Table 3.

Model parameters

Parameter	Description	Value	Units	Source
Qpc	Alveolar ventilation	18.9a	l h−1 kg−1	Brown et al. (1997)
Rv : co	Ventilation–perfusion ratio	1.0	Unitless	Calculated from Borghoff et al. (1996)
Compartment volumesb
BW	Body weight	0.14–0.24	kg	Measured
FVblood	Fraction of body weight as blood	0.074	Unitless	Brown et al. (1997)
FVf	Fraction of body weight as fat	0.35·bw + 0.00205	Unitless	Brown et al. (1997)
FVk	Fraction of body weight as kidney	0.0073	Unitless	Brown et al. (1997)
FVk	Fraction of kidney as blood	0.16	Unitless	Brown et al. (1997)
FVl	Fraction of body weight as liver	0.037	Unitless	Brown et al. (1997)
$F{V}_{\mathit{pp}}^{\mathit{\text{total}}}$	Total fraction of body weight that is poorly perfused tissuesc	0.757	Unitless	Brown et al. (1997)
FVpp	$=F{V}_{\mathit{pp}}^{\mathit{\text{total}}}-F{V}_f$	0.755–0.35·bw	Unitless	Brown et al. (1997)
$F{V}_{\mathit{rp}}^{\mathit{\text{total}}}$	Total fraction of body weight that is richly perfused tissuesd	0.165	Unitless	Brown et al. (1997)
FVrp	$=F{V}_{\mathit{rp}}^{\mathit{\text{total}}}-F{V}_k-F{V}_l-F{V}_{\mathit{\text{blood}}}$	0.046	Unitless	Brown et al. (1997)
FVrob	Fraction of rest of bodye	0.078	Unitless	Brown et al. (1997)
Blood flowsf
Qcc	Cardiac index	Qpc/Rv : co	l h−1 kg−1	Calculated
FQf	Fraction cardiac output to fat	0.07	Unitless	Brown et al. (1997)
FQl	Fraction cardiac output to liver (hepatic and portal)	0.174	Unitless	Brown et al. (1997)
FQk	Fraction cardiac output to kidney	0.14	Unitless	Brown et al. (1997)
$F{Q}_{\mathit{pp}}^{\mathit{\text{total}}}$	Fraction cardiac output to poorly perfused tissues	0.53	Unitless	Brown et al. (1997)
FQpp	$=F{Q}_{\mathit{pp}}^{\mathit{\text{total}}}-F{Q}_f$	0.46	Unitless	Brown et al. (1997)
$F{Q}_{\mathit{rp}}^{\mathit{\text{total}}}$	Fraction cardiac output to richly perfused tissues	0.47g	Unitless	Brown et al. (1997)
FQrp	$=F{Q}_{\mathit{rp}}^{\mathit{\text{total}}}-F{Q}_l-F{Q}_k$	0.157	Unitless	Brown et al. (1997)
Mass transfer coefficients
$P_{\mathit{\text{blood}}:\mathit{air}}^{\mathit{\text{ETBE}}}$	ETBE blood/air partition coefficient	11.6	Unitless	Kaneko et al. (2000)
$P_{f:\mathit{\text{blood}}}^{\mathit{\text{ETBE}}}$	ETBE fat/blood partition coefficient	11.7	Unitless	Kaneko et al. (2000)
$P_{\mathit{\text{kidney}}:\mathit{\text{blood}}}^{\mathit{\text{ETBE}}}$	ETBE kidney/blood partition coefficient	2.9h	Unitless	Kaneko et al. (2000)
$P_{\mathit{\text{liver}}:\mathit{\text{blood}}}^{\mathit{\text{ETBE}}}$	ETBE liver/blood partition coefficient	2.9	Unitless	Kaneko et al. (2000)
$P_{\mathit{pp}:\mathit{\text{blood}}}^{\mathit{\text{ETBE}}}$	ETBE poorly perfused/blood partition coefficient	1.9	Unitless	Kaneko et al. (2000); set equal to muscle
$P_{\mathit{rp}:\mathit{\text{blood}}}^{\mathit{\text{ETBE}}}$	ETBE richly perfused/blood partition coefficient	2.9	Unitless	Set equal to richly perfused
$P_{\mathit{\text{blood}}:\mathit{air}}^{\mathit{TBA}}$	TBA blood/air partition coefficient	481	Unitless	Borghoff et al. (1996)
$P_{f:\mathit{\text{blood}}}^{\mathit{TBA}}$	TBA fat/blood partition coefficient	0.40	Unitless	Borghoff et al. (1996)
$P_{\mathit{\text{kidney}}:\mathit{\text{blood}}}^{\mathit{TBA}}$	TBA kidney/blood partition coefficient	0.83	Unitless	Borghoff et al. (1996)
$P_{\mathit{\text{liver}}:\mathit{\text{blood}}}^{\mathit{TBA}}$	TBA liver/blood partition coefficient	0.83	Unitless	Borghoff et al. (1996)
$P_{\mathit{pp}:\mathit{\text{blood}}}^{\mathit{TBA}}$	TBA poorly perfused/blood partition coefficient	1.0	Unitless	Borghoff et al. (1996)
$P_{\mathit{rp}:\mathit{\text{blood}}}^{\mathit{TBA}}$	TBA richly perfused/blood partition coefficient	0.83	Unitless	Set equal to liver
$k_{\mathit{abs}}^{\mathit{\text{ETBE}}}$	ETBE first order absorption constant	1.6	h−1	Leavens and Borghoff (2009) for MTBE
$k_{\mathit{abs}}^{\mathit{TBA}}$	TBA first order absorption constant	5.0	h−1	Salazar et al. (2015)
$F_{\mathit{\text{absorbed}}}^{\mathit{TBA}}$	Fraction of TBA absorbed in alveolar region	0.6	Unitless	Medinsky et al. (1993)
$C{l}_{\mathit{\text{urinary}}}^{\mathit{TBA}}$	Urinary clearance of TBA	0.015	l h−1 kg–0 .75	Estimated
Metabolic parameters
$V_{\mathit{mc}}^{\mathit{\text{ETBE}}}$	Scaled maximum metabolic rate of ETBE	499	μmol h−1 kg–0 .75	Rao and Ginsberg (1997)
$K_m^{\mathit{\text{ETBE}}}$	Michelis–Menten constant for ETBE	1248	μmol l−1	Rao and Ginsberg (1997)
$V_{\mathit{mc}}^{\mathit{TBA}}$	Scaled maximum metabolic rate of TBA	54	μmol h−1 kg−1	Borghoff et al. (1996); Rao and Ginsberg (1997)
$K_m^{\mathit{TBA}}$	Michelis–Menten constant for ETBE	379	μmol l−1	Borghoff et al. (1996); Rao and Ginsberg (1997)
$\mathit{\text{In}}{d}_{\max }^{V_{\mathit{mc}}^{\mathit{TBA}}}$	Maximum percentage increase in $V_{\mathit{mc}}^{\mathit{TBA}}$	124.9	unitless	Leavens and Borghoff (2009)
$K_{\mathit{\text{induction}}}^{\mathit{\text{Vmctba}}}$	Rate constant for ascent to $\mathit{\text{In}}{d}_{\max }^{\mathit{\text{Vmctba}}}$	0.3977	day−1	Leavens and Borghoff (2009)
α2u–globulin binding parameters
$C_{k_{\mathit{ss}}}^{\alpha 2u}$	Steady‐state concentration of free α2u–globulin in kidney	550i	μmol l−1	Leavens and Borghoff (2009)
$K_{\mathit{\text{hydrolysis}}}^{\mathit{\text{free}}}$	First order rate constant for hydrolysis of free α2u–globulin	0.32	h−1	Leavens and Borghoff (2009)
$K_{\mathit{\text{hydrolysis}}}^{\mathit{\text{bound}}}$	First order rate constant for hydrolysis of bound α2u–globulin	0.11	h−1	Leavens and Borghoff (2009)
$K_b^{\mathit{TBA}}$	Second order binding rate constant for TBA to α2u–globulin	1.3	l μmol− 1 h−1	Leavens and Borghoff (2009)
$K_d^{\mathit{TBA}}$	α2u–globulin dissociation constant for TBA	120	μmol l−1	Leavens and Borghoff (2009)
$K_{\mathit{ub}}^{\mathit{TBA}}$	First order rate constant for unbinding of TBA from α2u–globulin	$K_b^{\mathit{TBA}}\cdot K_d^{\mathit{TBA}}$	h−1
$K_b^{\mathit{\text{ETBE}}}$	Second order binding rate constant for ETBE to α2u–globulin	0.15	l μmol− 1 h−1	Leavens and Borghoff (2009)
$K_d^{\mathit{\text{ETBE}}}$	α2u–globulin dissociation constant for ETBE	1	μmol l−1	Leavens and Borghoff (2009)
$K_{\mathit{ub}}^{\mathit{\text{ETBE}}}$	First order rate constant for unbinding of ETBE from α2u–globulin	$K_b^{\mathit{\text{ETBE}}}\cdot K_d^{\mathit{\text{ETBE}}}$	h−1	Leavens and Borghoff (2009)

ETBE, ethyl tertiary‐butyl ether; MTBE, methyl tertiary‐butyl ether; TBA, tertiary‐butyl alcohol.

^aLower limit of of alveolar ventilation values for rat reported in Brown et al. (1997).

^bTotal volume of the body weight of the rat was divided fractionally as follows: $1.0=F{V}_{\mathit{rp}}^{\mathit{\text{total}}}+F{V}_{\mathit{pp}}^{\mathit{\text{total}}}+F{V}_{\mathit{rob}}$

^cPoorly perfused tissues were defined as those having relative flow rates <100 ml min⁻¹ 100 g, including muscle, skin, fat and bone.

^dRichly perfused tissues were defined as those having relative flow rates of ≥100 ml min⁻¹ 100 g, including adrenal, blood , brain, gastrointestinal tissues, heart, kidney, liver, lungs and thyroid.

^eRest of body not perfused, including gut contents, hair, nails and urine.

^fTotal cardiac output was divided between the total richly perfused and poorly perfused: $1.0=F{Q}_{\mathit{rp}}^{\mathit{\text{total}}}+F{Q}_{\mathit{pp}}^{\mathit{\text{total}}}$

^gBrown et al. (1997) only accounted for 94% of cardiac output for fraction of flows. For this model, the unaccounted 6% was assumed to be in the richly perfused tissues.

^hETBE kidney/blood ratio measured in male rats was reported to be 11 (Kaneko et al., 2000). For a rapidly perfused tissue, this is a high value that suggests that uptake into this tissue is most likely dependent on solubility and an active process such as binding, which was the case for MTBE by Poet and Borghoff (1997). As such, the partition coefficient in kidney was set to rapidly perfused tissues and binding of ETBE to α2u–globulin described within the male, but not female rat kidney.

ⁱValues in literature range from ~160 to 1000 μm for α2u–globulin kidney concentration (Carruthers et al., 1987; Charbonneau et al., 1987; Olson, Garg et al., 1987; Stonard et al., 1986).