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CHE3BPH Biopharmaceutics

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Question:

A patient weighing 73 kg received a 250 mg dose of drug via an IV injection. Blood samples were taken from the patient at regular intervals and the drug plasma concentration was determined for each sample (see the table below).
Time (hr) Cp (mg/L)
0.25 11.6
0.5 8.4
0.75 7.2
1.00 6.1
1.50 4.2
2.00 3.2
3.00 1.9
4.00 1.0
6.00 0.3

(a) Plot the data and determine the elimination rate constant for this drug.
(b) Determine both the half-life (in both minutes and hours) and the volume of distribution (in both L and L/kg) for this drug.
(c) The minimum therapeutically active concentration of the drug is 10 μg/mL. What is the duration of action of this drug?
(d) If the dose of the drug was doubled, what will be the increase in its duration of action?
(e) How long would it take for: (i) 50.0%, (ii) 75.0 %, and (ii) 99.9% of this drug to be eliminated from the body?
(f) Plot the data and estimate the clearance of the drug using the area under the curve method.
(g) If 45% of the drug is excreted unchanged in the urine, determine both the renal and metabolic clearances.

Question 2
An 80 kg patient is to be given a 1.5 mg/kg body weight dose of gentamicin intravenously over 1 hour every 8 hours. Assume the half-life of gentamicin and volume of distribution in the patient are 2.6 hours and 0.25 L/kg respectively.
(a) List the main reasons why a patient would be prescribed IV administration of gentamicin.
(b) How long will it take for gentamicin to reach steady state plasma concentration?
(c) Calculate the peak and trough plasma concentrations of gentamicin after: (i) 1 dose, (ii) 2 doses, and (iii) 5 doses.
(d) Calculate the steady state peak and trough plasma concentrations of gentamicin.
 
What is the purpose of giving a loading dose to a patient? In the light your peak and trough plasma concentration calculations, do you think it is necessary for a loading dose of gentamicin to be used in treating this patient?
(e) If the dose of gentamycin given in a 24 hour period remains the same, but dosing frequency is decreased to 12 hour intervals, determine the steady state peak and trough plasma concentrations.Comment on your results and whether changing the dosing interval has affected steady state peak and trough plasma concentrations.

(f) If the dose of gentamycin was halved, what is the change observed in the steady state peak and trough plasma concentrations (providing the elimination rate constant, volume of distribution, and dosing interval remain the same as in part (a) of the question)
(g) If the volume of distribution decreases by 50%, what is the change observed in the steady state peak and trough plasma concentrations (providing the dose elimination rate constant, and dosing interval remain the same as in part (a) of the question)?
Question 3
A 70.0 kg patient is given a 2.6 mg/kg dose of a drug by intravenous injection. Blood samples were taken from the patient at regular intervals and the drug plasma concentration was determined for each sample (see the table below).
Time (min) Cp (mcg/mL)
2.0 93.08
7.0 69.11
10.0 63.82
15.0 54.79
20.0 48.73
30.0 38.63
45.0 27.85
60.0 22.92
75.0 19.12
90.0 13.62
105.0 11.43
120.0 9.04
(a) The pharmacokinetics of the drug displays two-compartment model kinetics. Plot the data for the drug and determine the rate constants for the both distribution phase and the elimination phase.(b) Give a brief description of the two-compartment model. In your answer include definitions for the terms “distribution phase” and “elimination phase” and indicate on your graph where these regions occur.
(c) Explain why the distribution phase rate constant is greater than the elimination phase rate constant.

Question 4 
Phenytoin is being taken by a patient to control seizures. A daily dose of 300 mg at bedtime results in a steady state plasma concentration of 8 mg/L. When the dose is increased to 400 mg, the steady state plasma concentration changes to 22 mg/L. Assuming Michaelis-Menten kinetics, determine the daily dose that would give a steady state plasma concentration changes of 15 mg/L. Include a plot of the data and the Michaelis-Menten parameters that you used to calculate your answer.

Question 5
(a) A small drop of oleic acid is placed on the surface of a beaker of water. Determine the spreading coefficient and the contact angle of the oleic acid with the surface of the water. Does the oleic acid will spread spontaneously over the surface of the water? Give a brief explanation to support your answer.
Note: ϒ(water) = 72.9 mN m-1
; ϒ(oleic acid) = 32.5 mN m-1
; ϒ(oleic acid-water) = 15.6 mN m-1 at 20 °C.
 
(b) You have 120.0 g of a 30.0 % w/w paraffin aqueous mixture in a sealed bottle and the bottle is shaken to from an emulsion. Determine the amount of work that would be required to form an emulsion where the disperse phase consisted of paraffin droplets with an average particle diameter of 25 μm. ϒ(water-liquid paraffin) = 52 mN m-1 at 20 
(c) A small amount of polysorbate 80 is then added to the mixture (in part (b) of the question). The interfacial tension is measured and is now 22.4 mN m-1 Determine the work now required to produce an emulsion with paraffin droplets with an average particle diameter of 25 μm. Explain why the presence of polysorbate 80 changes the amount of work required to produce an emulsion with an average particle diameter of 20 μm.

(d) Draw the structure of polysorbate 80 and explain why it is more soluble in water at lower temperatures?
Question 6 
(a) You have been asked to prepare a suspension of a drug that is available in tablet form. To prepare your suspension you first crush the tablets in a pestle and mortar. What excipients would you use to prepare a pharmaceutical suspension of this drug that is suitable for oral use? Provide reasons for your choice of excipients. Include in your answer a description of the general requirements for an acceptable pharmaceutical suspension.
(b) List all of the physical parameters that affect the rate at which solid spherical particle settles out in a suspension.
 
(c) Unfortunately, the tablet powder in your suspension is very hard to re-suspend even with considerable shaking. However, after consulting several references you decide to add a small amount of sodium citrate to the suspension. The sediment that forms is now much less dense and also much easier to re-suspend.From your knowledge of charged surfaces in solution, explain how the addition of sodium citrate to the suspension improves the ability of the tablet powder to be re-suspended.
(d) Often, a surfactant is added to a suspension mixture in order to make it easier to re-suspend the solid
particles. With the aid of diagrams, describe the mechanisms to explain how this occurs
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