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Subject: Re: Convolution and Deconvolution techniques to assess Bioavailability
Can someone explain what these techniques are? Where these should be
used and what are the advantages/disadvantages of using these techniques.
Please also post any references and/or books about these techniques.
Thanks
Masood Bhatti
Faculty of Pharmacy
University of Alberta
Edmonton, Alberta
Canada
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Convolution and deconvolution techniques are not necessarily used to
answer the question of bioavailability. The Wagner Nelson method and
Loo-Reigelman methods are forms of deconvolution. Deconvolution
techniques are used to assess rates of absorption and require I.V. data.
Some names to get you started are W. J. Jusko and P. V. Peterson.
However, this is a fairly complicated subject.
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>Convolution and deconvolution techniques are not necessarily used to
>answer the question of bioavailability. The Wagner Nelson method and
>Loo-Reigelman methods are forms of deconvolution. Deconvolution
Same area but slightly different direction. I had thought of WN and LR as
specialized examples of deconvolution and had included them as such under
Deconvolution in my book which was published earlier this year. One
reviewer expressed the opinion that this was incorrect. Do any others on
the PharmPK list have an opinion about this? Thanks.
David Bourne (david-bourne.-at-.uokhsc.edu)
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Dear colleague,
All arguments presented below are based on the assumption that the
disposition kinetics of the drug is linear.
The drug bioavailability in the circulatory system after extravascular
administration is defined in two ways, i.e. as the extent of
bioavailability and the rate of bioavailability (1).
The system describing the drug input into the circulatory system after
extravascular administration can be defined in the Laplace s-domain by
Eq.1
H_{c}(s) = X_{c}(s)/Y_{ex}(s) (1)
where H_{c}(s), X_{c}(s) and Y_{ex}(s) are the system transfer
function, output and input, respectively (2). X_{c}(s) represents the
drug input into the circulatory system. Since this input is not
available for measurement, to estimate the system transfer function
the following systems can be used:
The system describing the drug input into the circulatory system
after intravascular administration can be defined in the Laplace
s-domain by Eq.2
H_{iv}(s) = X_{p,iv}(s)/Y_{iv}(s), (2)
where H_{iv}(s), X_{p,iv}(s) and Y_{iv}(s) are the system transfer
function, output and input, respectively. X_{p,iv}(s) represents the
peripheral system output.
The system describing the drug input into the circulatory system after
extravascular administration can be defined in the Laplace s-domain by
Eq.3
H_{ex}(s) = X_{p,ex}(s)/Y_{ex}(s), (3)
where H_{ex}(s), X_{p,ex}(s) and Y_{ex}(s) are the system transfer
function, output and input, respectively. X_{p,ex}(s) represents the
peripheral system output.
Since
H_{ex}(s) = H_{iv}(s).H_{c}(s), (4)
the transfer function H_{c}(s) can be expressed in the form of Eq.5,
using the definitions given by Eqs.2 and 3
H_{c}(s) = (X_{p,ex}(s).Y_{iv}(s))/ (X_{p,iv}(s).Y_{ex}(s)). (5)
For the equal inputs,
Y_{iv}(s)=Y_{ex}(s) (6)
Eq.5 can be rewritten in the simple form of Eq.7
H_{c}(s) = (X_{p,ex}(s))/(X_{p,iv}(s)) (7)
Eqs.5 and 6 enable to estimate the drug bioavailability on the basis
of the measured functions X_{p,ex}, Y_{iv}, X_{p,iv} and Y_{ex}. The
gain parameter (2) of the model of the transfer function H_{c}
approaches the extent of the drug bioavailability. The model of the
weighting function, corresponding to the model of this transfer
function approaches the rate of the drug availability after
extravascular administration.
In the specific case of equal intravascular and extravascular inputs
(Eq.6), the weighting function can be estimated using deconvolution
methods in the time domain. The literature on numerical and analytical
deconvolution methods is extensive. Analytical deconvolution methods
are mostly devoted to relatively simple models (3) which do not
contain shunt and time delays and which models of transfer functions
do not contain complex poles (2,4). The CXT program, described in our
study (5) and available at
http://www.cpb.uokhsc.edu/pkin/pkin.html
option: software,
enables to estimate the system weighting function for equal and/or non
equal intravascular and extravascular inputs.
Sincerely,
Dedik, Ladislav DEDIK.-a-.KAM1.VM.STUBA.SK
Durisova, Maria EXFAMADU.-at-.SAVBA.SK
REFERENCES
1. Wagner, J.: Fundamentals of Clinical Pharmacokinetics, The Hamilton
Press, Inc. Hamilton, Illinois, 1975.
2. Dedik, L., and Durisova, M.: Frequency response method in
pharmacokinetics. J. Pharmacokin. Biopharm., 22, 1994, 293-307.
3. Gillespie, W.R., and Veng-Pedersen, P: A polyexponential
deconvolution method. Evaluation of the "gastrointestinal
bioavailability" and mean in vivo dissolution time of some ibuprofen
dosage forms on appropriate constraints on the initial input response
when applying deconvolution. J. Pharmacokin. Biopharm., 13, 1985,
289-307.
4. Dedik, L., Durisova, M., and Balan, M.: Building a structured model
of a complex pharmacokinetic system with time delay. Bull. Math.
Biol., 57, 1995, 787-808.
5. Dedik, L., Durisova, M.: CXT - a programme for analysis of linear
dynamic systems in the frequency domain. Int. J. Bio-Med. Comput.,
39, 1995, 231-241.
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