CN103077296B - Based on the in-vitro simulated method of the intravenous injection pharmacokinetic model of velocity of flow adjust - Google Patents

Abstract

The invention belongs to external pharmacokinetics/pharmacodynamic studies field, relate to a kind of in-vitro simulated method of the intravenous injection pharmacokinetic model based on velocity of flow adjust; The method is based on intellectuality and can regulates the flow relocity calculation method of the peristaltic pump of flow velocity stage by stage or in real time, comprises equation and recurrence method.The invention solves the in-vitro simulated problem of body internal jugular vein drug administration by injection compartment model, effectively reduce the dependence of external pharmacokinetics simulation to Internal pharmacokinetics model structure, expand the scope that external pharmacokinetic model is simulated Internal pharmacokinetics, for raising external pharmacokinetics/pharmacodynamic studies technical merit, especially the external pharmacokinetics/pharmacodynamic studies of antibacterials is significant.

Description

Based on the in-vitro simulated method of the intravenous injection pharmacokinetic model of velocity of flow adjust

Technical field

The invention belongs to external pharmacokinetics/pharmacodynamics (Pharmacokinetic/pharmacodynamic, PK/PD) research field, relate to a kind of in-vitro simulated method of the intravenous injection pharmacokinetic model based on velocity of flow adjust.

Background technology

External pharmacokinetics/pharmacodynamics (Pharmacokinetic/pharmacodynamic, PK/PD) technology is one of new drug research means of rising in recent decades, utilize pharmacokinetics process and the pharmacodynamics thereof of device outside drugs, working out for dosage regimen reasonable in body provides foundation; This technology needs the In vivo kinetics process of aids drug simultaneously can to meet again the device outside that pharmacodynamics dynamically observes requirement, i.e. external pharmacokinetic model based on a set of.In the research of this area, often need aids drug pharmacokinetics process in vivo in a set of device outside, study the pharmacodynamics of this medicine in concentration dynamic changing process simultaneously; Wherein, medicine usual process in vivo comprises: a compartment model and two compartment models, can be divided into again intravenous injection model, drip-feed model and extravascular administration model (such as oral model) according to administering mode.The pharmacodynamic study that it is effective object that described technology is particularly suitable for the life entity such as microorganism, tumour cell, because the requirement that can realize in pharmacokinetics simulation and dynamic pharmacodynamic observation two in such research relatively easily in an airtight cultivating system.

The core texture of described external pharmacokinetic model comprises (as shown in Figure 1) such as fresh fluid reservoir, reaction chamber, waste liquid cylinder, peristaltic pump, silicone tube and stirrers; Described reaction chamber is the space that drug concentration dynamic change, medicine and action target react to each other; Because drug efficacy study needs, reaction chamber is often placed in specific environment, or structurally has special modification; Liquid is pumped into reaction chamber from fluid reservoir by certain flow rate as drive system by peristaltic pump, the quantity of fluid such as to have again discharge thus the specific change of forming reactions room drug concentration in simultaneous reactions room under pressure; Described silicone tube is as the connecting tube of each parts, and stirrer acts on the liquid system in reaction chamber, makes drug distribution and is uniformly dispersed to acting in whole system of target.

In addition, the key of described external pharmacokinetics model investigation technology comprises PK simulation and PD simulates two aspects: the key of PK analogue technique be how by control liquid measure in reaction chamber, flow rate of liquid and by the modification of apparatus structure with the simulation of realization to Internal pharmacokinetics; The key of PD analogue technique is the transformation to reaction chamber structure, can meet the requirement of dynamic pharmacodynamic observation.Described PK simulation is simulated with PD and is often mutually conflicted to the demand of model structure, the accuracy meeting PK simulation often needs adds reaction chamber and increases servicing unit thus cause the sacrifice of model operability even also can have influence on pharmacodynamic observation, such as, meet periphery compartment that two chamber models simulate increase outward and result in operation easier increase and also result in the circulation of bacterium in reaction chamber and periphery compartment simultaneously and then affect count of bacteria in reaction chamber.Equally, meet PD research purpose and simultaneously also can bring impact due to the change of structure to PK simulation, such as, in order to avoid the bacterium hollow fiber column model adopted that runs off can be simulated because Drug absorbability affect PK.

At present, the in-vitro simulated of described pharmacokinetics is in basic status in whole external PK/PD research, the degree of accuracy of PK simulation is directly connected to the holistic approach quality of external PK/PD.Current, external PK/PD technology is also confined to the simulation of linear pharmacokinetics the simulation of PK but also needs to do in form to simplify, and is namely removed according to the speed of specifying by certain density medicine based on non-compartment model parameter; Described simulation has only been paid close attention to medicine maximum concentration in blood and has overallly been eliminated the half life period, have ignored the details of medicine in dynamic process, particularly has relatively large deviation when the simulation to two Room, three compartment model pharmacokinetics; Although introducing auxiliary chamber can realize the simulation to two Room, three compartment model pharmacokinetics, and said method can make the structure of whole external model and operability thereof become very complicated.In addition, during the measure that bacterium or tumour cell etc. circulate between central compartment and periphery compartment if do not take precautions against in model structure, said method can not make accurate evaluation to pharmacodynamics; Therefore, also stay in theory or approximate simulation stage at present to the simulation of two Room, three compartment model pharmacokinetics, how in vitro accurate analog medicine dynamic process in vivo ensures that the operability of model is the key issue that the art needs to solve simultaneously.

Summary of the invention

The object of the invention is the defect and the deficiency that overcome prior art, a kind of in-vitro simulated method of the intravenous injection pharmacokinetic model based on velocity of flow adjust is provided.

The present invention using the flow velocity of external pharmacokinetic model as breach with overcome PK simulation to study with PD between conflict, accurate analog body internal jugular vein drug administration by injection pharmacokinetics in simple mechanism is realized, such as a Room, two Room or three compartment model etc. by flow velocity dynamic adjustments; In-vitro simulated method of the present invention can make external PK simulation significantly reduce the dependence of reaction chamber structure, makes external model device have larger transformation space to meet drug efficacy study demand.

Specifically, the present invention is the flow relocity calculation method based on the adjustable peristaltic pump of flow velocity, and its feature is, comprising: adopt equation and recurrence method;

Described equation, recurrence method are all applicable to the flow relocity calculation in pharmacokinetics (comprise a chamber, two chambers and three compartment models, and the zero-order pharmacokinetics model) simulation of various single intravenous injection administration:

(1) equation

Described equation is the method directly calculating external model flow velocity based on pharmacokinetic parameters, in-vitro simulated for linear pharmacokinetic model, and its general flow relocity calculation formula is as follows:

$F=V_C\·\frac{\underset{i=1}{\overset{n}{\Σ}}{A}_i\·k_i\·e^{-k_{i}t}}{\underset{i=1}{\overset{n}{\Σ}}{A}_i\·e^{-k_{i}t}}---\left(1\right)$

Wherein, F and V _cbe respectively flow velocity and reaction chamber liquid measure, n represent the room number of phases (i=1,2,3 ...), A _iand k _irepresent intercept and the respective rate constant of the i-th phase respectively;

In-vitro simulated for a chamber, two chambers and three chambers quiet note pharmacokinetics, flow relocity calculation uses formula (2) ~ formula (4) statement respectively:

F＝k _e·V _C(2)

$F=V_C\·\frac{{\mathrm{A\αe}}^{-\mathrm{\α}t}+{\mathrm{B\βe}}^{-\mathrm{\β}t}}{{\mathrm{Ae}}^{-\mathrm{\α}t}+{\mathrm{Be}}^{-\mathrm{\β}t}}---\left(3\right)$

$F=V_C\·\frac{{\mathrm{A\αe}}^{-\mathrm{\α}t}+{\mathrm{B\βe}}^{-\mathrm{\β}t}+{\mathrm{R\γe}}^{-\mathrm{\γ}t}}{{\mathrm{Ae}}^{-\mathrm{\α}t}+{\mathrm{Be}}^{-\mathrm{\β}t}+{\mathrm{Re}}^{-\mathrm{\γ}t}}---\left(4\right)$

Wherein, V _cfor reaction chamber liquid volume, its numerical value is determined according to the actual requirements; K in formula (2) _efor elimination rate constant, A and B representative distribution in formula (3) and elimination phase intercept, α and β is respective rate constant, A, B and R in formula (4) are respectively distribution phase, fast elimination eliminates phase intercept mutually and slowly, and corresponding rate constant represents with α, β and γ respectively;

In-vitro simulated for zero-order pharmacokinetics, flow relocity calculation formula is:

$F=\frac{V_C\·k_e}{c_0-k_{e}t}---\left(5\right)$

Wherein, k _efor concentration descending slope in time, initial concentration c ₀represent;

(2) recurrence method

Described recurrence method is the method for based on concentration values m-during Internal pharmacokinetics, different time points flow velocity being carried out to recursion, and its recursion formula is:

$F_i=V_C\·(1-\frac{c_{i+1}}{c_i})\·\frac{1}{t_{i+1}-t_i}---\left(32\right)$

Wherein, F _iit is the flow velocity of the i-th moment point; V _cfor the liquid volume in reaction chamber, it is the designated value done according to the actual requirements; c _i+1and c _irepresent that medicine is at t respectively _i+1and t _iblood concentration in the body in moment, its exact value can calculate according to the compartment model Pharmacokinetic Formula of reality and obtain;

For the quiet note pharmacokinetic model of a chamber, two chambers and three chambers, the bulk concentration c in the i-th moment _iformula (33) ~ formula (35) is used to calculate respectively:

$c_i=c_0\·e^{-k_e{x}_i}---\left(33\right)$

$c_i=A\·e^{-{\mathrm{\αt}}_i}+B\·e^{-{\mathrm{\βt}}_i}---\left(34\right)$

$c_i=A\·e^{-{\mathrm{\αt}}_i}+B\·e^{-{\mathrm{\βt}}_i}+R\·e^{-{\mathrm{\γt}}_i}---\left(35\right)$

Wherein, the c in formula (33) ₀and k _ebe respectively initial drug concentrations and elimination rate constant, A and B representative distribution in formula (34) and elimination phase intercept, α and β is respective rate constant, A, B and R in formula (35) are respectively distribution phase, fast elimination eliminates phase intercept mutually and slowly, and corresponding rate constant represents with α, β and γ respectively;

For zero-order pharmacokinetics model, the bulk concentration c in the i-th moment _icalculate by formula (36):

c _i＝c ₀-k _et _i(36)

Wherein, c ₀for initial drug concentrations, k _erepresent concentration descending slope in time.

In the present invention, described equation and recurrence method are all applicable to the flow relocity calculation in pharmacokinetics (comprise a chamber, two chambers and three compartment models, and the zero-order pharmacokinetics model) simulation of various single intravenous injection administration.

In the present invention, also deduce described equation and recurrence method, step is as follows:

(1) equation

Realize external pharmacokinetic model and need meet following two conditions to the accurate analog of Internal pharmacokinetics curve: reaction chamber medicine initial concentration (C in (1) external model ₀) and drug disposition initial concentration (c ₀) equal, i.e. C ₀=c ₀; (2) external model drug concentration supersession rate (dC/dt) is equal with vivo medicine concentration supersession rate (dc/dt), i.e. dC/dt=dc/dt; Therefore, following formula is set up:

$\frac{dC/dt}{C}=\frac{dc/dt}{c}---\left(6\right)$

Wherein, (dC/dt)/C and (dc/dt)/c represent the relative change rate of in vitro and in vivo drug concentration versus time, elimination rate constant k in its implication and quiet note one compartment model _esimilar; For a compartment model, the relative change rate of concentration vs. time keeps constant; For two Room and above compartment model, relative change rate passes in time and reduces gradually; Vivo medicine concentration-equation of time and drug concentrations in vitro-equation of time are substituted into above formula, the flow relocity calculation formula under various in-vitro simulated situation can be derived;

In external pharmacokinetics model equipment as shown in Figure 1, the pharmacokinetics of simulation intravenous administration compartment model, medicine directly joins reaction chamber, fresh medium enters central compartment with flow rate F, there is again equivalent to mix liquid in reaction chamber to be discharged, thus medicine index elimination form in vivo can be simulated; The parameter determined is needed to comprise nutrient solution flow velocity (F) in described model equipment, liquid volume (V in central compartment _c) and dosage (D); Wherein, V _cnumerical value is designated value, and D equals c ₀× V _c, F value need be determined according to calculating; Dose (X) in described model equipment central compartment changes the differential equation that available formula (7) is illustrated:

$\frac{dX}{dt}=-\frac{F}{V_C}X---\left(7\right)$

Wherein, the initial value of X is dosage (D).Concentration C is by X and V _cratio obtain;

The above-mentioned differential equation is obtained the calculating formula of drug concentration in model central compartment through Induction Solved by Laplace Transformation solution:

$C=\frac{D}{V_C}\·e^{-\frac{F}{V_C}t}---\left(8\right)$

Can obtain external model drug concentration relative change rate in time by differentiate, its expression formula is as follows:

$\frac{dC/dt}{C}=-\frac{F}{V_C}---\left(9\right);$

In the present invention, described equation flow relocity calculation in varied situations, comprising:

1) flow relocity calculation that intravenous injection one compartment model is in-vitro simulated

The densimeter formula of intravenous injection one compartment model is:

$c=c_0\·e^{-k_e\·t}---\left(10\right)$

The expression formula of drug concentration relative change rate is in time obtained by differentiate:

$\frac{dc/dt}{c}=-k_e---\left(11\right)$

Make formula (11) equal with formula (9), can F=V be obtained _ck _e, therefore formula (2) is set up;

Result shows, can simulate body internal jugular vein injection one compartment model pharmacokinetics process in analogue means as shown in Figure 1;

2) flow relocity calculation that intravenous injection two compartment model is in-vitro simulated

The densimeter formula of intravenous injection two compartment model is:

c＝Ae ^-αt+Be ^-βt(12)

Wherein A, B represent distribution and elimination phase intercept respectively, α and β is for distribution phase and eliminate phase rate constant;

The expression formula of drug concentration relative change rate is in time obtained by differentiate:

$\frac{dc/dt}{c}=-\frac{\mathrm{\α}\·{\mathrm{Ae}}^{-\mathrm{\α}t}+\mathrm{\β}\·{\mathrm{Be}}^{-\mathrm{\β}t}}{{\mathrm{Ae}}^{-\mathrm{\α}t}+{\mathrm{Be}}^{-\mathrm{\β}t}}---\left(13\right)$

Make formula (13) equal with formula (9), formula (3) can be obtained;

Result shows, can simulate body internal jugular vein injection two compartment model pharmacokinetics process in analogue means as shown in Figure 1;

3) flow relocity calculation that intravenous injection three compartment model is in-vitro simulated

The densimeter formula of intravenous injection three compartment model is:

c＝Ae ^-αt+Be ^-βt+Re ^-γt(14)

Wherein A, B, R are respectively the phase that distributes, fast elimination phase and slow elimination phase intercept, and α, β and γ are the phase that distributes, eliminate phase and slow elimination phase rate constant soon;

By differentiate to the expression formula to drug concentration relative change rate in time:

$\frac{dc/dt}{c}=-\frac{{\mathrm{A\αe}}^{-\mathrm{\α}t}+{\mathrm{B\βe}}^{-\mathrm{\β}t}+{\mathrm{R\γe}}^{-\mathrm{\γ}t}}{{\mathrm{Ae}}^{-\mathrm{\α}t}+{\mathrm{Be}}^{-\mathrm{\β}t}+{\mathrm{Re}}^{-\mathrm{\γ}t}}---\left(15\right)$

Make formula (15) equal with formula (9), formula (4) can be obtained;

Result shows, can simulate body internal jugular vein injection three compartment model pharmacokinetics process in analogue means as shown in Figure 1;

4) flow relocity calculation that intravenous injection zero-order pharmacokinetics is in-vitro simulated

The concentration computing formula of zero-order pharmacokinetics model is:

c＝c ₀-k _et(16)

Wherein, c ₀and k _ebe respectively initial drug concentrations and drug concentration fall off rate constant in time;

The expression formula of drug concentration relative change rate is in time obtained by differentiate:

$\frac{dc/dt}{c}=-\frac{k_e}{c}---\left(17\right)$

Make formula (17) equal with formula (9), formula (16) is substituted into and arranges, formula (5) can be obtained;

Result shows, can simulate body internal jugular vein injection zero-order pharmacokinetics process in analogue means as shown in Figure 1.

(2) recurrence method

When vitro reactions room drug concentration (C) is equal with Ti Nei central compartment's drug concentration (c), simultaneously, vitro reactions room drug concentration rate of change (dC/dt) and Ti Nei central compartment drug concentration when rate of change (dc/dt) is identical in time in time, can realize the external accurate analog of quiet note pharmacokinetics in body, therefore formula (6) is set up;

Vivo medicine concentration is in time in relative change rate [(dc/dt)/c], and when dt → 0, dc/dt ≈ Δ c/ Δ t sets up, and this formula forward-difference method is launched, obtains:

$\frac{dc/dt}{c}{|}_{dt\→0}=(\frac{c_{i+1}}{c_i}-1)\·\frac{1}{t_{i+1}-t_i}---\left(37\right);$

Formula (8), in time in relative change rate [(dC/dt)/C], substitutes into, gets the i-th moment (t by drug concentrations in vitro _i) result of calculation, obtain:

$\frac{dC/dt}{C}{|}_{t=t_i}=-\frac{F_i}{V_C}---\left(38\right)$

Making the right item of above-mentioned two formula equal, formula (32) can be obtained through arranging; Central compartment's drug concentration in the i-th moment and the i-th+1 moment and time are substituted into the flow velocity (F that this formula just can calculate for the i-th moment _i), obtain the time dependent adjustment curve of flow velocity;

Work as t _i+1-t _iwhen trending towards 0, F can be obtained _iapproximate exact value, can obtain by recursion the flow velocity approximate continuity linear regulation value meeting the compartment model pharmacokinetics such as two Room, three Room, realize the real-time adjustment of flow velocity; Work as t _i+1-t _itime wider, the adjustment stage by stage of flow velocity can be realized; In addition, when drug concentration constantly declines, simultaneously its concentration is not when rule meets linear pharmacokinetics or zero-order pharmacokinetics over time, such as meet the non-linear pharmacokinetics of meter Man equation, formula (32) still can be adopted to make flow relocity calculation, to realize the real-time of Internal pharmacokinetics or simulation by periods.

The present invention also verifies described equation, and its step comprises:

The collocation principle of analogue means according to Fig. 1, equation is as follows over time can to derive reaction chamber drug concentration:

$\frac{dC}{dt}=-\frac{F}{V_C}\·C---\left(18\right)$

1) when simulating an Atrium Model in model in vitro,

Formula (2) is substituted into formula (18), can obtain:

$\frac{dC}{dt}=-k_e\·C---\left(19\right)$

Laplace transform and corresponding inverse transformation are implemented to above formula both sides, obtain:

$C=C_0\·e^{-k_{e}t}---\left(20\right)$

Work as C ₀=c ₀time, described equation meets the quiet note pharmacokinetic model of a chamber in body, identical with described formula (10) form, therefore confirms, can simulate body internal jugular vein injection one compartment model pharmacokinetics process in analogue means as shown in Figure 1;

2) when simulating two Atrium Models in model in vitro,

Formula (3) is substituted into formula (18), obtains:

$\frac{dC}{dt}=-\frac{C}{V_C}\·\[V_C\·\frac{\mathrm{\α}\·{\mathrm{Ae}}^{-\mathrm{\α}t}+\mathrm{\β}\·{\mathrm{Be}}^{-\mathrm{\β}t}}{{\mathrm{Ae}}^{-\mathrm{\α}t}+{\mathrm{Be}}^{-\mathrm{\β}t}}\]---\left(21\right)$

Therefore draw:

$\frac{dC}{C}=-\frac{\mathrm{\α}\·{\mathrm{Ae}}^{-\mathrm{\α}t}+\mathrm{\β}\·{\mathrm{Be}}^{-\mathrm{\β}t}}{{\mathrm{Ae}}^{-\mathrm{\α}t}+{\mathrm{Be}}^{-\mathrm{\β}t}}\·dt---\left(22\right)$

Above formula can be expressed as further:

d(lnC)＝d[ln(Ae ^-αt+Be ^-βt)](23)

Definite integral is made in above formula both sides in 0-t time domain, makes initial value C ₀for A+B, obtain:

C＝Ae ^-αt+Be ^-βt(24)

Described equation meets the quiet note pharmacokinetic model of two chambers in body, identical with formula (12) form, therefore confirms, can simulate body internal jugular vein injection two compartment model pharmacokinetics process in analogue means as shown in Figure 1;

3) when simulating three Atrium Models in model in vitro

Formula (4) substituted into formula (18) and arrange, obtaining:

$\frac{dC}{C}=-\frac{\mathrm{\α}\·{\mathrm{Ae}}^{-\mathrm{\α}t}+\mathrm{\β}\·{\mathrm{Be}}^{-\mathrm{\β}t}+\mathrm{\γ}\·{\mathrm{Re}}^{-\mathrm{\γ}t}}{{\mathrm{Ae}}^{-\mathrm{\α}t}+{\mathrm{Be}}^{-\mathrm{\β}t}+{\mathrm{Re}}^{-\mathrm{\γ}t}}\·dt---\left(25\right)$

Above formula can be written as further:

d(lnC)＝d[ln(Ae ^-αt+Be ^-βt+Re ^-γt)](26)

Definite integral is made in above formula both sides in 0-t time domain, with seasonal initial value C ₀=A+B+R, obtains:

C＝Ae ^-αt+Be ^-βt+Re ^-γt(27)

Described formula meets the quiet note pharmacokinetic model of three chambers in body, identical with formula (14) form, therefore confirms, can simulate body internal jugular vein injection three compartment model pharmacokinetics process in analogue means as shown in Figure 1;

4) when simulating zero level pharmacokinetic model in model in vitro

Formula (5) is substituted into formula (18), obtains:

$\frac{dC}{dt}=-\frac{k_e\·C}{c_0-k_{e}t}---\left(28\right)$

Above formula is arranged, obtains:

$\frac{dC}{C}=-\frac{k_e}{c_0-k_{e}t}dt---\left(29\right)$

Above formula can be expressed as further:

d(lnC)＝d[ln(c ₀-k _et)](30)

Definite integral is done to above formula both sides, makes initial value C ₀=c ₀, therefore draw:

C＝C ₀-k _et(31)

Described formula meets zero-order pharmacokinetics model in body, is equal to, therefore confirms with formula (16) form, can simulate body internal jugular vein injection zero-order pharmacokinetics process in analogue means as shown in Figure 1.

In the present invention, described in-vitro simulated method, finally can be consecutive variations value form to the assignment of flow velocity and also can be multistage mean value formation; This in-vitro simulated method can be used for flow relocity calculation when single-dose or multiple dosing.

The in-vitro simulated method of the intravenous injection pharmacokinetic model based on velocity of flow adjust of the present invention, can be used for external pharmacokinetics/pharmacodynamics model technology and relate in other technical field of similar principles, especially can be used for the external pharmacokinetics/pharmacodynamic studies of antibacterials, its application form is calculate based on the artificial calculating of the Equivalent Form of formula (1) ~ (5), (37) or identical reasoning thought or software.

The in-vitro simulated method of the intravenous injection pharmacokinetic model based on velocity of flow adjust of the present invention, solve the in-vitro simulated problem of body internal jugular vein drug administration by injection compartment model, comprise the in-vitro simulated problems such as a chamber, two chambers, three chambers and zero-order pharmacokinetics model; Described in-vitro simulated method effectively reduces the dependence of external pharmacokinetics simulation to Internal pharmacokinetics model structure, expand the scope that external pharmacokinetic model is simulated Internal pharmacokinetics, for raising external pharmacokinetics/pharmacodynamic studies technical merit, especially the external pharmacokinetics/pharmacodynamic studies of antibacterials is significant

For the ease of understanding, be described in detail below by the in-vitro simulated method of the drawings and specific embodiments to the intravenous injection pharmacokinetic model based on velocity of flow adjust of the present invention.It is important to note that specific embodiments and the drawings are only to illustrate, obvious those skilled in the art according to illustrating, can carry out various correction or change to the present invention herein, and these are revised and change and also will include within this patent scope.

Accompanying drawing explanation

Fig. 1 is the structural representation of the external pharmacokinetics model equipment of medium sized vein drug administration by injection compartment model of the present invention.

Fig. 2 is the in-vitro simulated design sketch of quiet note one compartment model of the present invention, wherein,

A: constant coordinate diagram; B: semilog plot;

Conc is calculating concentration, and C-Equ is equation gained simulated concentration, and C-Rec is recurrence method gained simulated concentration.

Fig. 3 shows the contrast situation of the in-vitro simulated flow relocity calculation result of quiet note one Room pharmacokinetic model of the present invention, and wherein, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Fig. 4 shows the in-vitro simulated variance analysis of quiet note one Room pharmacokinetic model of the present invention, wherein,

R is reference line (ratio is 1), and R-Equ is the ratio of equation gained simulated concentration and calculating concentration, and R-Rec is the ratio of recurrence method gained simulated concentration and calculating concentration.

Fig. 5 is the in-vitro simulated design sketch of quiet note two Room pharmacokinetic model of the present invention, wherein,

A: constant coordinate diagram; B: semilog plot;

Conc is calculating concentration, and C-Equ is equation gained simulated concentration, and C-Rec is recurrence method gained simulated concentration.

Fig. 6 shows the contrast situation of the in-vitro simulated flow relocity calculation result of quiet note two Room pharmacokinetic model of the present invention, and wherein, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Fig. 7 shows the in-vitro simulated variance analysis of quiet note two Room pharmacokinetic model of the present invention, wherein,

R is reference line (ratio is 1), and R-Equ is the ratio of equation gained simulated concentration and calculating concentration, and R-Rec is the ratio of recurrence method gained simulated concentration and calculating concentration.

Fig. 8 is the in-vitro simulated design sketch of quiet note three Room pharmacokinetic model of the present invention, wherein,

A: constant coordinate diagram; B: semilog plot;

Conc is calculating concentration, and C-Equ is equation gained simulated concentration, and C-Rec is recurrence method gained simulated concentration.

Fig. 9 shows the contrast situation of the in-vitro simulated flow relocity calculation result of quiet note two Room pharmacokinetic model of the present invention, and wherein, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Figure 10 shows the in-vitro simulated variance analysis of quiet note two Room pharmacokinetic model of the present invention, wherein,

R is reference line (ratio is 1), and R-Equ is the ratio of equation gained simulated concentration and calculating concentration, and R-Rec is the ratio of recurrence method gained simulated concentration and calculating concentration.

Figure 11 is the in-vitro simulated design sketch of quiet note zero-order pharmacokinetics model of the present invention, wherein,

Conc is calculating concentration, and C-Equ is equation gained simulated concentration, and C-Rec is recurrence method gained simulated concentration.

Figure 12 shows the contrast situation of the in-vitro simulated flow relocity calculation result of quiet note zero-order pharmacokinetics model of the present invention, and wherein, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Figure 13 shows the in-vitro simulated variance analysis of quiet note zero-order pharmacokinetics model of the present invention, wherein,

R is reference line (ratio is 1), and R-Equ is the ratio of equation gained simulated concentration and calculating concentration, and R-Rec is the ratio of recurrence method gained simulated concentration and calculating concentration.

Figure 14 is the in-vitro simulated design sketch of the non-linear pharmacokinetic model of quiet note of the present invention, wherein,

Conc is calculating concentration, and C-Rec is recurrence method gained simulated concentration.

Figure 15 shows the result of calculation adopting recurrence method of the present invention to calculate the in-vitro simulated flow velocity of the non-linear pharmacokinetic model of quiet note.

Figure 16 shows the in-vitro simulated variance analysis of the non-linear pharmacokinetic model of quiet note of the present invention, wherein,

R is reference line (ratio is 1), and R-Rec is the ratio of recurrence method gained simulated concentration and calculating concentration.

Figure 17 is the in-vitro simulated figure regulating flow velocity to realize quiet note pharmacokinetics in the present invention.

Embodiment

The flow relocity calculation that embodiment 1 quiet note one compartment model is in-vitro simulated

If dosage is 240mg, apparent volume of distribution (V _d) be 60L, elimination rate constant is k _efor 0.5h ^-1, external pharmacokinetics model reaction room amount of liquid V _cbe set to 250mL.

Dosage calculates: according to principle conversion external model dosage equal with drug concentrations in vitro in body, calculating formula: D _invivo× V _c/ V _d, obtaining vitro reactions room dosage is 1mg.

(1) equation

1) according to formula (2) F=V _ck _ecalculate F value, the numerical value obtaining flow rate F is 2.083mL/min (as shown in Figure 3);

2) the F value obtained is substituted into external model concentration calculating stepping type (formula (39)) and ask calculation simulated concentration, result is as shown in the crunode (×) in Fig. 2;

c _i+1＝c _i·[1-F _i·(t _i+1-t _i)/V _C](39)

(2) recurrence method

1) calculate blood concentration in body according to formula (10), result as shown in dashed line in figure 2;

2) with zero moment point for starting point, computing time gradient (t _i+1-t _i) be set to 0.02h, make the recurrence calculation of flow rate F by formula (32), obtaining its numerical value perseverance is 2.073mL/min (as shown in Figure 3).

3) obtained F value is substituted into external model concentration calculating stepping type (formula (39)) and ask calculation simulated concentration, acquired results is as shown in the hollow dots (zero) in Fig. 2.

As shown in Figure 2, described equation overlaps with recurrence method gained flow velocity result substantially, and result shows, the F value that described two kinds of methods obtain can simulate Internal pharmacokinetics well; Calculate the ratio of above-mentioned two kinds of method gained simulated concentrations and vivo medicine concentration, result as shown in Figure 4, recurrence method gained simulated concentration overlaps completely with vivo medicine concentration, equation gained simulated concentration is a little less than vivo medicine concentration, described deviation has passed certain increase trend in time, and deviation amplitude controls in the scope being less than 7%.

Model estimation is done to simulated concentration-time data that equation and recurrence method obtain, ask and calculate one compartment model pharmacokinetic parameters, and make comparisons with setting value, calculate mean relative deviation (ARD), average error (ME) and root-mean-square error (RMSE), result is as shown in table 1, recurrence method gained pharmacokinetic parameters is identical with setting value, equation parameters obtained estimated value and setting value are very close, ARD is no more than 0.3%, ME and RMSE value is less than 0.002, result shows, two kinds of described methods all can be used for the in-vitro simulated of quiet note one Room pharmacokinetic model.

The external pharmacokinetic parameters estimated value of table 1. quiet note one compartment model compares with Internal pharmacokinetics pre-set parameter

Note 1:k _eelimination rate constant, V _dapparent volume of distribution;

Note 2:ARD mean relative deviation; ME average error; RMSE root-mean-square error, calculating formula is followed successively by: ARD=∑ (y _i'/y _i-1)/m, ME=∑ (y _i-y _i')/m, RMSE=[∑ (y _i-y _i') ²/ m] ^0.5; y _iand y _i' be respectively setting value and estimated value, m data amount check.

The flow relocity calculation that embodiment 2 quiet note two compartment model is in-vitro simulated

If dosage is 240mg, apparent volume of distribution (V _d) be 60L, distribution phase rate constant (α) is 0.774h ^-1, eliminating phase rate constant (β) is 0.026h ^-1, distribution phase intercept A is 3.604mg/L, and eliminating phase intercept B is 0.396mg/L, external model reaction chamber amount of liquid V _cbe set to 250mL.

Dosage calculates: with embodiment 1, obtaining external model reaction chamber dosage is 1mg.

Flow relocity calculation:

(1) equation

1) directly calculate F value by formula (3), result is as shown in the crunode (×) in Fig. 6, and flow velocity is passed in time and reduced gradually;

2) obtained F value is substituted into external model concentration calculating stepping type (39) and ask calculation simulated concentration, acquired results is as shown in the crunode (×) in Fig. 5;

(2) recurrence method

1) according to formula (12) c=Ae ^{-α t}+ Be ^{-β t}make plasma concentration curve, result as shown in broken line in fig. 5;

2) be the first point with 0 moment point, computing time gradient (t _i+1-t _i) be set to 0.02h, by formula (37) recursion F value, as shown in the hollow dots (zero) in Fig. 6;

3) obtained F value is substituted into external model concentration to calculate in stepping type (39), ask calculation simulated concentration, acquired results is as shown in the hollow dots (zero) in Fig. 5.

Result shows, the flow velocity that equation and recurrence method obtain is basically identical (as shown in Figure 6), and as shown in Figure 5, the F value that two kinds of described methods obtain can simulate Internal pharmacokinetics well; Actual concentrations in recursion concentration and body is made ratio calculation (as shown in Figure 7), the deviation all very little (<2%) of actual concentrations in simulated concentration under described two kinds of computing method instruct and body, wherein recurrence method gained simulated concentration overlaps completely with vivo medicine concentration.

Model fit is done to simulated concentration-time data that described equation and recurrence method obtain, estimate quiet note two compartment model pharmacokinetic parameters, and make comparisons with setting value, calculate mean relative deviation (ARD), average error (ME) and root-mean-square error (RMSE), result is as shown in table 2, recurrence method gained pharmacokinetic parameters is almost identical with setting value, equation parameters obtained estimated value and setting value are also very close, ARD value is-0.1%, ME and RMSE value is all less than 0.005, these two kinds of methods are pointed out all to can be used for the in-vitro simulated of quiet note two Room pharmacokinetic model.

The external pharmacokinetic parameters estimated value of table 2. quiet note two compartment model compares with Internal pharmacokinetics pre-set parameter

Note 1: α distribution phase rate constant, β eliminates phase rate constant, and A distribution phase intercept, B eliminates phase intercept, V _dapparent volume of distribution;

Note 2:ARD mean relative deviation; ME average error; RMSE root-mean-square error; Calculating formula is followed successively by: ARD=∑ (y _i'/y _i-1)/m, ME=∑ (y _i-y _i')/m, RMSE=[∑ (y _i-y _i') ²/ m] ^0.5;

Y _iand y _i' be respectively setting value and estimated value, m data amount check.

The flow relocity calculation that embodiment 3 quiet note three compartment model is in-vitro simulated

If dosage is 240mg, apparent volume of distribution (V _d) be 70.59L, fast distribution phase rate constant (α) is 0.5h ^-1, slow distribution phase rate constant (β) and elimination phase rate constant (γ) are respectively 0.1 and 0.02h ^-1, fast distribution phase intercept A is 2mg/L, and slow distribution phase intercept B is 1.2mg/L, and eliminating phase intercept R is 0.2mg/L, external model reaction chamber liquid measure V _cbe set to 250mL.

Dosage calculates: obtaining vitro reactions room dosage with embodiment 1 is 0.85mg.

Flow relocity calculation:

(1) equation

1) directly calculate F value as shown in the crunode (×) in Fig. 9 by formula (4), along with passage of time, flow velocity reduces gradually, roughly maintains floor level after administration 15h;

2) obtained F value is substituted into external model concentration to calculate in stepping type (39), ask calculation simulated concentration, acquired results is as shown in the crunode (×) in Fig. 8;

(2) recurrence method

1) according to formula (14) c=Ae ^{-α t}+ Be ^{-β t}+ Re ^{-γ t}make plasma concentration curve, result as indicated by the dotted lines in figure 8;

2) be the first point with 0 moment point, computing time gradient (t _i+1-t _i) be set to 0.02h, by formula (32) recursion F value as shown in the hollow dots (zero) in Fig. 9;

3) obtained F value is substituted into external model concentration to calculate in stepping type (39), ask calculation simulated concentration, acquired results is as shown in the hollow dots (zero) in Fig. 8.

The flow velocity that described equation and recurrence method obtain is basically identical (as shown in Figure 9); The F value that described two kinds of methods obtain as seen from Figure 5 can simulate Internal pharmacokinetics well; Calculate the ratio (as shown in Figure 10) of actual concentrations in recursion concentration and body, can find described two kinds of computing method instruct under simulated concentration and body in the deviation all very little (<1%) of actual concentrations, wherein the in-vitro simulated concentration of recurrence method gained overlaps completely with vivo medicine concentration.

Model fit is done to simulated concentration-time data that equation and recurrence method obtain, estimate three compartment model pharmacokinetic parameters, and make comparisons with setting value, calculate mean relative deviation (ARD), average error (ME) and root-mean-square error (RMSE), result is as shown in table 3, recurrence method gained pharmacokinetic parameters and setting value are almost coincide, equation parameters obtained estimated value and setting value are also very close, ARD value is less than 0.2%, ME and RMSE value is all less than 0.003, points out these two kinds of methods all can good quiet note three Room pharmacokinetics in analogue body.

The external pharmacokinetic parameters estimated value of table 3. quiet note three compartment model compares with Internal pharmacokinetics pre-set parameter

Note 1: α distributes phase rate constant soon, and β distributes phase rate constant slowly, and γ eliminates phase rate constant, and A distributes phase intercept soon, and B distributes phase intercept slowly, and R eliminates phase intercept, V _dapparent volume of distribution;

Note 2:ARD mean relative deviation; ME average error; RMSE root-mean-square error;

Calculating formula is followed successively by: ARD=∑ (y _i'/y _i-1)/m, ME=∑ (y _i-y _i')/m, RMSE=[∑ (y _i-y _i') ²/ m] ^0.5;

Y _iand y _i' being respectively setting value and estimated value, m is data amount check.

The flow relocity calculation that embodiment 4 zero-order pharmacokinetics model is in-vitro simulated

If vivo medicine-feeding amount is 240mg, apparent volume of distribution is 60L, and drug concentration fall off rate is in time 0.08mg/ (hL).In external pharmacokinetic model, the amount of liquid of reaction chamber is 250mL.

Dosage calculates: with embodiment 1, obtaining vitro reactions room dosage is 1mg.

Flow relocity calculation:

(1) equation

1) calculate flow rate F according to formula (5), acquired results is as shown in the crunode (×) in Fig. 9; Result shows, and along with passage of time, increasing appears in flow rate F, and the trend constantly risen that gathers way;

2) obtained F value is substituted into external model concentration to calculate in stepping type (45), ask calculation simulated concentration, acquired results is as shown in the crunode (×) in Fig. 8;

(2) recurrence method

1) according to formula (16) c=c ₀-k _et, calculates blood concentration, as shown in phantom in Figure 11;

2) with zero moment for starting point, computing time gradient (t _i+1-t _i) be set to 0.02h, calculate flow rate F according to recursion formula (32) _i, acquired results is as shown in the hollow dots (zero) in Figure 12;

3) by obtained F _ivalue substitutes into external model concentration and calculates in stepping type (39), and ask calculation simulated concentration, acquired results is as shown in the hollow dots (zero) in Figure 11.

Result as shown in figure 12, shows that equation and recurrence method gained flow speed value overlap completely, does not almost have difference between gained simulated concentration; Simulated concentration variance analysis result shows, and described equation and the in-vitro simulated concentration of recurrence method gained overlap completely with vivo medicine concentration, and concentration proportion is constant was 1 (as shown in figure 13); The above results shows, all can realize the in-vitro simulated of zero-order pharmacokinetics in body well by equation and recurrence method; Flow velocity over time feature shows as numerical value and passes in time and increase.

Model fit is done to simulated concentration-time data that equation and recurrence method obtain, estimation apparent volume of distribution and drug concentration speed over time, and make comparisons with setting value, calculate mean relative deviation (ARD), average error (ME) and root-mean-square error (RMSE), result is as shown in table 4, the pharmacokinetic parameters that recurrence method and equation obtain is identical with setting value, and ARD, ME and RMSE value is minimum by (10 ^-5the order of magnitude), result shows, two kinds of described methods all can be used for the in-vitro simulated of zero-order pharmacokinetics.

The outer pharmacokinetic parameters estimated value of table 4. zero-order pharmacokinetics model compares with Internal pharmacokinetics pre-set parameter

Note 1:k _edrug concentration fall off rate in time, V _dapparent volume of distribution;

Note 2:ARD mean relative deviation; ME average error; RMSE root-mean-square error;

Calculating formula is followed successively by: ARD=∑ (y _i'/y _i-1)/m, ME=∑ (y _i-y _i')/m, RMSE=[∑ (y _i-y _i') ²/ m] ^0.5;

Y _iand y _i' being respectively setting value and estimated value, m is data amount check.

The flow relocity calculation that the non-linear pharmacokinetic model of embodiment 5 is in-vitro simulated

If certain drug administration dosage is 240mg, meet a compartment model in vivo after intravenous injection, elimination process meets a meter Man equation, maximum supersession rate (V _max) be 9mg/h, Michaelis constant k _m(50%V _maxcorresponding medication amount) be 5mg, apparent volume of distribution (V _d) be 60L.

The calculating of treated in vitro dosage: with embodiment 1, obtaining reaction chamber dosage is 1mg.

Flow relocity calculation:

1., according to the physiological disposition of this medicine, the pharmaco-kinetic properties that following equation describes described medicine can be listed:

$\frac{dx}{dt}=-\frac{V_{max}x}{k_m+x}---\left(40\right)$

Wherein, x represents Ti Nei central compartment dose.When dt → 0, dx/dt ≈ Δ x/ Δ t sets up, and launches this formula, obtain by forward-difference method:

$x_{i+1}=x_i-\frac{V_{max}{x}_i}{k_m+x_i}(t_{i+1}-t_i)---\left(41\right)$

Wherein, x _irepresent the i-th moment (t _i) dose, relative medicine concentration c _iaccording to x _iwith V _dratio obtains.By V _maxand k _mnumerical value substitutes into this formula, and substitutes into drug concentration calculation relational expression, can obtain drug concentration curve over time in central compartment's under different time points; Above-mentioned variable (x is realized by data assignment in Excel worksheet _iand c _i) calculating, computing time gradient (t _i+1-t _i) being set to 0.02h, the Ti Nei central compartment pharmaceutical concentration-time curve obtained is as shown in the dotted line in Figure 14;

2. with zero moment point for starting point, computing time, gradient was still 0.02h, according to recursion formula (32) calculate flow rate F _i, gained flow rate versus time curve as shown in figure 15;

3. obtained flow speed value is updated to external model concentration to calculate in stepping type (39), asks and calculate simulated concentration C _i, acquired results is as shown in the hollow dots (zero) in Figure 14.

The ratio of calculating simulation concentration and vivo medicine concentration, as shown in figure 16, Ratio invariableness is 1 to acquired results, and result shows, the in-vitro simulated concentration obtained by recurrence method overlaps completely with blood concentration in body.

As shown in figure 14, result also shows the in-vitro simulated concentration obtained by recurrence method and overlaps completely with blood concentration in body, result shows that the hollow dots of simulated concentration has all dropped on and represents on the dotted line of vivo medicine concentration, the release rate passing drug concentration is in time accelerated gradually, and passing in time with flow velocity constantly increases corresponding (as shown in figure 15).

Model fit is made by simulated concentration-time data, estimation pharmacokinetic model parameter, and make comparisons with setting value, calculate mean relative deviation (ARD), average error (ME) and root-mean-square error (RMSE), result is as shown in table 5, and parameter estimation value almost overlaps with setting value, ARD value is only-0.024%, ME and RMSE value is less than 0.003, and result shows, can realize the in-vitro simulated of the non-linear pharmacokinetics of quiet note well by recurrence method.

The external pharmacokinetic parameters estimated value of the non-linear pharmacokinetic model of the quiet note of table 5. compares with Internal pharmacokinetics pre-set parameter

Note 1:V _maxmaximum supersession rate, k _mmichaelis rate constant (dose that 50% maximum supersession rate is corresponding), V _dapparent volume of distribution;

Note 2:ARD mean relative deviation; ME average error; RMSE root-mean-square error. calculating formula is followed successively by: ARD=∑ (y _i'/y _i-1)/m, ME=∑ (y _i-y _i')/m, RMSE=[∑ (y _i-y _i') ²/ m] ^0.5;

Y _iand y _i' being respectively setting value and estimated value, m is data amount check.

The result of above-described embodiment shows, in-vitro simulated method of the present invention solves the in-vitro simulated problem of body internal jugular vein drug administration by injection compartment model, comprises the in-vitro simulated problems such as a chamber, two chambers, three chambers and zero-order pharmacokinetics model; Described in-vitro simulated method effectively reduces the dependence of external pharmacokinetics simulation to Internal pharmacokinetics model structure, expand the scope that external pharmacokinetic model is simulated Internal pharmacokinetics, for raising external pharmacokinetics/pharmacodynamic studies technical merit, especially the external pharmacokinetics/pharmacodynamic studies of antibacterials is significant.

Claims (7)

1. based on an in-vitro simulated method for the intravenous injection pharmacokinetic model of velocity of flow adjust, it is characterized in that, it comprises: adopt equation and recurrence method;

Described equation directly calculates external model flow velocity based on pharmacokinetic parameters, wherein,

In-vitro simulated for linear pharmacokinetic model, flow relocity calculation formula is:

$F=V_C\&CenterDot;\frac{\underset{i=1}{\overset{n}{\&Sigma;}}{A}_i\&CenterDot;k_i\&CenterDot;e^{-k_{i}t}}{\underset{i=1}{\overset{n}{\&Sigma;}}{A}_i\&CenterDot;e^{-k_{i}t}}---\left(1\right)$

Wherein, F and V _cbe respectively flow velocity and reaction chamber liquid measure, n represent the room number of phases (i=1,2,3 ...), A _irepresent the i-th phase intercept, k _irepresent the i-th phase rate constant, e and t is respectively natural constant (2.718) and time;

In-vitro simulated for a chamber, two chambers and three chambers quiet note pharmacokinetics, the flow relocity calculation that formula (1) is illustrated can use formula (2) ~ formula (4) specifically to state respectively:

F＝k _e·V _C(2)

$F=V_C\&CenterDot;\frac{{\mathrm{A\&alpha;e}}^{-\mathrm{\&alpha;}t}+{\mathrm{B\&beta;e}}^{-\mathrm{\&beta;}t}}{{\mathrm{Ae}}^{-\mathrm{\&alpha;}t}+{\mathrm{Be}}^{-\mathrm{\&beta;}t}}---\left(3\right)$

$F=V_C\&CenterDot;\frac{{\mathrm{A\&alpha;e}}^{-\mathrm{\&alpha;}t}+{\mathrm{B\&beta;e}}^{-\mathrm{\&beta;}t}+{\mathrm{R\&gamma;e}}^{-\mathrm{\&gamma;}t}}{{\mathrm{Ae}}^{-\mathrm{\&alpha;}t}+{\mathrm{Be}}^{-\mathrm{\&beta;}t}+{\mathrm{Re}}^{-\mathrm{\&gamma;}t}}---\left(4\right)$

Wherein, V _cfor reaction chamber liquid volume, its numerical value is determined according to the actual requirements; K in formula (2) _efor elimination rate constant, A and B representative distribution phase intercept in formula (3) and elimination phase intercept, α and β is for distribution phase rate constant and eliminate phase rate constant, A, B and R in formula (4) are respectively distribution phase intercept, fast elimination phase intercept and slow elimination phase intercept, α, β and γ are followed successively by distribution phase rate constant, fast elimination phase rate constant and slow elimination phase rate constant, e and t is respectively natural constant (2.718) and time;

In-vitro simulated for zero-order pharmacokinetics, flow relocity calculation formula is:

$F=\frac{V_C\&CenterDot;k_e}{c_0-k_{e}t}---\left(5\right)$

Wherein, k _efor concentration descending slope in time, initial concentration c ₀represent, t represents the time;

Described recurrence method carries out recursion based on concentration values m-during Internal pharmacokinetics to different time points flow velocity, and its recursion formula is:

$F_i=V_C\&CenterDot;(1-\frac{c_{i+1}}{c_i})\&CenterDot;\frac{1}{t_{i+1}-t_i}---\left(32\right)$

Wherein, F _iit is the flow velocity of the i-th moment point; V _cfor the liquid volume in reaction chamber, it is the designated value done according to the actual requirements; c _i+1and c _irepresent that medicine is at t respectively _i+1and t _iblood concentration in the body in moment, its exact value calculates according to the compartment model Pharmacokinetic Formula of reality and obtains.

2., by in-vitro simulated method according to claim 1, it is characterized in that, in described recurrence method,

For the quiet note pharmacokinetic model of a chamber, two chambers and three chambers, the i-th moment (t _i) bulk concentration c _iformula (33) ~ formula (35) is used to calculate respectively:

$c_i=c_0\&CenterDot;e^{-k_e{t}_i}---\left(33\right)$

$c_i=A\&CenterDot;e^{-{\mathrm{\&alpha;t}}_i}+B\&CenterDot;e^{-{\mathrm{\&beta;t}}_i}---\left(34\right)$

$c_i=A\&CenterDot;e^{-{\mathrm{\&alpha;t}}_i}+B\&CenterDot;e^{-{\mathrm{\&beta;t}}_i}+R\&CenterDot;e^{-{\mathrm{\&gamma;t}}_i}---\left(35\right)$

Wherein, the c in formula (33) ₀and k _ebe respectively initial drug concentrations and elimination rate constant, A and B representative distribution phase intercept in formula (34) and elimination phase intercept, α and β is followed successively by distribution phase rate constant and eliminates phase rate constant, A, B and R in formula (35) are respectively distribution phase intercept, fast elimination phase intercept and slow elimination phase intercept, α, β and γ are followed successively by distribution phase rate constant, fast elimination phase rate constant and slow elimination phase rate constant, and e represents natural constant (2.718);

For zero-order pharmacokinetics model, the i-th moment (t _i) bulk concentration c _icalculate by formula (36):

c _i＝c ₀-k _et _i(36)

Wherein, c ₀for initial drug concentrations, k _erepresent concentration descending slope in time.

3., by in-vitro simulated method according to claim 1, it is characterized in that, the assignment of described flow velocity is consecutive variations value form or multistage mean value formation.

4., by in-vitro simulated method according to claim 1, it is characterized in that, described flow velocity be calculated as single-dose or multiple dosing time flow relocity calculation.

5. the purposes of in-vitro simulated method according to claim 1 in vitro in pharmacokinetics or pharmacodynamics model flow relocity calculation.

6. by purposes according to claim 5, it is characterized in that, its application form be artificial calculating based on the Equivalent Form of formula (1) ~ (5), (32) or software calculating.

7., by purposes according to claim 5, it is characterized in that, described external pharmacokinetics or pharmacodynamics are the external pharmacokinetics of antibacterials or pharmacodynamics.