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Dear pk-professionals,
In the moment I have a problem with the interpretation of serum
concentration profiles of a new drug. More than 90% of the drug is
metabolized by conjugation, the conjugate is excreted renally:
After 2-min infusion of increasing doses (by infusion pump using an
indwelling cannula) some subjects showed tmax-values up to 0.5 or even 1
hour. The cmax is lower than predicted from 15 min infusion data. The
analytical method (HPLC with fluorescence detection) is selective (checked
by LC-MS-MS), there is no evidence for enterohepatic circulation after oral
dosing.
Here are 2 examples:
time [h], c_10_mg, c_20_mg, c_40_mg
0.050, 4.3, 20.2, 76.0
0.083, 55.3, 37.4, 98.0
0.167, 66.7, 53.8, 90.7
0.250, 36.3, 36.5, 75.6
0.500, 19.2, 34.8, 76.8
1.000, 14.2, 35.3, 73.7
2.000, 11.2, 27.4, 63.6
4.000, 7.8, 17.0, 48.6
6.000, 5.0, 12.0, 27.5
10.00, 2.8, 5.8, 13.6
time [h], c_10_mg, c_20_mg, c_30_mg
0.050, 15.2, 26.3, 61.4
0.083, 29.2, 37.4, 47.9
0.167, 23.1, 33.5, 43.5
0.250, 22.4, 32.1, 52.9
0.500, 18.4, 37.5, 57.2
1.000, 15.6, 41.5, 56.5
2.000, 12.4, 31.7, 49.8
4.000, 9.1, 24.2, 35.7
6.000, 5.5, 15.0, 22.5
10.00, 2.4, 4.9, 8.2
Is there anybody able to help me to find the (may be trivial) explanation?
I had expected some turbulence in the first sample points (3, 5 and 10
minutes) but no increasing concentrations ....
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Dear Dr. Ossig,
what is the solubility of the drug? Are you sure that there is no
precipitation after infusion?
Subsequent systemic dissolution can create profiles like the ones you saw.
Gerhard H.
Roche, Basel
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Group,
Lipid soluble benzodiazepines and barbiturates undergo redistribution
after IV administration, where uptake into less vascular tissues (especially
muscle and fat) leads to a decline in the concentration of durg in the
plasma and brain. A similar redistribution phenomenon could be taking
place here.
Two compartment analysis of the data as if an infusion took place up
until the peak plasma concentrations, indicates that there is a decrease
in to two compartment characteristics with Increasing doses. The k12 and
k12 decrease with increasing doses indicating a saturation of the peripheral
compartment.
Although I have only read about similar phenomenon,,this type of data
might indicate an initial distribution into a preferred compartment, and
then redistibution into the plasma. It would appear at least, that there
is change in the distribution properties of the drug with increasing doses.
Ko=10mg/0.03333hr= 300mg/hr for T=0.03333hr
A= RXo(alpha)/Ko(1-e-alphaT) 10mg dose Sub 1
58.18494153
B= SXo(beta)/Ko(1-e-betaT)
17.22363161
Vc= Xo/(A+b) 49.01273 R
0.132610917 10.59955 alpha
k21= (alphaA +betaB)/(A+b) 17.16428 S
8.224536062 0.20125 beta
K10=alpha*beta/k21
0.259365398
K12= alpha+ beta-k21-k10
2.316899877
Vb=k10*Vc/beta
0.170905228
Ko=40mg/0.03333hr= 1200mg/hr for T=0.03333hr
A= RXo(alpha)/Ko(1-e-alphaT) 40mg Dose Sub 1
53.70058
B= SXo(beta)/Ko(1-e-betaT)
32.24054
Vc= Xo/(A+b) 53.53319 R
0.465435 0.181437 alpha
k21= (alphaA +betaB)/(A+b) 32.14004 S
0.181437 0.181437 beta
K10=alpha*beta/k21
0.181437
K12= alpha+ beta-k21-k10
0
Vb=k10*Vc/beta
0.465435
Mike Leibold, PharmD, RPH
ML11439.-a-.goodnet.com
References
1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker
1975
2) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker
1982
3) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug
Intelligence Publications 1975
4) Godfrey, Keith, Compartment Models and Their Application, New York,
Academic Press 1983
5) Wagner, J.G., Pharmacokinetics for the Pharmaceutical Scientist, Lancaster,
Technomic Publishing Co 1993
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Group,
Here is a slight change in the two compartment analysis as
if an infusion took place up until 0.5 hours in subject 1, at
two different doses of 10mg and 40mg, which resulted in the
following change in the data. Basically, the same decrease in two
compartment characteristics occurs in the data, again indicating
a change in distribution properties (a saturation of a
preferred compartment?).
Ko=10mg/0.03333hr= 300mg/hr for T=0.03333hr
A= RXo(alpha)/Ko(1-e-alphaT) 10mg dose Sub 1
13.77935
B= SXo(beta)/Ko(1-e-betaT)
15.34182
Vc= Xo/(A+b) 13.10631 R
0.343393 3.024355 alpha
k21= (alphaA +betaB)/(A+b) 15.2945 S
1.525579 0.179443 beta
K10=alpha*beta/k21
0.355734
K12= alpha+ beta-k21-k10
1.322485
Vb=k10*Vc/beta
0.680753
Ko=40mg/0.03333hr= 1200mg/hr for T=0.03333hr
A= RXo(alpha)/Ko(1-e-alphaT) 40mg Dose Sub 1
51.18065
B= SXo(beta)/Ko(1-e-betaT)
29.72178
Vc= Xo/(A+b) 51.02111 R
0.494423 0.181437 alpha
k21= (alphaA +betaB)/(A+b) 29.62913 S
0.181437 0.181437 beta
K10=alpha*beta/k21
0.181437
K12= alpha+ beta-k21-k10
1.09E-13
Vb=k10*Vc/beta
0.494423
Mike Leibold, PharmD,RPh
ML11439.aaa.goodnet.com
References
1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker
1975
2) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker
1982
3) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug
Intelligence Publications 1975
4) Godfrey, Keith, Compartment Models and Their Application, New York,
Academic Press 1983
5) Wagner, J.G., Pharmacokinetics for the Pharmaceutical Scientist, Lancaster,
Technomic Publishing Co 1993
Back to the Top
Group,
When including the plasma levels before the peak, the best
fitting model is a two compartment with a first order dissolution term.
That is, a model which allows for dissolution of the IV administered
drug in the plasma after it has been administered. This is the only
model which fits the increase in plasma concentrations that occurs
before the peak.
Here is the triexpoenential model which was fitted to the data,
but the first term is negative, representing the first order dissolution
term of the equation. An ordinary three compartment model would not fit
the plasma concentrations before the peak.
Nonlinear Regression of Cp = Qe-pt + Re-at +Se-bt
Q pi R alpha S
-835.0134346 18.99610185 551.7020564 11.43598543
16.97809179 beta
0.178897821
Predicted Conc Time Concentration
SS function Minimized
5.270679896 0.05 4.3 0.000292109
57.70270585 0.083 55.3 0.035570097
63.19889347 0.167 66.7 0.301764167
40.63117962 0.25 36.3 0.311086177
17.27579577 0.5 19.2 0.423790259
14.20288683 1 14.2 0.050400387
11.87135267 2 11.2 0.000132097
8.300639105 4 7.8 2.39696E-06
5.803939269 6 5 0.041752943
2.83756301 10 2.8 0.006232451
1.171023083 Sum
Mike Leibold, PharmD, RPh
ML11439.-a-.goodnet.com
References
1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker
1975
2) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker
1982
3) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug
Intelligence Publications 1975
4) Godfrey, Keith, Compartment Models and Their Application, New York,
Academic Press 1983
5) Wagner, J.G., Pharmacokinetics for the Pharmaceutical Scientist, Lancaster,
Technomic Publishing Co 1993
---
Sender: PharmPK.at.boomer.org
Reply-To: ml11439.aaa.goodnet.com (Michael J. Leibold)
From: ml11439.-a-.goodnet.com (Michael J. Leibold)
Date: Sat, 9 Sep 2000 03:17:30 -0700 (MST)
To: david.aaa.boomer.org
Subject: Re: PO-kinetics after 2-min infusion?
Group,
Fitting the data to a triexpoential equation with the
first term being a negative first order dissolution term seems
to fit the data adequately. The first order dissolution with
a two compartment model can predict the initial low plasma
concentrations which increase to a peak, as well as explain
what seemed to be decrease in two compartment characteristics
with the higher 40mg dose. This would be mathematically
equivalent to the two compartment first order absorption model,
and kinetically similar to activation of a prodrug.
The following data resulting from a 40mg dose in subject
one were fitted to a triexponential equation with a negative
first order dissolution term. The fit seemed as good as
with the 10mg dose, and the fit indicated the same two
compartment characteristics.
40mg dose Sub 1
2min Infusion
Nonlinear Regression of Cp = Qe-pt + Re-at +Se-bt
Q pi R alpha S
-866.3538907 33.86616619 521.9578591 24.85520409
85.38710337 beta
0.175312971
Predicted Conc Time Concentration
SS function Minimized
81.70453204 0.05 76 4.62601E-05
100.2539897 0.083 98 0.00138804
88.22444089 0.167 90.7 0.073684107
82.59464127 0.25 75.6 0.645936614
78.22308832 0.5 76.8 0.026369485
71.65637351 1 73.7 0.056667696
60.13362278 2 63.6 0.188927218
42.34893146 4 48.6 0.804029999
29.82411358 6 27.5 0.196418325
14.79168741 10 13.6 0.104420506
2.097888249 Sum
SSW 1/C Function Minimized
2.097888249
Mike Leibold, PharmD, RPh
ML11439.-a-.goodnet.com
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Dear Dr. Joachim!
I met similar problems with Cmax achieved some time following IV bolus
administration while injecting VPA derivatives to dogs. The problem to my
understanding was solubility of the compound in plasma. So what may happen
after the injection is that the compound will sediment inside the blood
vessel and afterwards redissolve in the blood current over a period of
several minutes, which will subsequently cause Cmax achievement not in time
zero. On the other hand if your compound is freely water soluble it is
probably some other reason that caused this particular phenomenon of yours.
Matthew Wasserman.
Dissolution+/-Prodrug? Corrected textBack to the Top
Joachim,
When including the plasma levels before the peak, the best
fitting model is a two compartment with a first order dissolution term.
That is, a model which allows for dissolution of the IV administered
drug in the plasma after it has been administered. This is the only
model which fits the increase in plasma concentrations that occurs
before the peak.
Here is the triexpoenential model which was fitted to the data,
but the first term is negative, representing the first order dissolution
term of the equation. An ordinary three compartment model would not fit
the plasma concentrations before the peak.
Nonlinear Regression of Cp = Qe-pt + Re-at +Se-bt
Q pi R alpha S
-835.0134346 18.99610185 551.7020564 11.43598543
16.97809179 beta
0.178897821
Predicted Conc Time Concentration
SS function Minimized
5.270679896 0.05 4.3 0.000292109
57.70270585 0.083 55.3 0.035570097
63.19889347 0.167 66.7 0.301764167
40.63117962 0.25 36.3 0.311086177
17.27579577 0.5 19.2 0.423790259
14.20288683 1 14.2 0.050400387
11.87135267 2 11.2 0.000132097
8.300639105 4 7.8 2.39696E-06
5.803939269 6 5 0.041752943
2.83756301 10 2.8 0.006232451
1.171023083 Sum
Fitting the data to a triexpoential equation with the
first term being a negative first order dissolution term seems
to fit the data adequately. The first order dissolution with
a two compartment model can predict the initial low plasma
concentrations which increase to a peak, as well as explain
what seemed to be decrease in two compartment characteristics
with the higher 40mg dose. This would be mathematically
equivalent to the two compartment first order absorption model,
and kinetically similar to activation of a prodrug.
The following data resulting from a 40mg dose in subject
one were fitted to a triexponential equation with a negative
first order dissolution term. The fit seemed as good as
with the 10mg dose, and the fit indicated the same two
compartment characteristics.
40mg dose Sub 1
2min Infusion
Nonlinear Regression of Cp = Qe-pt + Re-at +Se-bt
Q pi R alpha S
-866.3538907 33.86616619 521.9578591 24.85520409
85.38710337 beta
0.175312971
Predicted Conc Time Concentration
SS function Minimized
81.70453204 0.05 76 4.62601E-05
100.2539897 0.083 98 0.00138804
88.22444089 0.167 90.7 0.073684107
82.59464127 0.25 75.6 0.645936614
78.22308832 0.5 76.8 0.026369485
71.65637351 1 73.7 0.056667696
60.13362278 2 63.6 0.188927218
42.34893146 4 48.6 0.804029999
29.82411358 6 27.5 0.196418325
14.79168741 10 13.6 0.104420506
2.097888249 Sum
SSW 1/C Function Minimized
2.097888249
Mike Leibold, PharmD, RPh
ML11439.-at-.goodnet.com
References
1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker
1975
2) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker
1982
3) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug
Intelligence Publications 1975
4) Godfrey, Keith, Compartment Models and Their Application, New York,
Academic Press 1983
5) Wagner, J.G., Pharmacokinetics for the Pharmaceutical Scientist, Lancaster,
Technomic Publishing Co 1993
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)