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Toxicokinetics 1
Crispin Pierce, Ph.D.
University of Washington
[email protected]
(206) 616-4390
Exposure to Exogenous Substances
Food
SECRETION OF
ENDOGENOUS
SUBSTANCES
Drugs
Toxicants
ABSORPTION THROUGH THE
GI TRACT, LUNGS, SKIN AND
VENOUS CIRCULATION
DISTRIBUTION WITHIN THE BODY
PHYSIOLOGIC EFFECT
AT A TARGET SITE
Pharmaco- and
Toxicodynamics
METABOLISM
STORAGE
ELIMINATION
Pharmaco- and
Toxicokinetics
Absorption
Absorption assumes
primary importance
in oral, inhalation,
and dermal
exposures. The two
kinetic parameters of
concern are the rate
of absorption and the
extent of absorption
(or bioavailability).
Rate of Absorption
The rate of absorption determines the time of
onset and the degree of acute toxicity. This is
largely because time to peak (Tpeak) and
maximum concentration (Cmax) after each
exposure depend on the rate of absorption.
Rate the following processes in order of
fastest to slowest: ORAL, DERMAL,
INHALATION, INTRAVENOUS EXPOSURE.
A
C-max
Conc.
minimum toxic conc.
B
T-peak
Slowing of absorption
(AB)
- prolonged Tp
- lower Cmax
Time
In instances when the absorption rate is slower
than elimination rate, the rate of washout of
toxicant becomes rate-limited by absorption rather
than by elimination (i.e., a depot effect).
Absorption faster than elimination
Elimination faster than absorption
i.v. dose
i.v. dose
log
Conc.
non-i.v. dose
log
Conc.
non-i.v. dose
Time
Time
?
How does having pizza with your beer get
you drunk more slowly?
Systemic Availability
The actual extent of exposure as defined by
the amount of toxicant reaching the systemic
circulation is determined by (1) entry barrier
permeability, and (2) the extent of "first-pass"
metabolism.
The fraction of dose reaching the system
circulation in intact form, or systemic
availability (F), is estimated from either the
AUCs,
F = (AUCroute/AUCi.v.)
Or from the amount of intact toxicant excreted
in urine or exhaled via the lungs (Aex).
F = (Aex-route/Aex-i.v.)
?
Is mercury amalgam in tooth fillings
dangerous?
Modeling Absorption
Intravenous dosing
IVrate = IVdose / Timeinf
 and input into venous blood.
Percutaneous dosing
Percrate = (Percdoseexp(-KA,percTime))KA,perc
and input into venous blood
Oral dosing
Oralrate = (Oraldoseexp(-KAoralTime)) KA oral
and input into liver
Inhalation dosing
Inhalationrate = CartQc
Qp * (Cinh- Calv) = Qc * (Cart - Cven)
kblood/air = Pblood/air = Cart / Calv
Cart = (QpPb/aCinh + CvenPb/aQc)/(QcPb/a + Qp)
Volume of Distribution
The Volume of
Distribution is the
apparent volume into which
a drug or toxicant
distributes, and provides a
proportionality constant
between blood (or plasma)
concentration and the
amount in the body:
Volume of Distribution =
Amount / Concentration
Co
Ln of
Blood (or
Plasma)
Conc.
The volume of distribution
can be readily calculated
V = Dose / Co
after an intravenous bolus
dose of a substance that
exhibits "one-compartment
model" characteristics:
Time
Volume of Distribution =
Dose / Initial Concentration
V = Dose / k•AUC
Ln of Blood
(or Plasma)
Conc.
slope = -k
AUC
Time
However, because of
the uncertainty in the
estimate of Co,
volume can be more
accurately estimated
by V = Dose /
(kAUC), where AUC
is the area under the
concentration-time
curve.
The volume of distribution does not
necessarily correspond to any
physiologic volume, and is influenced by
binding to plasma and tissue constituents.
Volume can range from about 3 liters (as
is seen with Tolbutamide, which is
distributed in blood only, to about 50,000
liters (as is seen with Quinacrine, which
distributes and binds to many tissues).
The volume of distribution relates blood
conc. to the total body burden of a
toxicant, i.e., ABody = VCblood
Physiologic Meaning? A measure of
extravascular distribution.
Two determinants of distribution into a
tissue region:
Tissue or organ volume Vti
Distribution or Partition ratio Ptissue/blood =
Cti/Cblood a constant @ pseudo-distribution
equilibrium or steady state.
Accordingly, ith Tissue Load = VtiCti =
Vti(Pi,Cblood)
Total Tissue Load = VtiPiCblood
Total Body Load = Amount in blood +
Amount in tissues
ABody = VbloodCblood + VtiPiCblood =
(Vblood + VtiPi)Cblood
V = ABody/Cblood = Vblood + VtiPi where
Vblood, Vti and Pi are constant.
Since Pi can assume a value ~0-, V
varies from a minimum of Vblood to many
times the body size. Because the volume
of distribution reflects the degree of
xenobiotic dispersal and binding to all
tissues, the following relationship is
observed:Vinitial< Vsteady-state< Vterminal phase
?
Would a chemical that is highly soluble in
water, such as ethanol, have a large or
small volume of distribution?
How about a chemical that is highly
soluble in fat, such as dioxin (TCDD)?
Clearance
Clearance is a measure of the body's
ability to completely clear a drug or
toxicant from blood or plasma. Clearance
is the rate of elimination by all routes
relative to the concentration in a systemic
biologic tissue, and is measured in units of
flow, or volume per unit time.
CL (units of volume/time) = Rate of
elimination (units of mass/time) /
Concentration (units of mass/volume)
Clearance is normally measured by
collecting blood concentration-time data
following a known dose, and using the
following equation: CL (units of
volume/time) = F*Dose (units of mass) /
AUC (units of time-mass/volume) where
F is the bioavailability (fraction of dose
entering systemic circulation), and AUC is
the area under the blood concentrationtime curve.
Blood (or
plasma)
Concentration
CL = F·Dose/AUC
AUC
Time
Clearance also plays a role in determining
the steady-state concentration of a drug or
toxicant:
Csteady-state = Rate of administration/ CL
Area Under the Blood Concentration Time
Curve (AUC): an internal or systemic
exposure index.


AUC  o Cb dt  o C0 • e dt  C0 / k
 kt
& since C0 = Dose/V, then AUC = Dose/kV
The product kV is equal to clearance.
AUC = Dose/CL or CL = Dose/AUC
i.e., clearance governs the extent of
systemic exposure as represented by
AUC for a given dose of toxicant.
Physiologic Basis of Clearance
Blood clearance can be resolved into components
representing the various metabolic and excretory
pathways of elimination, e.g., CL = CLmetabolism +
Clexhalation
or further resolved into organ clearances, e.g., CL =
(CLliver + CLg.i. tract + CLkidney + CLlung + ...)
Individual organ clearance can in turn be related to
organ blood flow (Qi) and extraction efficiency (Ei).
For instance, Hepatic Clearance (CLliver) = QliverEh,
note that Eh varies from 0–1 (i.e., 0 to 100%
extraction)
?
Would rapid breathing increase the
clearance of a substance that leaves the
body through the breath (such as nitrous
oxide used in dentistry)?
Half-Life
Ln of
Blood
(or
Plasma)
Conc.
C
1/2 C
Half-life
Time
The Half-life is a
measure of how rapidly
a steady-state
concentration will be
achieved during
constant rate dosing,
and conversely how
rapidly the
concentration will fall
after cessation of
exposure.
Half-life is related to the elimination rate
constant k by the formula: t1/2 = ln 2 / k
The elimination rate constant, like the
clearance, is a fractional rate of decline: k
= Rate of elimination / Amount
Since CL = Rate of
elimination/Concentration, the elimination
rate constant can be estimated: k = CL /
Volume of Distribution
Half-life can then be found by t1/2 = ln 2/ k
= ln 2 * V / CL
Elimination Half-life (t0.5, t1/2) is a
characteristic of First-order kinetics. For a
one-compartment model: dABody= - k ABody
 Since ABody declines with time, elimination
rate also decreases!
However, the fractional rate is a constant, i.e.,
- 1
ABody
-dABody/ABody
 —— ———  ——————— = k (time-1)
 ABody dt
dt
Upon integration, ABody = A0e-kt
A0 = Body load @ t=0
But blood conc. rather than body load is
measured.
ABody ~ Cblood and ABody = VCblood
Cblood = C0e-kt
or Ln Cblood = Ln C0 kt where C0=Blood conc. @ t=0
Note that when Cblood = 1/2C0, t = 0.693/k =
t1/2
It always takes 1 t1/2 to reach 50% of any
starting conc. (i.e., t1/2 independent of C0)
Takes about 3-4 t1/2s to effect 90% of
elimination or to achieve 90% of the
steady-state value under constant
exposure.
For compounds with multicompartmental
kinetics, there will be a t1/2 estimate for
each of the exponential phases. The
terminal t1/2 is often quoted as the
"Elimination t1/2," whereas the t1/2s of the
earlier phases are referred to as
"Distribution t1/2s.”
For example, in a two compartment model
described by Cblood = Ae-at + Be-bt , t1/2,a =
0.693/a and t1/2,b = 0.693/b
?
How would half-life be affected if a
condition such as kidney failure doubled
the volume of distribution for a particular
drug?
Does drinking coffee or another source of
caffeine help you to sober up? (Hint:
caffeine does not affect the volume of
distribution or clearance of ethanol.)
Why are certain subpopulations (e.g.,
pregnant women, children) more
susceptible to methyl mercury toxicity?
(Hint: Might certain populations get
higher doses of chemicals, possibly
concentrated in smaller masses of tissue?)