Download kinetics of iv bolus: urine data

LEARNING OBJECTIVES
Understand the role of renal excretion on the drug elimination
Know the routes of drug elimination and relevant elimination rateconstants
Identify the equations to estimate kinetic parameters from the
urine concentration-time data and plasma concentration-time data
after IV bolus
Appreciate the reasonable urine collection period to estimate the
total amount of drug excreted in urine
Review renal clearance
Compile the data to determine the renal clearance
Understand the pros and cons of cumulative and urinary excretion
rate methods used to calculate fraction-dose excreted
Calculate the following parameters using the urine data
 Half-life and elimination rate-constant
 Total amount of drug excreted in the urine
 Unchanged fraction-drug excreted in the urine
 Urinary excretion rate constant
ROUTES OF DRUG ELIMINATION
The term ‘drug elimination’
encompasses all the processes
involved in the removal of a drug
from the body
Two major processes of drug
elimination are
 Renal excretion
 Metabolism in the liver (primary)
The kidney in conjunction with
the liver eliminates over 90% of
drugs
The excretion of the parent drug
into the bile is the third major
route of drug elimination that
removes <10% of intact drugs
Drugs are also excreted in the
sweat and exhaled-air
RENAL ELIMINATION AND HEPATIC
METBAOLISM
Renal elimination
 Drug moves or excreted from the blood to the renal tubule
and then eliminated in the urine.
Metabolism
 The parent drug is converted to one or more molecular
entities, called, metabolites, via enzymatic action
Metabolites may again be metabolized and then
excreted in the urine and bile
Pharmacokinetics of metabolites
 When a drug becomes a metabolite, the drug is considered to
be eliminated
 If the metabolite has no pharmacological activity,
pharmacokinetics does not evaluate the elimination of
inactive metabolites
 The pharmacokinetics of active-metabolites is often studied
DRUG ELIMINATION KINETICS
Drug-elimination can be
monitored by the elimination rateconstant (k)
The slope of the plasma
concentration-time plot will give
you k
Drug elimination rate is
composed of two major
components
 Urinary excretion rate-constant (𝑘𝑟 )
 Metabolic rate-constant (𝑘𝑚 )
o 𝑘 = 𝑘𝑟 + 𝑘𝑚
The term ‘non-renal rate (𝑘𝑛𝑟 )’
include all possible elimination
pathways, although 𝑘𝑛𝑟 equals to
𝑘𝑚 under normal circumstances
 k can be written as
o 𝑘 = 𝑘𝑟 + 𝑘𝑛𝑟
CALCULATION OF ELIMINATION RELATED KINETIC
PARAMETERS
To calculate kinetic parameters related to elimination, we first
have to know how to manipulate urine data
I will use the data below to explain the concept
 Cumulative urinary excretion plot
 Urinary excretion-rate plot
 Sampling of urine
THE CUMULATIVE URINARY EXCRETION
PLOT AND FRACTION-DOSE EXCRETED
A plot of total intact drug excreted in the urine, during a
certain time-period, against the collection time is called the
cumulative urinary excretion plot
Consider the urinary data (Table next slide) of a 200 mg IV
bolus injection
After 96 h, no drug was in the urine
The line flattened out after 96 hr
The total amount excreted is 144 mg
Fraction-dose excreted unchanged is 0.72; 72% of
the dose
 𝑓𝑒 =
𝐴∞
𝑢
𝐷𝑜𝑠𝑒
=
144
200
= 0.72
THE CUMULATIVE URINARY
EXCRETION PLOT
PLASMA HALF-LIFE FROM THE URINE
DATA
When the plasma data are not available, you can use urine
data to calculate the half-life and rate-constant
Plasma data may not be available for a number of reasons:
 No good assay method to quantitate the drug in the
plasma
 To avoid invasive plasma sampling in some patients such
as pediatrics
A plot of the urinary-excretion-rate vs time is used to
calculate plasma half-life from the urine data.
URINARY EXCRETION RATE-PLOT
 The relation between urinary excretion rate (

𝑑𝐴𝑢
𝑑𝑡
𝑑𝐴𝑢
)
𝑑𝑡
and time is written as
= 𝑘𝑟 × 𝐷
 You can rearrange this equation to a straight line equation
 𝐴 = 𝐴0 × 𝑒 −𝑘𝑡 = 𝐷𝑜𝑠𝑒 × 𝑒 −𝑘𝑡


𝑑𝐴𝑢
=
𝑑𝑡
𝑑𝐴
ln 𝑢
𝑑𝑡
𝑘𝑟 × 𝐷𝑜𝑠𝑒 × 𝑒 −𝑘𝑡
= l𝑛 𝑘𝑟 × 𝐷𝑜𝑠𝑒 − 𝑘𝑡
 A plot of log urinary excretion rate vs time will give a straight-line
 Slope ‘-k’ of this line is the same as the slope of log plasma
concentration-time plot
 The 𝑡1/2 from the urinary-excretion-rate plot equals the plasma 𝑡1/2
 The urinary-excretion-rate cannot be determined at a particular time
because the urine is collected over a time-interval (e.g. from 0-2 h).
 The excretion-rate for an interval is plotted against the midpoint (time) of
the collection interval (e.g. 1 h)
GRAPHING OF THE URINARY EXCRETION RATE
PLOT AND CALCULATIONS OF PLASMA k AND 𝑡1/2
 First, you calculate the excretion rates by dividing the drug amount in the
urine for every collection period by the duration of time for that interval.
 The midpoint time is the middle of the collection time
 The half-life is 8.9 hr and overall rate-constant is 0.0778 hr-1
 The slope of this line (-k) is similar to the slope of plasma-concentrationtime on a log-graph
Au means Du
DURATION FOR URINE SAMPLE
COLLECTION
To estimate the cumulative amount of urinal drug
excretion(𝑨∞
𝒖 ), you first determine the duration, for
collection of urine samples, after which little or no
drug will come out in the urine .
We have two methods to decide the timespan for
urine collection
 Plasma half-life
 Fraction-dose un-excreted
HALF-LIFE TO DETERMINE THE TIMESPAN FOR
URINE COLLECTION
U
The extent of urinal drug (𝐴∞
𝑢 ) excretion depends on drug’s halflife
The urinal drug excretion represents the fraction-drug eliminated
from the plasma by all the methods of elimination
Since 50% of the dose is eliminated after one half-life, 50% of
total urinal drug excretion (𝐴∞
𝑢 ) is assumed to be excreted in the
urine, although 50% of 𝐴∞
𝑢 may not represent 50% of the dose
because drug elimination also occurs via routes other than urinal
elimination
After 4 plasma t1/2, 93.7% of the dose will be eliminated that
represent 93.7% total urinal excretion (𝐴∞
𝑢)
Urine collection up to ≥4 half-lives gives us a good estimate of 𝐴∞
𝑢
 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 − 𝑑𝑜𝑠𝑒 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 =
1
2
n
For data presented in table (slide 10), 36 (4x9) hrs would be an
appropriate timespan for sample collection.
FRACTION-DOSE UNEXCRETED TO DETERMINE
THE TIMESPAN FOR URINE COLLECTION
To determine the timespan for urine collection from the
fraction-dose un-excreted (the dose remaining in the body),
you can use the expression ‘𝑒 −𝑘𝑡 ’
Assume you want to determine the timespan for 95% 𝐴∞
𝑢
that represent elimination of 95% of the drug
Thus the fraction-dose un-excreted (𝑒 −𝑘𝑡 ) is 0.05 (1 − 0.95)
 𝑒 −𝑘𝑡 = 0.05; −𝑘𝑡 = ln 0.05; −0.0.0778 𝑡 = −3.0; 𝑡 =
38.6ℎ
The timespan of 38.6 hr, for 95% 𝐴∞
𝑢 , is close to the 4 halflives (36 hr) for estimation of ~93.7% of the drug
This expression ′𝑒 −𝑘𝑡′ is used to estimate the timespan to
reach any fraction of 𝐴∞
𝑢
ESTIMATION OF Kr AND K IN THE ABSENCE OF
CUMULATIVE URINARY EXCRETION PLOT
You may not always be able to construct a cumulative
urinary excretion plot for a number of reasons:
 Missing urine samples for one or more intervals
 Short sample collection time.
You can still construct the urinary excretion-rate plot using
available samples
You can find the half-life or k from the slope and kr from the
intercept
fe can be estimated from the urinary excretion rate plot using
the following equation:
 𝑓𝑒 =
𝑘𝑟
𝑘
CALCULATION OF 𝑘𝑟 FROM EXCRETION
RATE PLOT
The intercept of the urinary excretion rate plot gives
𝑘𝑟
Intercept on the log-graph= 𝑘𝑟 𝑑𝑜𝑠𝑒 = 11.9 mg/h.
If you know the dose (200 mg), you can estimate 𝑘𝑟
 𝐷𝑜𝑠𝑒 ∙ 𝑘𝑟 =
11.9𝑚𝑔
𝑜𝑟
ℎ
𝑘𝑟 =
11.9𝑚𝑔/ℎ
200𝑚𝑔
= 0.0595ℎ−1
CALCULATION OF 𝑘𝑟 FROM THE
CUMULATIVE AMOUNT EXCRETED
 The relation among, dose, cumulative amount
excreted (𝐴∞
𝑢 ), 𝑘, 𝑘𝑒 , and fraction-intact-drug
excreted 𝑓𝑒 is written as
 𝑓𝑒 =
𝐴∞
𝑢
𝑑𝑜𝑠𝑒
=
𝑘𝑟
𝑘
 This equation gives 𝑘𝑟 , when you know other
parameters
 𝑓𝑒 =

𝐴∞
𝑢
𝑑𝑜𝑠𝑒
𝑘𝑟
0.0778ℎ −1
=
𝑘𝑟
𝑘
= 0.72
= 0.72
 𝑘𝑟 = 0.0560/ℎ𝑟
RENAL CLEARANCE
Renal clearance measures the efficiency of the kidneys in
excreting the drug
Renal clearance relates the urinary excretion-rate with the
plasma concentration as follows

𝑑𝐴𝑢
𝑑𝑡
= 𝐶𝑙𝑟 ∙ 𝐶
This equation may be rearranged to estimate 𝐶𝑙𝑟
 𝐶𝑙𝑟 =
𝑑𝐴𝑢 /𝑑𝑡
𝐶
You need both plasma-concentration and urinary excretion
rate (𝑑𝐴𝑢 /𝑑𝑡) to estimate 𝐶𝑙𝑟 .
For this method, you determine 𝑑𝐴𝑢 /𝑑𝑡 using the data from
urine samples collected for a period of time (between t1 and
t2)
You have to collect a plasma sample in the middle of urine
collection (between t1 and t2) period.
For creatinine clearance, urine is collected for 24 hr and a
plasma sample is collected at 12 hr.
RENAL CLEARANCE USING AUC
The integration of (𝐶𝑙𝑟 =
following equation:
 𝐶𝐿𝑟 =
𝐴𝑡1−𝑡2
𝑢
𝐴𝑈𝐶𝑡1−𝑡2
=
𝑑𝐴𝑢 /𝑑𝑡
𝐶
) leads to the
𝐴∞
𝑢
𝐴𝑈𝐶0−∞
 Assume the AUC for this drug is 13.2 mg.hr/L, then
 𝐶𝐿𝑟 =
𝐴∞
𝑢
𝐴𝑈𝐶0−∞
=
144 𝑚𝑔
13.2 𝑚𝑔 ℎ/𝐿
= 10.9 𝐿/ℎ
CUMULATIVE METHOD
 Advantages:
 Deals with real the time-points (no 𝑡𝑚𝑖𝑑 )
 Incomplete bladder emptying does not impact the
outcome much
 Avoid frequent sampling when you want to estimate 𝐴∞
𝑢
 Disadvantages:
 Sampling should be for at least 4 half-lives in order to
estimate 𝐴∞
𝑢 (problem for drugs with long-half life
drugs)
 𝐴∞
𝑢 cannot be estimated in case of accidental sample loss
URINARY EXCRETION RATE METHOD
Advantages:
 Sample loss does not impact the outcome
 One misplaced samples eliminate one data point but the
existing data points are still useful
 Sample collection for ≥ 4 half lives is not required.
Disadvantages:
 Use of 𝑡𝑚𝑖𝑑 instead of sampling time
 Shorter interval to relate rate to 𝑡𝑚𝑖𝑑
 Incomplete bladder emptying affect each data point
APPLICATION OF URINE DATA
The drug half-life from the urine data can predict the time a
drug takes
 To exit the body
 To reach a steady plasma profile after multiple dosing.
The amount of urinal-excretion of intact drug can determine
the relative bioavailability or bioequivalence of two products
The fraction-dose excreted in the urine and the renal
clearance are used determine the role of kidneys in drug
elimination
If much of the intact drug is excreted via the kidneys, kidney
dysfunction would affect drug excretion
If urinal drug excretion is minimal, renal dysfunction does
not affect drug elimination