Download Calculation of k from Urinary Excretion Data

CHAPTER 5
DETERMINATION OF PK
PARAMETERS FROM
URINARY DATA
1
Calculation of kel from Urinary Excretion
Data after I.V. Injection
 kel can be calculated from urinary
excretion data.
 The excretion rate of the drug is
assumed to be first order.
 ke is the renal excretion rate
constant.
 Du is the amount of drug excreted
unchanged in the urine.
2
Elimination
kel = ke + km
3
Scheme of the Model
For a single i.v. dose,
IV Dose
DB = CpVd
ke
Du
km
dDu/dt = keDB
4
Rate of Drug Excretion in the Urine
Equations
dDu = keDB
dt
But DB= DB0e-kelt
dDu
  kel t
 k e DB e
dt
Therefore,
dDu

ln
 ln k e DB  k el t
dt
5
Plotting on a Semilog Paper
Plot dDu/dt vs. Time
dDu/dt
keDB
Slope= -kel
Time
6
Example
Time
Du/t
mg/hr
t* (hr)
0.25
Du
(mg)
160
160/0.25
640
0.125
0.5
140
140/0.25
560
0.375
1.0
200
200/0.5
400
0.750
2.0
250
250/1
250
1.50
4.0
188
188/2
94
3.0
6.0
46
46/2
23
5.0
7
Difference between t and t*
 t is the time interval for collection of urine
sample.
 t* is the midpoint of collection period.
 Assuming renal clearance is constant, Du/t
is proportional to plasma drug conc, and
plotting Du/t vs. t* is like plotting Cp vs. time.
 The measured urinary excretion rate reflects
the average plasma concentration during
the collection interval.
8
Why t* ?
 Because the drug urinary excretion rate
(dDu/dt) cannot be determined
experimentally at any given instant.
 In practice, urine is collected over a
specified time interval, and the urine
specimen is analyzed for drug.
 An average urinary excretion rate is then
calculated for that collection period.
 The average dDu/dt is then plotted against
the average time (t*).
9
Determination of the non-renal rate
constant (knr)
knr= is the elimination rate constant for any
route of elimination other than renal excretion.
kel - ke = knr
Since drug elimination occurs mainly through
renal excretion and metabolism,
knr  km
kel = ke + km
10
Determination of renal clearance
Renal clearance, ClR, is defined as the
volume of plasma that is cleared of drug
per unit of time through the kidney
ClT  k el  Vd
Cl R  k e  Vd
11
Sigma-Minus Method
 Also called the Amount of Drug Remaining to
be Excreted Method.
 It is an alternative method for the calculation
of kel from urinary excretion data.
 It is more accurate than the previous method.
 ke/kel is the fraction of drug excreted
unchanged in the urine.
 (ke/kel)*Dose= total amount of drug excreted
unchanged in the urine.
12
Sigma-Minus Method (cont)
Equations
ke D0
 k el t
Du 
(1  e )
kel
Where,
o Du is the cumulative amount of drug excreted
unchanged in the urine until time t.
o (1- e-kelt) is the fraction of drug lost from the
body.
13
Sigma-Minus Method (cont)
The amount of drug that is ultimately excreted
at time infinity will be equal to Du
Du = ke/kel (D0) (2)
By substituting in the previous equation (1)
Du - Du = Du e-kelt
(3)
To obtain a linear equation:
Ln (Du - Du) = ln Du - kelt
(4)
Where, (Du - Du) is the amount of drug
remaining to be excreted.
14
Sigma-Minus Plot
On a semilog paper:
Du-Du
Du
Slope= -kel
Time
15
Example
Use these data to calculate kel
Time (hr)
Du (mg)
Du (cum)
Du - Du
0.25
160
160
824
0.5
140
300
684
1.0
200
500
484
2.0
250
750
234
4.0
188
938
46
6.0
46
984
0
16
Cumulative Amount of Drug Excreted
in the Urine
Cumulative amount excreted
Plot
Du
Time
One needs to
collect urine
samples for a
minimum of 710 half-lives of
the drug to
assure all the
drug is excreted
into the urine.
17
Renal clearance
Renal clearance can be determined from
model independent equation

u
D
ClR 

[ AUC]0
18
Fraction of drug excreted
The fraction of drug excreted unchanged in
the urine (fe) can be calculated as follows:

u
D
ke
fe 

Dose kel
ke
ClR 
ClT  f eClT
kel
19
Comparison between the Rate and
the Sigma-Minus Method
1- In the rate method, Du need not be known,
and the loss of one urine specimen does not
invalidate the entire study.
2- The sigma-minus method needs accurate
determination of Du which requires urine
collection until drug excretion is complete.
3- Fluctuations in the rate of drug elimination
and experimental errors (such as incomplete
bladder emptying) cause considerable
departure from linearity in the rate method. 20
Comparison (cont)
4- The sigma-minus is less affected by
fluctuations in the rate of drug elimination.
5- The rate method is applicable to zero-order
elimination process, while sigma-minus
method is not.
6- The ke can be obtained from the rate
method but not from the sigma-minus method.
21
Problems in Obtaining Valid Urinary
Excretion Data
1- A significant fraction of unchanged drug
must be excreted in the urine( at least 20 % ).
2- The assay technique must be specific.
3- Frequent sampling is necessary for a good
curve description.
4- Urine samples should be collected until
almost all drug is excreted(7 t half)
5- Variation in urinary pH and volume cause
significant variation in urinary excretion rates.
6- Subjects should be instructed to the
importance of complete bladder emptying. 22