Human PBPK model for dioxin: Difference between revisions
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=== Tuomisto et al === | === Tuomisto et al === | ||
This model is based on one-compartment kinetics with a dioxin intake trend (r %/a decrease). The amount of dioxin in the body now (m<sub> | This model is based on one-compartment kinetics with a dioxin intake trend (r %/a decrease). t<sub>i</sub> means the distance in time between timepoint i (in the history) and now. The amount of dioxin in the body now (m<sub>n</sub>) from a dose d<sub>i</sub> at timepoint i is calculated as follows, if the dose during time decreases at a constant rate r: | ||
:<math> | :<math>m_n = d_i e^{-k t_i} = d_n e^{r t_i} e^{-k t_i} = d_n e^{(r-k) t_i}.</math> | ||
The total amount of dioxin M<sub> | The total amount of dioxin M<sub>n</sub> from all doses during the time period is | ||
:<math> | :<math>M_n = \Sigma_{i=1}^n d_n e^{(r-k) t_i} = \int_0^n d_n e^{(r-k) t}dt | ||
= | = d_n \frac{e^{(r-k) t}}{r-k} - d_n \frac{e^{(r-k) 0}}{r-k} = \frac{d_n}{r-k} (e^{(r-k) t}-1).</math> | ||
There may also be previous dioxin load at t<sub>i</sub>, and this is denoted m<sub>i</sub>: | There may also be previous dioxin load at t<sub>i</sub>, and this is denoted m<sub>i</sub>: | ||
:<math> | :<math>M_n = \frac{d_n}{r-k} (e^{(r-k) t}-1) + m_i e^{-k t}.</math> | ||
Also, there may be a breast feeding period during the observed time span | |||
:<math> | :<math>M_n = (\frac{d_n}{r-k} (e^{(r-k) t}-1) + m_i e^{-k t}) (1 - (1-e^{-k_B t_B})(e^{-k t_S})),</math> | ||
where d<sub> | where k<sub>B</sub> is the elimination constant caused by breast feeding, t<sub>B</sub> is the duration of breast feeding, and t<sub>S</sub> is the time since the breast feeding. | ||
If the intake is constant and there is no breast feeding, this simplifies into | |||
:<math>M_n = \frac{d_n}{k} (1 - e^{-k t}) + m_i e^{-k t},</math> | |||
where d<sub>n</sub>/k is the steady state amount at constant intake, (1 - e<sup>-k t</sup>) is the relative deviation from the steady state, and m<sub>i</sub> e<sup>-k t</sup> is the additional burden from before. | |||
;Assumptions | ;Assumptions | ||
Revision as of 14:42, 13 January 2015
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Question
How to calculate dioxin concentrations in human tissues after a given exposure pattern?
Answer
These are several approaches available.
Tuomisto et al model
- This model was previously on page Dioxin.
| Obs | Congener | Market basket | TEF | Elimination constant | Half life |
|---|---|---|---|---|---|
| 1 | TCDD | 2 | 1 | 0.00026 | 7.3 |
| 2 | 12378PeCDD | 2 | 1 | 0.00017 | 11.2 |
| 3 | 123678HxCDD | 5 | 0.1 | 0.000145 | 13.1 |
| 4 | 1234678HpCDD | 7 | 0.001 | 0.00039 | 4.9 |
| 5 | OCDD | 60 | 0.0003 | 0.00028 | 6.8 |
| 6 | TCDF | 8 | 0.1 | 0.0009 | 2.1 |
| 7 | 23478PeCDF | 16 | 0.3 | 0.00027 | 7.0 |
Dioxin kinetics with Bayes
Aylward et al model
TOXI/INERIS model
| Dioxin PBPK model |
|---|
| The results are total amounts (ng) of dioxin, except blood concentration (ng/l). |
The input data used for this variable:
|
Rationale
Tuomisto et al
This model is based on one-compartment kinetics with a dioxin intake trend (r %/a decrease). ti means the distance in time between timepoint i (in the history) and now. The amount of dioxin in the body now (mn) from a dose di at timepoint i is calculated as follows, if the dose during time decreases at a constant rate r:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_n = d_i e^{-k t_i} = d_n e^{r t_i} e^{-k t_i} = d_n e^{(r-k) t_i}.}
The total amount of dioxin Mn from all doses during the time period is
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_n = \Sigma_{i=1}^n d_n e^{(r-k) t_i} = \int_0^n d_n e^{(r-k) t}dt = d_n \frac{e^{(r-k) t}}{r-k} - d_n \frac{e^{(r-k) 0}}{r-k} = \frac{d_n}{r-k} (e^{(r-k) t}-1).}
There may also be previous dioxin load at ti, and this is denoted mi:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_n = \frac{d_n}{r-k} (e^{(r-k) t}-1) + m_i e^{-k t}.}
Also, there may be a breast feeding period during the observed time span
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_n = (\frac{d_n}{r-k} (e^{(r-k) t}-1) + m_i e^{-k t}) (1 - (1-e^{-k_B t_B})(e^{-k t_S})),}
where kB is the elimination constant caused by breast feeding, tB is the duration of breast feeding, and tS is the time since the breast feeding.
If the intake is constant and there is no breast feeding, this simplifies into
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M_n = \frac{d_n}{k} (1 - e^{-k t}) + m_i e^{-k t},}
where dn/k is the steady state amount at constant intake, (1 - e-k t) is the relative deviation from the steady state, and mi e-k t is the additional burden from before.
- Assumptions
- WHO-TEQ intake 57 pg/d average (Kiviranta et al, Env Int 2004:30:923)
- low intake 40 pg/d (42,05)
- high intake 160 pg/d (168,2)
- Average distribution 56 pg/d animal products, 1 pg/d plant products (ibid)
- low intake 39 pg/d animal products, 1 pg/d plant products
- high intake 157 pg/d animal products, 3 pg/d plant products
- Congener distribution as pg TEQ (rounded)
- low intake TCDD 7,9, 12378PCDD 7,9, 123678HxCDD 2, 1234678HpCDD 0,03, OCDD 0,07, TCDF 3,2, 23478PeCDF 19 pg/d WHO-TEQ
- high intake TCDD 32, 12378PCDD 32, 123678HxCDD 8, 1234678HpCDD 0,1, OCDD 0,3, TCDF 12,6, 23478PeCDF 76 pg/d WHO-TEQ
- Congener distribution as pg (rounded, rounded numbers used in other sheets)
- low intake TCDD 7,9, 12378PCDD 7,9, 123678HxCDD 20, 1234678HpCDD 28, OCDD 237, TCDF 32, 23478PeCDF 63 pg/d
- high intake TCDD 32, 12378PCDD 32, 123678HxCDD 80, 1234678HpCDD 111, OCDD 948, TCDF 126, 23478PeCDF 253 pg/d
- Congener elimination constants (d-1) TCDD 0,00026, 12378PCDD 0,00017, 123678HxCDD 0,000145, 1234678HpCDD 0,00039, OCDD 0,00028, TCDF 0,0009, 23478PeCDF 0,00027
- Half lives from Milbrath et al., Environ. Health Persp. 2009:117:417-425
TOXI/INERIS
Basic info
| Last modification: | 04/07/2007 | Model version : | |
| Software status : | Free software | OS : | Linux |
| Supplier : | INERIS | Installation : | See source |
| Possible developments : | yes | Source : | TOXI/INERIS web site [3] |
| Supplier address: | INERIS Verneuil en Halatte, France | Referent(s)* : | S. MICALLEF (INERIS)
Sandrine.micallef@ineris.fr |
Discipline : keywords: toxicokinetic model, 2,3,7,8-tétra-chloro-p-dioxin (TCDD), PBPK
Scope of the mode
Physiologically Based Toxicokinetic (PBTK) model for Dioxine. The presented PBTK model allows to simulate ingestion exposures to 2,3,7,8-tétra-chloro-p-dioxin (TCDD) for a woman over her whole life. TCDD is a persistent chemical found in trace amounts all over the globe. It accumulates in animal fat all along the trophic chain. Human exposure to TCDD is therefore almost unavoidable, even if in trace amounts. TCDD has multiple effects on health.
Model description
The proposed model is based on a previous one proposed by van der Molen and colleagues in 1996[4]. The model computes various measures of internal dose as a function of time. The superposition of a peak exposure to a time-varying background intake can be described. All ingested TCDD is supposed to be absorbed. TCDD is supposed to distribute between blood, fat, muscles and skin, and viscera. The model equations are solved dynamically (by numerical integration) with the MCSim simulation package to give a good precision both on short-term and long-term scales. The body mass and the volume of the various body tissues change with the age of the simulated individual.
Figure 1 : Toxicokinetic model used to describe TCDD toxicokinetic in the human body[4]. compartments are characterized with volume V and partition coefficient P. Exchanges between are governed by blood flows, F. Elimination is assumed proportional to the elimination constant, ke. The set value of each parameter is given in Table 1. The ingested quantity by unit of time ki (in ng/min), is determined by the exposure scenario.
Table 1 : Numerical values of the parameters of the toxicokinetic model for TCDD in the woman.
| Parameter(a) | Symbol | Numerical Value |
| Ventilation rate | Fp | 8,0 |
| Blood over air ventilation rate | R | 1,14 |
| Blood flow rates | ||
| Fat | Ff | 0,09 |
| Liver | Fl | 0,24 |
| Muscles and skin | fm | 0,18 |
| Viscera | fv | – (b) |
| Volumes | ||
| Total body volume | Vt | – (c) |
| Fat | Vf | – (c) |
| Liver | Vl | – (c) |
| Muscles and skin | Vm | – (c) |
| Viscera | Vv | – (c) |
| Partition Coefficient | ||
| Fat | Pf | 300 |
| Liver | Pl | 25 |
| Muscles and skin | Pm | 4 |
| Viscera | Pv | 10 |
| Elimination constant | ke | 8,45?10-8 (d) |
(a) Units : volumes (L), blood flow (L/min), et elimination constant (min-1). (b) Blood flow rate to viscera is calculated by difference between 1 and the sum of blood flow rates toward the other compartments. (c) Volumes evolve with time. (d) Corresponds to a half-life of 15,6 years.
Figure 1 gives a graphical representation of the model used. Only ingestion exposure is described in this model (the totality of the exposure dose is assumed to be absorbed). The TCDD is supposed to be distributed into different compartments of the body : blood, fat, muscles and skin. The original formulation of van der Molen and coll.[4] regards all these compartments as being with balance in an instantaneous way. This assumption is acceptable only if slow evolutions of absorption are the limiting factor of the kinetics of the product. Since the simulation of a short peak of exposure interests us, we developed a traditional dynamic formulation[5], specifies at the same time on short scales of time and the long-term.
Model equations Equations defining the proposed model are the following : For quantites of TCDD in fat, viscera, muscle and skin, and liver : (1) (2) (3) (4) La concentration artérielle est calculée par : (5)
The cardiac output, Ft, is proportinal to the ventilation rate, Fp : (1) The body volume evolve as a function of age : (6) The volume of fat, viscera, liver also evolve as a function of age[4]: (7) (8) (9) Volume of "muscles and skin" compartment is calculated as the difference between 90% of the total body volume (because bones are not included) and the other compartments : (10) Units used are : quantities of TCDD are expressed in ng, TCDD concentrations in ng/L, age in years volumes in liter, flows in L/min, the elimination constant in min-1, the ingested quantity by unit of time in ng/min. The body density is assumed equal to 1.
Figure 2 presents the temporal evolution of these parameters for a woman (the evolution is overall similar for a man). The reference averaged values used for the parameters not evolving with time are given in Table 1. The equations of the model were coded using the MCSim software[6].
Figure 2 : Temporal evolution of volumes for the woman[4].
Validation
To be done
Applications examples
Example of the use of this model can be found in the paper by Bois[7]
See also
- Van der Molen GW, Kooijman BALM, Wittsiepe J, et al. Estimation of dioxin and furan elimination rates with a pharmacokinetic model
JOURNAL OF EXPOSURE ANALYSIS AND ENVIRONMENTAL EPIDEMIOLOGY 10 (6): 579-585 Part 1 NOV-DEC 2000.
- Van der Molen GW, Kooijman SALM, Michalek JE, et al. The estimation of elimination rates of persistent compounds: A re-analysis of 2,3,7,8-tetrachlorodibenzo-p-dioxin levels in Vietnam veterans CHEMOSPHERE 37 (9-12): 1833-1844 OCT-NOV 1998.
Model inputs
All intakes are given in ng/min. A typical unit is pg/d; to change from the latter to the former, divide by 1440000.
Background exposure parameters:
- dose1: intake of dioxin during age 0 - 5 years
- dose2: intake of dioxin during age 5 - 10 years
- dose3: intake of dioxin during age 10 -15 years
- dose4: intake of dioxin during age 15 - 40 years
- dose5: intake of dioxin during age 40 - years
Peak exposure parameters (in addition to the background)
- peakstart: start of the peak exposure period (in days of age)
- peakend: end of the peak exposure period (in days of age)
- peakdose: Additional intake of dioxin during the peak period (in ng/min)
References
- ↑ Aylward LL et al. (2005a) Concentration-dependent TCDD eliminationi kinetics in humans: toxicokinetic modeling for moderately to highly exposed adults from Seveso, Italy, and Vienna, Austria, and impact on dose estimates for the NIOSH cohort. Journal of Exposure Analysis and Environmental Epidemiology 15: 51-65.
- ↑ Aylward LL et al. (200b) Exposure reconstruction for the TCDD-exposed NIOSH cohort using a concentration- and age-dependent model of elimination. Risk Analysis 25: 4: 945-956.
- ↑ http://toxi.ineris.fr/activites/toxicologie_quantitative/toxicocinetique/modeles/dioxine/sub_dioxine.php
- ↑ 4.0 4.1 4.2 4.3 4.4 Van der Molen, G. W., S. A. L. M. Kooijman and W. Slob (1996). "A generic toxicokinetic model for persistent lipophilic compounds in humans: an application to TCDD." Fundamental and Applied Toxicology 31: 83-94.
- ↑ Gerlowski, L. E. and R. K. Jain (1983). "Physiologically based pharmacokinetic modeling: principles and applications." Journal of Pharmaceutical Sciences 72: 1103-1127.
- ↑ Bois, F. Y. and D. Maszle (1997). "MCSim: a simulation program." Journal of Statistical Software 2(9): [1].
- ↑ Bois, F. Y. (2003). "Modélisation toxicocinétique de la concentration sanguine de 2,3,7,8-tetrachloro-p-dioxine après ingestion chez la femme." Environnement, Risques et Santé 2(1). [Toxicokinetic modelling of 2,3,7,8-tétrachloro-p-dioxin blood concentration after ingestion by women. Environnement, Risque et Santé, (2003) 2:45-53. ]