6. PHARMACOKINETICS 6-1

6.1. INTRODUCTION 6-1

6.2. DAILY BACKGROUND LEVELS 6-2

6.2.1. Basis for Calculation 6-2

6.2.2. Daily Intakes 6-7

6.3. COMPARTMENTAL MODELING 6-14

6.3.1. Pharmacokinetic Model 6-14

6.3.2. Model Utilization 6-17

6.3.3. Determining Liver Concentrations from Fat Levels 6-20

6.4. INTAKES THROUGH DAILY EXPOSURE 6-25

6.4.1. Determination of Daily Intake Dose from Exposure Concentrations 6-25

6.4.2. Dose Through Lactation 6-26

6.4.2.1. Concentration in the Milk 6-26

6.4.2.2. Dose to Infant 6-28

The pharmacokinetic profiles of CDDs and the CDFs are quite complex. A thorough analysis and understanding of these pharmacokinetic data would be very helpful in ensuring that exposure assessments for these compounds are reliable. In addition, such information would be useful in providing enhanced knowledge and understanding for the purposes of risk assessment. Previous drafts of this chapter included a discussion on bioavailability of CDD/Fs. Since this topic is only loosely related to pharmacokinetics, it was decided to move this discussion to an appendix and it now appears in Appendix C of this Volume.

Exposure to 2,3,7,8-TCDD and related compounds results in numerous species and tissue specific toxic and biological responses. Many, if not, all of these responses are mediated by a soluble intracellular protein, the aryl hydrocarbon (Ah) receptor, to which 2,3,7,8-TCDD binds with high affinity. After 2,3,7,8-TCDD and related compounds bind to this Ah receptor the complex undergoes a transformation process involving dissociation of hsp90. The transformed receptor complex is then able to bind with high affinity to a specific DNA sequence referred to as a dioxin responsive enhancer (DRE). The conserved nature of the DRE and Ah receptor is also indicated by the ability of transformed 2,3,7,8-TCDD: Ah receptor complexes from a wide variety of species to bind to the DRE. Studies also indicate a similarity in DNA recognition by Ah receptor from a variety of species suggestive of a functional role of this sequence in 2,3,7,8-TCDD responsiveness (Denison et al., 1991; Gasiewicz and Henry, 1991; Perdew and Hollenbeck, 1990; Andersen and Greenlee, 1991). Thus the definition of "disposition" may have to be extended to include suborgan or subcellular sites in order to more fully describe the congener, species, and train specific pharmacokinetics (dosimetry) of these compounds.

Pharmacokinetic analysis may be used in several ways to aid in the exposure and dose assessment of foreign chemicals. They may, for example, allow for predicting the time and profile of elimination of chemicals from the body. The redistribution of CDDs among the various tissues and organs, which may occur during elimination, can be accounted for and tracked. Effects on disposition which may result from altered physiology, such as sudden weight loss or from lactation, can be incorporated and thus adequately considered in exposure and risk assessments. Lactation is known to be an efficient route for the transfer of many of these chemicals from mother to offspring (Nau et al., 1986; Bowman et al., 1989).

Pharmacokinetic analyses can be used to estimate background exposure levels from body burden data. They can also be used to estimate uptake rates from various food sources, elimination rates and times from the body, and to estimate tissues levels from blood and adipose tissue monitoring. In addition, with the appropriate data on several congeners, estimates can be made for other congeners about which less data are available.

The remainder of this chapter will cover areas of pharmacokinetics pertinent to exposure assessment. Background levels and daily uptake of 2,3,7,8-TCDD will be reviewed and discussed; a method for the calculation of uptake of other congeners from food will be outlined; use of a compartmental model to estimate daily uptake will be demonstrated; a method will be outlined and reviewed for determining internal tissue concentrations from monitored blood and/or adipose tissue; exposure through lactation will also be discussed.

Physiologically based pharmacokinetic (PBPK) models are convenient and useful methods for describing and predicting disposition of foreign chemicals in the body. These models take into account physiologic and biochemical processes such as blood flows, metabolism, and renal clearance, and describe the body according to its normal anatomy. PBPK models can, given adequate data, predict disposition from one exposure scenario to another and even from species to species. One such model was developed for 2,3,7,8-TCDF (King et al., 1983) and is used here with some modifications. The anatomic regions depicted in the King model are the blood, liver, fat, skin, and muscle. The remaining organs of the body are lumped together as the "carcass." Input may be by a variety of routes, but for the purposes of this discussion is considered to occur through the gastrointestinal system by continuous chronic dosing. This is consistent with the findings of Chapters 4 and 5 that most of these compounds enter the body through the gastrointestinal tract as a result of the consumption of products containing animal fat. The pertinent equations follow.

For the liver:

Where,

V_L = Volume of the liver

C_B = Concentration of toxin in blood

C_L = Concentration of toxin in liver

t = Time

Q_L = Blood flow to liver

R_L = Equilibrium concentration ratio between liver and blood

KL = Clearance term (L/time)

D = Input or dosing function

The clearance in the liver is considered to be by metabolic processes.

For the fat:

Where all terms are analogous as those in Equation 6-1.

Note that there is no metabolic elimination assumed. The only disappearance of material from the fat is assumed to be diffusion driven and is accounted for in the above mass balance equation. Equations for the skin, carcass, and muscle are analogous to that for fat.

The equation for the blood is:

Where,

Q = Blood Flows

C = Concentrations

R = Equilibrium Concentration Ratios between tissue and blood

Subscripts:

B, L, F, M, S, C refer to blood, liver, fat, muscle, skin and carcass.

Some assumptions may be made to simplify the model for use to estimate daily background doses. If steady state is assumed, then the equations for the individual organs can be summed. The resultant equation for the liver is then:

and at steady state

and

and hence

When clearance is expressed in days, D is the daily intake. Clearance can be approximated from the half-life information according to the following equations:

Where,

k_e = First order elimination rate constant

V_d = Volume of distribution

and

Where,

t_1/2 = Biological half-life of compound in body

The volume of distribution may be estimated as in King et al., (1983) according to:

Where,

V_d,i = Volume of distribution of organ, i

V_i = Actual volume of organ, i

R_i = Equilibrium concentration ratio between organ i and blood

With substitution equation (6-7) becomes:

Where,

V_i = Volume of the organ in which toxin is measured

C_i,ss = Steady state concentration of toxin in organ

It is important to note that two major assumptions are in effect when the above formula is used to calculate average daily uptake. First steady state conditions are assumed. Given that the half-life of some of these compounds (e.g., 2,3,7,8-TCDD) are at least 5 years, it would take well over 15 years to reach 90 percent of steady state, and over 30 years to reach 99 percent of steady state levels. Thus, the assumption of steady state is only reasonable if background environmental concentrations are relatively similar and constant throughout the nation. Under such conditions even the normal movement from one geographical location to another would result in relatively constant exposures. Also implicit in this assumption is that bioavailability is relatively constant through the nation. Given that the source of this background exposure is believed primarily due to consumption of foods containing animal fat (see Chapters 4 and 5), the assumption of steady state for adults might be considered a reasonable assumption. Exceptions are those individuals who may for a portion of their adult lives be consuming foods with unusually high levels of these compounds. It would be expected, however, that those individuals would have higher than average body burdens, and hence would not be considered to have only average background exposure, but would rather be considered part of a source-specific exposure group. Conditions such as sudden weight loss and lactation would also alter the steady state condition. However, for purposes of calculating daily background exposure levels the sampling of tissues for body burden must be so designed to account for such deviations in the average. In summary, for adults (over 25 years of age) not in a source-specific exposure group, the steady state assumption is a reasonable approximation. It should be remembered, however, that the longer the biological half-life the longer it would take to reach steady state. A compound with a half life of 10 years, for example, would take over 50 years to reach 90 percent of the steady state value.

The second major assumption is that these compounds are eliminated from the body by monophasic kinetics. Biphasic elimination is very possible for many of these compounds. Data gathered to calculate elimination rates or half-lives would only reveal biphasic elimination profiles if gathered several years after the last exposure. Using only the short term half-life would result in an underestimated value for half-life and an overestimate of daily intake. This is particularly problematic for those compounds with extremely long half-lives and for which few data exist. In Section 6.2.2., an approach to calculating half-lives for some of these compounds will be presented. Also, the elimination kinetics are assumed to be constant over the entire life of the individual. Sudden weight loss and lactation would, for example, be conditions which violate that assumption. Again, it would be assumed that for calculation of daily intake due to background exposure the body burden data from such individuals would be identified and calculations handled accordingly.

Figure 6-1 shows a sample calculation for 2,3,7,8-TCDD using the above procedure. A fat volume of 14 L was chosen, representing 20 percent of the body weight. Also, for the purposes of this example, 1 ml of tissue was assumed to be equivalent to 1 gm.

Table 6-1 shows the estimated daily intake of 2,3,7,8-TCDD at several conditions. The range of daily intakes calculated are in agreement with those reported elsewhere (Fürst et al., 1991; U.S. EPA, 1994).

In order to perform similar calculations for other congeners three pieces of information are necessary. First, concentrations in the adipose tissues must be known. Second, the half-lives of the compounds within the body must be known. Third, some understanding of the kinetics and exposure conditions to assure that steady state conditions were achieved at the time of monitoring.

Concentrations of various congeners in adipose tissues can be found in several sources (Stanley et al., 1986; Schecter, 1991). Values range from around 2 ppt for 2,3,7,8-TCDF to several hundred ppt for 1,2,3,4,6,7,8,9-OCDD.

Half-lives could be determined from elimination data, if available. Methods have been suggested to determine the half-lives of such compounds from uptake data relative to 2,3,7,8-TCDD. Schlatter (1991) has proposed one such method. The following has been adapted from that proposed method. Manipulation of Equation 6-11 results in:

Where,

C_TCDD = Concentration of TCDD in body

D_TCDD = Daily Intake of TCDD

t_1/2,TCDD = Half-life of TCDD in body

V = Volume of body compartment

For some other congener x:

Where symbols are same as for equation (6-12) and subscript x applies to compound x.

Thus the ratio of concentrations of TCDD to x can be described by:

With algebraic manipulation and simplification Equation 6-14 becomes:

Assuming intake, D, to be mostly from the food, especially animal fat products, D can be related to absorption from these foods according to:

Where,

k_a,TCDD = Absorption rate constant for TCDD

A_TCDD = Concentration of TCDD in animal fat (diet)

and

Where,

k_a,x = Absorption rate constant for x

A_x = Concentration of x in animal fat (diet)

As a result the half-life for compound x can be described by:

When the absorption rate constants for each congener are equal or when the difference between them is small compared to differences in other parameters (concentration, half-lives), Equation 6-18 can be further simplified to:

Before using the above approach to calculate half-lives for some of the other substances of interest it is well to briefly highlight one of the assumptions in this approach. The relationship of half-life to elimination as described in Equation 6-9 only applies to simple single compartment kinetics. These compounds would not necessarily be expected to behave in such a manner. However, the error introduced by such an assumption is not great if the one phase predominates over the other, or if it is remembered that the calculation applies to one phase only. In fact, as will be discussed in a subsequent section, it is believed that for these chemicals the relationship between half-life and elimination as described here is a reasonable approximation.

It should be noted that for some of these substances exposure is expected from other than food sources. For such cases Equation 6-18 would be modified to include these other sources as follows:

Where,

k_a,i,TCDD = Absorption rate constants for TCDD from each of the i media

A_i,TCDD = Concentration of TCDD in each of the i media

k_a,i,x = Absorption rate constants for x from each of the i media

A_i,x = Concentration of x in each of the i media

Other symbols: As previously defined

Again, if the differences between the absorption rate constants for TCDD and x are judged to be small, then the variation of Equation 6-19 can be used, presented as Equation 6-21, Table 6-2 shows the results of some half-lives calculated in this manner.

The half-lives calculated using Equation 6-19 for the first three compounds in Table 6-2 agree with those calculated by Schlatter (1991). The large difference in the two calculations for OCDD is due to significant differences in absorption rates between the TCDD and the OCDD. Schlatter (1991) notes that for some compounds, including OCDD, corrections were made of differences in absorption. No explanation was offered on how this was done. In U.S. EPA (1993), results are summarized that indicate a possible several-fold greater oral

absorption of TCDD over OCDD. This adjustment would result in a calculated half-life closer to that calculated by Schlatter.

In summary, this section illustrates a method for calculating the half-lives of similar behaving compounds. Several pieces of information are necessary: 1) the concentration in the body of 2,3,7,8-TCDD; 2) the half-life of 2,3,7,8-TCDD; 3) the concentration of the substance of interest in the body; 4) the concentration of the substance of interest in the media from which exposure occurs; and 5) the differential absorption rates for TCDD and the substance of interest.

From the half-life information, average daily intakes may be calculated, when steady state can be assumed, by using Equation 6-12. Caution should be exercised when calculating daily intakes for those compounds with very long half-lives such as OCDD in the above example.

As previously discussed and also discussed elsewhere (U.S. EPA, 1994), PBPK models are very useful for describing and predicting the disposition of chemicals in the body. They are generally designed for predicting some measure of dose at a target site. They are also used to extrapolate from one species to another, between different doses, and between different routes of exposure. Several PBPK models have been published specifically for 2,3,7,8-TCDD (Leung et al., 1990; Leung et al., 1988). Also, as previously discussed, a model for 2,3,7,8-TCDF (King et al., 1983) is also available and from which were derived the equations for estimating daily intake from body concentrations at steady state conditions. Most of these models have been developed to describe in great detail the metabolism and binding of TCDD within the body, for the purpose of estimating target tissue dose.

Assuming a linear relationship between the concentrations in the fat and the body at low exposure concentrations and the near linear elimination profile, a simpler model relating exposure, whole body elimination, and whole body concentration is developed here. As described earlier, after a prolonged exposure most of the body's organs can be assumed to have very similar kinetic profiles and can thus be lumped together. The fat, while sharing such a similar profile, is kept separate because of its important role in storing most of the body burden and because it has been the most typically monitored tissue. The three compartments in this model are blood, fat, and a "body" representing all other tissues. The model is a flow- or perfusion-limited model with the assumption that the toxin is well stirred or uniformly distributed within each compartment. The pertinent equations for the model follow. The rate of change of concentration of toxin in the body is estimated by:

Where:

dC_bo/dt = Rate of change of concentration of toxin in body (bo)

Q_bo = Blood flow (volume/time) to body

C_B = Concentration of toxin in blood (B)

R_bo = Equilibrium concentration ratio of toxin between body and blood

K = Clearance (volume/time) of toxin from body

V_bo = Volume of body

D = Intake of toxin

The rate of change of concentration of toxin in the fat is estimated by Equation 6-23 below:

Where,

dC_F/dt = Rate of change of concentration of toxin in fat (F)

Q_F = Blood flow (volume/time) to fat

R_F = Equilibrium concentration ratio of toxin between fat and blood

V_F = Volume of fat

The integral of the above differential equation (Eq. 6-23) over time gives the actual concentration.

The rate of change of concentration of toxin in blood is estimated by Equation 6-24 below:

Where,

dC_b/dt = Rate of change of concentration of toxin in blood (B)

It should be noted that the description of intake is somewhat different than what is typically found in most PBPK models. D here is actually a dose rate. That is, D is in terms of pg/kg/day coming into the body as a dose, not just a concentration in the food, drinking water, or air. The usual description for gastrointestinal absorption of toxin from food would be

Where,

k_a = Absorption rate constant

F_c = Concentration of toxin in food

In this case, because of inadequate knowledge regarding the absorption rate constants for many of the congeners, a dose rate is used instead. This does not allow for estimation of body burden directly from environmental concentrations (e.g., F_c in Equation 6-25). As more data are collected, more accurate values of the parameters and descriptions of absorption functions can be input into Equation 6-22. For the present, other approaches can be used to relate concentration in the environmental media to daily intake (see Section 6.4.1).

Most of the model's parameters are known or can be estimated from experimental data for many of these toxins. For example, the equilibrium concentration ratios between the fat and the body and between the fat and the blood for 2,3,7,8-TCDD are approximately 10 and 100, respectively, on a tissue basis. The blood flows and compartment volumes are well known. One parameter that had to be estimated when applying this model to 2,3,7,8-TCDD was the clearance term K. This was done by first allowing the model to simulate elimination as though exposure was suddenly terminated (D becomes zero). Initial concentrations for the tissues were taken as those typically expected in the general population (7.0 ppt in the fat). The value of K was then adjusted until the model predicted a half-life of 7 years. Values of clearance for the other compounds in this series would be determined similarly. The necessary information includes the equilibrium concentration distribution ratios, the half-lives of the compounds, and some reasonable approximation of steady state fat concentrations.

With an estimated value for the clearance, the model can now be used with various exposure inputs to establish body burdens of toxin. The model can also be used to estimate elimination profiles from the body. In addition, events such as lactation can be incorporated into the model with knowledge about the appropriate parameters.

Figure 6-2 shows the results of the model run describing the elimination of 2,3,7,8-TCDD from fat. The clearance rate was adjusted to predict a half-life of 7 years. The same clearance value was used with different starting conditions (concentration of TCDD in tissues) and the model produced a half-life of 7 years. Next, the model was used with a constant daily intake as an input. Figure 6-3 shows the resulting profile of 2,3,7,8-TCDD in the fat. Figure 6-3 shows the results of a model run using an input of 0.44 pg/kg/day. Note that the steady state fat concentrations are approximately 7.0 ppt. The clearance rate used in this model run had been independently determined in the previous run based on reported half-life values. Thus, for these conditions this model does an adequate job of

predicting tissue levels of 2,3,7,8-TCDD. Figure 6-4 shows a similar profile for a 0.30 pg/kg/day dose. The daily intakes chosen were similar to those calculated by the steady state equations in Section 6.1.2 (Table 6-1). Note that the steady state fat levels predicted by the pharmacokinetic model agree closely with those used as a starting point for the steady state calculation using seven years for the half-life. This three compartment model appears to provide reasonable approximations of body burden, at least under the circumstances that have been tested. The necessary information for use with other substances in this series include the equilibrium distribution ratios between fat and blood and between fat and the rest of the body. An estimate of the half-life is also needed in order to establish an appropriate value for the clearance term used in the model. Table 6-3 shows the results when the model was adjusted for other substances. The congener-specific TEQ intakes can be added together to arrive at a TEQ-based total daily intake for all the congeners of interest to a particular assessment.

Under certain circumstances, it might also be possible to use the compartmental model on a total TEQ basis. Considering, for example, a mixture of dioxins and furans whose collective biophysical properties are similar to those of 2,3,7,8-TCDD the model could be applied to approximate daily intake from steady-state fat levels. For example, Schecter (1991) reports the blood lipid levels in a sample of 85 persons from Germany to be 42 ppt TEQ (CDDs and CDFs). Using that figure and the parameters of 2,3,7,8-TCDD, the model calculates a daily intake of 2.64 pg TEQ/d/kg. Fürst et. al (1991), based on food consumption patterns of the German population, estimated a daily intake of 2.3 pg TEQ/d/kg. Obviously great caution should be taken before using such an approach. Such estimates should only be relied upon if there is strong evidence that the mix of congeners is such that the collective properties of the mixture result in properties similar to those of 2,3,7,8-TCDD.

As mentioned previously, higher resolution PBPK models are necessary to estimate and predict concentration at cellular and sub-cellular targets (vidae supra). At the present time, many of the data necessary to develop and apply these models to estimate target tissue or cellular dose in humans are lacking. Andersen and Greenlee (1991) provide an approach that uses the equations of a PBPK model (Leung et al., 1990) to predict liver concentrations from monitored fat concentrations. It should also be noted that blood or milk concentrations expressed on a per lipid basis could also be used. Basically the approach calculates the ratio of fat to liver concentration by dividing the tissue concentration equations of the PBPK model as follows:

Where,

C_L, C_F = Concentrations of toxin in liver and fat

C_VL, C_VF = Concentrations of toxin in venous blood from liver and fat

P_L, P_F = Liver:blood and Fat:blood partition coefficients of toxin

V_L = Volume of Liver compartment

BM₁, KB₁ = Forward and reverse binding constants for binding of toxin with Ah receptor

BM₂(T) = Forward binding constant with microsomal binding protein - time dependent upon the amount of inducible microsomal binding protein

KB₂ = Reverse binding constant for microsomal binding protein

Andersen and Greenlee (1991) further simplify Equation 6-26 for various limiting conditions. For the case of very low doses where CVL<<KB₁, KB₂ and their is no induction of the cytochrome P450 enzyme (microsomal binding protein), the equation simplifies to:

Where,

BM₂₍₀₎ = Basal level (non-induced) binding level of P450 (microsomal binding protein)

For the case where KB₂<<CVL<<KB₁, P450 is maximally induced but binding is less than half saturation, Equation 6-26 becomes:

Where,

BM_2(max) = Maximally induced binding level of P450

For the case where CVL>>KB₁, KB₂, Equation 6-26 becomes:

Andersen and Greenlee (1991) provide values for each of the above conditions for experimental animals. It can be readily observed from examining Equation 6-26 that when binding levels are very small the ratio of concentration between liver and fat is influenced mostly by the ratio of partitioning coefficients.

With this approach and by knowing the necessary parameters Equation 6-26 can be used to estimate liver concentrations from fat (including blood lipid and milk lipid) concentrations. Andersen and Greenlee (1991) further suggest that most of the necessary binding parameters can be determined from in-vitro studies. Further, the pharmacokinetic model from which Equation 6-26 was derived can be used to estimate and predict cellular concentrations (both free and bound) under various exposure conditions. The equations used by Leung et al. (1990) or other like equations provide estimates of amount bound to intracellular receptors sites, and can thus provide a relationship between multiple binding sites. Denison et al. (1991) suggest that binding to the Ah receptor is only one of several steps necessary for 2,3,7,8-TCDD to have an intracellular toxic effect. As further knowledge becomes available about the mechanism and kinetics of each step, the model can be expanded to include these other processes such as DNA enhancing and hormonal modulation. The pharmacokinetic model will therefore become a pharmacodynamic model which will more explicitly link exposure to effect. Also, other tissues can be more specifically described in the model, if the mechanism of action data so warrant.

6.4. INTAKES THROUGH DAILY EXPOSURE

As was discussed in Section 6.3.1, it would be most advantageous to know more about the kinetics of absorption in the various animal species and the human. This is necessary for both extrapolation between species in the risk assessment and for determining body burdens from levels in the exposure media. For the time being, until more data become available regarding the kinetic absorption constants, a slightly modified approach can be used. Basically, the needed information is the concentration of the toxins in the media, the fraction of toxin absorbed from each of the media, and the amount of media coming into contact with the body. The following equation describes this in more detail.

Where,

D = Daily Intake

f_i = Fraction absorbed from various i media

C_i = Concentration in various i media

U_i = Amount of contact of i media, (gm/time for food, L/time for air, etc.)

This approach should be used with caution. The major assumption which impacts upon Equation 6-30 is that the fraction absorbed is constant across various concentrations and doses. As discussed in Section 6.4.2 and in U.S. EPA (1994), this assumption cannot always be considered to be sound. It most probably only applies at low doses and within any one species. It is an approach which, with care, can be used for certain conditions to give estimates until more reliable kinetic absorption data become available.

There is great concern regarding the potential dose resulting from lactation. Given the body burdens discussed in previous chapters and sections, lipid soluble substances might be expected to compartmentalize into milk and thus be transferred to nursing infants. Methods are needed to assess this potentially important route of exposure into the body.

The first step to calculating the daily intake for infants is to determine the levels in mother's milk. There are two general methods that can be used as a basis. The first assumes that levels in maternal fat remain at steady-state and reach an equilibrium with milk fat. Under these assumptions, Equation 5-1 ( repeated here as Equation 6-31) can be used to calculate the levels in maternal milk:

where,

C_{milk fat} = Concentration in maternal milk (pg/kg of milk fat)

m = Average maternal intake of dioxin (pg/kg body weight/day)

h = Half-life of dioxin in adults (days)

f₁ = Proportion of ingested dioxin that is stored in fat

f₂ = Proportion of mother's weight that is fat

Application of this equation to 2,3,7,8-TCDD, where an intake of 0.5 pg/kg/day, a half-life of 2555 days (7 years), 0.9 for f₁ and 0.3 for f₂ are assumed, results in a concentration in maternal milk fat of 5.6 ppt. This is higher than the 3.3 ppt. reported by Schecter et al., (1989).

A second and theoretically more accurate approach uses some type of physiologically based pharmacokinetic model to estimate the dynamically changing concentrations in mother's milk. One way to accomplish this is to add a mammary compartment to the compartmental model described in Section 6.3. The model is then extended to depict the toxin's transport into the milk. In the simplest form the following two equations would be added:

where,

dC_ma /dt = Change in the concentration of dioxin in mammary compartment

Q_ma = Blood flow to mammary compartment

C_b = Concentration of dioxin in blood

R_ma = Mammary tissue to blood partition coefficient for dioxin

F_mi = Flow of milk

R_mi = Milk to mammary tissue partition coefficient for dioxin

V_ma = Volume of mammary compartment

and

where,

dC_mi/ /dt = Change in concentration of dioxin in mother's milk

V_mi = Volume of milk

Other symbols as previously defined.

When the model is actually implemented, the changes in proportion of body fat in the mother that normally occur during lactation are taken into account. Observation of the two previous equations quickly shows that several new parameters are now added to the compartmental model. Many of these parameters have not been determined for most of the congeners of interest. In fact, even some of the physiologic and anatomic parameters are not readily available. Thus, for the time being it may be best to use some type of steady-state model and Equation 6-31 or to actually use monitored data for calculating dose to a lactating infant. It should be noted that the model was applied for 2,3,7,8-TCDD and parameters were adjusted to predict levels near the 3.3 ppt value published by Schecter et al. (1989). This is not a validation of the model or its parameters; of interest, however, is that the model predicted the same ratio between milk lipids and plasma lipids as reported by Schecter et al. (1989).

There are a number of measures of dose that can be used to compare the impact of exposure through lactation versus exposure through background. A common measure of dose, described in Chapter 5, is to calculate an average daily dose (ADD). Equation 5-2 (repeated here as Equation 6-34) describes such a calculation for the infant:

where,

ADD_infant = Average daily dose to the infant (pg/kg/d)

IR_milk = Ingestion rate of breast milk (kg/d)

ED = Exposure duration (year)

BW_infant = Body weight of infant (kg)

AT = Averaging time (year)

f₃ = Fraction of fat in breast milk

f₄ = Fraction ingested contaminant which is absorbed

Assuming a concentration of 2,3,7,8-TCDD in milk fat of 3.3 ppt, values for f₃ and f₄ of 0.04 and 0.9, respectively, an average infant body weight of 10 kg, an exposure duration of one year, an ingestion rate of milk of 800 g/d, and an averaging time of one year, an ADD equal to 9.5 pg/kg/d is calculated. Using the same assumptions, except for an averaging time of 70 years (the entire assumed lifetime), an ADD equal to 0.135 pg/kg/d is calculated. Thus, depending upon the averaging time, lactation results in ADD similar to that resulting from background (0.135 pg/kg/d compared to 0.51 pg/kg/d) or an ADD over an order of magnitude higher (9.5 pg/kg/d compared to 0.51 pg/kg/d). Little agreement exists regarding the appropriate choice of an averaging time for less than lifetime exposures. This is especially true for cases where exposure is occurring in a particularly sensitive developmental period. Lifetime averaging may be used for long time or even lifetime exposures, but the logic of applying it to short exposures is not clear.

Equally unclear is the utility of the ADD calculation itself. The ADD is actually an average intake over an arbitrarily chosen period of time. The significance of the ADD is not apparent, especially in cases of compounds, such as the CDDs and CDFs, that reach steady-state levels during chronic exposure.

It is recommended that other measures of dose be examined. As advanced and new mechanistic knowledge develops, new measures of dose should be used and examined. Recent studies (Andersen and Greenlee, 1991; Andersen et al., 1993) show the importance of receptor-mediated processes. The actual toxicologically relevant dose may be related to the induced production of specific hepatic proteins. Scientific research is still needed to determine the exact role these play in the various toxic responses that may be caused by the CDDs and CDFs. As this type of mechanistic information develops, and its relevance to humans becomes better established, pharmacokinetic models will be expanded to become pharmacodynamic models and then more realistic measures of dose can be determined.

For the time being, macroscopic measures other than the ADD should also be examined for assessment purposes. One approach to estimating such measures is to use the compartmental model described in Section 6.3. For the case of infants and children, the model is modified to account for the changing body weight of the child during the first 20 years of life. The model is used here under each of the three following exposure conditions for 2,3,7,8-TCDD:

· One year lactational exposure at levels corresponding to a milk fat concentration of 3.3 ppt followed by 69 years exposure at levels corresponding to background daily intakes of 0.51 pg/kg/d.

· 70 year exposure at levels corresponding to background daily intakes of 0.51 pg/kg/d.

· One year lactation exposure at milk fat concentration of 3.3 ppt.

Results of the simulation reveals several things. Figures 6-5 through 6-7 show the fat concentration profiles after the above three exposure scenarios for 2,3,7,8-TCDD. Figure 6-5 shows the fat level to peak quickly during the lactation period and then diminish until it reaches the steady-state level of about 8.0 ppt (8000 pg/kg). This is contrasted to Figure 6-6 where only background (no lactation exposure) is simulated. Note that in both cases the steady-state fat levels are 8.0 ppt. Lactation causes a temporary peak that diminishes over the next several years. Figure 6-7 shows the results of the simulation for the lactational phase only. This scenario assumed no further exposure after lactation ceased and was performed to investigate the impact of the lactational exposure apart from background exposure. Note that the half-life during the childhood years is shorter than that for adults (discussed in previous sections). This shorter half-life may be attributed to the changing size of the body and the compartments represented in the model. In fact, after age 20 (after which the body weight is assumed to remain constant) the model predicts the same half-life as previously discussed (7 £ t_1/2 ³ 8 years). Careful inspection

of Figures 6-5 and 6-6 also reveals that the time to reach steady-state is the same as discussed in previous sections (> 30 years).

Other measures of dose can also be used for comparison purposes. Care should be taken when ascribing meaning to different measures of dose, especially when exposure patterns of widely different duration are compared. Additional complexity is added by the fact that the lactational exposure occurs during the early developmental period of the individual. Given, these caveats, it may still be worthwhile to look at time integral (area under the curve or AUCs) measures of mass that has resided in the body throughout the exposure period. This is not a simple calculation of intake, but rather a measure of cumulative mass within the body as calculated by the model. The time integral of the mass in the body compartment (AUCBO) is used here for discussion and comparison. Lactation exposure during the first year and background exposure during the remaining 69 years results in an AUCBO at 70 years of 3.01 X 10⁶ pg-years. Seventy years of background exposure with no lactational exposure results in 2.95 X 10⁶ pg-years. The one year lactation exposure results in 7,862 pg-year at the one year mark. Obviously, in terms of pg-years the contribution from lactation is minor compared to background exposure.

It is not clear, however, whether this is an appropriate measure of dose to compare exposure patterns occurring at very different times of the lifetime. This same measure of dose can be averaged over the exposure time and then compared. The results appear different when the above three AUCBOs are converted to a pg/kg/day basis. The AUCBO averaged over exposure for the combined lactation and background exposure is 1.68 pg/kg/day ([3.01 X 10⁶ pg-years]/70 kg/[365 d X 70 years]), 1.64 pg/kg/day for the background only case, and 2.15 pg/kg/day ([7,862 pg-years]/10 kg/365 d X 1 year]) for the lactational portion of exposure. Using this time-averaged measure, it appears that the one year lactational phase contributes slightly more, on a daily average basis, than the 69 year background phase. In addition, for some toxic end-points the first year of life may be more vulnerable than later years. How any of these measures are related to risk remains unknown and caution should be exercised before drawing conclusions. The goal here is to present different methods that might be used for comparison purposes. As mentioned previously, as the mechanisms of action become better elucidated other more appropriate measures of dose should be used to make relative risk comparisons.

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