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The flow of water in a sufficiently long capillary represents laminar flow, and is governed by Poiseuille's law [14]. According to this law, the flow rate,

In this equation,

If the vessel is cylindrical (Figure 1a),

where

If

Equation 3 is substituted with Eq.4, and can be represented by a differential equation as follows:

Equation 5 suggests that a cylindrical vessel can be used as a hydrodynamic model of the first-order irreversible reaction [3, 4, 6, 7, 10], and

If two cylindrical vessels are connected by a capillary (Figure 1b),

Substituting Eq.6 into Eq.1 gives

If

Equation 7 is substituted with Eqs.8 and 9, and can be represented by a differential equation as follows:

Equation 10 suggests that the apparatus shown in Figure 1b can be used as a hydrodynamic model of the first-order reversible reaction [6], and

If the capillary in Figure 1a is very long, and is almost vertically suspended, the magnitude of

Equation 11 suggests that the simple model can be used as a hydrodynamic model of the zero-order irreversible reaction, and

Figure 1. Schematic presentation of the two actual hydrodynamic models, which are components of the six simulated linear chemical/pharmaco-kinetic models presented here.

The flowchart for the simulation is shown in Figure 2. All calculations for the simulations were performed using the integral rate laws [1, 2, 16]. If necessary, the simulation can be stopped at predetermined intervals. For reference, the reaction progress is represented by an ordinary line graph. If you input new parameters of rate constants (

Figure 2. Flowchart for the computer simulation of hydrodynamic models for chemical/pharmaco-kinetics.

For the first-order irreversible process (Figure 1a), the variation in *k* value in Eq.4 is accomplished by changing the value of *L*; the values of *S* of all cylinders in a model are the same and are kept constant. For the first-order reversible process (Figure 1b), the variation in *k*_{1} value in Eq.8 is accomplished by changing the value of *L* (the value of *S _{A}* is kept constant), and that of

In the irreversible process, a trace of the drop discharged horizontally from the head of a capillary is represented by a parabolic curve [15] (Figure 1a and 3). The magnitude of

Figure 3 is a simulation scene of model 6 [2]. After a drug is introduced into the plasma compartment (cylinder A) by bolus intravenous injection, it starts to disperse in the tissue compartment (cylinder B). Simultaneously, the drug is eliminated (excreted or metabolized) from the plasma compartment into urine and bile (cylinder C). At the start, both the dispersion and elimination rates are high; this is seen from the large values of

Figure 3. A scene of the computer simulation of a hydrodynamic model for chemical/pharmaco-kinetics exemplified by the two-compartment open model with rapid intravenous injection. For details, see text.

In model 5, a clear equilibrium state was observed when t = ¥. Steady-states were observed in the B cylinders of models 3 and 4 [1, 2, 16]. In each simulation, this was easily seen from equal magnitudes of *Q* in both in- and out-going capillaries of the B cylinder. The other two hydrodynamic models were also simulated easily and realistically.

[ 2] Welling, P.G.,

[ 3] Lemlich, R.,

[ 4] Hecht, K.,

[ 5] Weigang, O.E.Jr.,

[ 6] Lago, R.M., Wei, J. and Prater, C.D.,

[ 7] Meiners, H.F.(Ed.),

[ 8] Vaidhyanathan, V.S.,

[ 9] Davenport, D.A.,

[10] Asahi, Y.,

[11] Ricci, R.W. and Van Doren, J.M.,

[12] Katzung, B.G.(Ed.),

[13] Sugata, S.,

[14] Munson, B.R., Young, D.F. and Okiishi, T.H.,

[15] Tippens, P.E.,

[16] Tebbutt, P.,

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