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Toxicokinetics 3 Computer Exercises
Crispin Pierce, Ph.D.
University of Washington
[email protected]
(206) 616-4390
The goal of these exercises is for you to
become familiar with using a software tool
(in this case PCCAL) to predict drug or
toxicant concentrations in the body. In
the four cases below, we are assuming
that the drug and toxicants distribute into
and are eliminated from a single
compartment.
 When the rate of elimination is proportional to the
concentration in the body (first-order elimination), the
concentration in a single compartment is given by C  C0e kt
where C is the concentration at time t, C0 is the
concentration at time = 0, and k is the elimination rate
constant. The half-life is given by t  ln 2 k . When the
mechanism of elimination has been saturated (e.g., there is
more chemical in the body than can be easily metabolized),
then the rate of elimination is limited and no longer
dependent on the concentration (zero-order elimination).
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 As you complete each case below, decide whether the rate
of elimination is first- or zero-order.
The Case of the Deathcap
Mushrooms
 You are a Harborview Hospital intern, when the attending ER
physician asks for your help in a deathcap mushroom (Aminita
phalloides) poisoning case. The patient gathered a number of
mushrooms in preparation for a meal he ate two hours ago. While
symptoms of serious mushroom poisoning don’t appear until about
12 hours after consumption, blood levels of chemicals in the
mushrooms are measurable earlier. The physician has taken two
blood samples to measure the concentration of the toxic ingredient,
with the following results:
Time (hours after exposure)
2.25
4.5
Concentration (mg/liter)
23
33
 She asks for your help in "back-predicting" the dose of mushrooms
that led to the measured concentrations in blood. Depending upon
your modeling results, she may or may not perform a liver
transplant to save the patient's life.
 Click on the "Simulations" button in the PCCAL
software, then on the "Oral Administration"
button, then on the "One Compartment Model Single Dose" button.
 Click on "Pharmacokinetic Model" and review the
meanings of the symbols used in this kind of
model.
Click on the right arrow in the lower right corner,
to go to the third page, "One Compartment Model
- Single Oral Dose: Linear Scale."
 In order to back-predict the dose, you will enter the information
known about this poison, then try different dose estimates to find
the value that results in the measured concentrations.
 By clicking on the "Set Bio" button (or using the
slider bar), set the value of F (bioavailability) to
0.85.
 Set the value of Vd (the volume of distribution) to
10 liters.
 Set the value of ka (the absorption rate constant)
to 0.2 hours-1.
 Set the value of k (the elimination rate constant)
to 0.1 hours-1.
By using the slider bar, or typing in values, try
different dose values (in mg) and click on the
"Plot" button to find the value that produces the
measured concentrations. Dose = ______ mg.
 The physician needs to know how much of the
mushrooms the patient ate. If he ate more than 50
grams, the transplant will be necessary.
 Assume that the dose of poison you backpredicted is 1% of the weight of the
mushrooms. What is the estimated weight of
the consumed mushrooms? ________
grams.
Should this patient have a liver transplant to
save his life? ________
The Case of the New
Antiepileptic Drug
 With your background in math modeling, a large drug company
invites you to serve as a paid intern over the summer. The
company has a new drug that is effective in suppressing seizures,
and would like your help in establishing a safe and effective dosing
regimen. Initial tests have found that below a concentration of 50
mg/liter, the drug does not prevent seizures, and above 75 mg/liter,
damaging side effects begin to appear.
 Find the page within the software entitled "One
Compartment Model - Multiple Oral Doses: Linear
Scale"
 Click on the "Adjust X scale" button and type in
168 hours, representing one week, the time for
drug concentrations to stabilize.
Enter the known information about the drug:
F=0.95, Vd= 25 liters, ka=0.5 hr-1, k=0.05 hr-1.
Pills can be manufactured containing 500,
1,000 and 2,000 mg of the drug. By
experimenting with the dose and dosing
interval, find a regimen that will be
effective (giving a concentration between
50-75 mg/liter) and relatively convenient
to the patients (taking pills at the longest
interval possible). Dose: ________ mg
taken every _______ hours.
The Case of Dietary Fat
Most of the toxic stuff that gets into our
bodies enters through the mouth. We’ll
examine a single oral dose of fat from a
McDaniel’s fatburger. Because oral
exposure involves an absorption
component, this route is similar to dermal
exposure.
Click on “Simulation Examples” and then on
“Single Oral Dose.” By clicking on the forward
button in the lower right hand corner, and the
“Continue” button, proceed through the tutorial
to learn how dose, bioavailability, the elimination
rate constant, and the absorption rate constant
affect predicted levels of drug or toxicant. The
elimination rate constant (k) represents a
clearance process and is given by kelimination
(min-1) = Clearance (L/min) / Volume (L). The
clearance represents the process through which
the body eliminates the chemical, and the
volume represents the space into which the
chemical distributes.
 Click on “Return to Menu” and then “Go to Package
Menu” then “Simulations,” “Oral Administration,” and
“One Compartmental Model – Single Dose.” Go to
“Simulation Plotted on Semilog Scale.”
 Give yourself a 2 g (2,000 mg) dose of fat (from just the
first bite!) by clicking on “Set Dose” or using the slider.
Set bioavailability to 0.9 (either that late-night TV "Fat
Blocker” is working a little bit, or more likely, some of
the fat is bound up in the gristle). Set the volume of
distribution to 7 L (we’ll assume the fat is digested into
fatty acids, which circulate primarily in blood). Enter an
absorption rate constant (ka) of 1 hr-1 (corresponding
to a half-life of about 45 min, k = 0.693/t1/2), and an
elimination rate constant (k) of 0.5 hr-1 (a half-life of
about 1.3 hours; elimination is usually slower than
absorption). Click on “Plot” and examine the curve.
 Now, what do you think will happen to the shape of the
curve – in terms of Tpeak (the time to reach the peak
concentration), Cpeak (the peak concentration), the AUC and
the slope of the terminal phase if you lower the
bioavailability (F)?
 Tpeak: Decrease ____ Stay the same ____ Increase ____
 Cpeak: Decrease ____ Stay the same ____ Increase ____
 AUC: Decrease ____ Stay the same ____ Increase ____
 Terminal phase slope: Decrease ____ Stay the same ____
Increase ____
 Pretend you took some psyllium-containing laxative prior to
the fatburger, which lowered fat bioavailability to 0.5.
Change F to 0.5, plot, and see if your predictions are
correct!
 Change F back to 0.9 and simulate what might happen if
you had a large salad before your burger, slowing the rate
of absorption (ka). What do you think will happen to Tpeak ,
Cpeak , the AUC and the slope of the terminal phase, when
you lower ka to 0.25 (smaller than the k value of 0.5)?
 Tpeak: Decrease ____ Stay the same ____ Increase ____
 Cpeak: Decrease ____ Stay the same ____ Increase ____
 AUC: Decrease ____ Stay the same ____ Increase ____
 Terminal phase slope: Decrease ____ Stay the same ____
Increase ____
The Case of the Inebriated
Student
Because the alcohol dehydrogenase enzymes
are rapidly saturated (after a single drink),
alcohol provides a good example of non-linear
kinetics -- the rate of decline is not related to
the amount of alcohol in the body.
Click “Return to Menu,” “Back to Simulations
Menu,” “Go to Package Menu,” and click on
“Simulation Examples” to go through the
“Nonlinear Elimination” tutorial. Note especially
what happens when the oral dose is increased.
 Click on “Return to Menu” and then “Go to Package
Menu” then “Simulations,” “Nonlinear Elimination,” and
“Single Oral Dose – Nonlinear Elimination.” Go to
“Simulation Plotted on Semilog Scale.” Click on “Adjust x
Scale” and set the value to 10 hours. Click on “Adjust y
Scale” and set the value to 10.
 Doses of ethanol are much higher than for most drugs
and toxicants, and so we’ll be using units of grams (g)
instead of milligrams (mg). Give yourself a 4.2 g dose (F
= 1) of ethanol (about a third of a glass of wine, can of
beer, or mixed drink), with a ka of 1 (hr-1), a volume of
50 L (total body water), a km (affinity constant between
alcohol and alcohol dehydrogenase) of 0.1 g/L, and a
Vmax (maximal rate of enzyme activity) of 10 g/hour.
Plot the results.
 Assuming that we are in a range where the enzyme is
beginning to be saturated, predict what the shape of the
curve will be (Tpeak , Cpeak , the AUC and the slope of the
terminal phase) when you take a dose of 42 g (three
drinks). How do you think kinetic parameters will change
with this 10-fold dose?
 Tpeak: Decrease ____ Stay the same ____ Increase ____
 Cpeak: Less than 10-fold ____ 10-fold ____ More than 10fold ____
 AUC: Less than 10-fold ____ 10-fold ____ More than 10fold ____
 Terminal phase slope: Decrease ____ Stay the same ____
Increase ____
 Plot the results to see if you are correct. What happens
when you double the dose to 84 g (six drinks)?
 Under which of these three doses (if any) would you be
legally intoxicated, with a blood alcohol level of 0.08%
(0.08 g ethanol /100 g blood, remember that the y-axis
scale is g/L, or approximately g/1,000 g)?
______________
 How long would you have to wait before your blood
alcohol level declined to 0.08%? _________
 How would you characterize the rates of elimination in
the four cases that you solved?
Substance
First-Order
Zero-Order
Mushrooms


Antiepileptic
Drug
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
Fat
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
Ethanol
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