_BASIC PHARMACOKINETICS - CHAPTER 11: Multicompartment model*

`PHARMACOKINETICS: MAMMILLARY MODELS For many drugs, the equilibrium between drug concentrations in different tissues is not achieved rapidly. Thus, one of the assumptions of the one-compartment open model sometimes becomes invalid. A more complex mammillary open model is often necessary to describe mathematically the plasma concentration data (for example) seen after the administration of some drugs. The simplest mammillary open model is a two-compartment open model where the drug is both introduced into and exits from the central compartment ; for example:

• Compartment One (X1, the central compartment) can be sampled through the blood (or plasma, or serum). It may consist of organs or tissues which, being highly perfused with blood, are in rapid equilibrium distribution with the blood.

• Compartment Two (X2, the peripheral compartment) cannot normally be sampled. It may consist of organs or tissues which, being poorly perfused with blood, are in slow equilibrium distribution with the blood.

• The Body is the sum of both compartments.

1. Intravenous Bolus Administration: Plasma Concentration Data

Recall that for a one-compartment open model, the plasma concentration follows the equation:

( )0

kTCp Cp e −= (11.1.1)

i.e., the concentration of drug in the plasma declines mono-exponentially with time (one straight line on semi-log paper.)

k12

X1 X2

k21

k10

X0

Plasma Concentration vs. Time

10

100

1000

0 5 10 15 20 25 30

Time

Plas

ma

Con

cent

ratio

n

2. Bi-exponential Properties of Two-Compartment Open Model Following an intravenous bolus injection, the plasma concentration against time profile has two phases: a. Initial phase - (α - phase) b. Terminal phase - (β - phase)

On semilogarithmic paper (logarithm on the Y axis), the terminal phase is linear, indicating that initial distribution has been completed and that equilibrium has been attained. The terminal half life (T½β ) can be measured from the terminal phase.

For a two-compartment open model, The plasma concentration follows the equation:

( ) ( )1 1

T TCp A e B eα β− −= + (11.1.2)

i.e., the concentration of drug in the plasma declines bi-exponentially with time.

2.1 Symbols

i. A1 and B1 are intercept constants (m/L3)

ii. α and β are hybrid rate constants (T-1) iii. V1 is the apparent volume of unchanged drug distribution in compartment

1 (L3) iv. k10, k12, and k21 are the “micro” rate constants (T-1)

Plasma Concentration vs. Time

10

100

1000

0 5 10 15 20 25 30

Time

Plas

ma

Conc

entra

tion Alpha Phase

Beta Phase

2.2 Relationships:

( ) ( ) ( )( )210 12 21 10 12 21 10 21

1 42

k k k k k k k kα = + + + + + − (11.1.3)

( ) ( ) ( )( )210 12 21 10 12 21 10 21

1 42

k k k k k k k kβ = + + − + + − (11.1.4)

( )( )

211

1

D kA

Vαα β

−=

− (11.1.5)

( )( )

211

1

D kB

Vβ

α β−

=−

(11.1.6)

0 1 1Cp A B= + (11.1.7) 12 10 21k k kα β+ = + + (11.1.8) 10 21k kαβ = (11.1.9)

2.3 Obtaining Pharmacokinetic Parameters by “Feathering”

By convention, α > β a. Plot Cp against t on semilogarithmic paper b. Find t½ from the linear terminal phase: see “Intravenous

Administration,” section A1.4a c. Calculate the terminal hybrid rate constant (β); in reality it

contains both distributive (k12 and k21) and elimination (k10) factors.

1 2

ln(2)( )t β

β = (11.1.10)

d. Draw a straight line through the linear terminal elimination phase and extrapolate this line to t = 0. The intercept is equal to B1.

e. Read extrapolated plasma concentrations pC from the plot at times equal to those given for values of Cp which are prior to the terminal phase.

f. At each of these times, calculate:

diffp p pC C C= − (11.1.11)

g. Plot diffpC against t on semilogarithmic paper. The plot is a

“feathered” line and should decline linearly. h. Find the half-life of the plot. It will refer to the initial phase.

Calculate,

1 2

ln(2)( )t α

α = (11.1.12)

i. Measure the intercept of the “feathered” line; it will be equal to A1 (note that A1 ≠ B1, even theoretically).

j. Calculate (Cp)o from Eq. (11.1.7) k. Calculate V1 by

01

0 1 1

X DoseVCp A B

= =+

(11.1.13)

Theory (Why does feathering work?)

When t is large, e-αt < e-βt. Hence, Eq (11.1.2) becomes ( )

1TCp B e β−= (11.1.14)

i.e., when t is large, the concentration of the drug in the plasma declines exponentially with time.

The extrapolated plasma concentrations are ( )

1TCp B e β−= (11.1.15)

Substituting from Eqs. (11.1.2)and (11.1.15) into Eq.(11.1.11), ( )

1diff

TpC A e α−= (11.1.16)

i.e., the difference between observed and extrapolated drug concentrations in the plasma declines exponentially with time.

Note: The micro rate constants in terms of the graphical variables are:

1 121

1 1

B AkA B

α β+=

+ (11.1.17)

( )1 110

21 1 1

A Bk

k B Aαβαβα β

+= =

+ (11.1.18)

( )( )( )

21 1

12 10 211 1 1 1

A Bk k k

B A A Bα β

α βα β

−= + − − =

+ + (11.1.19)

2.4 Clearance and Volume Concepts

If model-independent equations can be used to define these terms, this is preferred. a. Systemic Clearance (C1) may be calculated by,

0

DoseClAUC∞= (11.1.20)

b. The volume terms are more complex than in a one-compartment open model. There are two terms of interest: The apparent volume of distribution in compartment one (V1) -

This is calculated using Eq.(11.1.15) The apparent volume of distribution at pseudo-distribution equilibrium (Vβ)

This volume may be defined only in relation to the terminal phase (β-phase), when initial distribution has been completed. It may be calculated by,

0

DoseVAUCβ β ∞= (11.1.21)

As Vβ requires calculation of the total area under the plasma concentration against time curve, it is also known as Varea.

c. Comparing Eqs. (11.1.20)and (11.1.21), Cl Vββ= (11.1.22)

It may also be shown that, 10 1Cl k V= (11.1.23)

This follows as systemic clearance is always given by the elimination rate constant out of the body multiplied by the apparent volume of distribution in the compartment from which drug leaves the body. Comparing Eqs. (11.1.22) and (11.1.23),

101

kV Vβ β= (11.1.24)

Note that k10 (the elimination rate constant) is not the same as β (the terminal hybrid rate constant).

2.5 Bioavailability

Find (AUC)0 using trapezoidal rule and, if necessary, the calculation for the terminal area.

00

lastlast

tpC

AUC AUCβ

∞ = +∑ (11.1.25)

This is a model-independent equation. 2.6 Dosage Regimens

The maintenance dose (DoseM) is given by the same model-independent equation as before,

( )M p ssDose C Clτ= (11.1.26)

Where ( )p ssC has its same previous definition.

The loading dose (DoseL) achieves a steady-state condition quite rapidly, but only after initial distribution has been completed. It is given by the previous equation,

( )1

21

ML N

DoseDose =−

(11.1.27)

As may be expected, equations relating (Cmax)ss and (Cmin)ss to ( )ss

Cp are

as before.

All dosage regimen equations strictly apply only when,

12

10 21

1 1kk kβ

+ ≈

(11.1.28)

Eq. (11.1.28) has the value of 0.947 for digoxin 0.990 for warfarin 0.846 for cephalexin

This is why, despite the fact that an open two-compartment model is the better description of the pharmacokinetics of these drugs, a simple one-compartment model may often be assumed for dosage regimen purposes.

3. Intravenous Bolus Administration: Compartment Two

It is not normally possible to measure drug concentrations in compartment two. However, the mass of drug can be predicted based on the drug concentrations observed in compartment one.

( ) ( )( )122

T Tk DoseX e eβ α

α β− −= −

− (11.1.29)

Note that the equation form bears a similarity to that seen for plasma concentrations after oral administration into a one-compartment open model.

When t is large, e-αt < e-βt. Hence, Eq. (11.1.29) becomes,

( )( )122

Tk DoseX e β

α β−=

− (11.1.30)

This is compared to the mass modification of Eq.(11.1.14), ( )

1 1 1TX V B e β−= (11.1.31)

Thus, when t is large, the masses of drug in each compartment decline exponentially, and in parallel, with time. This indicates that equilibrium attained. If the value of X2 reflects drug concentrations at the active site, the time of maximum concentration (and maximum pharmacological effect) is:

max

Lnt

αβ

α β

=

− (11.1.32)

4. Other Dosage Forms

The equations become complex and it is therefore difficult to obtain useful parameter values without the aid of a computer. Fortunately, because the complexity of the equations is greater than the experimental accuracy of the assays warrants, drugs that strictly require a mammillary model can be described adequately by an open one-compartment model for the purposes of calculating dosage regimens.

4.1 Intravenous Infusion

The plasma concentrations at first rise faster than an open one-compartment model profile would suggest. Later, the rise is slower. The decline, following the cessation of infusion, is bi-exponential.

( )

( )( ) ( )( )21 21

1

1 1t tk e k eQCpV

β αβ α

α β β α

− − − − − − = −

− (11.1.33)

Where α is as before in equation (11.1.3) β is as before in equation (11.1.4) Q is the infusion rate V1 is as before in equation (11.1.2) Cpss would be given by setting time equal to infinity and reducing

equation (11.1.33) to

1 10

ssQ QCp

V k Clearance= = (11.1.34)

If theer infusion was terminated at time T, the concentration at time T would be given by substituting T for t in equation (11.1.33) and the concentration after time T would be given by

( )

( )( ) ( )( )21 21

1

1 1T t T tk e e k e eQCpV

β β α αβ α

α β β α

− − − − − − = −

− (11.1.35)

4.2 Oral Administration

10

100

0 2 4 6 8 10 12

Time

Con

cent

ratio

n

At a time just after tmax the plasma concentration may exhibit a “nose,” when compared to the profile of an open one-compartment model if the absorption rate is significantly larger than α and β . The terminal rate constant will be reflected by the smallest rate constant usually β but sometimes it could be Γ, the absorption rate constant.

1 1 1

t t tCp A e B e C eα β γ− − −= + + (11.1.36) Where α is as before in equation (11.1.3) β is as before in equation (11.1.4) γ = ka, the absorption rate constant

( )( )( )

211

1

D kA

Vα γ

γ α β α−

=− −

(11.1.37)

( )( )( )

211

1

D kB

Vβ γ

γ β α β−

=− −

(11.1.38)

( )( )( )

211

1

D kC

Vγ γ

α γ β γ−

=− −

(11.1.39)

0 1 1 1 0Cp A B C= + + = (11.1.40)

SELECTED REFERENCES Riegelman, S., Loo, J.C.K., and Rowland, M., Shortcomings in pharmacokinetic analysis by conceiving the body to exhibit properties of a single compartment, J. Pharm. Sci., 57, 117-123 (1968). Riegelman, S., Loo, J.C.K., and Rowland, M., Concept of a volume of distribution and possible errors in evaluation of this parameter, J. Pharm.Sci., 57, 128-133 (1968). Benet, L.Z. and Ronfeld, R.A., Volume terms in pharmacokinetics, J. Pharm. Sci., 58, 639-641 (1969). Gibaldi, M., Nagashima, R., and Levy, G., Relationship between drug concentrations in plasma or serum and amount of drug in the body, J. Pharm.Sci., 58, 193-197 (1969). Metzler, C.M., Usefulness of the two-compartment open model in pharmacokinetics, J. Amer. Stat. Assn., 66, 49-54 (1971). Gibaldi, M. and Perrier, D., Drug elimination and apparent volume of distribution in multicompartment systems, J. Pharm. Sci., 61, 952-954 (1972). Gillette, J.R., The importance of tissue distribution in pharmacokinetics, J. Pharmacokin. Biopharm., 1, 497-520 (1973).

Drug Disposition: Volume Terms As apparent volumes of distribution are proportionality constants, and not physilological spaces, more than one term is of value.

1. Apparent Volume of sampled compartment (V1) This relates the concentration of drug on the sampled compartment with the mass of drug in that compartment. It may be calculated after an intervenous dose by:

( )0

1

0p

Dose DoseVC K AUC ∞= = (11.2.1)

It may be calculated after an intervenous infusion by

( )

11

ss ss

ss

p p

X QVC K C

= = (11.2.2)

2. Apparent Volume at Pseudo-Distribution Equilibrium (Vβ)

This volume term (sometimes known as the apparent volume of distribution of the drug in the body) requires the assumption that the drug is evenly distributed throughout the body which is clearly not true in most cases. Thus Vβ is only defined in relationship to the terminal phase (β phase) after equilibrium has been attained. It is calculated by:

( )0

DoseVAUC

ββ ∞= (11.2.3)

3. Relationships between apparent volumes:

Clearance (Cl) is calculated by the first order rate constant for the removal of the drug from the body multiplied by the volume of distribution of the drug in the compartment from which the drug leaves the body:

1r rCl k V= (11.2.4) 1m mCl k V= (11.2.5) 1sCl KV= (11.2.6)

However, systemic clearance is calculated by:

( )0

sDoseCl

AUC ∞= (11.2.7)

Comparing Eqs (11.2.3) and (11.2.7) we find: sCl Vββ= (11.2.8) And comparing Eqs (11.2.6) and (11.2.8) we find

1KV Vβ β

= (11.2.9)

As K > β, then Vβ >> V1. Note that if the pharmacokinetics cam be described by the one compartment model, then β = K and Vβ = V1.

Selected References Riegelman, S., Loo, J.C.K. and Rowland, M., Concept of volume of distributions and possible errors in evaluation of this parameter, J. Pharm. Sci., 57, 128-133 (1968) Benet, L.Z. and Ronfeld, R.A., Volume terms in pharmacokinetics, J. Pharm. Sci. 58, 639-641 (1969) Gibaldi, M., Nagashima, R., and Levy, G., Relationship between drug concentrations in plasma or serum and the amount of drug in the body. J. Pharm. Sci., 58, 193-197 (1969) Perrier, D. and Gibaldi, M., Relationship between plasma or serum drug concentrations and the amount of drug in the body at steady state upon multiple dosing, J. Pharmacokin. Biopharm., 1, 17-22 (1973) Oie, S. and Tozer, T.N., Effect of altered plasma protein binding on apparent volumes of distribution, J. Pharm. Sci., 68, 1203-1205 (1979)

Linear Mamillary Models and the LaPlace Transform Drug is usually sampled from the central compartment, designated as compartment one.

1. Laplace transform for Compartment One ,1 ,1( )( )s sA in d= (11.3.1)

Where: A s,1 is the Laplace transform for the mass of the drug in

compartment one s is the Laplace Operator in is the input function ds,1 is the disposition function for compartment one.

2. Input functions (Note: Input need not be into compartment one)

a. IV Bolus ( )in D= (11.3.2)

Where: D is the dose.

b. IV Infusion

(1 )( )sbQ ein

s

−−= (11.3.3)

Where: Q is the zero oder infusion rate, b =t when t<Term b=T when t>=Term

and Term is the termination time of the infusion

c. First order absorption

( ) ( )a

a

k FDins k

=+

(11.3.4)

Where: ka is the first order absorption rate constant F is the fraction of the dose that ultimately reaches

systemic absorption.

d. Dissolution and absorption (Type 1)

( ) ( )( )r a

r a

k k FDins k s k

=+ +

(11.3.5)

Where: kr is the first order dissolution rate constant

e. Dissolution and absorption (Type 2)

( ) ( )0 (1 )sb

a

a

k k eins s k

−−=

+ (11.3.6)

Where: k0 is the zero order dissolution rate constant, ceasing at time T

f. Others More complex functions can be derived simply by the serial addition of the above functions, e.g.:

(1 )( )sbQ ein D

s

−−= + (11.3.7)

Denote the simultaneous commencement of an IV bolus and IV infusion.

3. Disposition Function for Compartment One A driving force compartment has one or more exit rate constants; for example, in compartment i, the sum of the first order rate constants is Σi. Then:

( )( )

( ) ( )

12

,1

1 1221

i n

q iii q

s

j ni n m n

i j j mmjim j

k s

d

s k k s

=

=≠

== =

===≠

+ Σ

= + Σ − + Σ

∏

∑∏ ∏

(11.3.8)

Where: q is the compartment into which the input occurs

n is the number of driving force compartments i,j are counters (maximum of n) kq1 is the first order rate constant for transfer of

drug from the input compartment into compartment one

k1j, kj1 are the first order rate constants for drug transfer from compartment one to compartment j and visa versa.

a. Using the disposition function: i. If q = 1, then kq1 = 1

ii. Πi and Πm are continued products. The value equals one when the counter I or m takes on a forbidden number. For example i=1 is forbidden in the numerator and m=1 and m=j are forbidden in the denominator.

b. Examples i. One compartment open model (n=1,q=1)

,1 1sd = (11.3.9) ii. Two compartment open models (n=2,q=1)

( )( )( )

2,1

1 2 12 21s

sd

s s k k+ Σ

=+ Σ + Σ −

(11.3.10)

iii. Three compartment open models (n=3,q=2)

( )( )( )( ) ( ) ( )

21 3,1

1 2 3 12 21 3 13 31 2s

k sd

s s s k k s k k s+ Σ

=+ Σ + Σ + Σ − + Σ − + Σ

(11.3.11)

c. Simplifying the denominator The number of exponential terms in the final integrated equation will be equal to the number of driving force compartments (n.) This is also equal to the maximum power to which the LaPlace operator (s) would appear if the denominator were

multiplied out. Hence, the denominator is simplified to become ( )1

i n

ii

s k=

=

+∏ where

ki is a composite rate constant. Thus for the: One compartment model:

( ),1

1

1sd

s k=

+ (11.3.12)

Two compartment models

( )( )( )

2,1

1 2s

sd

s k s k+ Σ

=+ +

(11.3.13)

Three compartment models

( )( )( )( )

21 3,1

1 2 3s

k sd

s k s k s k+ Σ

=+ + +

(11.3.14)

The exact meaning of ki for any model depends on the equalities evident in the denominators. For example for the two compartment model

( )( ) ( )( )1 2 1 2 12 21s k s k s s k k+ + = + Σ + Σ − (11.3.15) And the right side of equation (11.3.15) can be multiplied out to the resultant quadratic equation 2as bs c+ + which is subsequently factored using the equation

to solve for the roots of a quadratic equation 2 4

2ib b ack

a− ± −

=

4. Method of partial fractions This method is used to solve the LaPlace transform provided that there are NO repeating factors in the denominator. E.g. NO s2 or (s+ki)2.

a. Prepare the LaPlace transform, e.g. IV Bolus into the two compartment model:

( )( )( )

2,1

1 2s

D sa

s k s k+ Σ

=+ +

(11.3.16)

b. Obtain the roots For (s+k1) the root is –k1 For (s+k2) the root is –k2 If the factor is s the root is 0.

c. The “Hidden Hand” Method i. Deal with each factor in turn.

ii. Cover each factor and remember its root. iii. Whenever the LaPlace operator occurs in the uncovered transform,

substitute the root for s iv. Multiply the result by est, again substituting the root for s. v. After doing 2 through 4 for each factor, simplify.

For the two compartment model the result would be:

( )( )

( )( )

11 2 2 2 21

1 2 2 1

k t k tD k D kX e e

k k k k− −− + Σ − + Σ

= +− + − +

(11.3.17)

which can take the form of: 1 1 1

t tC A e B eα β− −= + (11.3.18) with the exact meanings of the variables dependent on the form of the model.

5. LaPlace Transfom for peripheral compartments

This is analogous to that of employed when using the LaPlace transform table. a. Draw the model. b. Write the differential equation using all the arrows which touch the box

(compartment) in question. c. Take the transform of each side of the equation using the table where necessary. d. Use algebra to get the single time dependent variable on the left side and

everything else on the right side. e. Substitute for any know transformed dependent variables on the right side of the

equation. f. Solve using the “Hidden Hand” method above and simplify.

6. Method if the denominator contains the factor s2.

The “Hidden Hand” method is not applicable for the factor s2 as it has no simple root. The S2 factor may show up in terminal compartments, such as urine, following an IV infusion.

a. Example (n=2,q=1, exit from compartment one)

( )( )

( )( )2

, 10 21 2

1 sb

s u

e sa k Q

s s k s k

−− + Σ=

+ + (11.3.19)

where: k10 is the first order excretion rate constant from compartment one.

and this results in:

210

1 2

....ubX k Q

k kΣ

= + (11.3.20)

where Xu is the cumulative mass of drug excreted into the urine and the other factors are handled by the “Hidden Hand” method as above.

b. Example (n=3,q=1, exit from compartment one)

( )( )( )

( )( )( )2 3

, 10 21 2 3

1 sb

s u

e s sa k Q

s s k s k s k

−− + Σ + Σ=

+ + + (11.3.21)

and this results in:

2 310

1 2 3

...bXu k Qk k kΣ Σ

= + (11.3.22)

References L.Z.Benet, General treatment of linear mamilary models with elimination from any compartment as used in pharmacokinetics, J. Pharm. Sci., 61 536-541 (1972) D.P. Vaughan, D.J.H. Mallard, A. Trainor, and M. Mitchard, General pharmacokinetic equations for linear mammillary models with drug absorption into peripheral compartments, Europ. J. Clin. Pharmacol., 8, 141-148 (1975) D.P. Vaughn and Trainor, Derivation of general equations for linear mammillary models when drug is administered by different routes, J/ Pharmacokin. Biopharm., 3, 203-218 (1975)

Aspirin Fu, C., Melethil, S., and Mason, W., "The pharmacokinetics of aspirin in rats and the effect of

buffer", Journal of Pharmacokinetics and Biopharmaceutics, Vol. 19, (1991), p. 157 - 173. Aspirin is an analgesic/ antipyretic commonly used to relieve minor pain and is used in such conditions as rheumatic fever, rheumatoid arthritis, and osteoarthritis. The major metabolite of aspirin is salicylic acid. The following set of data was collected using rats which weighed 250 - 300 g. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr) Time(min) Cp(mg/L) 0.000 0.000 15.8200.001 0.065 15.1520.005 0.324 12.8530.011 0.648 10.6500.022 1.296 7.7320.032 1.943 5.9810.058 3.466 3.8300.116 6.931 1.8150.173 10.397 0.9050.289 17.329 0.2260.433 25.993 0.0400.578 34.657 0.007

weight of rat 275 g Dose 5 mg/kg IV

A1 8.58 µgmL

α 1.07 min−1

B1 7.24 µgmL

β 0.2 min−1

AUC 38.8 µgmL

⋅ min

AUMC 116.0 µgmL

min⋅ 2

1. What is AUCα ? 2. What is AUCβ ? 3. What is your patient's clearance? 4. What is your patients MRT? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is your patient's Vd ss ? 8. What is ( )t1

2α ?

9. What is ( )t12

β ? 10. What is k21? 11. What is k10 ? 12. What is k12 ? 13. What is Cpo

? 14. What is the tmax in the peripheral compartment? 15. What percent of the dose is in the peripheral compartment at equilibrium? 16. Can this drug be treated as a one-compartment model for dosing purposes? 17. If this drug can be treated as a one-compartment model, what is K ? 18. What would be the Cpmax and Cpmin if the patient were dosed as above by IV

bolus every four hours?

Buprenorphine Ohtani, M., et al., "Pharmacokinetic analysis of enterohepatic circulation of buprenorphine and

its active metabolite, norbuprenorphine, in rats", Drug Metabolism and Disposition, Vol. 22, (1994), p. 2 - 7.

Buprenorphine is a morphine derivative which has twice the duration of action and 30 times the potency of morphine. Buprenorphine is partially metabolized to norbuprenorphine which is also active in the body. In this study, buprenorphine was given to rats weighing 280 - 300 g. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr) Time(min) Cp(mg/L) 0.000 0.000 0.0510.018 1.069 0.0480.089 5.346 0.0390.178 10.691 0.0300.356 21.382 0.0190.535 32.074 0.0142.558 153.464 0.0055.115 306.929 0.0037.673 460.393 0.001

Weight of rat 290 g Dose 0.06 mg/kg IV

A1 41 ngmL

α 3.89 hr −1

B1 10 ngmL

β 0.271 hr −1

AUC 48.3 ngmL

h⋅

AUMC 135.24 ngmL

h⋅ 2

1. What is AUCα ? 2. What is AUCβ ? 3. What is your patient's clearance? 4. What is your patients MRT? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is your patient's Vd ss ? 8. What is ( )t1

2α ?

9. What is ( )t12

β ? 10. What is k21? 11. What is k10 ? 12. What is k12 ? 13. What is Cpo



Caffeine Shi, J., et al., "Pharmacokinetic-pharmacodynamic modeling of caffeine: Tolerance to pressor

effects", Clinical Pharmacology and Therapeutics, Vol. 53, (1993), p. 6 - 14. This study looks at the cardiovascular effects of caffeine. Caffeine is known to increase blood pressure upon its withdrawl. This study looks at how tolerance to caffeine and its pressor effects develops and disappears with time. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr) Time(min) Cp(mg/L)

0.000 0.000 19.650 0.014 0.849 18.914 0.071 4.244 16.413 0.141 8.488 14.084 0.283 16.975 11.164 0.424 25.463 9.573 3.014 180.821 4.550 6.027 361.642 2.275 9.041 542.463 1.138 15.068 904.105 0.284 22.603 1356.158 0.050 30.137 1808.210 0.009

Patient weight 80 kg Dose 4 mg/kg oral

A1 10.55 µgmL

α 4.9 hr −1

B1 9.1 µgmL

β 0.23 hr −1 f 98.4 %

1. What is AUCα ? 2. What is AUCβ ? 3. What is AUCtotal ? 4. What is your patient's clearance? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is ( )t1

2α ?

8. What is ( )t12

β ? 9. What is k21? 10. What is k10 ? 11. What is k12 ? 12. What is your patient's Vd ss ? 13. What is Cpo



Cefazolin Nightingale, C., et al., "Changes in pharmacokinetics of cefazolin due to

stress", Journal of Pharmaceutical Sciences, Vol. 64, (1975), p. 712 - 714. Cefazolin is a cephalosporin antibiotic used in the treatment of many types of infections. This study looks at the effect of stress on the pharmacokinetics of cefazolin. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr) Time(min) Cp(mg/L) 0.000 0.000 329.4400.014 0.861 314.6060.072 4.303 264.0120.143 8.607 216.4970.287 17.214 155.9400.430 25.821 121.8991.210 72.581 62.0782.419 145.162 30.7423.629 217.743 15.3706.048 362.904 3.8439.073 544.356 0.679

12.097 725.809 0.120

Patient weight 56.3 kg

Dose 1 g IV

A1 206.48 µgmL

α 4.832 hr −1

B1 122.96 µgmL

β 0.573 hr −1 1. What is AUCα ? 2. What is AUCβ ? 3. What is AUCtotal ? 4. What is your patient's clearance? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is ( )t1

2α ?

8. What is ( )t12




Ceftazidime Ackerman, B., et al., "Effect of decreased renal function on the pharmacokinetics of ceftazidime", Antimicrobial Agents and Chemotherapy, Vol. 25, (1984), p. 785 - 786.

Ceftazidime is a cephalosporin antibiotic. This study explores the effect of compromised renal function on the pharmacokinetics of ceftazidime. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 246.2000.008 0.506 233.3700.042 2.530 189.9460.084 5.059 149.8440.169 10.119 100.5840.253 15.178 74.9151.415 84.875 29.1022.829 169.750 14.5504.244 254.625 7.2757.073 424.376 1.819

10.609 636.564 0.32214.146 848.752 0.057

Dose 1 g IV bolus

A1 188 mgL

α 8.22hr −1

B1 58.2 mgL


2α ?

8. What is ( )t12




2-Chloro-2-deoxyadenosine Liliemark, J. and Juliusson, G., "On the pharmacokinetics of 2-Chloro-2-deoxy-

adenosine in humans", Cancer Research, Vol. 51, (1991), p. 5570 - 5572.

Two-Chloro-2-deoxyadenosine is an antitumor agent used in the treatment of hairy cell leukemia and other lymphoproliferative diseases. Infusions of 0.14 mg/kg over 12 hours were administered to 12 patients with various lymphoproliferative diseases for 5 consecutive days. Answer the remaining questions given this analysi of the data.

Patient weight 65 kg Dose 0.14 mg/kg over 12 hours

A1 177.0 nM α 1.04 hr −1

B1 21.0 nM β 0.10 hr −1

1. What is AUCα ? 2. What is AUCβ ? 3. What is AUCtotal ? 4. What is your patient's clearance? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is ( )t1

2α ?

8. What is ( )t12




Clentiazem Shah, A., et al., "Pharmacokinetics of clentiazem after intravenous and oral administration in

healthy subjects", Journal of Clinical Pharmacology, Vol. 33, (1993), p. 354 - 359. Clentiazem is an derivative of diltiazem which is under investigation for its use in the treatment of angina pectoris and hypertension. Clentiazem blocks calcium channels resulting in a decrease in peripheral vascular resistance which subsequently leads to a decrease in blood pressure. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 0.0540.026 1.540 0.0510.128 7.702 0.0430.257 15.403 0.0350.513 30.807 0.0250.770 46.210 0.0208.887 533.190 0.008

17.773 1066.380 0.00426.660 1599.570 0.00244.433 2665.951 0.001

Patient weight 77 kg

Dose 20 mg IV bolus

A1 37.52 ngmL

α 2.7 hr −1

B1 16.17 ngmL


2α ?

8. What is ( )t12




Cocaine Levine, B. and Tebbett, I., "Cocaine pharmacokinetics in ethanol-pretreated rats", Drug

Metabolism and Disposition, Vol. 22, (1994), p. 498 - 500. This study looks into several reports which claim that the euphoric effects of cocaine can be enhanced when taken in conjunction with alcohol. This effect may be the result of higher cocaine blood levels or a reduced elimination of cocaine or a combination of both. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 1.6350.003 0.191 1.5560.016 0.957 1.2910.032 1.915 1.0480.064 3.830 0.7540.096 5.744 0.607

15.403 924.196 0.23130.807 1848.392 0.11646.210 2772.589 0.05877.016 4620.981 0.014

115.525 6931.472 0.003

Weight of rat

Dose 2 mg/kg cocaine (also 1 g/ kg ethanol)

A1 1172.6 ngmL

α 0.362 min −1

B1 462 ngmL


2α ?

8. What is ( )t12




1,2-Diethyl-3-Hydroxypyridine-4-One Epemolu, O., et al., "The pharmacokinetics of 1,2-Diethyl-3-Hydroxypyridine-4-One

(CP94) in rats, Drug Metabolism and Disposition, Vol. 20, (1992), p. 736 - 741.

1,2-Diethyl-3-Hydroxypyridine-4-One (CP94) is an iron chelator which is orally active. It is being investigated for use in the treatment of hemoglobinopathic disorders. In this study, rats weighing 250 - 300 g were given doses 50 mg /kg intravenously and the following data was collected: Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.


13.681 820.832 0.04518.241 1094.443 0.008

Weight of rat 275 g Dose 50 mg/kg IV

A1 30.9 mgL

α 2.03 hr −1

B1 8.13 mgL

β 0.38 hr −1 Assume that the rat ( which weighs 275 g) is suffering from thalassemia and his iron levels are very high. The rat is prescribed CP94 to restore the iron levels to normal. 1. What is AUCα ? 2. What is AUCβ ? 3. What is AUCtotal ? 4. What is your patient's clearance? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is ( )t1

2α ?

8. What is ( )t12




2,2-dimethylaziridine Lalka, D., Jusko, W., and Bardos, T., "Reactions of 2,2-dimethylaziridine-type alkylating agents in biological systems II: Comparative pharmacokinetics in dogs", Journal of Pharmaceutical

Sciences, Vol. 64, (1975), p. 230 - 235.

The 2,2-dimethylaziridine alkylating agents are used for their antitumor capability as antineoplastic agents. In this study, male mongrel dogs, weighing 20 - 28 kg, were each given a dose of 12 mg/kg of ethyl bis (2,2-dimethylaziridinyl) phosphinate intraveneously. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 50.5000.003 0.169 47.5520.014 0.847 37.5410.028 1.695 28.2360.056 3.389 16.6600.085 5.084 10.4940.122 7.296 6.3740.243 14.593 2.2320.365 21.889 1.0680.608 36.481 0.2660.912 54.722 0.0471.216 72.963 0.008

Weight of dog 24 kg Dose 12 mg/kg IV

A1 42 µgmL

α 0.409 min −1

B1 8.5 µgmL

β 0.095 min −1 1. What is AUCα ? 2. What is AUCβ ? 3. What is AUCtotal ? 4. What is your patient's clearance? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is ( )t1

2α ?

8. What is ( )t12




Flurbiprofen Menzel-Soglowek, S., et al., "Variability of inversion of (R)-flurbiprofen in different species",

Journal of Pharmaceutical Sciences, Vol. 81, (1992), p. 888 - 891. Flurbiprofen is an anti-inflammatory and analgesic agent. This study compares the pharmacokinetics of the (R)-isomer of flurbiprofen to the those of the (S)-isomer. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 107.1800.030 1.785 103.6270.149 8.925 91.4670.297 17.849 79.9530.595 35.699 65.0030.892 53.548 56.2583.961 237.650 29.3457.922 475.301 14.670

11.883 712.951 7.33519.804 1188.252 1.83429.706 1782.378 0.32439.608 2376.505 0.057

Weight of rat 260 g

Dose 10 mg/kg IV

A1 48.5 mgL

α 2.33 hr −1

B1 57.68 mgL


2α ?

8. What is ( )t12




Furosemide Tilsone, W., and Fine, A., "Furosemide kinetics in renal failure", Clinical Pharmacology and

Therapeutics, Vol. 23, (1978), p. 644 - 650. Furosemide is an agent which is used for its diuretic action to treat such conditions as renal and cardiac edema. In this study, normal subjects were given an intravenous bolus dose of 22 mg of furosemide. Blood samples were taken at various intervals and the following data was obtained: Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.


Dose 22 mg IV

A1 2.1 mgL

α 6.9 hr −1

B1 0.77 µgmL


2α ?

8. What is ( )t12




Glycyrrhizin Tsai, T., et al., "Pharmacokinetics of glycyrrhyzin after intravenous administration to rats",

Journal of Pharmaceutical Sceinces, Vol. 81, (1992), p. 961- 963. Glycyrrhizin is a component of licorice which is proposed to have anti-inflammatory, anti-hepatotoxic, interferon-inducing, anti-viral, and anti-ulcer activity. It also causes pseudoaldosteronism. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.


12.090 725.387 0.38616.120 967.182 0.068

Weight of rat 275 g Dose 20 mg/kg

A1 91.23 mgL

α 4.16 hr −1

B1 69.90 µgmL


2α ?

8. What is ( )t12




Human Deoxyribonuclease Mohler, M., et al., "Altered pharmacokinetics of recominant human deoxyribonuclease in rats due to the

presence of a binding protein", Drug Metabolism and Disposition, Vol. 21, (1993), p. 71 - 75. Deoxyribonucleases are found in human serum, urine, and a variety of tissues. These endonucleases catalyze the hydrolysis of DNA to oligonucleotides. It has been suggested that increased levels of serum deoxyribonucleases may predict malignancies. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 24147.0000.008 0.483 22848.8650.040 2.415 18463.8730.081 4.830 14432.5480.161 9.661 9532.2300.242 14.491 7039.7663.027 181.611 2448.5006.054 363.221 1224.2509.081 544.832 612.125

15.134 908.053 153.03122.701 1362.080 27.05230.268 1816.106 4.782

Patient weight 260 g Dose 1 mg/kg IV bolus

A1 19250 mgL

α 8.61 hr −1

B1 4897 ngmL


2α ?

8. What is ( )t12




Human Granulocyte Colony-Stimulating Factor Tanaka, H., and Kaneko, T., "Pharmacokinetic and pharmacodynamic comparisons between human granulocyte colony-stimulating factor purified from human bladder carcinoma cell line 5637 culture

medium and recombinant human granulocyte colony-stimulating factor produced in Escherichia coli", The Journal of Pharmacology and Experimental Therapeutics, Vol. 262, (1992), p. 439 - 444.

Human Granulocye Colony-Stimulating Factor (hG-CSF) is used to stimulate the proliferation of precursor cells and their subsequent differentiation in the bone marrow. This article compares the pharmacokinetics of hG-CSF produced by two different methods. In the first method, the hG-CSF was obtained from human bladder carcinoma cell line 5637 culture medium. In the second method, the hG-CSF was produced by Escherichia coli. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 116.3090.024 1.440 108.5260.120 7.200 82.2660.240 14.400 58.1920.480 28.800 29.1290.720 43.200 14.5931.270 76.200 3.0162.540 152.400 0.1013.810 228.600 0.0146.350 381.000 0.0039.525 571.500 0.001

Weight of rat 250 g

Dose 10 µg/kg IV

A1 116.21 mgL

t 12( )α 0.24 hours

B1 99.228 ngmL

t 12( )β 1.27 hours

1. What is AUCα ? 2. What is AUCβ ? 3. What is AUCtotal ? 4. What is your patient's clearance? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is α? 8. What is β? 9. What is k21? 10. What is k10 ? 11. What is k12 ? 12. What is your patient's Vd ss ? 13. What is Cpo



Hydrocortisone Derendorf, H., et al., "Pharmacokinetics and oral bioavailability of hydrocortisone",

Journal of Clinical Pharmacology, Vol. 31, (1991), p. 473 - 476. This study looks at both the two-compartment model pharmacokinetics and the oral bioavailability of hydrocortisone. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.


11.682 700.935 2.42515.576 934.580 0.429

Dose 20 mg IV

A1 430 mgL

α 13.1 hr −1

B1 439 µgmL


2α ?

8. What is ( )t12




Levodopa Sasahara, K., et al., "Dosage form design for improvement of bioavailability of levodopa II:

Bioavailability of marketed levodopa preparations in dogs and parkinsonian patients" Journal of Pharmaceutical Sciences, Vol. 69, (1980), p. 261 - 265.

Levodopa is an agent used in the treatment of Parkinson's disease. This study looks at various dosage forms of levodopa and compares the pharmacokinetic parameters of each. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.


Dose 50 mg IV

A1 8.63 mgL

α 13.3 hr −1

B1 2.97 µgmL


2α ?

8. What is ( )t12




Meropenem Chimata, M., et al., "Pharmacokinetics of meropenem in patients with various degrees of renal

function, including patients with end-stage renal disease", Antimicrobial Agents and Chemotherapy, Vol. 37, (1993), p. 229 - 233.

Meropenem is a carapenem antibiotic which has a broad spectrum of activity. It is used in the treatment of infections caused by both Gram-positive and Gam-negative bacteria and is active against Enterobacteriaceae and Pseudomonas aeruginosa. Meropenem is 60% renally and 40% hepatically eliminated. Answer the remaining questions using the analysis given.


10.335 620.112 0.11013.780 826.816 0.020

Dose 500 mg IV infusion over 40

minutes

A1 21 mgL

α 1.85 hr −1

B1 20 µgmL


2α ?

8. What is ( )t12




N-Methylpyridinium-2-Carbaldoxime Chloride Bodor, N., and Brewster, M., "Problems of delivery of drus to the brain", International

Encyclopedia of Pharmacology and Therapeutics, Vol. 120, (1975) N-methylpyridinium-2-cabaldoxime chloride (2-PAM) is the drug of choice for the treatment of orgaonphosphate poisoning. It is mostly renally excreted. This article considers the fact that this agent is highly hydrophilic and thus has difficulty reaching the brain. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.


Weight of dog 40 kg

Dose 7.0 mg/kg

A1 5.356 mgL

α 0.28796 hr −1

B1 35.983 mgL


2α ?

8. What is ( )t12




Pyrazine Diazohydroxide Vogelzang, N., et al., "Phase I and pharmacokinetic study of a new antineoplastic agent: pyrazine

diazohydroxide (NSC 361456)", Journal of Cancer Research , Vol. 54, (1994), p. 114 - 119. Pyrazine diabhohydroxide is an agent which forms a reactive pyrazine dizonium ion in vivo which acts to destroy tumor cells. This study looks at the pharmacokinetic parameters of this agent in advanced cancer patients whose cancer was not curable by any other type of therapy. They were given a dose of 18 mg/m2/day for 5 days every 4 weeks. Most of the following data was collected for a 66 year old male subject. The remaining data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.


Patient Body Surface Area

1.82 m2

Dose 18 mg/ m2

A1 8063 µgmL

α 0.195 min −1

B1 1186 µgmL

β 0.0257 min −1 1. What is AUCα ? 2. What is AUCβ ? 3. What is AUCtotal ? 4. What is your patient's clearance? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is ( )t1

2α ?

8. What is ( )t12




Rhizoxin Graham, M., et al., "Preclinical and phase I studie with rhizoxin to apply a pharmacokinetically guided dose-escalation scheme", Journal of the National Cancer Institute, (1991), p. 494 - 499.

Rhizoxin is a lactone which was obtained from the fungus, Rhizopus chinensis. It has anti-tumor activity against a broad spectrum of tumor types including LOX melanoma, A549 lung tumors, and MX-1 mammary tumors. This study looks at dosing of rhizoxin. Patients with nontreatable tumors who had a life expectancy of more than 12 weeks were given doses of 12 mg/ m2. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(µMol/mL)0.000 0.000 1.6700.017 1.040 1.5660.087 5.199 1.2150.173 10.397 0.8930.347 20.794 0.5030.520 31.192 0.3075.975 358.524 0.060

11.951 717.049 0.03017.926 1075.573 0.01529.877 1792.622 0.00444.816 2688.933 0.001

Patient Body Surface

Area 1.82 m2

Dose 12 mg/ m2

A1 1.55 µMmL

α 4.00 hr −1

B1 0.12 µMmL


2α ?

8. What is ( )t12




Terbinafene Kovarik, J., et al., "Dose-proportional pharmacokinetics of terbinafine and its N-demethylated metabolite in healthy volunteers", British Hournal of Dermatology, Vol. 126, (1992), p. 8 - 13.

Terbinafene is an antifungal agent which acts by interfering with ergosterol biosynthesis. It is active against Trichophyton, Epidermophyton, and Microsporum. Approximately 70% of an oral dose is absorbed. Terbinafene has an N-demethylated metabolite which is active. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 2.5000.136 8.139 2.3390.678 40.694 1.7961.356 81.387 1.2982.713 162.774 0.6964.069 244.161 0.393

31.223 1873.371 0.05162.446 3746.742 0.02693.669 5620.112 0.013

156.114 9366.854 0.003

Dose 750 mg

A1 2398 ngmL

α 0.511 hr −1

B1 102 ngmL


2α ?

8. What is ( )t12




Verrucarol Barel, S., Yagen, B., and Bailer, M., "Pharmacokinetics of the trichothecen mycotoxin verrucarol

in dogs", Journal of Pharmacetuical Seciences, Vol. 79, (1990), p. 548 - 550. Verrucarol is a toxin which is related to toxins which have anti-tumor activity. This study looks at the pharmacokinetics of verrucarol in dogs. The following data was approximated from the graph given in this article. Graph the data and find A1, α, B1, β. Check your answers with the answers given below and answer the remaining questions using the correct answers.

Time(hr)Time(min) Cp(mg/L) 0.000 0.000 0.6670.028 1.670 0.6500.139 8.351 0.5890.278 16.702 0.5250.557 33.405 0.4260.835 50.107 0.3521.221 73.271 0.2762.442 146.543 0.1353.664 219.814 0.0686.106 366.357 0.0179.159 549.535 0.003

Weight of Dog 22.5 kg

Dose 0.4 mg/ kg

A1 126.05 ngmL

α 0.0415 min−1

B1 540.58 ngmL

β 0.00946min −1 1. What is AUCα ? 2. What is AUCβ ? 3. What is AUCtotal ? 4. What is your patient's clearance? 5. What is your patient's Vβ ? 6. What is your patient's V1? 7. What is ( )t1

2α ?

8. What is ( )t12




Answers

Aspirin Caffeine Ceftazidime Cocaine 1. 8.019 µg

mL⋅min 1. 2.15 µg h

mL⋅ 1. 22.87 mg h

L⋅ 1. 3239.2 ng min

mL⋅

2. 36.2 µgmL⋅min 2. 39.57 µg h

mL⋅ 2. 118.78 mg h

L⋅ 2. 10266.7 ng min

mL⋅

3. 31.1 mLmin

3. 41.72 µg hmL

⋅ 3. 141.65 mg hL

⋅ 3. 13505.89 ng min

mL⋅

4. 2.62 minutes 4. 7.67 Lh

4. 7.0598 Lh

4. 44.43 mLmin

5. 155.48 mL 5. 33.35 L 5. 14.41 L 5. 987.2 mL

6. 86.92 mL 6. 16.28 L 6. 4.06 L 6. 367.1 mL

7. 81.57 mL 7. 0.141 hours 7. 0.0843 hours 7. 1.91 minutes

8. 0.648 min 8. 3.014 hours 8. 1.415 hours 8. 15.4 minutes

9. 3.47 min 9. 2.39 h-1 9. 2.32 h-1 9. 0.1346 min-1

10. 0.598 min-1 10. 0.471 h-1 10. 1.738 h-1 10. 0.1210 min-1

11. 0.358min-1 11. 2.266 h-1 11. 4.65 h-1 11. 0.1514 min-1

12. 0.314min-1 12. 19.65 µgmL

12. 246.2 mgL

12. 1634.6 ngmL

13. 15.82 µgmL

13. 0.655 hours 13. 0.365 hours 13. 8.35 minutes

14. 1.928 minutes 14. 51.2% 14. 39.2% 14. 59.2%

15. 44.1% 15. Yes 15. Yes 15. No

16. Yes

17. 0.381 min-1

Buprenorphine Cefazolin Clentiazem 1,2-Diethyl-3-hydroxpyridine-4-one

1. 10.54 ng hmL

⋅ 1. 42.73 µg hmL

⋅ 1. 13.9 ng hmL

⋅ 1. 15.22 mg hL

⋅

2. 36.9 ng hmL

⋅ 2. 214.59 µg hmL

⋅ 2. 207.3 ng hmL

⋅ 2. 21.39 mg hL

⋅

3. 47.4 ng hmL

⋅ 3. 257.32 µg hmL

⋅ 3. 221.2 ng hmL

⋅ 3. 36.62 mg hL

⋅

4. 366.8 mLh

4. 3.89 Lh

4. 90.4 Lh

4. 375.5 mLh

5. 2.85 hours 5. 6.78 L 5. 1159.2 L 5. 988.2 mL

6. 1.35 L 6. 3.035 L 6. 372.5 L 6. 352.3 mL

7. 0.34 L 7. 0.143 hours 7. 0.257 hours 7. 0.341 hours

8. 0.178 hours 8. 1.21 hours 8. 8.89 hours 8. 1.824 hours

9. 2.58 hours 9. 2.163 h-1 9. 0.868 h-1 9. 0.724 h-1

10. 0.981 h-1 10. 1.28 h-1 10. 0.243 h-1 10. 1.066 h-1

11. 1.075 h-1 11. 1.96 h-1 11. 1.67 h-1 11. 0.62 h-1

12. 2.11 h-1 12. 329.44 µgmL

12. 53.69 ngmL

12. 39.03 mgL

13. 51 ngmL

13. 0.50 hours 13. 1.35 hours 13. 1.016 hours

14. 0.736 hours 14. 55.2% 14. 47.4% 14. 55.4%

15. No

15. 74.9% 15. Yes 15. Yes

16. No

17. Can't be calc

2,2-dimethylaziridine Furosemide Human Deoxyribonuclease

Hydrocortisone

1. 102.7 µg minmL⋅ 1. 0.304 mg h

L⋅ 1. 2235.78 ng h

mL⋅ 1. 32.8 mg h

L⋅

2. 89.47 µg minmL⋅ 2. 0.802 mg h

L⋅ 2. 21384.3 ng h

mL⋅ 2. 986.5 mg h

L⋅

3. 192.16 µg minmL⋅ 3. 1.106 mg h

L⋅ 3. 23620.1 ng h

mL⋅ 3. 1019.3 mg h

L⋅

4. 1498.7 mLmin

4. 19.88 Lh

4. 11.01 mLh

4. 19.62 mLh

5. 15.78 L 5. 20.71 L 5. 48.07 mL 5. 44.1 mL

6. 5.7 L 6. 7.67 L 6. 10.77 mL 6. 23.01 mL

7. 1.695 minutes 7. 0.1005 hours 7. 0.0805 hours 7. 0.053 hours


9. 0.148 min-1 9. 2.55 h-1 9. 1.929 h-1 9. 6.838 h-1

10. 0.263 min-1 10. 2.59 h-1 10. 1.0223 h-1 10. 0.853 h-1

11. 0.093 min-1 11. 2.71 h-1 11. 5.89 h-1 11. 5.85 h-1 12. 50.5 µg

mL 12. 2.87 mg

L 12. 24147 ng

mL 12. 869 mg

L


14. 56.5% 14. 62.99% 14. 28.9% 14. 47.8%

15. No 15. No 15. Yes 15. Yes

Flurbiprofen Glycyrrhizin Human Granulocyte Colony-Stimulating

Factor

Levodopa

1. 20.82 mg hL

⋅ 1. 21.93 mg hL

⋅ 1. 40.24 ng hmL

⋅ 1. 0.649 mg hL

⋅

2. 329.6 mg hL

⋅ 2. 162.56 mg hL

⋅ 2. 181.81 ng hmL

⋅ 2. 2.61 mg hL

⋅

3. 350.42 mg hL

⋅ 3. 184.5 mg hL

⋅ 3. 222.05 ng hmL

⋅ 3. 3.25 mg hL

⋅

4. 7.42 mLh

4. 29.8 mLh

4. 11.26 mLh

4. 15.37 Lh

5. 42.4 mL 5. 69.33 mL 5. 20.62 mL 5. 13.48 L

6. 24.5 mL 6. 34.13 mL 6. 11.6 mL 6. 4.31 L

7. 0.297 hours 7. 0.167 hours 7. 2.89 h-1 7. 0.052 hours

8. 3.96 hours 8. 1.61 hours 8. 0.546 h-1 8. 0.61 hours

9. 1.35 h-1 9. 2.048 h-1 9. 1.625 h-1 9. 4.25 h-1

10. 0.303 h-1 10. 0.873 h-1 10. 0.971 h-1 10. 3.56 h-1

11. 0.856 h-1 11. 1.67 h-1 11. 0.839 h-1 11. 6.62 h-1 12. 106.18 mg

L 12. 161.13 mg

L 12. 215.44 ng

mL 12. 11.6 mg

L

13. 1.2 hours 13. 0.61 hours 13. 0.711 hours 13. hours

14. 42.2% 14. 50.8% 14. 43.8% 14. 68.0%

15. Yes 15. Yes 15. Yes 15. Yes

Meropenem Pyrazine Diazohydroxide Verrucarol 1. 11.35 mg h

L⋅ 1. 41348.7

µg minmL⋅

1. 3037.35 ng minmL⋅

2. 39.76 mg hL

⋅ 2. 46147.9 µg min

mL⋅

2. 57143.8 ng min

mL⋅

3. 51.11 mg hL

⋅ 3. 87496.6 µg min

mL⋅

3. 60181.1 ng minmL⋅

4. 9.78 Lh

4. 0.3744 mLmin

4. 149.5 mLmin

5. 19.45 L 5. 14.57 mL 5. 15.81 L

6. 12.20 L 6. 3.542 mL 6. 13.5 L

7. 0.375 hours 7. 3.55 minutes 7. 16.7 minutes


9. 1.16 h-1 9. 0.0474 min-1 9. 0.0155 min-1

10. 0.802 h-1 10. 0.106 min-1 10. 0.0253 min-1

11. 0.391 h-1 11. 0.0676 min-1 11. 0.0101 min-1

12. 41 mgL

12. 9249 µgmL

12. 666.63 ngmL


14. 37.3% 14. 75.7% 14. 28.1%

15. No 15. No 15. Yes

N-methylpyridinium-2-carbaldoxime chloride

Terbinafene

1. 18.6 mg hL

⋅ 1. 4692.8 ng hmL

⋅

2. 3.106 mg hL

⋅ 2. 4594.6 ng hmL

⋅

3. 21.71 mg hL

⋅ 3. 9287.4 ng hmL

⋅

4. 12.9 Lh

4. 80.75 Lh

5. 1.11 L 5. 3637.6 L

6. 6.77 L 6. 300 L

7. 2.41 hours 7. 1.36 h

8. 0.0598 hours 8. 31.2 h

9. 1.752 h-1 9. 0.0421 h-1

10. 1.905 h-1 10. 0.2692 h-1

11. 8.218 h-1 11. 0.222 h-1

12. 41.339 mgL

12. 2500 ngmL

13. 0.327hours 13. 6.42 hours

?14. 45.5% 14. 91.8%

15. Yes 15. No

_BASIC PHARMACOKINETICS - CHAPTER 11: Multicompartment model*

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