![Page 1: Intravenous bolus administration: monitoring drug in urine Dr Mohammad Issa](https://reader033.vdocument.in/reader033/viewer/2022061614/56649f3e5503460f94c5e3ee/html5/thumbnails/1.jpg)
Intravenous bolusadministration: monitoring
drug in urine
Dr Mohammad Issa
![Page 2: Intravenous bolus administration: monitoring drug in urine Dr Mohammad Issa](https://reader033.vdocument.in/reader033/viewer/2022061614/56649f3e5503460f94c5e3ee/html5/thumbnails/2.jpg)
Renal and Non-renal elimination pathways
KR
KNR
Renal drug elimination (Drug appear unchanged in the urine)
Dose
Non-Renal drug elimination (e.g. hepatic metabolism)
X
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Methods to computePK parameters from urinary data1. the ‘‘amount remaining to be excreted’’
method (ARE); also known as the sigma-minus method
2. The rate of excretion method.
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Sigma-Minus Method
• Amount of unchanged or excreted drug in urine (Xu) is given by:
where K is the elimination rate constant, Kr is the renal elimination constant and X0 is the dose, is the cumulative amount of drug excreted in the urine at t = ∞
)1( )1( utt KK eXe
K
XKXu
or
uX
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Sigma-Minus Method
• Previous equation can be represented as:
where “ ” is the amount of the drug remaining to be excreted
303.2log)log(
KtXXX uuu
uu XX
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Sigma-Minus Method (Example)
• An intravenous bolus dose of 120 mg of a drug was administered. The drug is one that is partially eliminated by urinary excretion of unchanged drug following one-compartment model distribution and first-order elimination.
• The following Table provides the urinary data in a tabulated form.
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Sigma-Minus Method (Example)
Time
interval
(h)
Volume
(mL)
Concentration
(mg/mL)
0-1 200 0.200
1-2 50 0.400
2-3 50 0.200
3-4 100 0.050
4-5 25 0.100
5-6 125 0.010
6-12 250 0.005
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Sigma-Minus Method : 1- Calculate amount of drug eliminated
Time
interval
(h)
Volume
(mL)
Concentration
(mg/mL)
Drug amount in the urine
(mg)
0-1 200 0.200 40
1-2 50 0.400 20
2-3 50 0.200 10
3-4 100 0.050 5
4-5 25 0.100 2.5
5-6 125 0.010 1.25
6-12 250 0.005 1.25
Amount = volume*conc
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Sigma-Minus Method : 2- Calculate cumulative amount of drug eliminated
Time
interval
(h)
Volume
(mL)
Concentration
(mg/mL)
Drug amount in the urine
(mg)
Cumulative
amount in the
urine
(mg)
0-1 200 0.200 40 40
1-2 50 0.400 20 60
2-3 50 0.200 10 70
3-4 100 0.050 5 75
4-5 25 0.100 2.5 77.5
5-6 125 0.010 1.25 78.75
6-12 250 0.005 1.25 80
uX
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Sigma-Minus Method : 3- Calculate amount remaining to be excreted (ARE)
Time
interval
(h)
Volume
(mL)
Concentration
(mg/mL)
Drug amount in the urine
(mg)
Cumulative
amount in the
urine
(mg)
ARE
(mg)
0-1 200 0.200 40 40 40
1-2 50 0.400 20 60 20
2-3 50 0.200 10 70 10
3-4 100 0.050 5 75 5
4-5 25 0.100 2.5 77.5 2.5
5-6 125 0.010 1.25 78.75 1.25
6-12 250 0.005 1.25 80 0
uu XX
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Sigma-Minus Method : 4- Plot time (end of interval) vs. log(ARE)
Time
(h)
ARE
(mg)
1 40
2 20
3 10
4 5
5 2.5
6 1.25
12 0
uu XX
y = -0.301x + 1.9031R2 = 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 1 2 3 4 5 6 7
time (hr)
log
(AR
E)
303.2log)log(
KtXXX uuu
Intercept Slope
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Sigma-Minus Method : 5- Estimate PK parameters from the values of the slope and the intercept
0.301- 303.2
K
Slope
1-hr 693.0303.2*0.301 K
9031.10
loglog
X
KrK
uXIntercept
1 462.0
9031.1
0
10120
693.010 hr
Interceptr X
KK
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The rate method
• The rate of urinary excretion is given by:
• Previous equation can be represented as:
tKr eXKXKt
Xuor
t
Xu
303.2loglog
KtKrXo
t
Xu
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The rate method
• Previous equation can be represented as:
303.2loglog
KtKrXo
t
Xu
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The rate method (Example)
• An intravenous bolus dose of 120 mg of a drug was administered. The drug is one that is partially eliminated by urinary excretion of unchanged drug following one-compartment model distribution and first-order elimination.
• The following Table provides the urinary data in a tabulated form.
![Page 16: Intravenous bolus administration: monitoring drug in urine Dr Mohammad Issa](https://reader033.vdocument.in/reader033/viewer/2022061614/56649f3e5503460f94c5e3ee/html5/thumbnails/16.jpg)
The rate method (Example)
Time
interval
(h)
Volume
(mL)
Concentration
(mg/mL)
0-1 200 0.200
1-2 50 0.400
2-3 50 0.200
3-4 100 0.050
4-5 25 0.100
5-6 125 0.010
6-12 250 0.005
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The rate method: 1- Calculate amount of drug eliminated
Time
interval
(h)
Volume
(mL)
Concentration
(mg/mL)
Drug amount in the urine
(mg)
0-1 200 0.200 40
1-2 50 0.400 20
2-3 50 0.200 10
3-4 100 0.050 5
4-5 25 0.100 2.5
5-6 125 0.010 1.25
6-12 250 0.005 1.25
Amount = volume*conc
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The rate method: 2- Calculate the change in time
Time
interval
(h)
Volume
(mL)
Concentration
(mg/mL)
Drug amount in the urine
(mg)
Δt
(hr)
0-1 200 0.200 40 1
1-2 50 0.400 20 1
2-3 50 0.200 10 1
3-4 100 0.050 5 1
4-5 25 0.100 2.5 1
5-6 125 0.010 1.25 1
6-12 250 0.005 1.25 6
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The rate method: 3- Calculate the rate of urinary excretion
Time
interval
(h)
Volume
(mL)
Concentration
(mg/mL)
Drug amount in the urine
(mg)
Δt
(hr)(mg/hr)
0-1 200 0.200 40 1 40
1-2 50 0.400 20 1 20
2-3 50 0.200 10 1 10
3-4 100 0.050 5 1 5
4-5 25 0.100 2.5 1 2.5
5-6 125 0.010 1.25 1 1.25
6-12 250 0.005 1.25 6 0.21
t
Xu
t
Xu
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303.2loglog
KtKrXo
t
Xu
The rate method: 4- Plot time (mid of interval) vs. log(dXu/dt)
Time
(h)(mg/hr)
0.5 40
1.5 20
2.5 10
3.5 5
4.5 2.5
5.5 1.25
9 0.21Intercept Slope
t
Xu
y = -0.301x + 1.7526R2 = 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 1 2 3 4 5 6
time (hr)
log
(dX
u/d
t)
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The rate method:5- Estimate PK parameters from the values of the slope and the intercept
0.301- 303.2
K
Slope
1-hr 693.0303.2*0.301 K
7526.1log KrXoIntercept
1 471.0
7526.1
0
10120
110
1 hrIntercept
r XK
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General comments on the use of urinary data in PK analysis
• Urine collection is a non-invasive technique• It is, perhaps, a more convenient method of
sample collection, and sample size is generally not a problem. The sampling time, however, reflects drug in urine collected over a period of time, rather than a drug concentration at a discrete time
• Urinary data allows direct measurement of bioavailability, both absolute and relative, without the need of fitting the data to a mathematical model.
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Limitations of the Sigma-Minus Method
1. Urine samples must be collected until such time that, practically, no additional drug appears in the urine (i.e.5-7 half-life)
2. No urine samples can be lost, or urine from any samples used in the determination of Xu (the exact volume of urine at each time interval must be known)
3. This is a time-consuming method for a drug with a long elimination half life (t1/2)
4. There is a cumulative build up of error
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General comment on rate method
• The method tends to give overestimate of intercept. The overestimation can be minimized by collecting urine samples more frequently (which is not always easy from practical consideration)
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