CN103077296A - Method for externally simulating intravenous injection pharmacokinetics model based on flow velocity regulation - Google Patents

Abstract

The invention belongs to the field of external pharmacokinetics/pharmacodynamics researches, and relates to a method for externally simulating an intravenous injection pharmacokinetics model based on flow velocity regulation. The method is a flow velocity calculation method based on an intelligent peristaltic pump which can regulate flow velocity in a stage or real-time manner, and comprises a formula method and a recurrence method. By utilizing the method, an external simulation problem of an internal intravenous injection administration compartment model is solved, the dependence of an external pharmacokinetics model on an internal pharmacokinetics model structure is effectively reduced, the application scope of the external pharmacokinetics model to internal pharmacokinetics simulation is widened, the external pharmacokinetics/pharmacodynamics research technological level is improved, and the method has a particularly important meaning in antibacterial drug external pharmacokinetics/pharmacodynamics researches.

Description

In-vitro simulated method based on the intravenous injection pharmacokinetics 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 pharmacokinetics model based on velocity of flow adjust.

Background technology

External pharmacokinetics/pharmacodynamics (Pharmacokinetic/pharmaco-dynamic, 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, for rationally dosage regimen formulation in the body provides foundation; But this Technology Need can satisfy the device outside that pharmacodynamics is dynamically observed requirement again simultaneously based on the body internal dynamics process of a cover aids drug, i.e. external pharmacokinetics model.In the research of this area, often need to overlap aids drug pharmacokinetics process in vivo in the device outside one, study simultaneously the pharmacodynamics of this medicine in the concentration dynamic changing process; Wherein, medicine common process in vivo comprises: a compartment model and two chamber models can be divided into again intravenous injection model, drip-feed model and extravascular administration model (for example oral model) according to administering mode.Described technology is particularly suitable for the pharmacodynamic study take life entities such as microorganism, tumour cells as effective object, because can realize relatively easily the requirement aspect pharmacokinetics simulation and the dynamic pharmacodynamic observation two in an airtight cultivating system in such research.

The core texture of described external pharmacokinetics 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 often places specific environment, or special modification is structurally arranged; Peristaltic pump pumps into reaction chamber from fluid reservoir by certain flow rate with liquid as drive system, thereby the quantity of fluid such as has again under pressure to discharge the specific change that forms the reaction chamber drug concentration in the simultaneous reactions chamber; Described silicone tube is as the connecting tube of each parts, and stirrer acts on the liquid system in the reaction chamber, so that drug distribution and to being uniformly dispersed in the whole system of acting on of target.

In addition, the key of described external pharmacokinetics model investigation technology comprises PK simulation and two aspects of PD simulation: the key of PK analogue technique how to be by the liquid measure in the control reaction chamber, flow rate of liquid and by to the modification of apparatus structure with the simulation of realization to pharmacokinetics in the body; The key of PD analogue technique is the transformation to reaction chamber structure, can satisfy the requirement of dynamic pharmacodynamic observation.Described PK simulation often conflicts to the demand of model structure mutually with the PD simulation, thereby the normal needs of accuracy that satisfy PK simulation add reaction chamber and increase servicing unit and cause the sacrifice of model operability even also can have influence on pharmacodynamic observation, for example satisfy two chamber models simulate outward the periphery compartment of increase caused operation easier to increase also causing simultaneously bacterium in reaction chamber and periphery compartment circulation so that affect count of bacteria in the reaction chamber.Equally, satisfying the PD research purpose simultaneously also can simulation brings impact on PK owing to the change of structure, and for example running off the hollow fiber column model that adopts for fear of bacterium can be because Drug absorbability affect PK simulates.

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 also is confined to the simulation of linear pharmacokinetics the simulation of PK but also needs simplify in form, namely take non-compartment model parameter as basic with the speed removing of certain density medicine according to appointment; Maximum concentration and whole eliminate half life period of medicine in blood only paid close attention in described simulation, ignored the details of medicine in dynamic process, particularly has relatively large deviation to the simulation of two Room, three compartment model pharmacokinetics the time; Although introducing auxiliary chamber can realize the simulation to two Room, three compartment model pharmacokinetics, said method can make the structure of whole external model and operability thereof become very complicated.In addition, if when not taking precautions against the measure that bacterium or tumour cell etc. circulate in the model structure between central compartment and periphery compartment, said method can not be made accurate evaluation to pharmacodynamics; Therefore, simulation to two Room, three compartment model pharmacokinetics also stays in theory or approximate simulation stage at present, how to guarantee simultaneously that at external accurate aids drug dynamic process in vivo the operability of model is the key issue that the art need to solve.

Summary of the invention

The objective of the invention is to overcome defective and the deficiency of prior art, a kind of in-vitro simulated method of the intravenous injection pharmacokinetics model based on velocity of flow adjust is provided.

The present invention with the flow velocity of external pharmacokinetics model as the breach with conflicting between overcoming the PK simulation and PD studying, realize accurate analogue body internal jugular vein drug administration by injection pharmacokinetics in simple mechanism, such as a Room, two Room or three compartment model etc. by the flow velocity dynamic adjustments; In-vitro simulated method of the present invention can make external PK simulation that the dependence of reaction chamber structure is significantly reduced, and makes the external model device larger transformation space be arranged to satisfy the drug efficacy study demand.

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

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

(1) equation

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

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

Wherein, F and V _CBe respectively flow velocity and reaction chamber liquid measure, n represent the chamber number of phases (i=1,2,3 ...), A _iAnd k _iThe intercept and the respective rate constant that represent respectively the i phase;

In-vitro simulated for the quiet notes pharmacokinetics of a chamber, two chambers and three chambers, flow relocity calculation is used respectively formula (2)～formula (4) statement:

F＝k _e·V _C (2)

$F=V_C\·\frac{\mathrm{A\α}{e}^{-\mathrm{\αt}}+\mathrm{B\β}{e}^{-\mathrm{\βt}}}{A{e}^{-\mathrm{\αt}}+B{e}^{-\mathrm{\βt}}}---\left(3\right)$

$F=V_C\·\frac{\mathrm{A\α}{e}^{-\mathrm{\αt}}+\mathrm{B\β}{e}^{-\mathrm{\βt}}+\mathrm{R\γ}{e}^{-\mathrm{\γt}}}{A{e}^{-\mathrm{\αt}}+B{e}^{-\mathrm{\βt}}+R{e}^{-\mathrm{\γt}}}---\left(4\right)$

Wherein, V _CBe the reaction chamber liquid volume, its numerical value is decided according to the actual requirements; K in the formula (2) _eBe elimination rate constant, representative distributes and eliminates the phase intercept A in the formula (3) with B, α and β are rate constant separately, and A, the B in the formula (4) is respectively distribution with R and eliminates mutually, soon phase and eliminate slowly mutually intercept, and corresponding rate constant represents with α, β and γ respectively;

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

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

Wherein, k _eBe concentration descending slope in time, initial concentration c ₀Expression;

(2) recurrence method

Described recurrence method for based in the body during pharmacokinetics meta-concentration numbers value the different time points flow velocity is carried out the method for recursion, 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 i moment point; V _CBe the liquid volume in the reaction chamber, be the designated value of doing according to the actual requirements; c _I+1And c _iRepresent that respectively medicine is at t _I+1And t _iBlood concentration in the body constantly, its exact value can calculate according to the compartment model Pharmacokinetic Formula of reality and obtain;

For a chamber, two chambers and the quiet notes pharmacokinetics of three chambers model, i bulk concentration c constantly _iUse respectively formula (33)～formula (35) to calculate:

$c_i={\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000102026200000013.png,HDA0000102026200000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0\&CenterDot;e^{-k_e{t}_i}---\left(33\right)$

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

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

Wherein, the c in the formula (33) ₀And k _eBe respectively initial drug concentration and elimination rate constant, representative distributes and eliminates the phase intercept A in the formula (34) with B, α and β are rate constant separately, A, B in the formula (35) is respectively distribution with R and eliminates mutually, soon phase and eliminate slowly mutually intercept, and corresponding rate constant represents with α, β and γ respectively;

For zero level pharmacokinetics model, i bulk concentration c constantly _iCalculate with formula (41):

c _i＝c ₀-k _et _i (36)

Wherein, c ₀Be initial drug concentration, k _eExpression concentration descending slope in time.

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

Among the present invention, also described equation and recurrence method are deduced, step is as follows:

(1) equation

Realize that external pharmacokinetics model need satisfy following two conditions to the accurate simulation of pharmacokinetic curve in the body: reaction chamber medicine initial concentration (C in (1) external model ₀) and drug disposition initial concentration (c ₀) equate i.e. C ₀=c ₀(2) external model Chinese traditional medicine concentration elimination speed (dC/dt) equates with vivo medicine concentration elimination speed (dc/dt), i.e. dC/dt=dc/dt; Therefore, following formula is set up:

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

Wherein, (dC/dt)/C with (dc/dt)/c represents that external and vivo medicine concentration is to the relative change rate of time, elimination rate constant k in its implication and the quiet notes one compartment model _eSimilar; For a compartment model, concentration keeps constant to the relative change rate of time; For two Room and above compartment model, the relative change rate passes in time gradually and reduces; With vivo medicine concentration-equation of time and medicine in-vitro substrate concentration-equation of time substitution following formula, can derive the flow relocity calculation formula under the various in-vitro simulated situations;

In the 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 the central compartment with flow rate F, there is again equivalent mixing liquid to be discharged from the reaction chamber, eliminates form thereby can simulate medicine index in vivo; The parameter that needs in the described model equipment to determine comprises nutrient solution flow velocity (F), liquid volume (V in the central compartment _C) and dosage (D); Wherein, V _CNumerical value is designated value, and D equals c ₀* V _C, the F value needs according to calculative determination; Dose (X) in the described model equipment central compartment changes the differential equation of available formula (7) signal:

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

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 the model central compartment through the Induction Solved by Laplace Transformation solution:

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

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

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

Among the present invention, the flow relocity calculation of described equation under different situations comprises:

1) the in-vitro simulated flow relocity calculation of intravenous injection one compartment model

The densimeter formula of intravenous injection one compartment model is:

$c={\mathrm{<figure-callout\; id="0"\; label="c"\; filenames="HDA0000102026200000013.png,HDA0000102026200000021.png"\; state="\{\{state\}\}">c</figure-callout>}}_0\&CenterDot;e^{-k_e\&CenterDot;t}---\left(10\right)$

Obtain in time relative change rate's expression formula of drug concentration by differentiate:

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

Make formula (11) equate with formula (9), can obtain F=V _CK _e, so formula (2) is set up;

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

2) the in-vitro simulated flow relocity calculation of intravenous injection two compartment model

The densimeter formula of intravenous injection two compartment model is:

c＝Ae ^-αt+Be ^-βt (12)

Wherein A, B represent respectively to distribute and eliminate the phase intercept, and α and β are for distributing mutually and elimination rate constant mutually;

Obtain in time relative change rate's expression formula of drug concentration by differentiate:

$\frac{\mathrm{dc}/\mathrm{dt}}{c}=-\frac{\mathrm{\&alpha;}{\&CenterDot;\mathrm{Ae}}^{-\mathrm{\&alpha;t}}+\mathrm{\&beta;}\&CenterDot;B{e}^{-\mathrm{\&beta;t}}}{A{e}^{-\mathrm{\&alpha;t}}+B{e}^{-\mathrm{\&beta;t}}}---\left(13\right)$

Make formula (13) equate with formula (9), can obtain formula (3);

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

3) the in-vitro simulated flow relocity calculation of intravenous injection three compartment model

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 distribution phase, eliminate mutually soon and eliminate slowly mutually intercept, and α, β are that distribution is eliminated mutually, soon phase and eliminated slowly mutually rate constant with γ;

Arrive in time relative change rate's expression formula of drug concentration by differentiate:

$\frac{\mathrm{dc}/\mathrm{dt}}{c}=-\frac{\mathrm{A\&alpha;}{e}^{-\mathrm{\&alpha;t}}+\mathrm{B\&beta;}{e}^{-\mathrm{\&beta;t}}+\mathrm{R\&gamma;}{e}^{-\mathrm{\&gamma;t}}}{A{e}^{-\mathrm{\&alpha;t}}+B{e}^{-\mathrm{\&beta;t}}+R{e}^{-\mathrm{\&gamma;t}}}---\left(15\right)$

Make formula (15) equate with formula (9), can obtain formula (4);

The 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 level pharmacokinetics is in-vitro simulated

The concentration computing formula of zero level pharmacokinetics model is:

c＝c ₀-k _et (16)

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

Obtain in time relative change rate's expression formula of drug concentration by differentiate:

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

Make formula (17) equate with formula (9), formula (16) substitution is also put in order, can obtain formula (5);

The result shows, can simulate body internal jugular vein injection zero level pharmacokinetics process in analogue means as shown in Figure 1.

(2) recurrence method

When vitro reactions chamber drug concentration (C) equates with central compartment's drug concentration (c) in the body, simultaneously, when vitro reactions chamber drug concentration temporal evolution rate (dC/dt) is identical with central compartment's drug concentration temporal evolution rate (dc/dt) in the body, can realize the external accurate simulation of quiet notes pharmacokinetics in the body, so formula (6) is set up;

Vivo medicine concentration is in time among relative change rate's [(dc/dt)/c], and when dt → 0, dc/dt ≈ Δ c/ Δ t sets up, and this formula is launched with forward-difference method, obtains:

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

The medicine in-vitro substrate concentration among relative change rate's [(dC/dt)/C], with formula (8) substitution, is got constantly (t of i in time _i) result of calculation, obtain:

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

Make right of above-mentioned two formulas equate, can obtain formula (32) through arrangement; The i moment and i+1 central compartment's drug concentration and this formula of time substitution constantly just can be calculated i flow velocity (F constantly _i), obtain the time dependent adjustment curve of flow velocity;

Work as t _I+1-t _iTrend towards at 0 o'clock, can obtain F _iThe approximate exact value, can obtain meeting the flow velocity approximate continuity linear regulation value of the compartment model pharmacokinetics such as two Room, three Room by recursion, realize the real-time adjusting of flow velocity; Work as t _I+1-t _iWhen wider, can realize the stage by stage adjusting of flow velocity; In addition, when drug concentration constantly descends, simultaneously its concentration is not when rule meets linear pharmacokinetics or zero level pharmacokinetics over time, the non-linear pharmacokinetics that for example meets meter Man equation, still can adopt formula (32) to make flow relocity calculation, to realize simulating in real time or stage by stage pharmacokinetics in the body.

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

According to the collocation principle of analogue means shown in Figure 1, equation is as follows over time can to derive the reaction chamber drug concentration:

$\frac{\mathrm{dC}}{\mathrm{dt}}=-\frac{F}{V_C}\&CenterDot;C---\left(18\right)$

When 1) in external model, simulating an Atrium Model,

With formula (2) substitution formula (18), can get:

$\frac{\mathrm{dC}}{\mathrm{dt}}=-k_e\&CenterDot;C---\left(19\right)$

Laplace transform and corresponding inverse transformation are implemented in the following formula both sides, obtain:

$C={\mathrm{<figure-callout\; id="0"\; label="C"\; filenames="HDA0000102026200000013.png,HDA0000102026200000021.png"\; state="\{\{state\}\}">C</figure-callout>}}_0\&CenterDot;e^{-k_{e}t}---\left(20\right)$

Work as C ₀=c ₀The time, described equation meets the quiet notes pharmacokinetics of chamber model in the body, and is 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;

When 2) in external model, simulating two Atrium Models,

With formula (3) substitution formula (18), obtain:

$\frac{\mathrm{dC}}{\mathrm{dt}}=-\frac{C}{V_C}\&CenterDot;[V_C\&CenterDot;\frac{\mathrm{\&alpha;}{\&CenterDot;\mathrm{Ae}}^{-\mathrm{\&alpha;t}}+\mathrm{\&beta;}\&CenterDot;B{e}^{-\mathrm{\&beta;t}}}{A{e}^{-\mathrm{\&alpha;t}}+B{e}^{-\mathrm{\&beta;t}}}]---\left(21\right)$

Therefore draw:

$\frac{\mathrm{dC}}{C}=-\frac{\mathrm{\&alpha;}{\&CenterDot;\mathrm{Ae}}^{-\mathrm{\&alpha;t}}+\mathrm{\&beta;}\&CenterDot;B{e}^{-\mathrm{\&beta;t}}}{A{e}^{-\mathrm{\&alpha;t}}+B{e}^{-\mathrm{\&beta;t}}}\&CenterDot;\mathrm{dt}---\left(22\right)$

Following formula can further be expressed as:

d(lnC)＝d[ln(Ae ^-αt+Be ^-βt)] (23)

Definite integral is made in the following formula both sides in the 0-t time domain, make initial value C ₀Be A+B, obtain:

C＝Ae ^-αt+Be ^-βt (24)

Described equation meets the quiet notes pharmacokinetics of two chambers model in the body, and is 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;

When 3) in external model, simulating three Atrium Models

With formula (4) substitution formula (18) and put in order, obtain:

$\frac{\mathrm{dC}}{C}=-\frac{\mathrm{\&alpha;}\&CenterDot;A{e}^{-\mathrm{\&alpha;t}}+\mathrm{\&beta;}\&CenterDot;B{e}^{-\mathrm{\&beta;t}}+\mathrm{\&gamma;}\&CenterDot;R{e}^{-\mathrm{\&gamma;t}}}{A{e}^{-\mathrm{\&alpha;t}}+B{e}^{-\mathrm{\&beta;t}}+R{e}^{-\mathrm{\&gamma;t}}}\&CenterDot;\mathrm{dt}---\left(25\right)$

Following formula can further be written as:

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

Definite integral is made in the following formula both sides in the 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 notes pharmacokinetics of three chambers model in the body, and is 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;

When 4) in external model, simulating zero level pharmacokinetics model

With formula (5) substitution formula (18), obtain:

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

Following formula is put in order, is obtained:

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

Following formula can further be expressed as:

d(lnC)＝d[ln(c ₀-k _et)] (30)

Definite integral is made on the following formula both sides, made initial value C ₀=c ₀, therefore draw:

C＝C ₀-k _et (31)

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

Among the present invention, described in-vitro simulated method, final assignment to flow velocity can be continuous changing value form and also can be multistage mean value form; Flow relocity calculation when this in-vitro simulated method can be used for single-dose or multiple dosing.

The in-vitro simulated method of the intravenous injection pharmacokinetics 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 to 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 pharmacokinetics 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, comprised the in-vitro simulated problems such as a chamber, two chambers, three chambers and zero level pharmacokinetics model; Described in-vitro simulated method has reduced external pharmacokinetics simulation effectively to the dependence of pharmacokinetics model structure in the body, expanded external pharmacokinetics model to the scope of pharmacokinetics simulation in the body, external pharmacokinetics/external pharmacokinetics/pharmacodynamic studies of pharmacodynamic studies technical merit, especially antibacterials is significant for improving

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 pharmacokinetics model based on velocity of flow adjust of the present invention.It needs to be noted, specific embodiments and the drawings only are in order to illustrate, obviously those skilled in the art can illustrate according to this paper, and the present invention is carried out various corrections or change, and these corrections and changing also will be included within this patent scope.

Description of drawings

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 notes 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 has shown the in-vitro simulated flow relocity calculation result's of quiet notes one Room pharmacokinetics model of the present invention contrast situation, and wherein, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Fig. 4 has shown the in-vitro simulated variance analysis of quiet notes one Room 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.

Fig. 5 is the in-vitro simulated design sketchs of quiet notes two Room pharmacokinetics models 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 has shown the in-vitro simulated flow relocity calculation result's of quiet notes two Room pharmacokinetics models of the present invention contrast situation, and wherein, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Fig. 7 has shown the in-vitro simulated variance analysis of quiet notes two Room pharmacokinetics models 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 sketchs of quiet notes three Room pharmacokinetics models 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 has shown the in-vitro simulated flow relocity calculation result's of quiet notes two Room pharmacokinetics models of the present invention contrast situation, and wherein, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Figure 10 has shown the in-vitro simulated variance analysis of quiet notes two Room pharmacokinetics models 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 notes zero level 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 has shown the in-vitro simulated flow relocity calculation result's of quiet notes zero level pharmacokinetics model of the present invention contrast situation, and wherein, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Figure 13 has shown the in-vitro simulated variance analysis of quiet notes zero level 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 pharmacokinetics model of quiet notes of the present invention, wherein,

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

Figure 15 has shown the result of calculation that adopts recurrence method of the present invention to calculate the in-vitro simulated flow velocity of the non-linear pharmacokinetics model of quiet notes.

Figure 16 has shown the in-vitro simulated variance analysis of the non-linear pharmacokinetics model of quiet notes 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 regulates the in-vitro simulated figure that flow velocity is realized quiet notes pharmacokinetics among the present invention.

Embodiment

The in-vitro simulated flow relocity calculation of embodiment 1 quiet notes one compartment model

If dosage is 240mg, apparent volume of distribution (V _d) be 60L, elimination rate constant is k _eBe 0.5h ^-1, external pharmacokinetics model reaction chamber amount of liquid V _CBe made as 250mL.

Dosage calculates: according to the principle conversion external model dosage that equates with the medicine in-vitro substrate concentration in the body, calculating formula: D _{In vivo}* V _C/ V _d, obtaining vitro reactions chamber dosage is 1mg.

(1) equation

1) according to formula (2) F=V _CK _eCalculate the F value, the numerical value that obtains flow rate F is 2.083mL/min (as shown in Figure 3);

2) the F value substitution external model concentration that obtains is calculated stepping type (formula (39)) and ask the calculation simulated concentration, the result is shown in the crunode (*) among 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 the body according to formula (10), the result is shown in the dotted line among Fig. 2;

2) take zero moment point as starting point, computing time gradient (t _I+1-t _i) be made as 0.02h, by formula (32) do the recursion calculating of flow rate F, obtain the permanent 2.073mL/min (as shown in Figure 3) of being of its numerical value.

3) resulting F value substitution external model concentration is calculated stepping type (formula (39)) and ask the calculation simulated concentration, acquired results is shown in the hollow dots among Fig. 2 (ο).

The result as shown in Figure 2, described equation overlaps substantially with recurrence method gained flow velocity, the result shows, the F value that described two kinds of methods obtain is the interior pharmacokinetics of analogue body well; Calculate the ratio of above-mentioned two kinds of method gained simulated concentrations and vivo medicine concentration, the result as shown in Figure 4, recurrence method gained simulated concentration overlaps fully with vivo medicine concentration, equation gained simulated concentration is a little less than vivo medicine concentration, described deviation has been passed certain increase trend in time, and deviation amplitude is controlled at less than in 7% the scope.

Equation and the resulting simulated concentration-time data of recurrence method are done the model estimation, ask and calculate the 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), the 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 approaching, ARD is no more than 0.3%, ME and RMSE value are less than 0.002, the result shows, described two kinds of methods all can be used for the in-vitro simulated of quiet notes one Room pharmacokinetics model.

The comparison of pharmacokinetic parameters setting value in the external pharmacokinetic parameters estimated value of the quiet notes one compartment model of table 1. and the body

Annotate 1:k _eElimination rate constant, V _dApparent volume of distribution;

Annotate the 2:ARD mean relative deviation; The ME average error; The RMSE root-mean-square error, calculating formula is followed successively by:

ARD=∑ (y _i'/y _i-1)/and m, ME=∑ (y _i-y _i')/m, RMSE=[∑ (y _i-y _i') ²/ m] ^0.5y _iAnd y _i' be respectively setting value and estimated value, m data amount check.

The in-vitro simulated flow relocity calculation of embodiment 2 quiet notes two compartment models

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, eliminating phase intercept B is 0.396mg/L, external model reaction chamber amount of liquid V _CBe made as 250mL.

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

Flow relocity calculation:

(1) equation

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

2) resulting F value substitution external model concentration is calculated stepping type (39) and ask the calculation simulated concentration, acquired results is shown in the crunode (*) among Fig. 5;

(2) recurrence method

1) according to formula (12) c=Ae ^{-α t}+ Be ^{-β t}Make plasma concentration curve, the result is shown in the dotted line among Fig. 5;

2) take 0 moment point as the first point, computing time gradient (t _I+1-t _i) being made as 0.02h, (37) recursion F value by formula is shown in the hollow dots among Fig. 6 (ο);

3) resulting F value substitution external model concentration is calculated in the stepping type (39), asked the calculation simulated concentration, acquired results is shown in the hollow dots among Fig. 5 (ο).

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

Described equation and the resulting simulated concentration-time data of recurrence method are made model fit, estimate quiet notes 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), the result is as shown in table 2, recurrence method gained pharmacokinetic parameters and setting value are almost identical, equation parameters obtained estimated value and setting value are also very approaching, the ARD value is-0.1%, ME and RMSE value point out these two kinds of methods all to can be used for the in-vitro simulated of quiet notes two Room pharmacokinetics models all less than 0.005.

The comparison of pharmacokinetic parameters setting value in the external pharmacokinetic parameters estimated value of the quiet notes two compartment model of table 2. and the body

Annotate 1: α distribution phase rate constant, β eliminates the phase rate constant, A distribution phase intercept, B eliminates phase intercept, V _dApparent volume of distribution;

Annotate the 2:ARD mean relative deviation; The ME average error; The RMSE root-mean-square error; Calculating formula is followed successively by: ARD=∑ (y _i'/y _i-1)/and 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 in-vitro simulated flow relocity calculation of embodiment 3 quiet notes three compartment models

If dosage is 240mg, apparent volume of distribution (V _d) be 70.59L, the phase that distributes soon rate constant (α) is 0.5h ^-1, the phase that distributes slowly rate constant (β) with eliminate mutually rate constant (γ) and be respectively 0.1 and 0.02h ^-1, the phase that distributes soon intercept A is 2mg/L, and the phase that distributes slowly intercept B is 1.2mg/L, and eliminating phase intercept R is 0.2mg/L, external model reaction chamber liquid measure V _CBe made as 250mL.

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

Flow relocity calculation:

(1) equation

1) by formula (4) directly calculate the F value shown in the crunode (*) among Fig. 9, and along with passage of time, flow velocity reduces gradually, roughly maintain floor level behind the administration 15h;

2) resulting F value substitution external model concentration is calculated in the stepping type (39), asked the calculation simulated concentration, acquired results is shown in the crunode (*) among Fig. 8;

(2) recurrence method

1) according to formula (14) c=Ae ^{-α t}+ Be ^{-β t}+ Re ^{-γ t}Make plasma concentration curve, the result is shown in the dotted line among Fig. 8;

2) take 0 moment point as the first point, computing time gradient (t _I+1-t _i) be made as 0.02h, by formula (32) recursion F value is shown in the hollow dots among Fig. 9 (ο);

3) resulting F value substitution external model concentration is calculated in the stepping type (39), asked the calculation simulated concentration, acquired results is shown in the hollow dots among Fig. 8 (ο).

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

Equation and the resulting simulated concentration-time data of recurrence method are made model fit, 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), the 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 approaching, the ARD value is less than 0.2%, ME and RMSE value be all less than 0.003, points out all good quiet notes three Room pharmacokinetics in the analogue body of these two kinds of methods.

The comparison of pharmacokinetic parameters setting value in the external pharmacokinetic parameters estimated value of the quiet notes three compartment model of table 3. and the body

Annotate 1: the α phase rate constant that distributes soon, the β phase rate constant that distributes slowly, γ eliminates the phase rate constant, the A phase intercept that distributes soon, the B phase intercept that distributes slowly, R eliminates phase intercept, V _dApparent volume of distribution;

Annotate the 2:ARD mean relative deviation; The ME average error; The RMSE root-mean-square error;

Calculating formula is followed successively by: ARD=∑ (y _i'/y _i-1)/and 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 in-vitro simulated flow relocity calculation of embodiment 4 zero level pharmacokinetics models

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

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

Flow relocity calculation:

(1) equation

1) calculate flow rate F according to formula (5), acquired results is shown in the crunode (*) among Fig. 9; Result's demonstration, along with passage of time, increasing appears in flow rate F, and the trend of the continuous rising that gathers way;

2) resulting F value substitution external model concentration is calculated in the stepping type (45), asked the calculation simulated concentration, acquired results is shown in the crunode (*) among 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) take zero constantly as starting point, computing time gradient (t _I+1-t _i) be made as 0.02h, calculate flow rate F according to recursion formula (32) _i, acquired results is shown in the hollow dots among Figure 12 (ο);

3) with resulting F _iValue substitution external model concentration is calculated in the stepping type (39), asks the calculation simulated concentration, and acquired results is shown in the hollow dots among Figure 11 (ο).

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

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

The comparison of pharmacokinetic parameters setting value in the outer pharmacokinetic parameters estimated value of table 4. zero level pharmacokinetics model and the body

Annotate 1:k _eDrug concentration fall off rate in time, V _dApparent volume of distribution;

Annotate the 2:ARD mean relative deviation; The ME average error; The RMSE root-mean-square error;

Calculating formula is followed successively by: ARD=∑ (y _i'/y _i-1)/and 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 in-vitro simulated flow relocity calculation of embodiment 5 non-linear pharmacokinetics models

If certain drug administration dosage is 240mg, meet in vivo a compartment model after the intravenous injection, the elimination process meets a meter Man equation, the maximum speed (V that eliminates _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 the reaction chamber dosage is 1mg.

Flow relocity calculation:

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

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

Wherein, x represents central compartment's dose in the body.When dt → 0, dx/dt ≈ Δ x/ Δ t sets up, and launches this formula by forward-difference method, obtains:

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

Wherein, x _iRepresent constantly (t of i _i) dose, the relative medicine concentration c _iAccording to x _iWith V _dRatio obtains.With V _MaxAnd k _mThis formula of numerical value substitution, and substitution drug concentration calculation relational expression can obtain under the different time points over time curve of central compartment's drug concentration; In the Excel worksheet, arrange by data and realize above-mentioned variable (x _iAnd c _i) calculating, computing time gradient (t _I+1-t _i) being made as 0.02h, central compartment's pharmaceutical concentration-time curve is shown in the dotted line among Figure 14 in the resulting body;

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

3. resulting flow speed value is updated to external model concentration and calculates in the stepping type (39), ask and calculate simulated concentration C _i, acquired results is shown in the hollow dots among Figure 14 (ο).

Calculate the ratio of simulated concentration and vivo medicine concentration, acquired results as shown in figure 16, Ratio invariableness is 1, the result shows, blood concentration overlaps fully in the in-vitro simulated concentration that is obtained by recurrence method and the body.

As shown in figure 14, the result shows that also blood concentration overlaps fully in the in-vitro simulated concentration that obtained by recurrence method and the body, the result shows that the hollow dots of simulated concentration has all dropped on the dotted line of expression vivo medicine concentration, pass in time the release rate of drug concentration and accelerate gradually, pass in time continuous increase corresponding (as shown in figure 15) with flow velocity.

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

The comparison of pharmacokinetic parameters setting value in the outer pharmacokinetic parameters estimated value of the non-linear pharmacokinetics model of the quiet notes of table 5. and the body

Annotate 1:V _MaxMaximum speed, the k of eliminating _mMichaelis rate constant (50% maximum dose corresponding to speed of eliminating), V _dApparent volume of distribution;

Annotate the 2:ARD mean relative deviation; The ME average error; The 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 has solved 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 level pharmacokinetics model; Described in-vitro simulated method has reduced external pharmacokinetics simulation effectively to the dependence of pharmacokinetics model structure in the body, expanded external pharmacokinetics model to the scope of pharmacokinetics simulation in the body, external pharmacokinetics/external pharmacokinetics/pharmacodynamic studies of pharmacodynamic studies technical merit, especially antibacterials is significant for improving.

Claims (7)

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

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

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

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

Wherein, F and V _CBe respectively flow velocity and reaction chamber liquid measure, n represent the chamber number of phases (i=1,2,3 ...), A _iAnd k _iThe intercept and the respective rate constant that represent respectively the i phase;

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

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

Wherein, k _eBe concentration descending slope in time, initial concentration c ₀Expression;

Described recurrence method based in the body during pharmacokinetics meta-concentration numbers value the different time points flow velocity is carried out recursion, 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 i moment point; V _CBe the liquid volume in the reaction chamber, be the designated value of doing according to the actual requirements; c _I+1And c _iRepresent that respectively medicine is at t _I+1And t _iBlood concentration in the body constantly, its exact value calculates acquisition according to the compartment model Pharmacokinetic Formula of reality.

2. by in-vitro simulated method claimed in claim 1, it is characterized in that, in the described equation,

For a chamber, two chambers and the quiet notes pharmacokinetics of three chambers model, i bulk concentration c constantly _iUse respectively formula (33)～formula (35) to calculate:

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

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

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

Wherein, the c in the formula (33) ₀And k _eBe respectively initial drug concentration and elimination rate constant, representative distributes and eliminates the phase intercept A in the formula (34) with B, α and β are rate constant separately, A, B in the formula (35) is respectively distribution with R and eliminates mutually, soon phase and eliminate slowly mutually intercept, and corresponding rate constant represents with α, β and γ respectively;

For zero level pharmacokinetics model, i bulk concentration c constantly _iCalculate with formula (41):

c _i＝c ₀-k _et _i (36)

Wherein, c ₀Be initial drug concentration, k _eExpression concentration descending slope in time.

3. by in-vitro simulated method claimed in claim 1, it is characterized in that, the assignment of described flow velocity is continuous changing value form or multistage mean value form.

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

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

6. by purposes claimed in claim 5, it is characterized in that, its application form is to calculate based on the artificial calculating of the Equivalent Form of formula (1)～(5), (37) or software.

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

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