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School

PMB

Subject Area & Catalogue

number

PHAR 2006

Course Name

Pharmacokinetics and Biopharmaceutics

Student ID

Given Name/s

Surname

If you are required to use a

calculator, please note the make

and model here

Make:

Model

Official Reading Time:

Writing Time:

10 Minutes

2:00 hr/s

Question

Value

Mark

1

30

2

20

3

26

4

24

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

Page 1 of 12

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.

Time (min)

Cp. (µg/L)

10

32.5

20

17.5

30

11.3

40

8.0

60

5.5

90

4.0

120

3.2

150

2.5

180

2.0

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)

(b)

Determine the equation that describes the plasma concentration (C) following the

dose, where concentration is in µg/L and time is in hours.

(5 marks)

(c) Calculate the plasma clearance (L/h) of the drug.

(4 marks)

(d) Calculate the initial Volume of Distribution (L).

(3 marks)

Page 2 of 12

(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)

Page 3 of 12

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

Renal clearance

80% of creatinine clearance

Non-renal clearance

0.14 ml.min-1.kg-1

Volume of distribution

0.42 L.kg-1

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)

Page 4 of 12

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)

Page 5 of 12

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

↓

↓

↔

↔

↔

↔

↑

Page 6 of 12

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)

Page 7 of 12

(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)

Page 8 of 12

(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)

Page 9 of 12

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

CL

=

Dose/AUC

Hepatic clearance

CLHb

=

QH

f .CL

Q + f .CL

u int

H u int

⎛⎜⎝

⎞⎟⎠

Renal clearance

CLR =

⎛⎜⎝

⎞⎟⎠

fu

.GFR +

QR.fu.CLI

QR + fu.CLI (1-FR)

Page 10 of 12

Volume of distribution

T

T

fu

P

Pharmacodynamic response

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

Incremental

= Vd (Cp desired – Cp initial)

Loading Dose

F

Average steady-state = F Dose/τ

plasma concentration Cl

(Cpssave)

Cpssmax =

(Dose) (F)

(Vd) (1-e-kτ )

Cpssmin =

(Dose) (F) x e-kτ

(Vd) (1-e-kτ)

Creatinine Clearance (CrCl)

CrCl (mL/min) =

(140-Age) x LBW (kg) x F

Serum Creatinine (micromol/L)

F= 1.23 (males) or 1.04 (females)

Page 11 of 12

Bioavailability

F = (AUC)oral x Dose iv

(AUC)iv x Dose oral

Non-linear Equations

(F) (Dose/τ) =

(Vm) (Cpss ave)

Km + Cpss ave

Cpssave

=

(Km) [(F) (Dose/τ)]

Vm – (F) (Dose/τ)

Page 12 of 12

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