- On 22 Dec 1998 at 13:46:09, ml11439.-a-.goodnet.com (Michael J. Leibold) sent the message

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Pharmacokinetic Discussion Group Letter:

To those who know:Monday, December 21, 1998

Could the duration of pharmacological effect of abciximab post infusion

and/or bolus be modeled after the reported half-life of the platelet

receptor-antibody complex? That is, in a March 1996 article in Annals of

Pharmacotherapy Gennetto& Mauro report that the monoclonal antibody blockade

of the GPIIB/IIIA receptor complex falls from 80% to 40% post bolus over 24

hours. However, post infusion (48-72 hour infusion) the half-life of the

platelet receptor-monoclonal antibody blockade is 5-6 days.

Given that the percent receptor blockade required for pharmacological

effect is 80%, could the duration of pharmacological effect be modeled under

the simple assumption that the half-life of the platelet receptor-antibody

complex is about one day following bolus dosing, but about 5 days following

prolonged infusions?

There must be a complex interplay between infusion, distribution,

platelet receptor binding, and elimination which might explain this

phenomenon. There is also some mention of a pharmacokinetic washout phase

post-infusion.

A multicompartment model might explain the difference between the

duration following a bolus or infusion, where the beta phase may predominate

in the later. However, perhaps more appropriate would be the application of

a "Modifed Nagashima Equation", where the pharmacological effect would be

modeled as some linear function of abciximab's concentration over Cmax

(concentration associated with antiplatelet activity resulting in receptor

occupancy of 80%). The Modified Nagashima Equation is of course used to

model the pharmacodynamics of warfarin. A similar investigation of the

pharmacodynamics of abciximab involving the measuring of antiplatelet

activity as function of percent receptor blockade would be necessary. The

effect of abciximab transferring from platelet to platelet might affect the

pharmacodynamics differently in the case of a prolonged continous infusion,

and the pharmacodynamic curve (M) may differ with prolonged infusions versus

bolus administration.

Pharmacodynamic Model: Modifed Nagashima Equation?

The pharmacodynamics of warfarin are really modeled as a linear function

of the "log" of the plasma concentrations, where:

Rsyn= -M[Ln(Ce-kt/Cmax)]

Rdeg= -KdP

dP/dt= -M[Ln)Ce-kt/Cmax)] - KdP

Where Ke= Ke for warfarin

Kd= degradation constant for PCA

P= prothrombin complex activity

Rsyn= rate of synthesis of PCA

Rdeg = rate of degradation of PCA

A similar mode for abciximab might be:

Percent platelet acitivity= -M[Ln(Ce-kt/Cmax)]

Decrease in physiological platelet activity= -KdPt

dPt/dt= -M[Ln)Ce-kt/Cmax)]- KdPt

Where K= Ke for abciximab

Kd= physiological rate of decline of platelet activity

Pt= percent platelet activity

A multicompartment model could be incoporated as:

C= Ae-at + Be-bt

Obviously, this would take considerable laboratory work to derive any

appropriate pharmacodynamic constants.

Abciximab Multicompartent Pharmacokinetics/Pharmacodynamics

The pharmacodynamic model for Abciximab would to seem best correlated with

amount in the tissue compartment of a three compartment model. Pharmacokinetic

data suggests that there is a washout phase which probably reflects the release

of antibody from platelets. No more than 5% of bolus dose remains in the plasma

two hours after administration, suggesting sequestering of the antibody by

platelets.

Two rapid distribution phases with half-lives of 10min and 30min are

followed

by a longer elimination phase which probably reflects the release of antibody

by platelets. The half-life for the percent antibodies bound by abciximab

following

prolonged infusion(48-72 hours) is 5-6 days. This probably reflects the

half-life

of the washout phase. Hence, the half-life of the terminal elimination constant

for the three compartment model would be 120 hours, and the accumulation and

elimination from the platelet-tissue binding compartment would be influenced

by this

constant.

Ctp= k13/Vtp( A[1-e-aT]e-at + B[1-e-bT]e-bt + G[1-e-gT]e-gt )

= k13/Vtp( Xc )

Xc= amount in central compartment

Vtp= volume of tissue-platelet compartment

Ctp= (k13/Vtp)(A' + B' + G[1-e-gT]) 2 hours into infusion

Ctp= (k13/Vtp)(A'e-at' + B'e-bt' + G(1-e-gT)e-gt')] Post infusion

Ctp= (k13/Vtp)(Ae-at+ Be-bt + Ge-gt) Post bolus

As can be seen, the difference in half-life in percent antibody blockade

between bolus and IV infusion administration probably reflects more

accumulation

with the infusion. Although the half-life of percent antibody blockade would

reflect the terminal half-life of abciximab, the critical factor would be the

concentration of abciximab in the platelet-tissue compartment. Abciximab would

continue to accumulate in the plaetelet tissue compartment according to the

above equations with continuing infusion.

Hence, pharmacodynamic modeling would predict a more prolonged effect with

the prolonged infusion, since there would be continuing accumulation in the

platelet-tissue compartment. The terminal elimination phase would be most

influential, and the model could be simplied to a one compartment version:

Ctp= k13'/Vtp(ko/g)(1-e-gT)e-gt')

Fraction normal platelet function(Pt)=

-M[ln((k13'/Vtp(ko/g)(1-e-gT)e-gt')/Cmax)]

Physiological platelet degration= -KdPt

dPt/dt= -M[ln((k13'/Vtp(ko/g)(1-e-gt)e-gt')/Cmax)] -KdPt

where g= the terminal elimination constant of the three compartment

model

Ctp= the concentration of abciximab in the platelet-tissue

compartment

Simplification: Above Cmax

As mentioned earlier, it may be that Abciximab is usually dosed above

the Cmax for inhibition of normal platelet activity. In this case than the

appropriate pharmacodynamic equation might be a simplification of the

modified Nagashima equation where:

Fraction Normal Platelet activity= None

Degradation of normal platelets= -KdPt

dPt/dt= zero

Time till recovery of platelet function:post infusion or post-bolus

Cmax= Ctpe-gt*

t*= [ln(Ctp/Cmax)]/g

The previously described Modified Nagashima Equation would apply when

the concentration of agciximab is falling below the Cmax.

Mike Leibold, PharmD

ML11439.-a-.goodnet.com - On 24 Dec 1998 at 17:30:26, ml11439.aaa.goodnet.com (Michael J. Leibold) sent the message
To those who know:

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Regarding the Abxiximab problem, there is a slight error in the

equations I would like to correct. The factors A, B and G in the following

equations are actually divided by (k31-a), (k31-b) and (k31-g). Such that

the equation Ctp= (K13/Vtp)Xc is incorrect, since each component of the

equation for Xc should be divided by the factor as above.

So, the corrected equations are as follows:

Ctp= k13/Vtp( A'[1-e-aT]e-at + B'[1-e-bT]e-bt + G'[1-e-gT]e-gt )

A', B', G': components of the polyexponential equation for the central

compartment divided by (k31-a), k31-b), k31-g) respectively

Ctp= (k13/Vtp)(A" + B" + G'[1-e-gT]) 2 hours into infusion

A", B": previous components when the terms (1-e-aT), (1-e-bT) approach 1.

Ctp= (k13/Vtp)(A"e-at' + B"e-bt' + G'(1-e-gT)e-gt')] Post infusion

Ctp= (k13/Vtp)(A'e-at+ B'e-bt + G'e-gt) Post bolus

As can be seen, the difference in half-life in percent antibody blockade

between bolus and IV infusion administration probably reflects more

accumulation with the infusion. Although the half-life of percent antibody

blockade would reflect the terminal half-life of abciximab, the critical

factor would be the

concentration of abciximab in the platelet-tissue compartment. Abciximab would

continue to accumulate in the plaetelet tissue compartment according to the

above equations with continuing infusion.

Hence, pharmacodynamic modeling would predict a more prolonged effect with

the prolonged infusion, since there would be continuing accumulation in the

platelet-tissue compartment. The terminal elimination phase would be most

influential, and the model could be simplied to a one compartment version:

Ctp= k13'/Vtp(ko/g)(1-e-gT)e-gt')

k13'= hybrid rate constant representing a combination of k13(G')

(actually part of G', since 1/g is in the above equation)

Fraction normal platelet

function(Pt)=-M[ln((k13'/Vtp(ko/g)(1-e-gT)e-gt')/Cmax)]

Physiological platelet degration= -KdPt

dPt/dt= -M[ln((k13'/Vtp(ko/g)(1-e-gt)e-gt')/Cmax)] -KdPt

where g= the terminal elimination constant of the three compartment

model

Ctp= the concentration of abciximab in the platelet-tissue

compartment

k13'= hybrid rate constant

Mike Leibold, PharmD

Ml11439.at.goodnet.com

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