Skip to main content
. 2014 Feb 26;9(2):e88517. doi: 10.1371/journal.pone.0088517

Table 1. Description of symbols used in the conceptual and functional representation of the kinetic model of permethrin and cypermethrin and their metabolites.

Parameters Definitions
goral(t) Oral dose (mol) bioavailable per unit of time which can describe time varying inputs
gdermal(t) Dermal dose (mol) bioavailable per unit of time which can describe time varying inputs
ginh(t) Inhalation dose (mol) bioavailable per unit of time which can describe time varying inputs
D(t) Amounts of cis- and trans-permethrin or cypermethrin (mol) bioavailable at skin surface as a function of time
GI(t) Amounts of cis- and trans-permethrin or cypermethrin (mol) bioavailable in the gastrointestinal tract as a function of time
R(t) Amounts of cis- and trans-permethrin or cypermethrin (mol) bioavailable in the respiratory tract as a function of time
Bcis(t) Burden of cis-permethrin or cypermethrin (mol) in blood and tissues in dynamical equilibrium with blood as a function of time
Btrans(t) Burden of trans-permethrin or cypermethrin (mol) in blood and tissues in dynamical equilibrium with blood as a function of time
Scis(t) Burden of cis-permethrin or cypermethrin (mol) in storage tissues (mol) as a function of time
Strans(t) Burden of trans-permethrin or cypermethrin (mol) in storage tissues (mol) as a function of time
Mcis-DCCA(t) Body burden of cis-DCCA (mol) as a function of time
Mtrans-DCCA(t) Body burden of trans-DCCA (mol) as a function of time
M3PBA(t) Body burden of 3-PBA (mol) as a function of time
Mnot observed(t) Body burden of non-monitored metabolites (mol) as a function of time
Ucis-DCCA(t) Cumulative amounts of cis-DCCA in urine (mol) as a function of time
Utrans-DCCA(t) Cumulative amounts of trans-DCCA in urine (mol) as a function of time
U3PBA(t) Cumulative amounts of 3-PBA in urine (mol) as a function of time
QUcis-DCCA(t) Urinary excretion rate of cis-DCCA in urine (mol) as a function of time = Mcis-DCCA(t)×kMU_cis
QUtrans-DCCA(t) Urinary excretion rate of trans-DCCA in urine (mol) as a function of time = Mtrans-DCCA(t)×kMU_trans
QU3PBA(t) Urinary excretion rate of 3-PBA in urine (mol) as a function of time = M3PBA(t)×kMU_3PBA
Fcis-DCCA(t) Cumulative amounts of cis-DCCA in feces (mol) as a function of time
Ftrans-DCCA(t) Cumulative amounts of trans-DCCA in feces (mol) as a function of time
F3PBA(t) Cumulative amounts of 3-PBA in feces (mol) as a function of time
fabs_oral_cis Oral absorption fraction of cis-permethrin or cypermethrin
fabs_oral_trans Oral absorption fraction of trans-permethrin or cypermethrin
fabs_dermal_cis Dermal absorption fraction of cis-permethrin or cypermethrin
fabs_dermal_trans Dermal absorption fraction of trans-permethrin or cypermethrin
kabs_oral_cis Oral absorption rate of cis-permethrin or cypermethrin (h−1)
kabs_oral_trans Oral absorption rate of trans-permethrin or cypermethrin (h−1)
kabs_dermal_cis Dermal absorption rate of cis-permethrin or cypermethrin (h−1)
kabs_dermal_trans Dermal absorption rate of trans-permethrin or cypermethrin (h−1)
kabs_inh_cis Respiratory absorption rate of cis-permethrin or cypermethrin (h−1)
kabs_inh_trans Respiratory absorption rate of trans-permethrin or cypermethrin (h−1)
kBS_cis Blood to storage tissues transfer rate of cis-permethrin (h−1)
kBS_trans Blood to storage tissues transfer rate of trans-permethrin (h−1)
kSB_cis Storage tissues to blood transfer rate of cis-permethrin (h−1)
kSB_trans Storage tissues to blood transfer rate of trans-permethrin (h−1)
kBM_cis Biotransformation rate of cis-permethrin or cypermethrin into cis-DCCA (h−1)
kBM_trans Biotransformation rate of trans-permethrin or cypermethrin into trans-DCCA (h−1)
kBM_3PBA_cis Biotransformation rate of cis- permethrin or cypermethrin into 3-PBA (h−1)
kBM_3PBA_trans Biotransformation rate of trans- permethrin or cypermethrin into 3-PBA (h−1)
kBM_NO_cis Biotransformation rate of cis-permethrin or cypermethrin into non-observed cis-derivative metabolites (h−1)
kBM_NO_trans Biotransformation rate of trans-permethrin or cypermethrin into non-observed trans-derivative metabolites (h−1)
kBM_NO_3PBA_cis
Biotransformation rate of cis-permethrin or cypermethrin into non-observed cis-phenoxy derivatives (h−1)
kBM_NO_3PBA_trans Biotransformation rate of trans-permethrin or cypermethrin into non-observed trans-phenoxy derivatives (h−1)
kMU_cis Transfer rate of cis-DCCA from the body to urine (h−1)
kMU_trans Transfer rate of trans-DCCA from the body to urine (h−1)
kMU_3PBA Transfer rate of 3-PBA from the body to urine (h−1)
kMF_cis Transfer rate of cis-DCCA from the body to feces (h−1)
kMF_trans Transfer rate of trans-DCCA from the body to feces (h−1)
kMF_3PBA Transfer rate of 3-PBA from the body to feces (h−1)
kmetabolism_cis Biotransformation rate of cis-permethrin or cypermethrin into cis-metabolite forms or 3-PBA ( = kBM_cis+kBM_NO_cis) (h−1)
kmetabolism_trans
Biotransformation rate of trans-permethrin or cypermethrin into trans-metabolite forms or 3-PBA ( = kBM_trans+kBM_NO_trans) (h−1)
kelim_cis Total excretion rate of cis-DCCA = (kMU_cis+kMF_cis) (h−1)
kelim_trans Total excretion rate of trans-DCCA = (kMU_trans+kMF_trans) (h−1)
kelim_3PBA Total excretion rate of 3-PBA = (kMU_3PBA+kMF_3PBA) (h−1)
ωcis kBM_cis×kMU_cis
ωtrans kBM_trans×kMU_trans
ω3PBA kBM_3PBA×kMU_3PBA