Pharmacokinetics and Biopharmaceutics

Instructions to Candidates:
Graph paper is provided. Please write your name on the graph paper.
A list of symbols and equations is provided at the back of the exam.
The mark allocated to each question is shown in the table above.
Ensure that your answers are in the correct units.
Permitted Materials
Non-programmable calculator
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Question 1
The following plasma data was obtained following the intravenous injection of 1.5 mg of
Drug X into a 70 kg healthy volunteer.

Urine was collected for 8 hours after the dose and found to contain 0.1 mg of unchanged
drug.
Previous in vitro studies have demonstrated that the blood to plasma ratio (λ) is 0.3 and the
fraction unbound is 0.7. The drug is known to be a weak acid.
(a) Plot the data on the graph paper provided (5 marks)

(5 marks)
(c) Calculate the plasma clearance (L/h) of the drug.
(4 marks)
(d) Calculate the initial Volume of Distribution (L).
(3 marks)
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(e) Calculate the terminal Volume of Distribution (L). (3 marks)
(f) If a second dose of the drug (1.5 mg) was to be given four hours after the first dose,
what would the concentration (µg/L) be immediately following the second injection:
(3 marks)
(g) Using appropriate calculations, explain whether a change in urine pH is likely to
affect the renal clearance of Drug X.
(4 marks)
(h) Following this, do you consider that alkalinisation of the urine is likely to have a
significant effect on drug clearance in the case of an overdose?
(3 marks)
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Question 2
The aminoglycoside antibiotics, administered intravenously, are widely used in hospitals
for the treatment of serious systemic gram-negative bacterial infections. The
aminoglycosides are unusual in that therapeutic benefit (bacterial killing) is associated
with maximum concentrations of at least 10 mg.l-1, while trough (minimum)
concentrations of below 0.5 mg.l-1 are required to prevent toxicity to the patient’s
kidneys. You are a hospital pharmacist required to design a dosing regimen for a 72 kg
male patient who is 50 yr old. His serum creatinine concentration is 79 micromolL-1.
Pharmacokinetic parameters

Showing your calculations, answer the following questions:
a What is the total clearance in this subject? Show your calculations. (2 marks)
b What dosing interval would you choose? Justify your answer. (5 marks)
c Given the answer to (b):
i What steady-state concentration (Cpss, ave) would be associated with a target
steady-state AUC of 72 mg.hr.L-1? (2 marks)
ii What maintenance dose would you employ to achieve this concentration?
(3 marks)
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d For the regimen in (c), What are:
i. Cpss, max
ii Cpss, min (2 marks)
e Are these acceptable concentrations? Briefly justify you answer. (2 marks)
f If a patient suffered from toxicity due to trough concentrations that were too high:
i What impact would the toxicity have on the pharmacokinetics of the drug? Briefly
justify your answer. (2 marks)
ii Briefly, what procedure would you employ to redesign the dosing protocol using
information about the patient? (2 marks)
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Question 3.
Complete the table below to show tendencies by marking: ↑ for increase, ↓ for decrease,
for little or no change, ‘Low’ for a low hepatic extraction ratio drug, or ‘High’ for a high
extraction ratio drug.
Assume a blood to plasma ratio of 1, fe of 0.001, complete absorption from the intestine, and
that there is no change in Clint.
(26 marks)

Hepatic Extraction Ratio	Hepatic Blood Flow	Fraction Unbound in Plasma	Fraction Unbound in Tissue	Total Clearance	Volume of Distribution	Elimination Half Life	Oral Bioavailability
High	↓
High		↑
High	↓	↑
Low			↓
Low	↓
Low	↓	↓
			↑

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Question 4
Consider the following schematic:
Ke = Kf + Ko
In the space provided, sketch the drug and the metabolite concentration-time profiles that
you would expect following a single oral dose in each of the following situations. Under
each sketch, write a few lines describing the key features of the profile.
(a) Ke is much smaller than Km, and Ka is much larger than Km. (6 marks)
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(b) Km is much smaller than Ke, and Ka is much larger than Ke. (6 marks)
(c) Ka is much smaller than either Ke or Km. Km is larger than Ke (6 marks)
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(d) Discuss whether the value of Km needs be taken into account when designing a dosing
and therapeutic drug monitoring regimen for a patient.
(6 marks)
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Equations and physiological values
Glomerular filtration rate = 120 mL/min
Hepatic blood flow = 1.5 L/min
Renal blood flow = 1.2 L/min
Cardiac output = 5 L/min
Haematocrit = 0.5
Plasma concentrations after an intravenous bolus
– monoexponential C = C(0).exp-k.t
– biexponential C = A.exp-α.t + B.exp-β.t
Plasma concentrations during an intravenous infusion (monoexponential only)
C = (Ro/CL).(1-exp(-k.t))
where Ro is the zero-order infusion rate
Plasma concentrations after an extravascular dose
[ ] tk tka
kkaVd
kaDoseF
C . expexp .
).(
..
– –
–
–
=
Half-life and elimination rate constant
k = Cl
Vd
t½ = ln2
k
k = – ln(Cp2/Cp1)
t2 – t1
Physiological determinants of clearance and volume of distribution

f .CL
Q + f .CL
u int
H u int
⎛⎜⎝
⎞⎟⎠
Renal clearance
CLR =
⎛⎜⎝
⎞⎟⎠
fu
.GFR +
QR.fu.CLI
QR + fu.CLI (1-FR)
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Volume of distribution

fu
+= VVVd
nn
n
CEC
CE
E
+
=
50
max .
Accumulation Index
⋅- τ
–
=
A k
Ass
exp1
1
1max,
max
Oral dosing equations
Loading Dose = Vd Cp
LD F

Average steady-state = F Dose/τ
plasma concentration Cl
(Cpssave)

Creatinine Clearance (CrCl)

F= 1.23 (males) or 1.04 (females)
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Bioavailability
F = (AUC)oral x Dose iv
(AUC)iv x Dose oral
Non-linear Equations

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