Basic PBPK (Physiologically Based PharmacoKinetic) model of Acetaminophen.

This is a basic model of Acetaminophen (APAP, Paracetamol) pharmacokinetics in humans. Many of the model parameters (compartment volumes, volumetric flow rates, etc.) are scaled allometrically based on the body weight (BW) raised to the 3/4 power. Because of that, the assigned values of many of the parameters are recalculated at run time and are different than the default values for the particular entity (e.g., the volume of a compartment and the volumetric flow rate between compartments).

APAP dose is initially given in grams (APAP_Dose_gram), which is converted to moles via the APAP molecular weight (APAP_MW). APAP quantities throughout the rest of the models are given in moles.

The base parameters are for a 70Kg human and a pharmacological oral dose of 1.4 gram of APAP. Metabolism is modelled as a single ODE in the liver compartment and the metabolite does not leave that compartment.

This model is loosely based on the model of Wambaugh and Shaw (PLoS Comput Biol. 2010 Apr 22;6(4):e1000756. doi: 10.1371/journal.pcbi.1000756. Pubmed ID: PMID- 20421935) with the following changes:

  1. The lung lumen compartment was omitted.
  2. A kidney compartment was added.
  3. Glomerular Filtration is from the kidney compartment.
  4. The APAP dose was changed to 1.4g.
  5. The gut adsorption rate constant (KGutabs), tissue partition coefficients and liver metabolism rate constant (CLmetabolism) were fit using the human in vivo data of Critchley (Critchley, J. A., Critchley, L. A. H., Anderson, P. J., and Tomlinson, B. 2005 Journal of clinical pharmacy and therapeutics, 30(2), 179-184).
  6. To model the extensive re-adsorption of APAP from the kidney tubules back into the blood the QGfr value is modified. This was done by changing the scaling parameter QGFR_ref value from 0.31 to 0.039, resulting in a decrease in the QGfr value of 8 fold (from 7.2 L/hr to 0.91 L/hr).

The parameters in this file are the REFSIM parameters from our publication.

Chelliah Vijayalakshmi viji@ebi.ac.uk EMBL-EBI Sluka James JSluka@indiana.edu Indiana University Fu Xiao fuxiao@umail.iu.edu Indiana University 2015-02-04T11:47:58Z 2017-05-23T10:32:07Z

Units of molecular weight: grams/mole

Reference body weight (Kg) for allometric scaling.

Compartments such as the liver, lungs, kidneys, ...

Blood only compartments such as the arteries and veins.

Lumen compartments such as in the lungs, gut and kidney.

Acetaminophen in all locations.

All metabolites of APAP in all locations.

Volume of the arterial blood. Note that this value is modified by allometric scaling in an initial assignment or rule equation.

Perfusable volume of the Gut (small intestine). The compartment volume is allometrically scaled and is assigned in an initialAssignment.

Lumen of the Gut. Note that the volume is arbitrary.

Perfusable volume of the Lungs. The compartment volume is allometrically scaled and is assigned in an initialAssignment.

Volume of the venous blood. The compartment volume is allometrically scaled and is assigned in an initialAssignment.

Perfusable volume of the Rest of the body, that is, all tissues and blood volumes not explicitly described by other compartments. The compartment volume is allometrically scaled and is assigned in an initialAssignment.

Perfusable volume of the Liver. The compartment volume is allometrically scaled and is assigned in an initialAssignment.

Perfusable volume of the Kidney. The compartment volume is allometrically scaled and is assigned in an initialAssignment.

Kidney (renal) Tubules (lumen). This, like the gut lumen, is treated as a volumeless compartment.

Amount of APAP in the arteries of the gut in moles.

Amount of APAP in the gut (small intestine) blood in moles.

Amount of APAP in the lumen of the gut in moles.

Amount of APAP in the lung blood in moles.

Amount of APAP in the venous blood in moles.

Amount of APAP in the "rest of the body" in moles.

Amount of APAP in the liver blood in moles.

Amount of APAP in the kidney blood in moles.

Amount of APAP in the Kidney Tubules in moles.

APAP dose in grams.

Acetaminophen molecular weight in grams/mole.

Acetaminophen dose in moles. = APAP_Dose_grams/APAP_MW. Note that this value is assigned by an initial assignment or rule equation.

Body weight, in Kg. This value, raised to the 3/4 power, is used in the allometric scaling equations

De-dimensionalization factor for the allometric scaling. Removes the non-integer exponent of the BW^(3/4) scaling factor in the allometric equations.

Total cardiac output reference value for individual of BW=BW_ref (70Kg) for allometric scaling. In Litres/hour.

Cardiac blood flow in Litres/hr. (aka arterial blood flow or QArt). Note that this value is modified by allometric scaling in an initial assignment or rule equation.

Allometric scaling coefficient for fraction of cardiac output (QCardiac) that flows through the Gut (QGut).

Volumetric blood flow through the gut in Litres/hour. Note that this value is modified by allometric scaling in an initial assignment or rule equation.

Allometric scaling coefficient for fraction of cardiac output (QCardiac) that flows through the Liver (QLiver).

Perfusable volume of the Liver in Litres/hr. Note that this value is modified by allometric scaling in an initial assignment or rule equation.

Allometric scaling coefficient for fraction of cardiac output (QCardiac) that flows through the Kidney (QKidney).

Kidney blood flow in Litres/hr. Note that this value is modified by allometric scaling in an initial assignment or rule equation.

Blood throw through all other tissues, Litres/hour. Note that this value is modified by allometric scaling in an initial assignment or rule equation.

Qgfr coefficient for allometric scaling.

NOTE: The normal value for this parameter is 21.7L/hr. The value shown here reflects the extensive re-adsorption of APAP from the kidney tubules back into the blood.

Granulocyte filtration rate in Litres/hour. Note that this value is modified by allometric scaling in an initial assignment or rule equation. In addition, this vlue is greatly reduced to simulate resorption of APAP from the tubules in the kidney.

Rate of metabolism of APAP in the liver. This single kinetic constant represents both Phase I (e.g., Cyp-2E1) and Phase II (glucurondiation and sulfation) metabolism.

Fraction of compound in plasma that is not bound by plasma proteins.

Ratio of the compound amount in (total) blood vs. plasma.

Partition coefficient for compound between the Liver and the blood plasma.

Partition coefficient for compound between the Kidney and the blood plasma.

Partition coefficient for compound between the Rest (of body) and the blood plasma.

Total perfusable volume of the body coefficient for allometric scaling. This is the lean fraction of Body Weight.

Total perfusable volume of the body in Litres. Note that this value is modified by allometric scaling in an initial assignment or rule equation.

Allometric scaling coefficient for fraction of total perfusable volume of the body (VTotal) represented by the Liver (VLiver).

Allometric scaling coefficient for fraction of cardiac output (QCardiac) that flows through the Arteries (QArt).

Allometric scaling coefficient for fraction of total perfusable volume of the body (VTotal) represented by the Lungs (VLung).

Allometric scaling coefficient for fraction of total perfusable volume of the body (VTotal) represented by the Veins (VVen).

Allometric scaling coefficient for fraction of total perfusable volume of the body (VTotal) represented by the Gut/stomach/small intestine (VGut).

Allometric scaling coefficient for fraction of total perfusable volume of the body (VTotal) represented by the Kidneys (VKidney).

Assignment of the perfusable volume (L) of the Arterial (Art) compartment after allometric scaling.

 VTotal VArt_fraction_VTotal

Assignment of the perfusable volume (L) of the Gut compartment after allometric scaling.

 VTotal VGut_fraction_VTotal

Assignment of the perfusable volume (L) of the Lung compartment after allometric scaling.

 VTotal VLung_fraction_VTotal

Assignment of the perfusable volume (L) of the Venous (Ven) compartment after allometric scaling.

 VTotal VVen_fraction_VTotal

Assignment of the perfusable volume (L) of the Liver compartment after allometric scaling.

 VTotal VLiver_fraction_VTotal

Assignment of the perfusable volume (L) of the Kidney compartment after allometric scaling.

 VTotal VKidney_fraction_VTotal

Assignment of the perfusable volume (L) of the Rest (of the body) compartment after allometric scaling.

 VTotal VArt VGut VKidney VLiver VLung VVen

Calculate APAP dose in moles based on the dose in grams (APAP_Dose_grams) and APAP moleuclar weight (APAP_MW).

 APAP_Dose_grams APAP_MW

Starting compartment for the APAP dose (moles) is the lumen of the gut/stomach/small intestine.

 APAP_Dose

Allometric calculation of the total cardiac output inL/hour (QCardiac) based on the body weight ( (BW/BW_ref)^(3/4) ).

 Cardiac_flow_ref BW BW_ref 0.75

Allometric calculation of the Gut blood flow rate (QGut) in L/hour based on the body weight ( BW^(3/4) ).

 QCardiac QGut_fraction_QCardiac

Allometric calculation of the Liver blood flow rate (QLiver) in L/hour based on the body weight ( BW^(3/4) ).

 QCardiac QLiver_fraction_QCardiac

Allometric calculation of the Kidney blood flow rate (QKidney) in L/hour based on the body weight ( BW^(3/4) ).

 QCardiac QKidney_fraction_QCardiac

Allometric calculation of the Rest of the body's blood flow rate (QRest) in L/hour based on the body weight ( BW^(3/4) ).

 QCardiac QGut QKidney QLiver

Allometric calculation of the Qgfr inL/hour based on the body weight ( (BW/BW_ref)^(3/4) ).

 QGFR_ref BW BW_ref 0.75

Allometric calculation of the total perfusable volume of the body in litres (VTotal) based on the body weight.

 VTotal_ref BW BW_ref

Blood born transfer of compound from the Arterial compartment (CArt) to the Gut (CGut) in moles/hour.

 QGut VArt CArt

First order adsorption of compound from the lumen of the gut (AGutlumen) to the gut compartment (CGut) in mole/hour.

 kGutabs AGutlumen

Blood born transfer of compound from the Lung compartment (CLung) to the Arterial blood compartment (CArt) in moles/hour.

 QCardiac VLung CLung

Blood born transfer of compound from the Venous compartment (CVen) to the Lung compartment (CLung) in moles/hour.

 QCardiac VVen CVen

Blood born transfer of compound from the Arterial compartment (CArt) to the Rest of the body compartment (CRest) in moles/hour.

 QRest CArt VArt

Blood born transfer of compound from the Rest compartment (CRest) to the Venous compartment (CVen) in moles/hour.

 QRest VRest CRest Ratioblood2plasma KRest2plasma Fraction_unbound_plasma

Blood born transfer of compound from the Arterial compartment (CArt) to the Liver compartment (CLiver) in moles/hour.

 QLiver VArt CArt

Metabolism of compound in the Liver compartment (CLiver) to metabolites (CMetabolized) in moles/hour. The metabolites stay in the liver compartment. This single first order ODE represents both Phase I (Cyp-P450 2E1, 1A2) and Phase II (glucuronidation and sulfation) reactions.

 CLmetabolism CLiver Kliver2plasma Fraction_unbound_plasma

Blood born transfer of compound from the Gut compartment (CGut) to the Liver compartment (CLiver) in moles/hour.

 QGut VGut CGut

Blood born transfer of compound from the Liver compartment (CLiver) to the Venous compartment (CVen) in moles/hour.

 QLiver QGut VLiver CLiver Ratioblood2plasma Kliver2plasma Fraction_unbound_plasma

Blood born transfer of compound from the Arterial compartment (CArt) to the Kidney compartment (CKidney) in moles/hour.

 QKidney VArt CArt

Transfer of compound from the Kidney compartment (CKidney) to the Kidney tubules (species CTubules in the compartment "KidenyTubules") in moles/hour.

 Qgfr VKidney CKidney Kkidney2plasma

Blood born transfer of compound from the Kidney compartment (CKidney) to the Venous compartment (CVen) in moles/hour.

 QKidney VKidney CKidney Ratioblood2plasma Kkidney2plasma Fraction_unbound_plasma