1 Compartment IV Analysis
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1 Compartment IV Analysis & Renal Elimination. 500 mg of tobramycin is administered by iv bolus to Mr BB, a 68 yr old male who weighs 75 kg. Blood samples were drawn following the dose and the plasma concentration determined. It is known that tobramycin is excreted primarily unchanged in

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Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

& Renal Elimination

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Graph Patient Data

100

60

30

10

6

4

2

1

Using semi-log paper,

graph the data following

Iv bolus of 500 mg of

tobramycin.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Graph Patient Data in Excel®

Using semi-log paper,

graph the data following

IV bolus of 500 mg of

tobramycin.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

What model best

describes this profile?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Graph Patient Data

100

60

30

10

6

4

2

1

What model best

describes this profile?

… a 1 compartment model

with iv bolus input

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation the will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?

What do you calculate first?

Cl

AUC

Vd

K


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?

What do you calculate first?

Cl Dose/AUC or K x Vd

T½ - 0.693 K

AUC –/ K

Vd - [ ]0 by back extrapolation of K

K …?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Graph Patient Data

Slope based on log of the

concentrations

100

60

30

10

6

4

2

1

Time ConcLog

(hr) (mg/L)Conc

119.51.29

214.41.16

55.80.76

82.40.38

120.7-0.15

18BLOQ

Slope = -K/2.303

Slope = (y2 – y1) / (x2 – x1)

=

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Graph Patient Data

Slope based on log of the

concentrations

100

60

30

10

6

4

2

1

Time ConcLog

(hr) (mg/L)Conc

119.51.29

214.41.16

55.80.76

82.40.38

120.7-0.15

18BLOQ

Slope = -K/2.303

Slope = (y2 – y1) / (x2 – x1)

= (-0.15 – 1.29)/(12-1)

= (- 1.44) / (11)

= -0.1309

- K= slope x 2.303

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Graph Patient Data

Slope based on log of the

concentrations

100

60

30

10

6

4

2

1

Time ConcLog

(hr) (mg/L)Conc

119.51.29

214.41.16

55.80.76

82.40.38

120.7-0.15

18BLOQ

Slope = -K/2.303

Slope = (y2 – y1) / (x2 – x1)

= (-0.15 – 1.29)/(12-1)

= (- 1.44) / (11)

= -0.1309

- K= slope x 2.303

= - 0.1309 x 2.303

K= 0.3015 hr-1

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Graph Patient Data

Slope based on log of the

concentrations

100

60

30

10

6

4

2

1

Time ConcLog

(hr) (mg/L)Conc

119.51.29

214.41.16

55.80.76

82.40.38

120.7-0.15

18BLOQ

Slope = -K/2.303

K= 0.3015 hr-1

T½= 0.693 / K

= 0.693 / 0.3015

= 2.298 hr

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

K


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation the will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?

Now calculate Volume.

Since it was an IV dose,

and appears to be a 1 compartment model,

we will assume instantaneous distribution

and so we will back-extrapolate to t=0

to determine the initial concentration.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Calculation of Volume

  • Back extrapolation can be

  • completed a number of ways

  • Graphically

100

60

30

10

6

4

2

1

Intercept

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Calculation of Volume

  • Back extrapolation can be

  • completed a number of ways

  • Graphically

  • By equation

100

60

30

10

6

4

2

1

Intercept

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

[ ]t= C0 e-Kt

or

[ ]0= C1 e+Kt

=

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Calculation of Volume

  • Back extrapolation can be

  • completed a number of ways

  • Graphically

  • By equation

100

60

30

10

6

4

2

1

Intercept

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

[ ]t= C0 e-Kt

or

[ ]0= C1 e+Kt

[ ]0= 19.5 e(0.3015 x 1)

= 26.36 mg/L

Volume = Dose / [ ]0

=

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Calculation of Volume

  • Back extrapolation can be

  • completed a number of ways

  • Graphically

  • By equation

100

60

30

10

6

4

2

1

Intercept

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

[ ]t= C0 e-Kt

or

[ ]0= C1 e+Kt

[ ]0= 19.5 e(0.3015 x 1)

= 26.36 mg/L

Volume = Dose / [ ]0

= 500 / 26.36

= 18.97 L

0 2 4 6 8 10 12 14


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

  • Back extrapolation can be

  • completed a number of ways

  • Graphically

  • By equation

  • By Excel

  • Using Intercept function

  • =10^(INTERCEPT(C5:C9,A5:A9))

Calculation of Volume


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation the will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?

Now calculate AUC.

Since it was an IV dose, we must realise

that the data set starting at 1 hour is missing

concentration data from 0 to 1 hour.

Therefore, AUC by trapezoidal rule must use

a time zero concentration of 26.38 mg/L.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Trapezoidal Rule

AUC =((C0+C1)/2)*(t1-t0)

The value of 9.75 for the AUC

is based on a noconcentration

or a concentration of 0.00

at time zero.

Was the Concentration zero?

Or should we determine

the time zero concentration

Calculation of AUC

Trapezoidal Rule (Excel)

AUC = ((B4+B5)/2)*(A5-A4)

The value of 9.75 in this cell

is based on a noconcentration

or a concentration of 0.00

at time zero in cell B4.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Trapezoidal Rule

If the initial concentration of

26.38 is used in the calculation

of AUC from time 0 to 1 hr, a

more appropriate AUC of

22.94 mg*hr/L is estimated.

AUC0-12h is 88.69 mg*hr/L.

Calculation of AUC

You must also

calculate AUC

from 12 hr to .

This can only

be done using

the PCK method:

[ ]LP/K.

 = 88.69


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

AUC from 12hr to 

Recall that K was calculated

as 0.3015 hr-1 using

concentrations at 1 hr and 12 hrs.

Using this K value, AUC12- is:

[ ]LP/K. = 0.7/0.3015

= 2.32 mg*hr/L.

Calculation of AUC

The sum of the

AUC (0-12hr)

and

AUC (12hr-).

is:

AUC (0-) = 88.69 + 2.32

= 91.01 mg*hr/L.

 = 88.69


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

  • Other Estimates of AUC (0-)

  • Several AUC (0-) estimates

  • are possible based on the

  • estimate of K

  • and the method used.

  • Kinetic method

  • Using the determined

  • back-extrapolated t=0

  • concentration of 26 .38 mg/L

  • AUC0-  can also be estimated as:

  • [ ]t=0/K. = 26.38/0.3015

  • = 87.496 mg*hr/L.

Calculation of AUC


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Other Estimates of AUC (0-)

Several AUC (0-) estimates

are possible based on the

estimate of K

and the method used.

2.Estimates of K

In the Excel sheet using the

last 2 … or last 3 …or last 4…

K values can be estimated

ranging from of 0.30809 hr-1

0.30245 hr-1

0.30185hr-1

and 0.301806 hr-1

(these are effectively the same

~ differ by less than 0.007 hr-1)

These variations will produce

small differences in AUC

Calculation of AUC


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Other Estimates of AUC

Excel sheet shows some

of the possible estimates

of K and using 0.0318 hr-1

and calculates AUC12h-

As 2.32 mg*hr/L.

Also shown are

Calculation of AUC


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Other Estimates of AUC

Excel sheet shows some

of the possible estimates

of K and using 0.0318 hr-1

and calculates AUC12h-

As 2.32 mg*hr/L.

Also shown are two

estimates of AUC0-:

1. Based on kinetic method

from the t=0

determined concentration

and

2. Based on sum

of Trap Rule AUC

& kinetic method from LP

Calculation of AUC


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Other Estimates of AUC

AUC0- is 91.01 mg*hr/L

calculated by trapezoidal rule.

But if we use the PCK method

from time zero (26.38 mg/L)

we would calculate

AUC0- as 87.41 mg*hr/L.

Which is more correct?

Calculation of AUC


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation the will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?

  • Now calculate Clearance.

  • This can be completed

  • by at least 2 methods:

  • Dose / AUC

  • K x Vd


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Calculation of Clearance

Estimates of Clearance

Although a variety of estimates

of K have been calculated

all are very close (~0.3018 hr-1)

Using the volume calculated

from the t=0 concentration

determined by back-extrap

using this K value (Excel Sheet)

Cl = K x Vd

= 0.3018 x 18.95 L

= 5.720 L/hr


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Calculation of Clearance

Estimates of Clearance

Although a variety of estimates

of K have been calculated

all are very close (~0.3018 hr-1)

Cl = 5.720 L/hr (K x V)

When we use AUC calculated

by the PCK method, clearance

estimate is identical to estimate

determined by K*Vd.

Clearance is 5.72 L/hr and

AUC0- of 87.41 mg*hr/L.

is the more correct estimate.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Equation describing profile

Profile is a 1 compartment

model with bolus input.

[ ]t= C0 e-Kt

Where K = 0.3018 hr-1

and C0 can always

be calculated from Dose/V

Ct= (Dose / V) e-Kt

and for our patient

K = 0.3018 hr-1

V = 18.95 L


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Equation describing profile

Profile is a 1 compartment

model with bolus input.

[ ]t= C0 e-Kt

Where K = 0.3018 hr-1

and C0 can always

be calculated from Dose/V

Ct= (Dose / V) e-Kt

and for our patient

K = 0.3018 hr-1

V = 18.95 L


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?

At time zero, immediately following

the dose, there should be

500 mg in the body.

The entire dose is delivered into the body.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Amount in the body at 12 hours

Ct= (Dose / V) e-Kt

and for our patient

K = 0.3018 hr-1

Dose = 500 mg

V = 18.95 L

So the concentration

at 12 hr would be:

C12hr=


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Amount in the body at 12 hours

Ct= (Dose / V) e-Kt

and for our patient

K = 0.3018 hr-1

Dose = 500 mg

V = 18.95 L

So the concentration

at 12 hr would be:

C12hr= (500 / 18.95) e(-0.3018 x 12)

= 28.38 e(-0.0267)

= 0.7054 mg/L

and the concentration reported

at 12 hours was 0.7 mg/L


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Amount in the body at 12 hours

C12hr= (500 / 18.95) e(-0.3018 x 12)

= 28.38 e(-0.0267)

= 0.7054 mg/L

and the concentration reported

at 12 hours was 0.7 mg/L

Since the volume is 18.95 L,

the amount in the body at 12 hours is:

Amount = [ ] x V

= 0.7 mg/L x 18.95 L

= 13.265 mg

Only 13.265 mg of the initial

500 mg dose remains.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Amount in the body at 12 hours

We could have also calculated the

amount in the body directly

from the equation:

Instead of

Ct= (Dose / V) e-Kt

We would have

Amtt=


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Amount in the body at 12 hours

We could have also calculated the

amount in the body directly

from the equation:

Instead of

Ct= (Dose / V) e-Kt

We would have

Amtt= Dose e-Kt

and for our patient

K = 0.3018 hr-1

Dose = 500 mg

So the amount in the body

at 12 hr would be:

Amt12hr= (500) e(-0.3018 x 12)

= 500 e(-0.0267)

= 13.36 mg


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

& Renal Elimination

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Where did the tobramycin go?

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

& Renal Elimination

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Where did the tobramycin go?

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Amount = [ ] x V

= 0.7 mg/L x 18.95 L

= 13.26 mg

Amt12hr= (500) e(-0.3018 x 12)

= 500 e(-0.0267)

= 13.36 mg

Only 13.3 mg of the initial

500 mg dose remains.

Does this mean that 486.7 mg is in the urine

in the first 12 hours following the dose?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

& Renal Elimination

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Since renal elimination appears

to be the only way tobramycin

is cleared from the body,

Total Body Clearance should

equal renal clearance…?

Clearance is 5.7 L/hr

Calculation of Clearance


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

At constant concentration, clearance

can be estimated from blood flow

and the difference between

arterial and venous concentrations.

ClH = Q [ (Ca – Cv) / Ca ]

But in our situation the concentration changing.

In the first hour concentration started at

26.38 mg/L and declined to 19.51 mg/L

and we collected 130.26 mg

of tobramycin in the urine.

In the second hour concentration started at

19.51 mg/L and declined to 14.43 mg/L

and we collected 96.33 mg

of tobramycin in the urine.

Equations

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

As the concentration declines we recover less

in the urine and because urinary excretion is

the only method of elimination, drug excretion

into the urine is tied to elimination from the body.

Rate of appearance of drug in the urine

is proportional to the amount in the body

Therefore:

Where X is the amount of drug in the body

at time t and Xu is the amount of drug

eliminated in the urine to time t.

Equations

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q

dXu

dt

--- = ke X


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Since X, the amount drug in the body

at time t changes according to

X = X0 e (-Kt)

or as we have previous written

Amtt = Dose e (-Kt)

Then …

and a semi-log plot of

excretion rate of drug

in the urine vs. time

should be linear and have a

slope of –K/2.303.

This is the same slope as

for a plasma concentration curve.

dXu

dt

--- = ke X0 e(-Kt)

Equations

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Evaluation of

excretion rate

vs. time.

Note:

Time scale expanded

Conc. & Amount/time

Difference produces

“Amount Lost”

both total and during

each 1 hour interval.

An excretion rate

per hour

(mg/hr)

is then calculated.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Plots of excretion rate (mg/hr) vs. time and concentration

vs. time are parallel. Slope of the log of excretion rate

vs. time is a function of the overall elimination rate (K),

NOT the urinary excretion rate constant – ke.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

The urinary excretion rates that were

calculated are not instantaneous rates,

Rather, they are average rates

determined over an interval.

The average excretion

rate closely approximates the

instantaneous rate seen at the mid-point

of the urine collection interval.

Therefore, urinary excretion rates

should be plotted at the midpoints

of the urine collection period.

dXu

dt

--- = ke X0 e(-Kt)

Xu

t

--- = ke X0 e(-Kt)

Equations

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Just as the plasma concentration-time

profile can be characterized by both an

elimination rate constant (K) and a

clearance term (ClT or TBC) , so can

urinary excretion data:

renal excretion rate constant (ke)

and a renal clearance term (ClR).

We have seen that the rate at which drug

is cleared into the urine is proportional to

the plasma concentration at the mid point

of the urine collection interval.

Equations

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q

(dXu / dt )

CMID

ClR =


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

We have seen that the rate at which drug

is cleared into the urine is proportional to

the plasma concentration at the mid point

of the urine collection interval.

In practice renal clearance is estimated by

dividing the urinary excretion rate by the

plasma concentration at the mid point

of the urinary collection interval.

where XU is the amount of

drug appearing in the urine

(dXu / dt )

CMID

ClR =

Equations

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q

(Xu / t )

CMID

ClR =


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

In practice renal clearance is estimated by

dividing the urinary excretion rate by the

plasma concentration at the mid point

of the urinary collection interval.

where XU is the amount of

drug appearing in the urine.

(Xu / t )

CMID

ClR =

Equations

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q

Rearrangement yields:

(Xu / t ) = ClR x CMID

which indicates that ClR will be the slope

of a straight-line relationship between

the amount recovered in the urine

during an interval and the

midpoint plasma concentration.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

The excretion rate

(mg/hr) has been

plotted against the

plasma

concentration at

the midpoint of

the interval.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

The slope is renal

clearance (ClR)

and you can see

that it equivalent

to total clearance (ClT)

calculated previously.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

The slope is renal

clearance (ClR)

and you can see

that it equivalent

to total clearance (ClT)

calculated previously.


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

In practice, renal clearance is calculated from a

series of urine collections with blood samples

taken at the mid-point of the interval.

Urinary Excretion Rate is calculated

from the urine volume,

the drug concentration in the urine

and period over which the urine is collected.

Example:

Blood Urine Urine Urine AmountExcretion

Sample CollectionVolume Conc. Excreted Rate

Time Interval

(hr)Start-Stop (mL)(mg/mL)(mg)(mg/hr)

1.0 0 – 2 hr 120 1.89226.6 113.6

4.0 2 – 6 hr 250 0.77192.5

9.0 6 – 12 hr 400 0.17


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

In practice, renal clearance is calculated from a

series of urine collections with blood samples

taken at the mid-point of the interval.

Urinary Excretion Rate is calculated

from the urine volume,

the drug concentration in the urine

and period over which the urine is collected.

Example:

Blood Urine Urine Urine AmountExcretion

Sample CollectionVolume Conc. Excreted Rate

Time Interval

(hr)Start-Stop (mL)(mg/mL)(mg)(mg/hr)

1.0 0 – 2 hr 120 1.89226.6 113.6

4.0 2 – 6 hr 250 0.77192.5 48.13

9.0 6 – 12 hr 400 0.1768.0 11.33


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Calculated

Renal

Clearance

5.723 L/hr


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Another method for calculating

Renal Clearance

Since dXu / dt is equivalent to keX,

Substitution in the equation:

Results in

Where X/C = V, and so…

ClR = keV

(dXu / dt )

CMID

ClR =

Equations

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q

(ke X )

CMID

ClR =


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

1 Compartment IV Analysis

& Renal Elimination

500 mg of tobramycin is administered by iv bolus to Mr BB, a

68 yr old male who weighs 75 kg. Blood samples were drawn

following the dose and the plasma concentration determined.

It is known that tobramycin is excreted primarily unchanged in

the urine. The following plasma concentrations were observed.

Time Plasma Conc

(hr) (mg/L)

119.5

214.4

55.8

82.4

120.7

18Below limit of detection

  • What model best describes this profile?

  • Calculate AUC, K, Vd, T½ and Cl.

  • Write an equation that will calculate

  • concentrations at anytime after the 1st dose.

  • How much is in the body at time zero?

  • How much is in the body at 12 hours?

  • Where did the tobramycin go?

  • How much is in the urine at 12 hrs?

  • What is the renal clearance of tobramycin?

  • Is tobra a high or low extraction drug?


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Renal blood flow = 25% CO

1.5 L/min.

Hct = 0.5 in our patient

Therefore, renal plasma flow is

Qplasma = 1.5 L/min x 0.5

= 0.75 L/min

= 45 L/hr.

Equation Summary

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q

(Xu / t ) = ClR x CMID

ClR = keV

Using plasma because

renal clearance was based

on plasma concentrations and

the volume of distribution

was based on

plasma concentrations


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Renal blood flow = 25% CO

1.5 L/min.

Hct = 0.5 in our patient

Therefore, renal plasma flow is

Qplasma = 1.5 L/min x 0.5

= 0.75 L/min

= 45 L/hr.

Tobramycin renal clearance

in our patient was 5.72 L/hr

ER = ClR / Qplasma

=

Equation Summary

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q

(Xu / t ) = ClR x CMID

ClR = keV


Time plasma conc hr mg l 1 19 5 2 14 4 5 5 8 8 2 4 12 0 7 18 below limit of detection

Renal Clearance of tobramycin

Renal blood flow = 25% CO

1.5 L/min.

Hct = 0.5 in our patient

Therefore, renal plasma flow is

Qplasma = 1.5 L/min x 0.5

= 0.75 L/min

= 45 L/hr.

Tobramycin renal clearance

in our patient was 5.72 L/hr

ER = ClR / Qplasma

= 5.72 / 45

= 0.127

Low Extraction … compare

Theophylline (liver) 5%

Creatinine (renal) 14.6%

Ciprofloxacin (renal) 71%

Equation Summary

Conc = Dose / V

V = Dose/Conc

Cl = Q x ER

ER = Cl / Q

(Xu / t ) = ClR x CMID

ClR = keV


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