Biopharmaceutics & Pharmacokinetics (Ultimate final note)

Intravenous Infusion (IV): Define intravenous infusion. Write down advantages and disadvantages of intravenous infusion,
Write down the pharmacokinetics of IV infusion, Calculate the plasma drug concentration at steady-state after IV infusion, Determine the half life (t1/2) by IV infusion method, Show that in case of IV infusion the time to reach 99% steady-state is 6.65 t1/2.
Multiple-Dosage Regimens: Write a short note on Multiple-Dosage Regimens. What are the basic considerations for multiple dosage regimen?, What are the purposes of multiple-dosage regimens (MDR)? Write down the importance of MDR, Write short note on repetitive intravenous injections, Prove that C∞av is not arithmetic average of C∞max and C∞min, Give brief description on superposition principle and Plateau principle?.
Individualization: Write down about individualization of drug dosing regimen? What are the advantages of individualization? How will you optimizing dosage regimen?, What are the sources of variability in drug response? What are the causes of Inter subject Pharmacokinetics Variability? Write down the steps involved in individualization of dosage regimen?, Write short note on – dosing of drug in obese patient and also discuss about dosing of drug in neonates, infants and children?, Write down about dosing of drug in elderly and hepatic disease? Give some examples of drugs who's conc. Changes due to hepatic impairment?, Explain some clinical experience with individualization and optimization based on plasma drug levels?
NON-linear pharmacokinetics: Derive the Michaelis-Menten Equation or Non-Liner pharmacokinetic and Linear pharmacokinetic model, Define non-linear pharmacokinetics. Why it is called dose dependent pharmacokinetics?, Why Michaelis-Menten equation is termed as mixed order kinetics?, A given drug is metabolized by capacity-limited pharmacokinetics. Assume KM is 50훍g/mL, Vmax is 20훍g/mL per hour and apparent VD is 20 L/kg, Differentiate between linear & non-linear Pharmacokinetics.
Non-compartment model: Briefly describe compartment model?, Briefly describe non-compartment model?, What is MRT? Write down the importance of MRT?, What is MAT? Write down the importance of MAT?, Compare between compartment model and non-compartment models.

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Gono Bishwabidyalay
Nolam, Saver, Dhaka
8
th
Semester
Assignment on: Biopharmaceutics &
Pharmacokinetics-II (Pharm 4802)
Assignment topic: Question Answer

Submitted To:
Mst. Mahfuza Khatoon A.F.M Mahmudul Islam
Senior Lecturer & Senior Lecturer
Department of Pharmacy Department of Pharmacy
Gono Bishwabidyalay Gono Bishwabidyalay

Submitted By:
Md. Nazmul Islam Tanmoy
Class Roll: 74
Exam Roll: 2064
Batch: 32
nd

Department of pharmacy, GB.
Submission date: 26
th
July 2021

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INDEX
SI.
NO
Chapters Questions Page

no



01


Intravenous
Infusion
(IV)
Define intravenous infusion. Write down advantages
and disadvantages of intravenous infusion



01-
08
Write down the pharmacokinetics of IV infusion
Calculate the plasma drug concentration at steady-
state after IV infusion.
Determine the half life (t1/2) by IV infusion method.
Show that in case of IV infusion the time to reach
99% steady-state is 6.65 t1/2.




02


Multiple-Dosage
Regimens
Write a short note on Multiple-Dosage Regimens.
What are the basic considerations for multiple
dosage regimen?




09-
15
What are the purposes of multiple-dosage regimens
(MDR)? Write down the importance of MDR
Write short note on repetitive intravenous injections.
Prove that C
∞
av is not arithmetic average of C
∞
max
and C
∞
min.
Give brief description on superposition principle
and Plateau principle?






03







Individualization
Write down about individualization of drug dosing
regimen? What are the advantages of
individualization? How will you optimizing dosage
regimen?







15-
23
What are the sources of variability in drug
response? What are the causes of Inter subject
Pharmacokinetics Variability? Write down the steps
involved in individualization of dosage regimen?
Write short note on – dosing of drug in
obese patient and also discuss about
dosing of drug in neonates, infants and
children?
Write down about dosing of drug in elderly and
hepatic disease? Give some examples of drugs
who's conc. Changes due to hepatic impairment?
Explain some clinical experience with
individualization and optimization based on
plasma drug levels?

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04





NON-linear
pharmacokinetics
Derive the Michaelis-Menten Equation or Non-
Liner pharmacokinetic and Linear pharmacokinetic
model.







23-
31
Define non-linear pharmacokinetics. Why it
is called dose dependent pharmacokinetics?
Why Michaelis-Menten equation is
termed as mixed order kinetics?
A given drug is metabolized by capacity-
limited pharmacokinetics. Assume KM is
50??????g/mL, Vmax is 20??????g/mL per hour
and apparent VD is 20 L/kg.
Differentiate between linear & non-linear
Pharmacokinetics.


05


Non-
compartment
model
Briefly describe compartment model?



31-
34
Briefly describe non-compartment model?
What is MRT? Write down the importance
of MRT?
What is MAT? Write down the importance
of MAT?
Compare between compartment model and
non-compartment models.

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Question 1: Define intravenous infusion. Write down advantages and
disadvantages of intravenous infusion.
Answer:
Intravenous infusion is a direct method by which the drug is administered
systematically into the body. Intravenous (IV) drug solutions may be given as a
bolus dose or infused slowly, at a constant or zero order.
Advantages: The main advantages of giving a drug by IV infusion are-
i. It allows precise control of plasma drug concentrations to fit the identical
needs of the patients.
ii. It is used for drugs with a narrow therapeutic window (e.g. Heparin).
iii. IV infusion maintains an effective constant plasma drug concentration by
eliminating wide fluctuations between the peek (maximum) and trough
(minimum) plasma drug concentration.
iv. The IV infusion of drugs. Such as antibiotics, may be given with IV fluids
that include electrolytes and nutrients.
Disadvantages:
i. Invasive procedure can cause infection, bleeding and ASE (add side effect).
ii. More costly than oral or sublingual.
iii. One IV site has limited use per time. Usually no more than 72hr.
Question 2: Write down the pharmacokinetics of IV infusion.
The pharmacokinetics of a drug given by constant IV infusion follows a zero-order
input process in which the drug is directly infused into the systemic blood
circulation. For most drugs, elimination of drug from the plasma is a first-order
process. Therefore, in this one-compartment model, the infused drug follows zero-
order input and first-order output. The change in the amount of drug in the body at
any time (dDB/dt) during the infusion is the rate of input minus the rate of output.

dDB
dt
= R – KDB …………(I)

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Or,
dDB
R – KDB
= dt
Or, ∫
d(−kDB)
R – KDB
��
0
= -k ∫�??????
??????
0
…………(II) (Multiplying by -K)
Or, [ ln (R – KDB) ]0
DB
= -Kdt
Or, ln (R – KDB) – ln R = -Kdt
Or, ln
R – KDB
R
= -Kdt
Or,
R – KDB
R
= �
−????????????

Or, R – KDB = R �
−????????????

Or, KDB = R – R �
−????????????

Or, KDB = R (1– �
−????????????
)
Or, DB =
R
K
(1– �
−????????????
)
Or, VD.CP =
R
K
(1– �
−????????????
) …………. (as we know, DB = VD.CP)
Thus, CP =
R
K.VD
(1– �
−????????????
) …………. (III)
Equation (III) gives plasma drug concentration at any time during the IV infusion.
Where, t is the time for infusion.
Question 3 : Calculate the plasma drug concentration at steady-state after IV
infusion.
The pharmacokinetics of a drug given by constant IV infusion follows a zero-order
input process in which the drug is directly infused into the systemic blood
circulation. For most drugs, elimination of drug from the plasma is a first-order
process. Therefore, in this one-compartment model, the infused drug follows zero-
order input and first-order output. The change in the amount of drug in the body at
any time (dDB/dt) during the infusion is the rate of input minus the rate of output.

dDB
dt
= R – KDB …………(I)

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Or,
dCP.VD
dt
= R – K CP.VD …………. (as we know, DB = CP.VD)
Or,
dCP
dt
=
R
VD
-
KCP.VD
VD
……………….(divided by VD)
Or,
dCP
dt
=
R
VD
– KCP …………(II)
At steady-state, the rate of infusion is equal to the rate of elimination. Therefore,
the rate of change in plasma drug concentration is equal to zero.
Thus, When

dCP
dt
= 0 ; CP = CSS
From equation (II);
0 =
R
VD
– KCSS
Or, KCSS =
R
VD

Or, CSS =
R
KVD
………. (III)
Equation (III) shows that steady-state concentration (CSS) is dependent on the
volume of distribution, the elimination rate constant, and the infusion rate. Altering
any of these factors can affect steady-state concentration.
Question 4 : Determine the half life (t1/2) by IV infusion method.
We know, the plasma drug concentration at any time offer IV infusion is ;
CP =
R
K.VD
(1– �
−????????????
) ………….. (I)
And we also know, the plasma concentration of steady-state level offer IV infusion
is –
CSS =
R
KVD
………. (II)
Now from equation (I) we get,

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CP = CSS (1– �
−????????????
)…………[ putting value from equation (II)]
Or, CP = CSS – CSS �
−????????????

Or, CSS �
−????????????
= CSS - CP
Or, �
−????????????
=
CSS − CP
CSS

Or, -Kt = ln (
CSS − CP
CSS
)
Or,
−Kt
2.303
= log (
CSS − CP
CSS
)
Or, Kt = -2.303 log (
CSS − CP
CSS
)
Or, K =
−2.303
t
log (
CSS − CP
CSS
)
By calculating the value we can indirectly calculate the value of t1/2 as follows;
t1/2 =
0.693
K

Question 5: Show that in case of IV infusion the time to reach 99% steady-state
is 6.65 t1/2.
We know the plasma concentration at steady-state level after IV infusion is –
CSS =
R
KVD
…………………… (I)
99% steady-state level is 99%
R
KVD

So, CSS = 99%
R
KVD
………………(II)
We also know, at steady-state the plasma concentration at any time after IV
infusion is-
CSS =
R
K.VD
(1– �
−????????????
) …………. (III)
From equation (II) & (III) we get;

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99%
R
KVD
=
R
K.VD
(1– �
−????????????
)
Or, 99% = 1– �
−????????????

Or, �
−????????????
= 1-
99
100

Or, �
−????????????
= 1 – 0.99
Or, �
−????????????
= 0.01
Or, -Kt = ln 0.01
Or, t99%SS =
ln0.01
−K

Or, t99%SS =
−4.61
−K

Or, t99%SS =
4.61
K

Or, t99%SS =
4.61
0.693
??????1/2

Or, t99%SS =
4.61
0.693
t1/2
So, t99%SS = 6.65 t1/2 ………………. (Shown)
From this equation we can say that, the time needed to reach steady-state is not
depended on rate of infusion, but only on the elimination half-life.

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Question 6: Write a short note on Multiple-Dosage Regimens. What are the
basic considerations for multiple dosage regimen?
Multiple-Dosage Regimens
After single-dose drug administration, the plasma drug
level rises above and then falls below the minimum
effective concentration (MEC), resulting in a decline in
therapeutic effect.
➢ To maintain prolonged therapeutic activity, many
drugs are given in a multiple-dosage regimen.
➢ The plasma levels of drugs given in multiple doses
must be maintained within the narrow limits of
the therapeutic window (CP above the MEC and
below the MTC) to achieve optimal clinical
effectiveness.

➢ Dosage regimen is established for drug to provide
the correct plasma level without excessive
fluctuation and drug accumulation outside the
therapeutic window.

Criteria for optimum dosage regimen:
I. The plasma levels of drug given must be maintained within the
therapeutic window.
▪ Ex. The therapeutic range of theophylline is 10-20µg/L. So, the best
is to maintain the CP around 15µg/L.
II. Should be convenient to the patient
▪ It is difficult to take I.V. injection every ½ hour or one tablet every 2
hour, this lead to poor compliance.

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Basic considerations for multiple dosage regimen (MDR)
Some basic consideration should be adjusted in developing a dosage regimen.
1) Size of dose of the drug.
2) Frequency of drug administration (time interval between doses).
3) Successive doses of the drug.
4) Dose interval should be such that the drug does not leave the body
completely before the next dose.
5) Steady state concentration must be maintained between the MEC and
MTC level.
6) Excessive fluctuation in drug level should not be allowed.
7) Drug should not be accumulated.
8) Desired plasma drug conc. must be related to therapeutic response.
9) Pharmacokinetic parameter should be obtained after single dose.
10) In MDR, it is necessary to decide whether successive does have any effect
on previous dose.
Example, common drug give in MDR.
-Antidiabetics (Insulin) -Antiasthmatics / Bronchodilator (Theophylline)
-Antibiotic (Ampicillin) -Antiepileptic (phenytoin)
-Anticancers -Anticonvulsant (Phenobarbital, phenytoin)
-Cardiotonics digoxin) -Contraceptives (Progestin) (Hormone)

Question 7: What are the purposes of multiple-dosage regimens (MDR)? Write
down the importance of MDR.
Purpose of multiple dose regimen
1. To maintain the plasma level within the therapeutic range.
2. To maintain the plasma level without excessive fluctuation and drug
accumulation.

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3. To maintain the maximum effective concentration (MEC).
4. To maintain the desired MTC (Antibiotic).
5. To maintain the steady-state plasma and tissue drug conc. for the long term
management of disease.
6. For achieving prolonged therapeutic activity.
7. Single dose is usually unsuitable to maintain the steady-state plasma drug conc.
So MDR is established.
8. For quickly metabolized drug (1st pass effect), MDR is necessary.
9. For prophylactic treatment of many disease.
10. To destroy the infected organism.
11. Narrow therapeutic index drugs may cause toxicity (phenytoin), in such
cases multiple dose is required.

Importance of MDR
• It helps to maintain plasma level of drug to completely eradicate the
infectious organism.
• It helps to continuously combat the symptom of the disease.
• To maintain a steady state plasma drug concentration for a long term
management of disease state.
• To maintain optimum fluctuation between Cmax and Cmin.

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Question 8: Write short note on repetitive intravenous injections.
Repetitive Intravenous Injections
The maximum amount of drug in the body following a single rapid IV injection is
equal to the dose of the drug. For a one-compartment open model, the drug will be
eliminated according to first-order kinetics.
DB = Do ??????
−????????????

If τ is equal to the dosage interval (the time between the first dose and the next
dose), then the amount of drug remaining in the body after several hours can be
determined with:
DB = Do ??????
−????????????

The fraction (f) of the dose remaining in the body is related to the elimination
constant (k) and the dosage interval (τ) as follows:
f = DB/ Do = ??????
−????????????

With any given dose, f depends on K and τ. If τ is large, f will be smaller because
DB (the amount of drug remaining in the body) is smaller.
To determine the concentration of drug in the body after multiple doses:
C
∞
max = D
∞
max/VD or C
∞
max = C
o
P / (1– ??????
−????????????
)
C
∞
min = D
∞
min/VD or C
∞
min = C
o
P ??????
−????????????
/ (1– ??????
−????????????
)
C
∞
av= D
∞
av/VD or C
∞
av = FD
0
/VDK??????

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Question 9: Prove that C
∞
av is not arithmetic average of C
∞
max and C
∞
min.
C
∞
av is not the arithmetic mean of C
∞
max and C
∞
min because plasma drug
concentration declines exponentially. The C
∞
av is equal to the AUC (∫????????????�??????
??????2
??????1
) for
a dosage interval at steady-state divided by dosage interval ?????? .
So, C
∞
av = [AUC]
t2
t1 / ?????? ……………….(I)
The AUC is related to the amount of drug absorbed divided by the total body
clearance as shown in the following equation;
[AUC]
t2
t1 =
??????�??????
�??????
=
??????�??????
????????????�
…………….(II)
From (I) & (II) , we get –
C
∞
av =
??????�??????
????????????�??????
……………….(III)
This equation is used to obtain C
∞
av after a multiple dosage regimen regardless of
the route of administration.
Question 10: Give brief description on superposition principle and Plateau
principle?
Superposition Principle
The superposition principle can be used when all the PK processes are linear.
That is when distribution, metabolism, and excretion (DME) processes are linear or
first order.
Thus, concentrations after multiple doses can be calculated by adding together the
concentrations from each dose. Also, doubling the dose will result in the
concentrations at each time doubling.

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Principle of superposition
➢ The basic assumptions are
(1) that the drug is eliminated by first-order kinetics and
(2) that the pharmacokinetics of the drug after a single dose (first dose) are
not altered after taking multiple doses.
Example:
Calculate drug concentration at 24 hours after the first dose of 200 mg. The second
dose of 300 mg was given at 6 hours and the third dose of 100 mg at 18 hours. The
apparent volume of distribution is 15 L and the elimination rate constant is 0.15
hr
-1

This method involved calculating contribution from each dose at 24 hours after
the first dose.
Plateau principle
If a drug is administered at a fixed dose and dosage interval, the amount of drug in
the body will increase and attain steady state level or plateau level where there is
no further appreciable change in the plasma drug concentration and this level is
higher than the initial peak plasma level obtained from the first dose.
At steady state level, maximum drug concentration and minimum drug
concentration are constant and do not further changes after repetitive
administration of drug.

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The speed at which the plateau level arises depends on the elimination rate
constant of the drug. The faster the elimination rate, the shorter the t1 / 2 value of
the drug and faster the attainment of plateau level.
The time required to attain the plateau level is almost equal to the time required to
disappear the initial dose of the drug.
Limitations of Plateau principle
• Plateau principle is very important to know dosage regimen i.e dose and dosage
interval.
• For the determination of infusion rate, plateau principle is important.
• We can calculate the amount of drug accumulate in the body by this principle.
• Toxic level of drug can be determined.
Question 11: Write down about individualization of drug dosing regimen? What
are the advantages of individualization? How will you optimizing dosage regimen?
Individualization of drug dosing regimen
It is the most accurate approach and is based on the pharmacokinetics of drug in the
individual patient. The approach is suitable for hospitalized patients but is quite
expensive. Same dose of drug may produce large differences in pharmacologic
response in different individuals, this is inter subject variability. In other words it
means that the dose required to produce a certain response varies from individual
to individual. The main objective of individualization is aimed at optimizing the
dosage regimen. An inadequate therapeutic response calls for a higher dosage
whereas drug related toxicity calls for a reduction in dosage. Thus in order to aid
individualization, a drug must be made available in dosage forms of different dose
strengths.
The number of dose strengths in which a drug should be made available depend
upon two major factors:
a) The therapeutic index of the drug, and
b) The degree of inter subject variability

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Smaller the therapeutic index and greater the variability more the number of dose
strengths require.
Advantages of Individualization
1. Individualization of dosage regimen help in development of dosage regimen
which is Specific for the patient.
2. Leads to decrease in Toxicity and side effects and increase in
pharmacological drug efficacy.
3. Leads to decrease in allergic reactions of the patient for the drug if any.
4. Patient compliance increases etc.
Optimizing dosage regimens
Incorporating the patient, characteristics in the process of initiating a drug dosage
regimen is an important step toward optimization of drug therapy, but it do not
guarantee the success of the therapy. We still need to evaluate the outcome of the
treatment and we still find in some case that the therapeutic objective has not been
achieved. Traditionally, the management of drug therapy has been accomplished by
monitoring the incidence and intensity of both desired therapeutic effect and
undesired adverse effects.
Question 12: What are the sources of variability in drug response? What are the
causes of Inter subject Pharmacokinetics Variability? Write down the steps
involved in individualization of dosage regimen?
SOURCES OF VARIABILITY
Pharmacokinetic Variability
• Due to difference in drug concentration at the site of action (as reflected from
plasma drug concentration) because of individual differences in Drug
absorption, Distribution, Metabolism and Excretion.
Pharmacodynamics Variability
• Which is attributed to differences in effect produced by a given drug
concentration.

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Causes of Inter subject Pharmacokinetics Variability
Major causes of Inter subject Pharmacokinetics Variability are:
1. Genetics
2. Diseases
3. Age
4. Body Weight and
5. Drug-Drug Interactions
Less important Causes are:
1. Pharmaceutical formulations
2. Route of administration
3. Environmental factors and Patient non-compliance

Steps Involved in Individualization of Dosage Regimen
Based on the assumption that all patients require the same plasma
conc. range for therapeutic effectiveness, the steps involved in the
individualization of dosage regimen are :
1. Estimation of Pharmacokinetic Parameters in individual
patients and to evaluate the degree of Variability.
2. Attributing the Variability to some measurable characteristics
such as hepatic or renal diseases, Age, weight etc.
3. Designing the new dosage regimen from the collected data.
The design of new dosage regimen involves
a. Adjustment of dosage or
b. Adjustment of dosing interval or
c. Adjustment of both dosage and dosing interval

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Question no 13: Write short note on – dosing of drug in obese
patient and also discuss about dosing of drug in neonates, infants
and children?
Answer:
Dosing of Drugs In Obese Patients
The apparent volume of distribution is greatly affected by changes in body weight
since the latter is directly related to vol. of various body fluids.
The Ideal Body Weight (IBW) for men and women can be calculated from following
formulae:
IBW (Men) = 50 kg +/- lkg/2.5cm above or below 150cm in height
IBW (Women) = 45kg +/- lkg/2.5cm above or below 150cm in height
Any Person Whose body Weight Is more than 25% above the IBW is considered
Obese.
Generalizations regarding drug distribution and dose distribution in obese
patients :
For drugs such as Digoxin that do not significantly distribute in excess body space,
Vd do not change and hence dose should be calculated on IBW basis. For polar drugs
like antibiotics (Gentamicin) which distribute in excess fat of obese patients to less
extent then other tissues the dose should be lower than per kg total body weight
basis but more than that on IBW basis.
Dosing of Drugs in Neonates, Infants and Children
Neonates, Infants and children require different dosages than that of adults because
of differences in the body surface area, TBW and ECF on per kg body weight basis.
Dose for such patients is calculated on the basis of their body surface area not on
body weight basis.
The surface areas in such patients are calculated by Mosteller's equation:
SA (in m
2
) = [{(Height) x (Weight)}
1/2
]

/ 60

Infants and children require larger mg/kg doses than adults because:

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Their body surface area per kg body weight is larger and hence
Larger volume of distribution (particularly TBW and ECF)
TBW - Total body water ECF - Extra cellular fluid
The child's Maintenance dose can be calculated from adult dose by the following
equation:
Child's dose = {(SA of child in m
2
) x (Adult dose)} / 1.73
Where 1.73 is surface area in m
2
of an avg. 70kg adult.
Since the surface area of a child is in proportion to the body weight according to the
following equation,
SA(in m
2
)= Body weight (in kg)
The following relationship can also be written for child's dose:
Child's dose = (weight of child in kg / 70) x (adult dose)
As the TBW in neonates is 30% more than that in adults,
• The Vd for most water-soluble drugs is larger in infants and
• The Vd for most lipid soluble drugs is smaller
Accordingly, the dose should be adjusted.

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Question no 14: Write down about dosing of drug in elderly and hepatic disease?
Give some examples of drugs who's conc. Changes due to hepatic impairment?
Answer:
Dosing of drugs in Elderly
Drug dose should be reduced in elderly patients because of general decline in body
function with age. The lean body mass decreases and body fat increases by almost
100% in elderly persons as compared to adults. Vd of water soluble drugs may
decrease and that of lipid soluble drugs like diazepam increases with age. Age
related changes in renal and hepatic functions greatly alters the clearance of drugs.
The equation that allows calculation of maintenance dose in such patients is given
as follows :
Patients dose = [{(weight in Kg)(140 - age in years)} / {1660}] x [adult dose]
Dosing of drugs in Hepatic diseases
The influence of Hepatic disorder on the drug bioavailability & disposition is
unpredictable because of the multiple effects that liver produces. The altered
response to drugs in liver disease could be due to decreased metabolizing capacity
of the hepatocytes, impaired biliary elimination, due to biliary obstruction (e.g.
Rifampicin accumulation in obstruction jaundice). Impaired Hepatic blood flow
leading to an increase in bioavailability caused by a reduction in first pass
metabolism (e.g. Bioavailability's of Morphine and Labetalol have been reported to
double in patients with Cirrhosis). Decreased protein binding and increased toxicity
of drugs highly bound to plasma protein (e.g. Phenytoin, Warfarin) due to impaired
albumin production, altered volume of distribution of drugs due to increased
extracellular fluid. Oedema in liver disease may be increased by drugs that cause fluid
retention (e.g. Acetylsalicylic acid, Ibuprofen, Prednisolone, Dexamethasone).
Generally, drug doses should be reduced in patients with hepatic dysfunction since
clearance is reduced & bioavailability is increased in such a situation.

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Examples of drugs who's conc. Changes due to hepatic impairment
High extraction ratio
• Antidepressants
• Chlorpromazine/haloperidol
• Calcium channel blockers
• Morphine
• Glyceryl trinitrates
• Levodopa
• Propranolol
Low extraction ratio
• Non-steroidal anti-inflammatory drugs
• Diazepam
• Carbamazepine
• Phenytoin
• Warfarin
Question no 15: Explain some clinical experience with
individualization and optimization based on plasma drug levels?
Answer:
Clinical experience with individualization and optimization based on
plasma drug levels
A: ANTIARRHYTHMIC DRUGS
Quinidine
It is useful for treatment of atrial and ventricular arrhythmia. It is usually
administered orally but may be given by intramuscular or intravenous injection. It
has a half-life of about 6 to 7 hrs. When usual dosages of quinidine are given to
patients on enzyme inducing drugs, such as phenobarbital, phenytoin, or rifampin,
low sub therapeutic blood levels of quinidine are likely to result. Higher than usual
dosages of quinidine are required in these patients. Quinidine concentrations of

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about 3 to 8µg/ml are considered therapeutic when nonspecific assay methods are
used. With a high performance liquid chromatography assay procedure
antiarrhythmic effects are associated with serum quinidine levels of 2 to 5 µg/ml.
The frequency of gastrointestinal disturbances increases with quinidine levels above
5 µg/ml; cardiovascular disturbances are a concern at concentrations exceeding 8
µg/ml.
B: ANTIBIOTICS
Aminoglycoside Antibiotics
The aminoglycoside antibiotics are effective in treating pneumonia, urinary tract,
soft tissue, burn wound, and other systemic infections caused by gram-negative
organisms. All aminoglycosides are ototoxic and nephrotoxic and have a relatively
low therapeutic index. The major elimination route for the aminoglycosides is renal
excretion, largely by way of glomerular filtration. The half-lives of gentamicin and
tobramycin in patients with normal renal function are variable but avg. about 2.5hr.
Patients with impaired renal function eliminate the aminoglycosides more slowly
and require reduced dosage. Infants less than 7 days of age and elderly patients also
require lower dosages.
C: ANTICONVULSANTS
Phenytoin
No drug has a greater need for therapeutic drug concentration monitoring and
individualized dosing than phenytoin. A relationship between drug concentration
in plasma and daily dose is almost nonexistent because phenytoin is poorly
absorbed, highly plasma protein bound, and subject to nonlinear, capacity-limited
metabolism. Despite these problems, it is the most frequently prescribed
anticonvulsant drug for the management of grandmal and partial seizures.
Optimum phenytoin efficacy is achieved in most patients with serum
concentrations in the range of 10 to 20µg/ml. Concentration-related CNS toxicity
of phenytoin is generally observed at serum concentrations above 20 µg/ml. As
serum levels rise, so do the frequency and severity of side effects. Children
metabolize phenytoin more rapidly than do adults and may require 2- or 3-times
larger mg/kg daily doses (up to 15 mg/kg per day) than do adults. The dosage of

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phenytoin may need to be increased during pregnancy because of the increased
clearance of the drug during this period.
Question no 16: Derive the Michaelis-Menten Equation or Non-Liner
pharmacokinetic and Linear pharmacokinetic model.
Answer:
Reaction Model: The enzyme reacts with the substrate by binding to its active
site to form the enzyme substrate complex, ES. That reaction followed by the
decomposition of ES to regenerate the free E and the new product P.


Michaelis-Menten Equation:



Here, Vo = Initial reaction velocity
Vmax = Maximum velocity
Km = Michaelis constant =
K−1 + K2
K1


Assumption 1: (Rate formation of ES complex)
Rate formation,


Assumption 2: (Rate of breakdown ES complex)

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-
{“- “negative sign indicates reduction of conc. Of [ES] complex with time}
Assumption 3: (Steady state assumption)
The rate of breakdown of ES complex very rapidly equal to the rate of formation
ES
Thus,


Or, K1 [E] [S] = K – 1 [ES] + K2 [ES] {From the equation 1 and equation}
Or, K1 [E] [S] = (K1 + K2) [ES]


Steady state assumption → [ES] is constant.
So, Formation of ES = Loss of ES.
We know that –
Michaelis constant Km is the substrate concentration at which the reaction rate is
at half maximum & is an inverse measure of the substrate’s affinity to the enzyme.
So,

The total amount of enzyme in the system must be the same throughout the
experiment but it can either be free (unbound) E or in complex with substrate, ES.
If we term the toral enzyme Et, this relationship can be written out:
[Et] = [E] + [ES]----------(4)

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From equation 3 and equation 4 we can write-
Or, [Et] [S] – [ES] [S] = KM [ES]
Or, [Et] [S] = KM [ES] + [ES] [S]
Or, [Et] [S] = ([S] + KM) [ES]
Vo is determined by the breakdown of ES to form product, which is denoted
by [ES].
Vo = K2 [ES]--------------(6)
From the equation 5 and equation 6 we can write,
The maximum rate, which can call Vmax, would be achieved when all of the
enzyme molecules have substrate bound. Under the conditions when [S] is much
greater than [E], it is fair to assume that all E will be in the form ES. Therefore [Et]
= [ES]. Thinking again about equation 6, we could substitute the term Vmax for
Vo and [Et] for [ES]. This would give us –
Vmax = K2 [Et]

From equation 7,

Is non-linear pharmacokinetic equation or Michaelis-Menten equation which
proves Non-linear behavior.

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If we flip the equation,

??????
????????????
=
????????????+[??????]
????????????????????????[??????]

Now it is linear pharmacokinetic equation which proves linear behavior.

Question no 17: Define non-linear pharmacokinetics. Why it is called
dose dependent pharmacokinetics?
Answer:

Non-linear Pharmacokinetics: The first order kinetics is usually transformed
into mixture of first order and zero order rate process and the pharmacokinetic
parameters are changed with the size of the administered dose. Pharmacokinetics
of these are said to be non-linear/mixed order/capacity-limited/dose dependent
pharmacokinetic.
Dose-dependent pharmacokinetics:
Phenytoin → 300 mg (50% increase) → 450 mg → CSS (10X increase)
Phenytoin undergoes capacity-limited kinetics at therapeutic drug concentrations
in the body. At steady state, the rate of drug metabolism is assumed to be the same
as the rate of drug input (dose/day). Therefore, Equation may be written for drug
metabolism in the body similar to the way drugs are metabolized in vitro.
Again, V0 = -
dc
dt

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1st Condition: when km = C
V0 =
Vmax.C
2C
=
Vmax
2

The rate of progress is equal to half life of its maximum

2
nd Condition: KM >>> C
KM + C = KM

is identical to first order kinetic
3
rd
Condition: KM <<< C
KM + C = C
∴ V0 = Vmax
No concentration available thus, zero order
kinetic
Linear pharmacokinetic is not dose dependent pharmacokinetics.
So, non-linear pharmacokinetics is dose dependent pharmacokinetics.

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Question no 18: Why Michaelis-Menten equation is termed as mixed
order kinetics?
Answer:



When the drug concentration is low relative to the enzyme concentration, there are
abundant enzymes to catalyze the reaction, and the rate of metabolism is a first-order
process.
So, If KM >>> [S] we can write–
KM + [S] = KM
From Michaelis-Menten Equation
Here,
KM = [S]
Or, KM + [S] = [S] + [S] = 2[S]

Or, V0 =
Vmax.[S]
2[S]
=
Vmax
2

Saturation of the enzyme usually occurs when the plasma drug concentration is
relatively high, all the enzyme molecules become complexed with drug, and the
reaction rate is at a maximum rate; the rate process then becomes a zero-order
process.
So, If KM <<< [S] we can write –

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KM + [S] = [S]
From Michaelis-Menten Equation
From the equation Vo = Vmax
Because of following 1st order and second order this kinetics is termed mixed
order.
Question no 19: A given drug is metabolized by capacity-limited
pharmacokinetics. Assume KM is 50??????g/mL, Vmax is 20??????g/mL per hour and
apparent VD is 20 L/kg.
a. What is the reaction order for the metabolism of this drug when given in a
single IV dose of 10 mg/kg?
b. How much time is necessary for the drug to be 50% metabolized?
Answer:
a. What is the reaction order for the metabolism of this drug when given in a
single IV dose of 10 mg/kg?
Here,
KM = 50??????g/mL
Vmax = 20??????g/mL per hour
VD = 20 L/kg = 20,000mL/kg
We know,
IV dose = 10 mg/kg
= 10,000 ??????g/kg
VD = 20 L/kg
= 20,000mL/kg

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Again we know that,
Because KM = 50 ??????g/mL we can write, CP <<< KM and we can say that the
reaction rate is first order.
So, the above equation can reduce to

Thus First order first order reaction.


b. How much time is necessary for the drug to be 50% metabolized?
Now,
For the first order reaction,

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Question no 20: Differentiate between linear & non-linear Pharmacokinetics.
Answer:
Topic Linear Pharmacokinetics Non-linear Pharmacokinetics
Parameters
changes
Linearly Non-linearly
Synonyms Dose independent Dose dependent, Michaelis
menten pharmacokinetics,
saturation pharmacokinetics,
Mix-order pharmacokinetics.
Clearance Remain constant Decreases
AUC Changes proportionally to
dose,
Changes dis-proportionally to
dose.
Half-life Always constant Increases
CSS Changes proportionally to
dose
Changes dis-proportionally to
dose.
TSS Constant Increases

Question no 21: Briefly describe compartment model?
Answer:
Compartment model:
Compartment models simulate drug absorption distribution and elimination.
They are a convenient oversimplification used to predict the concentration of a drug
at any given time in any given body fluid or tissue.

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In pharmacokinetics Compartmental modeling of pharmacokinetics describes the
fate of a drug in the body by dividing the whole body into one or more
compartments. A compartment involves several organs or tissues and is kinetically
homogenous. Different compartments do not have a direct anatomical or
physiological signification.
In pharmacokinetic three-compartment model divided the body into central
compartment and two peripheral compartments.
The central compartment (compartment 1) consists of the plasma and tissues where
the distribution of the drug is practically instantaneous.
Question no 22: Briefly describe non-compartment model?
Answer:
Non-compartment model:
Non-compartmental model thinks of an organism as only one homogenous
compartment. It presumes that a drug's blood-plasma concentration is a true
reflection of the concentration in other tissues and that the elimination of the drug is
directly proportional to the drug's concentration in the organism.
Non-compartmental analysis (NCA) is a simple and quick method for evaluating
the exposure of a drug. It allows you to evaluate things like linearity and in vivo
exposure. To illustrate this consider an antibody given in a subcutaneous injection.
Noncompartmental analysis (NCA) lets you compute pharmacokinetic (PK)
parameters of a drug from the time course of measured drug concentrations.
This approach does not require the assumption of a specific compartmental model.
Based upon this view, the pharmacokineticist makes certain assumptions and
develops models based upon nonlinear regression analysis to describe the PK of
the drug.

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Question no 23: What is MRT? Write down the importance of MRT?
Answer:
Mean Residence Time (MRT):
Understanding How Long Drug Molecules Stay in the Body Or the duration of
persistence of a mass or substance in a medium or place.
Importance of MRT:
It can be used to estimate the average time a drug molecule spends in the body. It
can also be used to help interpret the duration of effect for direct-acting molecules
(e.g. blood pressure lowering agents) and helps to determine;
1. AUC or AUMC
2. VSS
3. Cl
4. MAT (Mean absorption time)
Question no 24: What is MAT? Write down the importance of MAT?
Answer:
Mean absorption time (MAT) :
Mean absorption time corresponds to the time on. average that drug molecules
spend prior absorption.
When drug is applied via multiple routs MAT can be calculated by differences in
mean residence time of different mode of administration.
If dug is administered both instantaneous (IV) and non-instantaneous (NI) rout
then, MAT = MRTNI - MRTIV
Importance of MAT:
Both routes can be compared to understand drug’s time spend in body.

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Question no 25: Compare between compartment model and non-compartment
models.
Answer:
Compartment models Non-compartment model
Require elaborate assumption Do not require assumption
Curve fitting of experimental data using
computer, it is a tedious method.
Simple algebraic equations, no curve
fitting and no computers.
Time course change in C, can be
predicted precisely.
Time course change in C, cannot be
predicted precisely.
Applicable to linear and non-linear
pharmacokinetics
Applicable to linear pharmacokinetics
Number of compartments = Number of
curve exponentials
Use statistical moment theory
Mo=∫??????
∞
0
0
Cpdt= ∫
∞
0
Cpdt = AUC
These are useful for most of the
situations, though assumption of
modeling are involved.
Useful for clinical pharmacokinetics,
bioavailability, and bio-equivalence
studies.
VSS, Compartment model
1CMT VSS=V
2CMT VSS= V1+V2
3CMT VSS= V1+V2+V3
Noncompartmental model;
VSS= MRT.CL