- On 8 Jan 2005 at 04:27:53, Vlase Laurian (vlaselaur.at.yahoo.com) sent the message

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Hi,

I heard that (especially) for complex PK models, is better to use for

fitting algebraic equations instead of corresponding differential eq.

Is that true? Why?

Thank you,

laurian vlase

Vlase Laurian

Dept. of Pharmaceutical Technology and Biopharmaceutics

Faculty of Pharmacy

University of Medicine and Pharmacy "Iuliu Hatieganu"

13, Emil Isac

Cluj-Napoca, Cluj 3400, Romania

vlaselaur.at.yahoo.com

online on Yahoo Messenger

[Typically the algebraic equations can be solved more quickly than the

differential equations. However you have to know the equations from

somewhere, reference or derivation

(http://www.boomer.org/c/p3/c07/c0707.html). Developing algebraic

equations may require re-parameterization (e.g. k12,k21,k10 to

alpha/beta). With a fast computer and appropriate software (boomer

perhaps - http://www.boomer.org/ or see

http://www.boomer.org/pkin/soft.html for other software) testing

different models may be more efficient using an easily modified

differential equation format - db] - On 8 Jan 2005 at 13:52:05, "Gordi, Toufigh" (Toufigh.Gordi.-a-.cvt.com) sent the message

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The following message was posted to: PharmPK

Hi Vlase,

Just adding to David's comments, explicit equations would be your gold

standard, as they give you the exact answer to the problem. However,

many times it is impossible to get the explicit answer to various

equations and that's one of the main reasons differential equations are

used. With modern computer power and availability of various programs

for solving differential equations, it is more practical, and many times

less time-consuming, to set up the model using differential equations

and estimate the model parameters.

Toufigh Gordi - On 9 Jan 2005 at 00:54:27, Vlase Laurian (vlaselaur.-a-.yahoo.com) sent the message

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Thank you all for answer.

I'm asking that because I'm looking for some advantages for using

algebraic equations instead of differential.

Until now, I can say (please correct me if I wrong):

1. Advantafes for using diff:

-as Dr. Gordi says, is more practical and less time consuming

2. Advantages for using algebraic eq:

-for scientist: can examine the time course of a certain compound in a

certain place (compartment) and can see the dependence of concentration

versus all the model constants.

- the fitting, in case of complex models, can be more robust (?),

especially when the data is not reach or have large CV% (?).

I'm not talking about algebraic eq. of some simple models, but about

complex models, when the user probabely will never see the analytic

solution due to complex calculations.

For example, using a simple and fast method of calculation, we have

obtained the algebraic form of all the compound/in every compartment

from the next models:

-PK19, PK42 from PK/PD Data Analysis by Gabrielsson and Weiner

or, for more complex models, like the next one (absorption with

firt-pass effect and sistemic metabolisation):

http://www.geocities.com/vlaselaur/pk/_pk.doc

Please let me know your opinion

--

Vlase Laurian

Dept. of Pharmaceutical Technology and Biopharmaceutics

Faculty of Pharmacy

University of Medicine and Pharmacy "Iuliu Hatieganu"

13, Emil Isac

Cluj-Napoca, Cluj 3400, Romania

vlaselaur.at.yahoo.com

online on Yahoo Messenger

[The first advantage for algebraic isn't correct as this is also

possible with differential equations. With regard to the second

advantage of algebraic equations, differential equation solution will

be slower and numerical approximations, however there are common

situations were the algebraic solution are not robust. For example for

a simple one compartment model with oral absorption you need to include

additional equations as ka = kel. Many (most) algebraic solutions

include the difference between parameters in denominator - db] - On 10 Jan 2005 at 09:31:50, "Hans Proost" (j.h.proost.at.rug.nl) sent the message

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The following message was posted to: PharmPK

Dear Laurian,

With respect to the discussion about 'algebraic equations' (or 'explicit

equations') and differential equations, I do not fully agree with you:

> 2. Advantages for using algebraic eq:

> -for scientist: can examine the time course of a certain compound in a

> certain place (compartment) and can see the dependence of

concentration

> versus all the model constants.

This is a relative advantage; the information can be obtained also from

the

numerical solution of the differential equations.

> - the fitting, in case of complex models, can be more robust (?),

> especially when the data is not reach or have large CV% (?).

I don't think this is fully true. Algebraic solutions provide exact

solutions (depending on implicit numerical accuracy of the software),

which

is indeed an advantage. Numerical solutions are always approximations,

and

this may indeed cause problems, e.g. in the estimation of derivatives

(as

required for many fitting algorithms). This is mainly a technical

question

that usually can be solved adequately by proper design of the software.

If parameters have a large CV%, or if the fitting does not converge (I

trust

that you refer to these situations), the data do not contain sufficient

information about the model parameters, and this has nothing to do with

the

differential equations.

> I'm not talking about algebraic eq. of some simple models, but about

> complex models, when the user probabely will never see the analytic

> solution due to complex calculations.

The main problem with algebraic equations is that you have to derive

(and

test!) the equations for each individual model. Differential equations

describe the problem in relative simple equations, that can be written

easily. In addition, a set of differential equations can be easily

'fed' to

a computer program solving the differential equations numerically. This

allows to fit the parameters of very different and very complex models

with

a single program, by changing only the differential equations.

Please note that I do not see any objection against using algebraic

equations. On the contrary, these are still the gold standard, since the

testing of a program solving numerical equations is eventually done by

comparing the results to that of an algebraic solution. So, if you are

happy

using algebraic solutions, just continue! It is like horses; an

algebraic

solution is like a race-horse; it runs fast and elegant, but requires

much

attention, and needs a proper preparation for each race. A program for

solving differential equations numerically is a work-horse. It runs more

slowly and not really efficient, but it can do any job whatever you

want to

do.

Best regards,

Hans Proost

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Antonius Deusinglaan 1

9713 AV Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.aaa.rug.nl - On 10 Jan 2005 at 13:32:41, Peter.Wolna.aaa.merck.de sent the message

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Hi Laurian,

As a general statement and as a rule of thumb I'd like say:

1. In general PK-models are differential equations, or substantial

parts of the model are differential equations

2. In some cases there exist an explicit solution (algebraic form) of

that model. In these cases it is advantageous to do the calculations

using the explicit solution.

3. Using an algebraic equation, that is not the explicit solution of

the differential equation model, is in general disadvantageous, if

compared to the use of the differential equation model itself.

Maybe this is not an answer to your question, but it can help to find

out, what your problem is.

Kind regards

Peter

Peter Wolna

Merck KGaA, Clinical R&D / Clinical Statistics

Frankfurter Str 250

D-64293 Darmstadt

Phone: +49- 61 51- 72 61 68

Fax: +49- 61 51- 72 63 61

Email: peter.wolna.at.merck.de - On 10 Jan 2005 at 08:50:59, "Walt Woltosz" (walt.aaa.simulations-plus.com) sent the message

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The following message was posted to: PharmPK

I agree with Hans and Peter.

Analytical models are fast, but often require simplifying assumptions

and/or splitting the problem into different time segments to handle

discontinuities. Integrating differential equations provides the

greatest flexibility, as a single software package can be developed to

handle a wide variety of problems without the need to rederive

analytical solutions for every new twist.

Walt Woltosz

Chairman & CEO

Simulations Plus, Inc. (AMEX: SLP)

1220 W. Avenue J

Lancaster, CA 93534-2902

U.S.A.

http://www.simulations-plus.com

Phone: (661) 723-7723

FAX: (661) 723-5524

E-mail: walt.-at-.simulations-plus.com - On 14 Jan 2005 at 12:54:15, "Durisova Maria" (exfamadu.-a-.savba.sk) sent the message

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The following message was posted to: PharmPK

Hi Laurian,

my contribution to this discussion you can find at

http://www.uef.sav.sk/Reply_14_01.pdf

Kind regards,

Maria Durisova, PhD, DSc (Math/Phys)

Vice Director of Institute of Experimental Pharmacology

Slovak Academy of Sciences

and

Head of Department of Pharmacokinetics

Dubravska cesta 9

841 04 Bratislava

Slovak Republic

Tel./Fax: +421 2 54775928

http://www.uef.sav.sk/durisova.htm

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