OFlaherty 2001
Notes
Cr PBK (O'Flaherty et al. 2001):
Overview
| key | value |
|---|---|
| Modelled species/orgamism(s) | http://purl.obolibrary.org/obo/NCBITaxon_9606 |
| Model chemical(s) | http://purl.obolibrary.org/obo/CHEBI_155866 |
| Input route(s) | 1 (oral) |
| Time resolution | d |
| Amounts unit | mg |
| Volume unit | L |
| Number of compartments | 6 |
| Number of species | 12 |
| Number of parameters | 30 (14 external / 16 internal) |
Diagram
Compartments
| id | name | unit | model qualifier |
|---|---|---|---|
| GI | Gut compartment | L | http://purl.obolibrary.org/obo/PBPKO_00477 |
| Liver | Liver compartment | L | http://purl.obolibrary.org/obo/PBPKO_00558 |
| Plasma | Plasma compartment | L | http://purl.obolibrary.org/obo/PBPKO_00488 |
| RBC | Red blood cells compartment | L | http://purl.obolibrary.org/obo/PBPKO_00634 |
| Rest | Rest of body compartment | L | http://purl.obolibrary.org/obo/PBPKO_00450 |
| Feces | Feces compartment | L | http://purl.obolibrary.org/obo/PBPKO_00555 |
Species
| id | name | unit | model qualifier |
|---|---|---|---|
| AGI_Cr3 | Amount in gut | mg | http://purl.obolibrary.org/obo/PBPKO_00496 |
| AGI_Cr6 | Amount in gut | mg | http://purl.obolibrary.org/obo/PBPKO_00496 |
| ALiver_Cr3 | Amount in liver | mg | http://purl.obolibrary.org/obo/PBPKO_00497 |
| ALiver_Cr6 | Amount in liver | mg | http://purl.obolibrary.org/obo/PBPKO_00497 |
| Aplasma_Cr3 | Amount in plasma | mg | http://purl.obolibrary.org/obo/PBPKO_00502 |
| Aplasma_Cr6 | Amount in plasma | mg | http://purl.obolibrary.org/obo/PBPKO_00502 |
| ARBC_Cr3 | Amount in red blood cells | mg | http://purl.obolibrary.org/obo/PBPKO_00623 |
| ARBC_Cr6 | Amount in red blood cells | mg | http://purl.obolibrary.org/obo/PBPKO_00623 |
| ARest_Cr3 | Amount in rest of body | mg | http://purl.obolibrary.org/obo/PBPKO_00501 |
| ARest_Cr6 | Amount in rest of body | mg | http://purl.obolibrary.org/obo/PBPKO_00501 |
| AFeces_Cr3 | Amount in feces | mg | http://purl.obolibrary.org/obo/PBPKO_00273 |
| AFeces_Cr6 | Amount in feces | mg | http://purl.obolibrary.org/obo/PBPKO_00273 |
Transfer equations
| id | from | to | equation |
|---|---|---|---|
| _J0 | AGI_Cr6 | AGI_Cr3 | kred_GI * AGI_Cr6 |
| _J1 | AGI_Cr6 | ALiver_Cr6 | AGI_Cr6 * kabs_Cr6 |
| _J2 | AGI_Cr3 | ALiver_Cr3 | AGI_Cr3 * kabs_Cr3 |
| _J3 | AGI_Cr6 | AFeces_Cr6 | kfe * AGI_Cr6 |
| _J4 | AGI_Cr3 | AFeces_Cr3 | kfe * AGI_Cr3 |
| _J5 | ALiver_Cr6 | ALiver_Cr3 | kred_Liver * ALiver_Cr6 |
| _J6 | ALiver_Cr6 | Aplasma_Cr6 | kt_Plasma_Cr6 * ALiver_Cr6 / VL |
| _J7 | ALiver_Cr3 | Aplasma_Cr3 | kt_Plasma_Cr3 * ALiver_Cr3 / VL |
| _J8 | Aplasma_Cr6 | Aplasma_Cr3 | kred_Plasma * Aplasma_Cr6 |
| _J9 | Aplasma_Cr6 | ALiver_Cr6 | kt_Tissues_Cr6 * Aplasma_Cr6 / Vplasma |
| _J10 | Aplasma_Cr3 | ALiver_Cr3 | kt_Tissues_Cr3 * Aplasma_Cr3 / Vplasma |
| _J11 | ARBC_Cr6 | ARBC_Cr3 | kred_RBC * ARBC_Cr6 |
| _J12 | Aplasma_Cr6 | ARBC_Cr6 | kt_Tissues_Cr6 * Aplasma_Cr6 / Vplasma |
| _J13 | Aplasma_Cr3 | ARBC_Cr3 | kt_Tissues_Cr3 * Aplasma_Cr3 / Vplasma |
| _J14 | ARBC_Cr3 | Aplasma_Cr3 | kt_Plasma_Cr3 * ARBC_Cr3 / VRBC |
| _J15 | ARBC_Cr6 | Aplasma_Cr6 | kt_Plasma_Cr6 * ARBC_Cr6 / VRBC |
| _J16 | ARest_Cr6 | Aplasma_Cr6 | kt_Plasma_Cr6 * ARest_Cr6 / VRest |
| _J17 | ARest_Cr3 | Aplasma_Cr3 | kt_Plasma_Cr3 * ARest_Cr3 / VRest |
| _J18 | Aplasma_Cr6 | ARest_Cr6 | kt_Tissues_Cr6 * Aplasma_Cr6 / Vplasma |
| _J19 | Aplasma_Cr3 | ARest_Cr3 | kt_Tissues_Cr3 * Aplasma_Cr3 / Vplasma |
ODEs
\(\frac{d[\mathtt{AGI-Cr3}]}{dt} = \mathit{kred_{GI}}\cdot \mathit{AGI_{Cr6}} - \mathit{AGI_{Cr3}}\cdot \mathit{kabs_{Cr3}} - \mathit{kfe}\cdot \mathit{AGI_{Cr3}}\)
\(\frac{d[\mathtt{AGI-Cr6}]}{dt} = - \mathit{kred_{GI}}\cdot \mathit{AGI_{Cr6}} - \mathit{AGI_{Cr6}}\cdot \mathit{kabs_{Cr6}} - \mathit{kfe}\cdot \mathit{AGI_{Cr6}}\)
\(\frac{d[\mathtt{ALiver-Cr3}]}{dt} = \mathit{AGI_{Cr3}}\cdot \mathit{kabs_{Cr3}} + \mathit{kred_{Liver}}\cdot \mathit{ALiver_{Cr6}} - \frac{\mathit{kt\_Plasma\_Cr3}\cdot \mathit{ALiver_{Cr3}}}{\mathit{VL}} + \frac{\mathit{kt\_Tissues\_Cr3}\cdot \mathit{Aplasma_{Cr3}}}{\mathit{Vplasma}}\)
\(\frac{d[\mathtt{ALiver-Cr6}]}{dt} = \mathit{AGI_{Cr6}}\cdot \mathit{kabs_{Cr6}} - \mathit{kred_{Liver}}\cdot \mathit{ALiver_{Cr6}} - \frac{\mathit{kt\_Plasma\_Cr6}\cdot \mathit{ALiver_{Cr6}}}{\mathit{VL}} + \frac{\mathit{kt\_Tissues\_Cr6}\cdot \mathit{Aplasma_{Cr6}}}{\mathit{Vplasma}}\)
\(\frac{d[\mathtt{Aplasma-Cr3}]}{dt} = \frac{\mathit{kt\_Plasma\_Cr3}\cdot \mathit{ALiver_{Cr3}}}{\mathit{VL}} + \mathit{kred_{Plasma}}\cdot \mathit{Aplasma_{Cr6}} - \frac{\mathit{kt\_Tissues\_Cr3}\cdot \mathit{Aplasma_{Cr3}}}{\mathit{Vplasma}} - \frac{\mathit{kt\_Tissues\_Cr3}\cdot \mathit{Aplasma_{Cr3}}}{\mathit{Vplasma}} + \frac{\mathit{kt\_Plasma\_Cr3}\cdot \mathit{ARBC_{Cr3}}}{\mathit{VRBC}} + \frac{\mathit{kt\_Plasma\_Cr3}\cdot \mathit{ARest_{Cr3}}}{\mathit{VRest}} - \frac{\mathit{kt\_Tissues\_Cr3}\cdot \mathit{Aplasma_{Cr3}}}{\mathit{Vplasma}}\)
\(\frac{d[\mathtt{Aplasma-Cr6}]}{dt} = \frac{\mathit{kt\_Plasma\_Cr6}\cdot \mathit{ALiver_{Cr6}}}{\mathit{VL}} - \mathit{kred_{Plasma}}\cdot \mathit{Aplasma_{Cr6}} - \frac{\mathit{kt\_Tissues\_Cr6}\cdot \mathit{Aplasma_{Cr6}}}{\mathit{Vplasma}} - \frac{\mathit{kt\_Tissues\_Cr6}\cdot \mathit{Aplasma_{Cr6}}}{\mathit{Vplasma}} + \frac{\mathit{kt\_Plasma\_Cr6}\cdot \mathit{ARBC_{Cr6}}}{\mathit{VRBC}} + \frac{\mathit{kt\_Plasma\_Cr6}\cdot \mathit{ARest_{Cr6}}}{\mathit{VRest}} - \frac{\mathit{kt\_Tissues\_Cr6}\cdot \mathit{Aplasma_{Cr6}}}{\mathit{Vplasma}}\)
\(\frac{d[\mathtt{ARBC-Cr3}]}{dt} = \mathit{kred_{RBC}}\cdot \mathit{ARBC_{Cr6}} + \frac{\mathit{kt\_Tissues\_Cr3}\cdot \mathit{Aplasma_{Cr3}}}{\mathit{Vplasma}} - \frac{\mathit{kt\_Plasma\_Cr3}\cdot \mathit{ARBC_{Cr3}}}{\mathit{VRBC}}\)
\(\frac{d[\mathtt{ARBC-Cr6}]}{dt} = - \mathit{kred_{RBC}}\cdot \mathit{ARBC_{Cr6}} + \frac{\mathit{kt\_Tissues\_Cr6}\cdot \mathit{Aplasma_{Cr6}}}{\mathit{Vplasma}} - \frac{\mathit{kt\_Plasma\_Cr6}\cdot \mathit{ARBC_{Cr6}}}{\mathit{VRBC}}\)
\(\frac{d[\mathtt{ARest-Cr3}]}{dt} = - \frac{\mathit{kt\_Plasma\_Cr3}\cdot \mathit{ARest_{Cr3}}}{\mathit{VRest}} + \frac{\mathit{kt\_Tissues\_Cr3}\cdot \mathit{Aplasma_{Cr3}}}{\mathit{Vplasma}}\)
\(\frac{d[\mathtt{ARest-Cr6}]}{dt} = - \frac{\mathit{kt\_Plasma\_Cr6}\cdot \mathit{ARest_{Cr6}}}{\mathit{VRest}} + \frac{\mathit{kt\_Tissues\_Cr6}\cdot \mathit{Aplasma_{Cr6}}}{\mathit{Vplasma}}\)
\(\frac{d[\mathtt{AFeces-Cr3}]}{dt} = \mathit{kfe}\cdot \mathit{AGI_{Cr3}}\)
\(\frac{d[\mathtt{AFeces-Cr6}]}{dt} = \mathit{kfe}\cdot \mathit{AGI_{Cr6}}\)
Assignment rules
| variable | assignment |
|---|---|
| VL | VLc * BW |
| Vplasma | 0.55 * VRBC / 0.45 |
| VRBC | VRBCc * BW |
| VRest | BW - VL - VRBC - Vplasma |
| CGI_Cr3 | AGI_Cr3 / GI |
| CGI_Cr6 | AGI_Cr6 / GI |
| CLiver_Cr3 | ALiver_Cr3 / Liver |
| CLiver_Cr6 | ALiver_Cr6 / Liver |
| CPlasma_Cr3 | Aplasma_Cr3 / Plasma |
| CPlasma_Cr6 | Aplasma_Cr6 / Plasma |
| CRBC_Cr3 | ARBC_Cr3 / RBC |
| CRBC_Cr6 | ARBC_Cr6 / RBC |
| CRest_Cr3 | ARest_Cr3 / Rest |
| CRest_Cr6 | ARest_Cr6 / Rest |
| CFeces_Cr3 | AFeces_Cr3 / Feces |
| CFeces_Cr6 | AFeces_Cr6 / Feces |
Initial assignments
| variable | assignment |
|---|---|
| Liver | VL |
| Plasma | Vplasma |
| RBC | VRBC |
| Rest | VRest |
Parameters
| id | name | unit | model qualifier |
|---|---|---|---|
| VL | Volume of liver | L | http://purl.obolibrary.org/obo/PBPKO_00077 |
| Vplasma | Volume of plasma | L | http://purl.obolibrary.org/obo/PBPKO_00103 |
| VRBC | Volume of red blood cells | L | http://purl.obolibrary.org/obo/PBPKO_00108 |
| VRest | Volume of rest of body | L | http://purl.obolibrary.org/obo/PBPKO_00105 |
| BW | Bodyweight | kg | http://purl.obolibrary.org/obo/PBPKO_00008 |
| VLc | Volume fraction of liver | dimensionless | http://purl.obolibrary.org/obo/PBPKO_00078 |
| VRBCc | Volume fraction of red blood cells | dimensionless | not specified |
| CGI_Cr3 | Concentration in gut | mg/L | http://purl.obolibrary.org/obo/PBPKO_00538 |
| CGI_Cr6 | Concentration in gut | mg/L | http://purl.obolibrary.org/obo/PBPKO_00538 |
| CLiver_Cr3 | Concentration in liver | mg/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CLiver_Cr6 | Concentration in liver | mg/L | http://purl.obolibrary.org/obo/PBPKO_00539 |
| CPlasma_Cr3 | Concentration in plasma | mg/L | http://purl.obolibrary.org/obo/PBPKO_00549 |
| CPlasma_Cr6 | Concentration in plasma | mg/L | http://purl.obolibrary.org/obo/PBPKO_00549 |
| CRBC_Cr3 | Concentration in red blood cells | mg/L | http://purl.obolibrary.org/obo/PBPKO_00301 |
| CRBC_Cr6 | Concentration in red blood cells | mg/L | http://purl.obolibrary.org/obo/PBPKO_00301 |
| CRest_Cr3 | Concentration in rest of body | mg/L | http://purl.obolibrary.org/obo/PBPKO_00548 |
| CRest_Cr6 | Concentration in rest of body | mg/L | http://purl.obolibrary.org/obo/PBPKO_00548 |
| CFeces_Cr3 | Concentration in feces | mg/L | not specified |
| CFeces_Cr6 | Concentration in feces | mg/L | not specified |
| kabs_Cr6 | Rate constant for absorption of Cr(VI) from the GI tract | mg/d | http://purl.obolibrary.org/obo/PBPKO_00141 |
| kabs_Cr3 | Rate constant for absorption of Cr(III) from the GI tract | mg/d | http://purl.obolibrary.org/obo/PBPKO_00141 |
| kt_Plasma_Cr6 | Clearance of diffusible Cr(VI) from all other tissues into plasma (L/da) | L/d | not specified |
| kt_Plasma_Cr3 | Clearance of diffusible Cr(III) from all other tissues into plasma (L/da) | L/d | not specified |
| kt_Tissues_Cr6 | Clearance of diffusible Cr(VI) from plasma into all tissues (L/da) | L/d | not specified |
| kt_Tissues_Cr3 | Clearance of diffusible Cr(III) from plasma into all tissues (L/da) | L/d | not specified |
| kred_GI | Rate constant for reduction of Cr(VI) to Cr(III) in GI | mg/d | not specified |
| kred_Liver | Rate constant for reduction of Cr(VI) to Cr(III) in GI | mg/d | not specified |
| kred_RBC | Rate constant for reduction of Cr(VI) to Cr(III) in plasma | mg/d | not specified |
| kred_Plasma | Rate constant of reduction in plasma | mg/d | not specified |
| kfe | First-order rate constant for passage of Cr out of the absorption region of the GI tract | /d | not specified |