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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
To those who know:Back to the Top
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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