A physiologically based pharmacokinetic model for lactational transfer of PCB 153 with or without PCB 126 in mice

Abstract

Chemical exposure via breast milk is one of the great concerns in public health. Previously, we demonstrated that most body burden of PCB 153 can be transferred from the mother to the pups in mice during lactational period. Here we present a physiologically based pharmacokinetic (PBPK) model to describe the lactational transfer of PCB 153 with or without PCB 126 in mice. The model incorporated physiological changes on the volume and the blood flow into mammary tissues, and considered mechanistic information on the movement of PCB 153 from adipose tissue to the mammary gland during lactational period. The mechanistic consideration includes fat volume changes, binding of PCB 153 to very low density lipoprotein (VLDL) and increased uptake of VLDL in mammary tissues. Model parameters depicting physiological changes were obtained from research articles dealing with chemical transfer during lactational period in rodents. Chemical-specific parameters were derived from previous PBPK models focusing on the PCB disposition in rodents. The developed model adequately described the lactational transfer of PCB 153 with or without PCB 126 in mice. Our model will provide a useful mechanistic tool to estimate the disposition of PCBs in diverse experimental designs regarding PCB effects during developmental period and to improve quantitative risk assessment of PCBs in the developing organisms.

Appendix

The mathematical expressions of the model which described the mass balance on different compartments are formulated as outlined in Ramsey and Andersen (1984). Equation 1 represents a tissue mass balance equation for a flow-limited transport process.

$$ {\text{d}}A_{i} /{\text{d}}t = Q_{i}\times{\text{ }}(C_{{\text{B}}}-C_{{{\text{V}}i}} )\, $$

(1)

where A _i is amount in ith tissue; Q _i is blood flow to ith tissue. C _B is arterial blood concentration; C _Vi is venous blood concentration leaving ith tissue. C _Vi  = C _i /P _i , where P _i is tissue/blood partition coefficient, C _i is concentration in ith tissue.

C _i  = A _i /V _i ; where V _i is the volume of ith tissue.

Equations 2 and 3 are tissue mass balance equations for a diffusion-limited transport process; under this assumption, C _i /P _i does not equal to C _Vi .

$$ {\text{d}}A_{{i{\text{B}}}} /{\text{d}}t = Q_{i} \times (C_{{\text{B}}} - C_{{{\text{V}}i}} ) + P_{{{\text{A}}i}} \times ((C_{i} /P_{i} ) - C_{{{\text{V}}i}} )$$

(2)

$$ {\text{d}}A_{i} /{\text{d}}t = P_{{{\text{A}}i}} \times (C_{{{\text{V}}i}} - (C_{i} /P_{i} )) $$

(3)

where A _iB is amount in the blood compartment of ith tissue; Q _i is blood flow to ith tissue; P _Ai is the diffusion permeation constant of ith tissue.

For the liver compartment, additional terms were added to describe a first-order oral absorption of PCB 153 and to account for a first-order metabolism of PCB 153. The following equation described above-mentioned mass transfer.

$$ {\text{d}}A_{{\text{L}}}/{\text{d}}t = Q_{{\text{L}}} \times (C_{{\text{B}}} - C_{{{\text{VL}}}} ) + K_{{{\text{AS}}}} \times A_{{{\text{ST}}}} + K_{{{\text{AD}}}} \times A_{{{\text{DU}}}} - {\text{ }}K_{{{\text{FC}}}} \times C_{{{\text{VL}}}} $$

(4)

where K _AS is the first-order absorption rate constant from the stomach; K _AD is the first-order absorption rate constant from duodenum; A _ST is the amount in stomach; A _DU is the amount in duodenum; K _FC is the first-order metabolism constant in the liver.

$$ C_{{\text{L}}} = A_{{\text{L}}} /V_{{\text{L}}} $$

(5)

$$ C_{{{\text{VL}}}} = C_{{\text{L}}} /{\text{PL}} $$

(6)

For model development involving co-exposure with PCB 126, the partition coefficient in the liver (PL) was modified to a time-dependent equation, PL = 10 + KFL × T where KFL is the coefficient for time-dependent increase of partition coefficient and T is the hours after PCB 153 exposure, where 0 ≤ T ≤ 340 h (14 days).

Oral absorption of PCB 153 was described as follows.

$$ {\text{d}}A_{{{\text{ST}}}}/{\text{d}}t= - K_{{{\text{AS}}}} \times A_{{{\text{ST}}}} - K_{{{\text{DT}}}} \times A_{{{\text{ST}}}} $$

(7)

$$ {\text{d}}A_{{{\text{DU}}}}/{\text{d}}t = K_{{{\text{DT}}}} \times A_{{{\text{ST}}}} - K_{{{\text{AD}}}} \times A_{{{\text{DU}}}} $$

(8)

where K _DT is the transfer rate of PCB 153 from stomach to duodenum.

The rate change in the amount of PCB 153 in the milk compartment of lactating dams comprises two terms; one related to the maternal blood circulation and partitioning to the milk and the other to pup suckling. The equation for the mammary tissue/milk is

$$ {\text{d}}A_{{{\text{MA}}}} /{\text{d}}t = Q_{{{\text{MA}}}} \times (C_{{\text{B}}} - C_{{{\text{VMA}}}} ) - N \times {\text{d}}A_{{{\text{suck}}}} /{\text{d}}t $$

(9)

where A _MA is the amount in mammary/milk compartment; Q _MA is blood flow to mammary/milk; C _B is arterial blood concentration. N is the number of pups. C _VMA = C _MA/P _MA, where P _MA is mammary/milk tissue:blood partition coefficient. C _VMA is venous blood concentration leaving mammary/milk tissue. C _MA is concentration in mammary/milk tissue. The second term (dA _suck/dt) is identical to the pup litter suckling rate.

$$ {\text{d}}A_{{{\text{suck}}}} /{\text{d}}t = C_{{{\text{MA}}}} \times K_{{{\text{MILK}}}} $$

(10)

where K _MILK is the milk transfer rate to the pups and was assumed to equal the milk production rate.

The amount of PCB 153 transferred to the pup’s liver is modeled via Eq. 11:

$$ {\text{d}}A_{{{\text{LP}}}} /{\text{d}}t = Q_{{{\text{LP}}}} \times (C_{{{\text{BP}}}} - C_{{{\text{VLP}}}} ) + C_{{{\text{MA}}}} \times K_{{{\text{MILK}}}} $$

(11)

where A _LP is the amount in pup’s liver; Q _LP is blood flow to pup’s liver; C _BP is arterial blood concentration in the pups.

$$ C_{{{\text{VLP}}}} = C_{{{\text{LP}}}} /P_{{{\text{LP}}}} $$

(12)

where P _LP is partition coefficient and C _VLP is venous blood concentration leaving pup’s liver. For model development involving co-exposure with PCB 126, P _LP was modified to a time-dependent equation, P _LP = 20 + KFLP × T where KFLP is the coefficient for time-dependent increase of partition coefficient and T is the hours after PCB 153 exposure, where 0 ≤ T ≤ 340 h (14 days).

Physiological changes during lactational period were described using GRAPH function. For example, body weight changes of the dam and the pup were described as follows.

$$ {\text{BW}} = {\text{GRAPH }}({\text{TIME}}){\text{ }}(T_{i} ,{\text{BW}}_{i} ) \ldots (T_{f} ,{\text{BW}}_{f} ) $$

(13)

where T _i is the first measured time point; BW _i is the first measured body weight; T _f is the last measured time point; BW _f is the last measured body weight. For the body weight of pup, BW _p is used to discriminate from the dam. The changes of cardiac output (QCC), blood flow in mammary glands (QMAC), volume in mammary glands (VMAC), and fat volume (VFC) were also described in a same way.

$$ {\text{QCC}} = {\text{GRAPH }}({\text{TIME}}){\text{ }}(T_{i} ,{\text{QCC}}_{i} ) \ldots (T_{f} ,{\text{QCC}}_{f} ) $$

(14)

$$ {\text{QMAC}} = {\text{GRAPH }}({\text{TIME}}){\text{ }}(T_{i} ,{\text{QMA}}_{i} ) \ldots (T_{f} ,{\text{QMA}}_{f} ) $$

(15)

$$ {\text{VMAC}} = {\text{GRAPH }}({\text{TIME}}){\text{ }}(T_{i} ,{\text{VMA}}_{i} ) \ldots (T_{f} ,{\text{VMA}}_{f} ) $$

(16)

$$ {\text{VFC}} = {\text{GRAPH }}({\text{TIME}}){\text{ }}(T_{i} ,{\text{VFC}}_{i} ) \ldots (T_{f} ,{\text{VFC}}_{f} ) $$

(17)