DETERMINATION OF PK PARAMETERS FROM URINARY DATA

1
CHAPTER 5

• DETERMINATION OF PK PARAMETERS FROM URINARY DATA

2
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.

3
Elimination

• kel ke km

4
Scheme of the Model

• For a single i.v. dose,

DB CpVd
ke
IV Dose
Du
km
dDu/dt keDB
5
Rate of Drug Excretion in the Urine

• Equations
• But DB DB0e-kelt
• Therefore,

dt
6
Plotting on a Semilog Paper

• Plot dDu/dt vs. Time

7
Example
Time Du (mg) Du/t mg/hr t (hr)
0.25 160 160/0.25 640 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
8
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.

9
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).

10
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

11
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

12
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.

13
Sigma-Minus Method (cont)

• Equations
• Where,
• Du is the cumulative amount of drug excreted
• unchanged in the urine until time t.
• (1- e-kelt) is the fraction of drug lost from
  the
• body.

14
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.

15
Sigma-Minus Plot

• On a semilog paper

16
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
17
Cumulative Amount of Drug Excreted in the Urine

• Plot

One needs to collect urine samples for a minimum
of 7-10 half-lives of the drug to assure all the
drug is excreted into the urine.
Du?
Cumulative amount excreted
Time
18
Renal clearance

• Renal clearance can be determined from model
  independent equation

19
Fraction of drug excreted

• The fraction of drug excreted unchanged in the
  urine (fe) can be calculated as follows

20
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.

21
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.

22
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.