Available kinetic models

Physiologically based kinetic (PBK) models, or kinetic models for short, are mathematical representations of the animal or human body aimed at describing and predicting the time course distribution of chemicals in tissues and organs. Those internal dose metrics can usefully replace external exposure dose in the derivation of the quantitative dose-response relationships and following risk assessments. PBK models can simulate both internal doses from exposure scenarios (forward dosimetry) and external dose from biomonitoring data (reverse dosimetry).

The following generic PBK models are currently implemented in MCRA:

• EuroMix generic PBK model (Tebby et al. (2020)).

• bisphenol PBK model ETHZ (Karrer et al. (2019)).

The MCRA interface allows to run PBK models for any number of days and supplies an option to skip an initial number of days (build-up phase PBK model) in the calculation of the internal exposure.

In the original bisphenol PBK model of Karrer et al. (2019), doses were applied on fixed time points and only for the first four days. For oral exposure, three dosings per day with t = 0, 6 and 12 h, for dermal exposure to PCPs and TP, two dosings per day with t = 0 and 12 h. The steady state was reached after dosing on four consecutive days. Therefore, the bisphenol PBK model described in Karrer et al. should be run for four days to reached steady state and the number of initial days to be skipped should be set to 0. Note, no dosing is applied from day 5th onwards.

These restrictions were relaxed in a new implementation of the bisphenol PBK model (General Model BPA Re-implementation). In this new version the number of days is unlimited. Dosings are specified through the user interface including the definition on the non-stationary period, see settings kinetic models.

EuroMix Generic PBTK model v5

Cosmos version 5 (adapted 9/11/2018)

Model aliases: Cosmos4, CosmosV4, Cosmos5, CosmosV5.

Table 185 Exposure routes (forcings)

Id	Description	Unit	Order
Dietary	Dietary exposure	mmoles	0
Dermal	Dermal exposure	mmoles	1
Inhalation	Inhalatory exposure	mmoles	2

Table 186 Output

Id	Description	ScalingFactor	MultiplicationFactor	Unit	Order
CVen	Venous blood	scVBlood	0.66667	mM	0
CArt	Arterial blood	scVBlood	0.33333	mM	1
CFat	Fat tissues	scVFat		mM	2
CPoor	Muscle tissues			mM	3
CRich	Viscera	scVRich		mM	4
CLiver	Liver	scVLiver		mM	5
CSkin_u	Viable skin, unexposed			mM	6
CSkin_e	Viable skin, exposed	BSA, Height_vs, fsA_exposed		mM	7
CSkin_sc_u	Skin stratum corneum, unexposed			mM	8
CSkin_sc_e	Skin stratum corneum, exposed	BSA, Height_vs, fsA_exposed		mM	9

Table 187 Input

Id	Description	Unit	Type	Order
BM	Body mass	kg	Physiological	0
BSA	Body skin surface area	dm2	Physiological	1
scVFat	Fat as fraction of total body volume		Physiological	2
scVRich	Richly perfused tissues (viscera) as fraction of total body volume		Physiological	3
scVLiver	Liver as fraction of total body volume		Physiological	4
scVBlood	Blood as fraction of total body volume		Physiological	5
Height_sc	Skin thickness	decimeter	Physiological	6
Height_vs	Viable skin		Physiological	7
scFBlood	Total blood flow per unit mass	L/h/kg	Physiological	8
scFFat	Fat fraction of total blood flow going to compartments		Physiological	9
scFPoor	Poorly perfused tissues (muscles) fraction of total blood flow going to compartments		Physiological	10
scFLiver	Liver fraction of total blood flow going to compartments		Physiological	11
scFSkin	Skin fraction of total blood flow going to compartments		Physiological	12
Falv	Alveolar ventilation rate	L/h	Physiological	13
mic	Microsomal proteins content	mg/gr liver	Physiological	14
PCAir	Partition coefficient: blood over air		Partition coefficient	15
log_PCFat	Scaled parameter, partition coefficient: fat over blood		Partition coefficient	16
log_aPoor	Scaled parameter, partition coefficient: muscle over blood (poorly perfused tissue)		Partition coefficient	17
log_aRich	Scaled parameter, partition coefficient: viscera over blood (richly perfused tissue)		Partition coefficient	18
log_aLiver	Scaled parameter, partition coefficient: liver over blood		Partition coefficient	19
log_aSkin	Scaled parameter, partition coefficient: viable skin / blood		Partition coefficient	20
log_aSkin_sc	Scaled parameter, partition coefficient: viable skin / stratum corneum		Partition coefficient	21
Kp_sc_vs	Diffusion rate from stratum corneum to viable skin	decimeter/h	Metabolic	22
Ke	Renal excretion rate	L/h	Metabolic	23
Michaelis	Flag for Michaelis-Menten vs linear metabolism (0 = linear)		Metabolic	24
Vmax	Maximum rate of metabolism	mmoles/h/L liver	Metabolic	25
Km	Michaelis-Menten constant	mM	Metabolic	26
CLH	Hepatic clearance		Metabolic	27
fup	Unbound fraction in blood		Metabolic	28
Frac	Fraction absorbed by the gut		Metabolic	29
kGut	Oral 1st order absorption rate constant	1/h	Metabolic	30
Cinh	Inhalation		Metabolic	31
Tinh	Inhalation duration		Metabolic	32
fSA_exposed	Fraction of skin surface area actually exposed		Metabolic	35

EuroMix Generic PBTK model v6

Cosmos version 6 (received 3/27/2019)

Model aliases: Cosmos6, CosmosV6.

Table 188 Exposure routes (forcings)

Id	Description	Unit	Order
Dietary	Dietary exposure	mmoles	0
Dermal	Dermal exposure	mmoles	1
Inhalation	Inhalatory exposure	mmoles	2

Table 189 Output

Id	Description	ScalingFactor	MultiplicationFactor	Unit	Order
CTotal	Total concentration			mM	0
CVen	Venous blood concentration	scVBlood	0.66667	mM	1
CArt	Arterial blood concentration	scVBlood	0.33333	mM	2
CFat	Fat (adipose) tissue concentration	scVFat		mM	3
CPoor	Poorly perfused tissue (muscle) concentration			mM	4
CRich	Richly perfused tissue (viscera) concentration	scVRich		mM	5
CLiver	Liver concentration	scVLiver		mM	6
CSkin_u	Viable unexposed skin concentration			mM	7
CSkin_e	Viable exposed skin concentration	BSA, Height_vs, fsA_exposed		mM	8
CSkin_sc_u	Skin unexposed stratum corneum concentration			mM	9
CSkin_sc_e	Skin exposed stratum corneum concentration	BSA, Height_vs, fsA_exposed		mM	10

Table 190 Input

Id	Description	Unit	Type	Order
BM	Body mass	kg	Physiological	0
BSA	Body surface area (internally scaled by an allometric scaling factor s = 70/BM^0.3)	dm2	Physiological	1
scVFat	Fat as fraction of total body volume		Physiological	2
scVRich	Richly perfused tissues (viscera) as fraction of total body volume		Physiological	3
scVLiver	Liver as fraction of total body volume		Physiological	4
scVBlood	Blood as fraction of total body volume		Physiological	5
Height_sc	Skin thickness	decimeter	Physiological	6
Height_vs	Viable skin		Physiological	7
scFBlood	Total blood flow per unit mass	L/h/kg	Physiological	8
scFFat	Fat fraction of total blood flow going to compartments		Physiological	9
scFPoor	Poorly perfused tissues (muscles) fraction of total blood flow going to compartments		Physiological	10
scFLiver	Liver fraction of total blood flow going to compartments		Physiological	11
scFSkin	Skin fraction of total blood flow going to compartments		Physiological	12
Falv	Alveolar ventilation rate	L/h	Physiological	13
mic	Microsomal proteins content	mg/gr liver	Physiological	14
Kp_sc_vs	Diffusion rate from stratum corneum to viable skin	decimeter/h	Metabolic	22
Ke	Renal excretion rate	L/h	Metabolic	23
Michaelis	Flag for Michaelis-Menten vs linear metabolism (0 = linear)		Metabolic	24
Vmax	Maximum rate of metabolism	mmoles/h/L liver	Metabolic	25
Km	Michaelis-Menten constant for metabolism	mM	Metabolic	26
CLH	Hepatic metabolic clearance		Metabolic	27
fub	Unbound fraction in blood		Metabolic	28
Frac	Fraction absorbed by the gut		Metabolic	29
kGut	Oral 1st order absorption rate constant	1/h	Metabolic	30
Tinh	Inhalation duration		Metabolic	32
fSA_exposed	Fraction of skin surface area actually exposed		Metabolic	35
PCFat	Partition coefficient: fat over blood		Partition coefficient	55
PCPoor	Partition coefficient: muscle over blood (poorly perfused tissue)		Partition coefficient	56
PCRich	Partition coefficient: viscera over blood (richly perfused tissue)		Partition coefficient	57
PCLiver	Partition coefficient: liver over blood		Partition coefficient	58
PCSkin	Partition coefficient: viable skin over blood		Partition coefficient	59
PCSkin_sc	Partition coefficient: viable skin / stratum corneum		Partition coefficient	60

Generic Model BPA Re-implementation

Generic model Cecile Karrer, adapted by Waldo de Boer 22 april 2022

Model aliases: PBPKModel_BPAReimplemented.

Table 191 Exposure routes (forcings)

Id	Description	Unit	Order
Dietary	Dietary exposure	nmoles	0
Oral	Oral exposure	nmoles	1
Dermal	Dermal exposure	nmoles	2
Inhalation	Inhalation exposure	nmoles	3

Table 192 Output

Id	Description	ScalingFactor	MultiplicationFactor	Unit	Order
CPlasmaOut	Concentration in plasma			nmol/L	0
CGonadOut	Concentration in gonads			nmol/L	1
AurinebpaOut	Cumulative excretion of BPA in urine			nmol/L	2
AurinegOut	Cumulative excretion of BPA-g in urine			nmol/L	3
AurineTotalOut	Cumulative excretion of BPA and metabolites in urine			nmol/L	4

Table 193 Input

Id	Description	Unit	Type	Order
BW	Bodyweight	kg	Physiological	0
QCC	Cardiac output	L/min	Physiological	1
QgonadC	Fractional blood flow to gonads		Physiological	2
QliverC	Fractional blood flow to liver		Physiological	3
QfatC	Fractional blood flow to fat tissue		Physiological	4
QbrainC	Fractional blood flow to brain		Physiological	5
QskinC	Fractional blood flow to skin		Physiological	6
QmuscleC	Fractional blood flow to gonads		Physiological	7
VplasmaC	Fractional volume of plasma		Physiological	8
VfatC	Fractional volume of fat tissue		Physiological	9
VliverC	Fractional volume of liver tissue		Physiological	10
VbrainC	Fractional volume of brain tissue		Physiological	11
VskinC	Fractional volume of skin tissue		Physiological	12
VgonadC	Fractional volume of gonads		Physiological	13
VmuscleC	Fractional volume of muscle tissue		Physiological	14
VrichC	Fractional volume of richly perfused tissue		Physiological	15
VbodygC	Distribution volume of BPA-g		Physiological	16
pliver	Partition coefficient liver to blood		Partition coefficient	18
pfat	Partition coefficient fat to blood		Partition coefficient	19
pslow	Partition coefficient slowly perfused tissue to blood		Partition coefficient	20
prich	Partition coefficient richly perfused tissue to blood		Partition coefficient	21
pgonad	Partition coefficient gonads to blood		Partition coefficient	22
pbrain	Partition coefficient brain to blood		Partition coefficient	23
pskin	Partition coefficient skin to blood		Partition coefficient	24
geC	Gastric emptying	1/h/kg bw^-0.25	Metabolic	25
k0C	Oral uptake from the stomach into the liver	1/h/kg bw^-0.25	Metabolic	26
k1C	Oral uptake from the small intestine into the liver	1/h/kg bw^-0.25	Metabolic	27
k4C	Fecal elimination from small intestine after oral administration	1/h/kg bw^-0.25	Metabolic	28
kGIingC	Transport of glucuronide from enterocytes into serum	1/h/kg bw^-0.25	Metabolic	29
kGIinsC	Transport of sulfate from enterocytes into serum	1/h/kg bw^-0.25	Metabolic	30
kmgutg	Km of Glucuronidation in the gut	nM	Metabolic	31
vmaxgutgC	Vmax of Glucuronidation in the gut	nmol/h/kg bw	Metabolic	32
fgutg	Correction factor of glucuronidation in the gut		Metabolic	33
kmguts	Km of Sulfation in the gut	nM	Metabolic	34
vmaxgutsC	Vmax of Sulfation in the gut	nmol/h/kg bw	Metabolic	35
fguts	Correction factor of sulfation in the gut		Metabolic	36
met1g	Fraction of glucuronide in the liver taken up directly into serum (the rest undergoes EHR)		Metabolic	37
met1s	Fraction of sulfate in the liver taken up directly into serum		Metabolic	38
enterocytes	Sum of enterocytes weights in duodenum, jejunum and ileum	L	Metabolic	39
kmliver	Km of Glucuronidation in the liver	nM	Metabolic	40
vmaxliverC	Vmax of Glucuronidation in the liver	nmol/h/g liver	Metabolic	41
fliverg	Correction factor of glucuronidation in the liver		Metabolic	42
kmlivers	Km of Sulfation in the liver	nM	Metabolic	43
vmaxliversC	Vmax of Sulfation in the liver	nmol/h/g liver	Metabolic	44
flivers	Correction factor of sulfation in the liver		Metabolic	45
EHRtime	Time until EHR occurs	h	Metabolic	46
EHRrateC	EHR of glucuronide	1/h/kg bw^-0.25	Metabolic	47
k4C_IV	Fecal elimination of glucuronide from the EHR compartment	1/h/kg bw^-0.25	Metabolic	48
kurinebpaC	Clearance, urine excretion of parent compound	L/h/kg bw^0.75	Metabolic	49
kurinebpagC	Clearance, urine excretion of glucuronide	L/h/kg bw^0.75	Metabolic	50
kurinebpasC	Clearance, urine excretion of sulfate	L/h/kg bw^0.75	Metabolic	51
vreabsorptiongC	Vmax for renal reabsorption of glucuronide	nmol/h/kg bw^0.75	Metabolic	52
vreabsorptionsC	Vmax for renal reabsorption of sulfate	nmol/h/kg bw^0.75	Metabolic	53
kreabsorptiong	Km for renal reabsorption of glucuronide	nM	Metabolic	54
kreabsorptions	Km for renal reabsorption of sulfate	nM	Metabolic	55
kenterobpagC	EHR of parent compound due to biliary excretion of glucuronide	1/h/kg bw^-0.25	Metabolic	56
kenterobpasC	EHR of parent compound due to biliary excretion of sulfate	1/h/kg bw^-0.25	Metabolic	57
EoA_D	Extent of dermal absorption from TP		Physiological	59
aHL_D	Half-life for dermal penetration	h	External	60
EoA_D2	Extent of dermal absorption from PCPs		Physiological	62
aHL_D2	Half-life for dermal penetration from PCPs	h	External	63

Generic Model BPA

Generic model Cecile Karrer 23 juli 2018

Model aliases: PBPKModel_BPA, PBPKModelBPA, ModelBPA, BPA.

Table 194 Exposure routes (forcings)

Id	Description	Unit	Order
Dietary	Dietary exposure	nmoles	0
Oral	Oral exposure	nmoles	1
Dermal	Dermal exposure	nmoles	2
Inhalation	Inhalation exposure	nmoles	3

Table 195 Output

Id	Description	ScalingFactor	MultiplicationFactor	Unit	Order
CPlasmaOut	Concentration in plasma			nmol/L	0
CGonadOut	Concentration in gonads			nmol/L	1
AurinebpaOut	Cumulative excretion of BPA in urine			nmol/L	2
AurinegOut	Cumulative excretion of BPA-g in urine			nmol/L	3
AurineTotalOut	Cumulative excretion of BPA and metabolites in urine			nmol/L	4

Table 196 Input

Id	Description	Unit	Type	Order
BW	Bodyweight	kg	Physiological	0
QCC	Cardiac output	L/min	Physiological	1
QgonadC	Fractional blood flow to gonads		Physiological	2
QliverC	Fractional blood flow to liver		Physiological	3
QfatC	Fractional blood flow to fat tissue		Physiological	4
QbrainC	Fractional blood flow to brain		Physiological	5
QskinC	Fractional blood flow to skin		Physiological	6
QmuscleC	Fractional blood flow to gonads		Physiological	7
VplasmaC	Fractional volume of plasma		Physiological	8
VfatC	Fractional volume of fat tissue		Physiological	9
VliverC	Fractional volume of liver tissue		Physiological	10
VbrainC	Fractional volume of brain tissue		Physiological	11
VskinC	Fractional volume of skin tissue		Physiological	12
VgonadC	Fractional volume of gonads		Physiological	13
VmuscleC	Fractional volume of muscle tissue		Physiological	14
VrichC	Fractional volume of richly perfused tissue		Physiological	15
VbodygC	Distribution volume of BPA-g		Physiological	16
MW	Molecular weight	g/mol	Chemical property	18
pliver	Partition coefficient liver to blood		Partition coefficient	19
pfat	Partition coefficient fat to blood		Partition coefficient	20
pslow	Partition coefficient slowly perfused tissue to blood		Partition coefficient	21
prich	Partition coefficient richly perfused tissue to blood		Partition coefficient	22
pgonad	Partition coefficient gonads to blood		Partition coefficient	23
pbrain	Partition coefficient brain to blood		Partition coefficient	24
pskin	Partition coefficient skin to blood		Partition coefficient	25
geC	Gastric emptying	1/h/kg bw^-0.25	Metabolic	26
k0C	Oral uptake from the stomach into the liver	1/h/kg bw^-0.25	Metabolic	27
k1C	Oral uptake from the small intestine into the liver	1/h/kg bw^-0.25	Metabolic	28
k4C	Fecal elimination from small intestine after oral administration	1/h/kg bw^-0.25	Metabolic	29
kGIingC	Transport of glucuronide from enterocytes into serum	1/h/kg bw^-0.25	Metabolic	30
kGIinsC	Transport of sulfate from enterocytes into serum	1/h/kg bw^-0.25	Metabolic	31
kmgutg	Km of Glucuronidation in the gut	nM	Metabolic	32
vmaxgutgC	Vmax of Glucuronidation in the gut	nmol/h/kg bw	Metabolic	33
fgutg	Correction factor of glucuronidation in the gut		Metabolic	34
kmguts	Km of Sulfation in the gut	nM	Metabolic	35
vmaxgutsC	Vmax of Sulfation in the gut	nmol/h/kg bw	Metabolic	36
fguts	Correction factor of sulfation in the gut		Metabolic	37
met1g	Fraction of glucuronide in the liver taken up directly into serum (the rest undergoes EHR)		Metabolic	38
met1s	Fraction of sulfate in the liver taken up directly into serum		Metabolic	39
enterocytes	Sum of enterocytes weights in duodenum, jejunum and ileum	L	Metabolic	40
kmliver	Km of Glucuronidation in the liver	nM	Metabolic	41
vmaxliverC	Vmax of Glucuronidation in the liver	nmol/h/g liver	Metabolic	42
fliverg	Correction factor of glucuronidation in the liver		Metabolic	43
kmlivers	Km of Sulfation in the liver	nM	Metabolic	44
vmaxliversC	Vmax of Sulfation in the liver	nmol/h/g liver	Metabolic	45
flivers	Correction factor of sulfation in the liver		Metabolic	46
EHRtime	Time until EHR occurs	h	Metabolic	47
EHRrateC	EHR of glucuronide	1/h/kg bw^-0.25	Metabolic	48
k4C_IV	Fecal elimination of glucuronide from the EHR compartment	1/h/kg bw^-0.25	Metabolic	49
kurinebpaC	Clearance, urine excretion of parent compound	L/h/kg bw^0.75	Metabolic	50
kurinebpagC	Clearance, urine excretion of glucuronide	L/h/kg bw^0.75	Metabolic	51
kurinebpasC	Clearance, urine excretion of sulfate	L/h/kg bw^0.75	Metabolic	52
vreabsorptiongC	Vmax for renal reabsorption of glucuronide	nmol/h/kg bw^0.75	Metabolic	53
vreabsorptionsC	Vmax for renal reabsorption of sulfate	nmol/h/kg bw^0.75	Metabolic	54
kreabsorptiong	Km for renal reabsorption of glucuronide	nM	Metabolic	55
kreabsorptions	Km for renal reabsorption of sulfate	nM	Metabolic	56
kenterobpagC	EHR of parent compound due to biliary excretion of glucuronide	1/h/kg bw^-0.25	Metabolic	57
kenterobpasC	EHR of parent compound due to biliary excretion of sulfate	1/h/kg bw^-0.25	Metabolic	58
EoA_O	Extent of oral absorption		Physiological	61
period_O	uptake period	h	External	63
t0_O	time point at which dosing starts	h	External	65
EoA_D	Extent of dermal absorption from TP		Physiological	68
aHL_D	Half-life for dermal penetration	h	External	70
period_D	Uptake period dermal exposure from TP	h	External	72
t0_D	Time points at which dermal dosing from TP starts	h	External	74
EoA_D2	Extent of dermal absorption from PCPs		Physiological	77
aHL_D2	Half-life for dermal penetration from PCPs	h	External	79
period_D2	Uptake period dermal exposure from PCPs	h	External	81
t0_D2	Time points at which dermal dosing from PCPs starts	h	External	83
BW075	BW^0.75	kg^0.75	External	103
BW025	BW^0.25	kg^0.25	External	104

Note

Additional kinetic models can be implemented, please contact the MCRA administrator.