have a way to export this macro.	Clearance due to active and passive reabsorption.
We don't have a way to export this macro.	Clearance due to metabolism.

Equation 2-15: Perfusion-limited GastroPlus® PBPK lung tissue model calculations

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where:

Variable	Definition
We don't have a way to export this macro.	The total concentration of drug in the lung tissue, at time t.
We don't have a way to export this macro.	The total concentration of drug in lung tissue ELF, at time t.
We don't have a way to export this macro.	The saturable clearance rate of drug calculated using Michaelis-Menten kinetics. See Equation 2-3.

Equation 2-16: Hybrid perfusion-limited GastroPlus® PBPK lung tissue model calculations

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where:

Variable	Definition
We don't have a way to export this macro.	The total concentration of drug in the lung tissue, at time t.
We don't have a way to export this macro.	The total concentration of drug in ELF, at time t.
We don't have a way to export this macro.	The process of drug exchange between tissue and ELF via a combination of passive processes and transporter-mediated processes.
We don't have a way to export this macro. We don't have a way to export this macro.	Represent saturable carrier-mediated transport of drug between the lung tissue and ELF calculated using Michaelis-Menten kinetics.
We don't have a way to export this macro.	The neutral, unbound concentration of drug in the tissue.
We don't have a way to export this macro.	The neutral unbound concentration of drug in ELF.
Note: All other variables have been defined previously for Equation 2-15 and Figure 2-6.

Equation 2-17: Permeability-limited GastroPlus® PBPK lung tissue model calculations

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where:

Variable	Definition
We don't have a way to export this macro.	The saturable clearance rate of drug calculated using Michaelis-Menten kinetics.
We don't have a way to export this macro.	The total concentration of drug in the lysosomal compartments, at time t.
We don't have a way to export this macro.	The concentration of neutral, unbound drug in the intracellular space in the tissue compartment.
We don't have a way to export this macro.	The concentration of neutral, unbound drug in the lysosomal compartment.
We don't have a way to export this macro.	The total concentration of drug in ELF, at time t.
We don't have a way to export this macro.	The exchange of drug between tissue and ELF via a combination of passive processes and transporter-mediated processes.
We don't have a way to export this macro.	The concentration of unbound drug in ELF.
We don't have a way to export this macro.	The basolateral (permeability*surface area) product for passive diffusion between extracellular water and the intracellular space in the tissue compartment.
We don't have a way to export this macro.	The apical (permeability*surface area) product for passive diffusion between the intracellular space in the tissue compartment and ELF.
We don't have a way to export this macro. We don't have a way to export this macro.	The saturable, carrier-mediated transport of drug (into tissue and out of tissue, respectively) using Michaelis-Menten kinetics.
We don't have a way to export this macro. We don't have a way to export this macro.	The saturable, carrier-mediated transport of drug between the lung tissue and ELF calculated using Michaelis-Menten kinetics.

Equation 2-18: Default value for the fraction of drug unbound in ELF calculation

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where:

Variable

Definition

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The fraction of neutral, unbound drug at the pH of plasma.

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The fraction of neutral, unbound drug at the pH of ELF.

Tissue Distribution Calculations

Equation 2-19: Fraction of drug unbound in tissue calculation

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where:

Variable

Definition

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The fraction of unbound drug in plasma.

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The ratio of albumin concentration in tissue to the albumin concentration in plasma.

Note: When using Poulin’s method of tissue:plasma partition coefficients, RAt:p = 0.15 for adipose and RAt:p = 0.50 for all other tissues.

Equation 2-20: Calculation of tissue:plasma partition coefficients based on the Poulin homogeneous method

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where:

Variable	Definition
We don't have a way to export this macro.	The fraction of unbound drug in tissue.
We don't have a way to export this macro.	The fraction of unbound drug in plasma.
We don't have a way to export this macro.	The solvent/water partition coefficient or distribution coefficient for the drug, where: For adipose and yellow marrow, K = the distribution coefficient at pH = 7.4 in vegetable oil and water (logD_vo/w). For all other normal tissue, K = the partition coefficient in octanol and water (logP_oct/w).
We don't have a way to export this macro.	The volume fraction of neutral lipids in tissue.
We don't have a way to export this macro.	The volume fraction of neutral phospholipids in tissue.
We don't have a way to export this macro.	The volume fraction of total water in tissue.
We don't have a way to export this macro.	The volume fraction of neutral lipids in plasma.
We don't have a way to export this macro.	The volume fraction of neutral phospholipids in plasma.
We don't have a way to export this macro.	The volume fraction of total water in plasma.

Equation 2-21: Default GastroPlus® conversion of logP_oct/w to logD_vo/w

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Equation 2-22: Kp calculation for perfusion-limited tissues

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Equation 2-23: Kp calculation for permeability-limited tissues

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where:

Variable	Definition
We don't have a way to export this macro.	The volume of the extracellular space as a fraction of the total tissue volume.
We don't have a way to export this macro.	The fraction of unbound drug in tissue.
We don't have a way to export this macro.	The fraction of unbound drug in plasma.

Equation 2-24: Berezhkovskiy method of Kp calculation (modified Poulin calculation)

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Equation 2-25: Kpu calculation with acidic phospholipid binding for compounds with a base pKa > 7

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where:

Variable	Definition
We don't have a way to export this macro.	The volume fraction of extracellular water in individual tissues.
We don't have a way to export this macro.	The volume fraction of intracellular water in individual tissues.
We don't have a way to export this macro.	The solvent/water partition coefficient for the drug, where: For adipose and yellow marrow, K = the partition coefficient in vegetable oil and water (logPvo/w). For all other normal tissues, K = the partition coefficient in octanol and water (logPoct/w).
We don't have a way to export this macro.	The volume fraction of neutral lipids in individual tissues.
We don't have a way to export this macro.	The volume fraction of neutral phospholipids in individual tissues.
We don't have a way to export this macro.	The fraction of neutral drug in plasma (pH = 7.4).
We don't have a way to export this macro.	The association constant of a basic compound with acidic phospholipids. See Equation 2-27.
We don't have a way to export this macro.	The concentration of acidic phospholipids in individual tissues.
We don't have a way to export this macro.	The fraction of neutral drug in the intracellular space (water) of individual tissues (pH = 7).

Equation 2-26: Calculation of Kpu_{RBC/plasma water}

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where:

Variable	Definition
We don't have a way to export this macro.	The hematocrit.
We don't have a way to export this macro.	The blood/plasma drug concentration ratio.
We don't have a way to export this macro.	The fraction of unbound drug in plasma.

Equation 2-27: Calculation of Ka from Kpu_{RBC/plasma water}

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where:

Variable	Definition
We don't have a way to export this macro.	The fraction of neutral drug in the intracellular space of red blood cells (pH = 7.22).
We don't have a way to export this macro.	The fraction of neutral drug in plasma (pH = 7.4).
We don't have a way to export this macro.	The volume fraction of intracellular water in red blood cells.
We don't have a way to export this macro.	The volume fraction of neutral lipids in red blood cells.
We don't have a way to export this macro.	The volume fraction of neutral phospholipids in red blood cells.
We don't have a way to export this macro.	The concentration of acidic phospholipids in red blood cells.
We don't have a way to export this macro.	The solvent/water partition coefficient for the drug, where: For adipose and yellow marrow, K = the partition coefficient in vegetable oil and water (logP_vo/w). For all other normal tissues, K = the partition coefficient in octanol and water (logP_oct/w).

Equation 2-28: Kpu calculation with tissue protein binding for compounds with all base pKas <7

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where:

Variable	Definition
We don't have a way to export this macro.	The fraction of neutral drug in the intracellular space (water) of individual tissues (pH = 7).
We don't have a way to export this macro.	The fraction of neutral drug in plasma (pH = 7.4).
We don't have a way to export this macro.	The volume fraction of intracellular water in individual tissues.
We don't have a way to export this macro.	The volume fraction of extracellular water in individual tissues.
We don't have a way to export this macro.	The volume fraction of neutral lipids in individual tissues.
We don't have a way to export this macro.	The volume fraction of neutral phospholipids in individual tissues.
We don't have a way to export this macro.	The fraction of unbound drug in plasma.
We don't have a way to export this macro.	The volume fraction of neutral lipids in plasma.
We don't have a way to export this macro.	The volume fraction of neutral phospholipids in plasma.
We don't have a way to export this macro.	For ionizable drug compounds: The ratio of albumin concentration in tissue to the albumin concentration in plasma. For non-ionizable drug compounds: The ratio of lipoprotein concentration in tissue to the lipoprotein concentration in plasma.
We don't have a way to export this macro.	The solvent/water partition coefficient for the drug, where: For adipose and yellow marrow, K = the partition coefficient in vegetable oil and water (logPvo/w). For all other normal tissues, K = the partition coefficient in octanol and water (logPoct/w).

Equation 2-29: Final Kp calculation for all compounds

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Equation 2-30: Lukacova combined equation for Kp calculation

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where:

Variable	Definition
We don't have a way to export this macro.	The volume fraction of extracellular water in individual tissues.
We don't have a way to export this macro.	The fraction of neutral drug in the intracellular space (water) of individual tissues (pH = 7).
We don't have a way to export this macro.	The fraction of neutral drug in plasma (pH = 7.4).
We don't have a way to export this macro.	The solvent/water partition coefficient for the drug, where: For adipose and yellow marrow, K = the partition coefficient in vegetable oil and water (logPvo/w). For all other normal tissues, K = the partition coefficient in octanol and water (logPoct/w).
We don't have a way to export this macro.	The volume fraction of intracellular water in individual tissues.
We don't have a way to export this macro.	The volume fraction of neutral lipids in individual tissues.
We don't have a way to export this macro.	The volume fraction of neutral phospholipids in individual tissues.
We don't have a way to export this macro.	The fraction of drug without positive charge in plasma, where the zwitterions with total charge = 0 are not included in this fraction because they contain positive charge that would be associating with the acidic phospholipids.
We don't have a way to export this macro.	The volume fraction of neutral lipids in plasma.
We don't have a way to export this macro.	The volume fraction of neutral phospholipids in plasma.
We don't have a way to export this macro.	For ionizable drug compounds: The ratio of albumin concentration in tissue to the albumin concentration in plasma. For non-ionizable drug compounds: The ratio of lipoprotein concentration in tissue to the lipoprotein concentration in plasma.
We don't have a way to export this macro.	The fraction of drug with positive charge in plasma, including cations or zwitterions with at least one positive charge on the molecule, regardless of the total charge of the molecule.
We don't have a way to export this macro.	The association constant of a basic compound with acidic phospholipids.
We don't have a way to export this macro.	The concentration of acidic phospholipids in individual tissues.

Equation 2-31: NPI calculation

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where:

Variable

Definition

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The normalized error of prediction using the original two Rodgers and Rowland equations.

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The normalized error of prediction using the Lukacova combined equation.

Equation 2-32: Normalized error of prediction calculation

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where:

Variable

Definition

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The predicted volume of distribution.

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The experimental volume of distribution.

Equation 2-33: Lukacova method with lysosomes

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where:

Variable	Definition
We don't have a way to export this macro.	The fraction of neutral drug in lysosomes.
We don't have a way to export this macro.	The fraction of positive drug in lysosomes.
We don't have a way to export this macro.	The fraction of positive drug in intracellular water.
We don't have a way to export this macro.	The volume fraction of lysosomes in tissue.
Note: All other variables are as previously defined. See Equation 2-30.

Equation 2-34: Fraction unbound in plasma for Kp calculations

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where:

Variable	Definition
We don't have a way to export this macro.	The adjusted fraction of unbound drug in plasma that is used in Kp calculations.
We don't have a way to export this macro.	The experimental f_upvalue.
We don't have a way to export this macro.	The octanol/water distribution coefficient at pH=7.4, which is the pH of plasma.
We don't have a way to export this macro.	The volume fraction of total neutral lipid and total neutral phospholipid in plasma.
We don't have a way to export this macro.	The volume fraction of total water in plasma.

Equation 2-35: f_ut calculation for perfusion-limited tissue

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Equation 2-36: f_u(ext) calculation for permeability-limited tissue

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where:

Variable	Definition
We don't have a way to export this macro.	The fraction of neutral drug in plasma (pH = 7.4).
We don't have a way to export this macro.	The fraction of unbound drug in plasma.
We don't have a way to export this macro.	The tissue/plasma partition coefficient.
We don't have a way to export this macro.	The fraction of neutral drug in intracellular water (pH = 7) for a perfusion-limited tissue.
We don't have a way to export this macro.	The fraction of neutral drug in extracellular water (pH = 7.4) for a permeability-limited tissue.

Equation 2-37: f_u(int) calculation for permeability-limited tissue

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where:

Variable	Definition
We don't have a way to export this macro.	The fraction of unbound drug in the intracellular space (water) of the tissue.
We don't have a way to export this macro.	The fraction of cationic drug in plasma (pH = 7.4).
We don't have a way to export this macro.	The fraction of cationic drug in intracellular space (water) of the tissue (pH = 7.0).
Note: For the remainder of the variable definitions, see Equation 2-30.

Equation 2-38: f_ut in lysosomal compartments, permeability-limited tissue

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where:

Variable	Definition
We don't have a way to export this macro.	The fraction of cationic drug in plasma (pH = 7.4).
We don't have a way to export this macro.	The fraction of cationic drug in the lysosomal compartments.
We don't have a way to export this macro.	The concentration of acidic phospholipids in individual tissues.

Equation 2-39: Total concentration of drug entering a perfusion-limited tissue

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where:

Variable	Definition
We don't have a way to export this macro.	The concentration of non-ionized, unbound drug in extracellular water.
We don't have a way to export this macro.	The concentration of non-ionized, unbound drug in intracellular water.
We don't have a way to export this macro.	The concentration of ionized, unbound drug in extracellular water.
We don't have a way to export this macro.	The concentration of ionized, unbound drug in intracellular water.
We don't have a way to export this macro.	The concentration of neutral or anionic drug bound to tissue albumin in the extracellular space.
We don't have a way to export this macro.	The concentration of cationic drug bound to acidic phospholipids in the intracellular space.
We don't have a way to export this macro.	The concentration of neutral or anionic drug bound to neutral lipids in the intracellular space.
We don't have a way to export this macro.	The concentration of neutral or anionic drug bound to neutral phospholipids in the intracellular space.

Equation 2-40: Non-ionized, unbound concentrations of drug in extracellular and intracellular water

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Equation 2-41: Equilibria between non-ionized and ionized unbound concentrations of drug in extracellular and intracellular spaces

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Equation 2-42: Fraction of unbound drug in the extracellular space

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Equation 2-43: Cationic fraction of drug bound to acidic phospholipids

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Equation 2-44: Neutral fraction of drug bound to neutral lipids

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where, for simplicity in upcoming calculations, this value is abbreviated as f_nl.

Equation 2-45: Neutral fraction of drug bound to neutral phospholipids

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where, for simplicity in upcoming calculations, this value is abbreviated as f_npl.

Equation 2-46: Total fraction of unbound drug in the tissue

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Equation 2-47: Ratio of the drug concentrations in the extracellular region and intracellular region to the total drug concentration

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Equation 2-48: Total drug concentration in tissue

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Equation 2-49: Total concentration of drug in the intracellular and extracellular spaces

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Equation 2-50: Unbound, un-ionized concentration of drug in the intracellular and extracellular spaces

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Equation 2-51: Total, unbound intracellular concentration of drug (neutral and ionized forms)

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Equation 2-52: Total fraction of unbound drug in the intracellular space

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Kp Calculation Variable Assumptions

Equation 2-53: Steady state volume distribution calculation

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where:

Variable	Definition
We don't have a way to export this macro.	The total volume of plasma in the body.
We don't have a way to export this macro.	The total volume of erythrocytes in the body.
We don't have a way to export this macro.	The ratio of the total concentration of the drug in erythrocytes to the total concentration of the drug in plasma, calculated from the blood/ plasma drug concentration ratio and the hematocrit.
We don't have a way to export this macro.	The volume of a given tissue compartment.
We don't have a way to export this macro.	The tissue/plasma partition coefficient.
We don't have a way to export this macro.	The extraction ratio for a given tissue.

Equation 2-54: McNamara’s equation for infant physiologies

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where:

Variable	Definition
We don't have a way to export this macro.	The fraction of drug unbound in pediatric plasma.
We don't have a way to export this macro.	The fraction of drug unbound in adult plasma.
We don't have a way to export this macro.	The protein concentration in pediatric plasma.
We don't have a way to export this macro.	The protein concentration in adult plasma.

Equation 2-55: Infant R_b:p scaling

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where:

Variable	Definition
We don't have a way to export this macro.	The drug blood/plasma concentration ratio as indicated for infants (ped) or adults (adult).
We don't have a way to export this macro.	The hematocrit, expressed as a fraction, in pediatric blood.
We don't have a way to export this macro.	The hematocrit, expressed as a fraction, in adult blood.

Equation 2-56: Homeostasis of amniotic fluid

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where:

Variable	Definition
We don't have a way to export this macro.	The fetal urinary rate.
We don't have a way to export this macro.	The secretion rate from fetal tissue.
We don't have a way to export this macro.	The fetal swallowing rate.
We don't have a way to export this macro.	The active portion of the intra-membranous pathway.

Equation 2-57: Fetal pathway for perfusion-limited tissue (amniotic fluid)

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where:

Variable	Definition
We don't have a way to export this macro.	The total volume of the amniotic fluid.
We don't have a way to export this macro.	The total concentration of drug in the amniotic fluid.
We don't have a way to export this macro.	The concentration of unbound drug in the amniotic fluid.
We don't have a way to export this macro.	The total concentration of drug in the fetal tissue.
We don't have a way to export this macro.	The intra-membranous fluid transfer rate constant (defined in the amniotic fluid compartment) representing osmosis.
We don't have a way to export this macro.	The trans-membranous fluid transfer rate constant between the uterus and the amniotic fluid.
We don't have a way to export this macro.	The fetal tissue/plasma partition coefficient.
We don't have a way to export this macro.	The fraction of unbound drug in the fetal plasma.
We don't have a way to export this macro.	The total concentration of drug on the fetal side of the placenta.
We don't have a way to export this macro.	The tissue/plasma partition coefficient on the fetal side of the placenta.
We don't have a way to export this macro.	The fetal filtration clearance rate.
We don't have a way to export this macro.	The secretion rate from fetal tissue.
We don't have a way to export this macro.	The fetal swallowing rate.
We don't have a way to export this macro.	The total concentration of drug in the uterine tissue.
We don't have a way to export this macro.	The uterine tissue/plasma partition coefficient.
We don't have a way to export this macro.	The general clearance rate for the fetal tissue.

Unless otherwise noted, all variables are defined for the amniotic fluid or fetal tissue.

Equation 2-58: Fetal pathway for perfusion-limited tissue (fetal tissue)

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where:

Variable	Definition
We don't have a way to export this macro.	The total volume of the fetal tissue.
We don't have a way to export this macro.	The fetal blood flow.
We don't have a way to export this macro.	The total concentration of drug in arterial (in) blood in fetal tissue.
We don't have a way to export this macro.	The fetal blood/plasma drug concentration ratio.
We don't have a way to export this macro.	The fetal tissue/plasma partition coefficient.
We don't have a way to export this macro.	The intra-membranous fluid transfer rate constant (defined in the amniotic fluid compartment) representing osmosis and vesicular routes, respectively.
We don't have a way to export this macro.	The concentration of unbound drug in the amniotic fluid.
We don't have a way to export this macro.	The total concentration of drug in the fetal tissue.
We don't have a way to export this macro.	The fraction of unbound drug in the fetal plasma.
We don't have a way to export this macro.	The fetal filtration clearance rate.
We don't have a way to export this macro.	The secretion rate from fetal tissue.
We don't have a way to export this macro.	The fetal swallowing rate.
We don't have a way to export this macro.	The general clearance rate for the fetal tissue.

For the equations that describe the modeling of the fetal and maternal placenta tissue, the variables were defined according to the following rules:

Variable	Definition
We don't have a way to export this macro.	Represents concentration, amount (mass) and volume, respectively.
We don't have a way to export this macro.	The total concentration of drug in arterial (in) blood and venous (out) blood in tissue.
We don't have a way to export this macro.	Represents fetal, maternal, and total (across both fetal and maternal), respectively.
We don't have a way to export this macro.	The extracellular fluid to plasma partition coefficient.
We don't have a way to export this macro.	The (permeability*surface area) product for the tissue, which can be either on the apical side (api) or the basolateral side (baso).
We don't have a way to export this macro.	The tissue/plasma partition coefficient between maternal tissue and maternal plasma.
We don't have a way to export this macro.	The tissue/plasma partition coefficient between fetal tissue and maternal plasma.
We don't have a way to export this macro.	The tissue/plasma partition coefficient between fetal tissue and fetal plasma.
We don't have a way to export this macro.	The tissue/plasma partition coefficient between total placenta tissue (maternal and fetal) and maternal plasma.
We don't have a way to export this macro.	The total amount (mass) of drug in the maternal placenta and the fetal placenta, respectively.
We don't have a way to export this macro.	The maternal blood/plasma drug concentration ratio and the fetal blood/plasma concentration ratio, respectively.
We don't have a way to export this macro.	The tissue blood flow from the maternal side and the fetal side, respectively.
We don't have a way to export this macro.	The total maternal placenta tissue volume and the total fetal placenta tissue volume, respectively.
We don't have a way to export this macro.	Represents total, unbound, extracellular space, intracellular space, and the plasma compartment in the tissue, respectively.

Equation 2-59: Mass balance in perfusion-limited placenta tissue

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Equation 2-60: Total concentration in the placenta (maternal + fetal)

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Equation 2-61: Partition coefficient for total placenta tissue and maternal plasma

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Equation 2-62: General equation that describes the change in the amount of drug in the total perfusion-limited placenta tissue (maternal placenta + fetal tissue)

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where:

Variable	Definition
We don't have a way to export this macro.	The concentration of unbound drug in the amniotic fluid.
We don't have a way to export this macro.	The total concentration of drug in the fetal side of the placenta.
We don't have a way to export this macro.	The tissue/plasma partition coefficient on the fetal side of the placenta.
We don't have a way to export this macro.	The fraction of unbound drug in the fetal tissue.

Equation 2-63: Change in the amount of drug in the fetal placenta

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Equation 2-64: Initial equation for the change in the amount of drug in maternal placenta

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Equation 2-65: Fetal tissue placenta concentration

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Equation 2-66: Final equation for the change in the amount of drug in the maternal placenta

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Equation 2-67: Permeability-limited fetal placenta calculations

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Equation 2-68: Permeability-limited maternal placenta calculations

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We don't have a way to export this macro.

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where:

Variable	Definition
We don't have a way to export this macro.	The saturable clearance rate of drug calculated using Michaelis-Menten kinetics.
We don't have a way to export this macro.	The saturable, carrier-mediated transport rate of drug into the tissue using Michaelis-Menten kinetics.
We don't have a way to export this macro.	The saturable, carrier-mediated transport rate of drug out of the tissue using Michaelis-Menten kinetics.

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