CN103077295B - The in-vitro simulated method of oral administration pharmacokinetic model based on flow rate regulation - Google Patents

Abstract

The invention belongs to external pharmacokinetics/pharmacodynamic studies field, relate to a kind of in-vitro simulated method of oral administration pharmacokinetic model based on flow rate regulation；The method includes equation and recurrence method.The flow velocity of the pharmacokinetic model that the method for the present invention Room, two Room, the linear pharmacokinetics of three-compartment model and absorption after determining device in vitro accurate simulation oral administration or elimination process have nonlinear characteristic sets up scheme；Described in-vitro simulated method considerably simplify external oral pharmacokinetic model equipment, significant for improving the PK/PD investigative technique of the external PK/PD investigative technique level particularly antibacterials of medicine.

Description

The in-vitro simulated method of oral administration pharmacokinetic model based on flow rate regulation

Technical field

The invention belongs to pharmaceutical field, relate to external pharmacokinetics/pharmacodynamics (Pharmacokinetic/ Pharmacodynamic, PK/PD) technology, it is specifically related to the external of a kind of oral administration pharmacokinetic model based on flow rate regulation Analogy method.

Background technology

Prior art discloses medicine dynamic process in vivo and include a chamber, two chambers and three compartment models, with And zero order model and nonlinear model；And intravenous injection, intravenous drip and oral medicine can be further divided into according to administering mode Dynamic model etc. of learning, wherein, Oral administration, owing to having the advantages such as simple and fast, patient dependence are good, becomes medicine the most normal The administering mode seen, therefore, pharmacokinetics after drugs oral administration and pharmacodynamics are for formulating the oral administration side of medicine Case tool has very important significance.

External pharmacokinetics/pharmacodynamics (PK/PD) technology is the most conventional clinical pharmacology investigative technique, and this technology need to be one Set device outside simulates certain medicine pharmacokinetics process in vivo, and then studies the pharmacodynamics of this medicine on the basis of the above Change procedure, i.e. pharmacodynamic studies；During research, can be come by the Internal pharmacokinetics of external model aids drug and pharmacodynamics The rational use of drug scheme of drugs.At present, owing to being limited by model structure and computational methods, external PK/PD model for The model of oral administration is also limited only to one-compartment model, for two Room, three-compartment model and suction after the most common oral administration Receipts or elimination process do not meet the also the most corresponding accurately analogy method of pharmacokinetic model of first order kinetics.

Additionally, due to the effective object of antibacterials is that perch is in the antibacterial of human body so that its drug action can be easy to Ground is simulated in vitro, therefore, and most widely used general in antibacterials pharmacodynamic studies of external PK/PD technology；When Before, the pharmacodynamic study of existing substantial amounts of antibacterials uses above-mentioned technology in the world.

Prior art simulation oral administration one Atrium Model device outside, Primary containers include fluid reservoir, Absorption chamber, reative cell and waste liquid cylinder (as shown in Figure 1)；Fresh medium first pumps into absorption chamber from fluid reservoir by certain flow rate, so After in absorption chamber, by malleation, quantity of fluid such as grade is pumped into reative cell (in reative cell, liquid is mixed) by agitator effect, reaction Room continues through the quantity of fluid such as malleation discharge to waste liquid cylinder.Carry out oral pharmacokinetic in-vitro simulated time, medicine is initially injected suction Receiving room, pastille liquid is pumped to reative cell by absorption chamber, described process simulation drug absorption, and the pastille liquid in reative cell leads to Cross silica gel tube to be discharged to the process simulation medicine of waste liquid cylinder and eliminate process；Flow velocity is the fastest, represents drug absorption in vivo and disappears Except process is the fastest, otherwise then represent that drug absorption in vivo and release rate are the slowest.

Said apparatus needs the parameter determined to include in use: dose (D), absorption chamber liquid volume (V_A), reative cell liquid Body volume (V_C), flow velocity (F)；Wherein, V_CValue be direct designated value, according to the ratio etc. of internal dosage Yu apparent volume of distribution It is same as external dose and the reative cell liquid volume ratio external dose of conversion, it may be assumed that D=F_BA×Dose×V_C/V_d, wherein Dose is Vivo medicine-feeding dosage, F_BARepresent bioavailability, V_dFor medicine apparent volume of distribution in vivo.A described compartment model body Outer simulation, its flow rate F and absorption chamber liquid volume V_AFor steady state value, wherein F is according to medicine supersession rate in vivo and V_CProduct obtains Arrive.

Currently, under normal conditions, medicine process in vivo meets two chambers and three compartment models, therefore, above-mentioned Device is difficult to meet the external accurate simulation to common oral administration pharmacokinetics under existing flow conditions and parameter are arranged, The most accurately aids drug dynamic process in vivo avoids model operability to reduce simultaneously is that above-mentioned technology needs The key issue solved.

Summary of the invention

It is an object of the invention to overcome the defect of prior art and deficiency, it is provided that a kind of oral administration based on flow rate regulation The in-vitro simulated method of pharmacokinetic model；The method be oral disposition based on model equipment as shown in Figure 1 be administered a chamber, two Chamber and the in-vitro simulated flow relocity calculation method of three Atrium Models, the flow velocity obtained is consecutive variations value, so that Obtain the pharmacokinetics process of many compartment models after this device can accurately simulate oral administration.

Specifically, the in-vitro simulated method of the oral administration pharmacokinetic model based on flow rate regulation of the present invention, it is special Levy and be, including following method equation and recurrence method；

(1) equation

Pharmacokinetic model linear for n chamber, is calculated as follows flow rate F:

$\frac{\frac{F}{V_C}{e}^{-\frac{F}{V_C}t}-\frac{F}{V_A}{e}^{-\frac{F}{V_A}t}}{e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t}}=\frac{\underset{i=0}{\overset{n}{\Σ}}{A}_i\·k_i\·e^{-k_{i}t}}{\underset{i=0}{\overset{n}{\Σ}}{A}_i\·e^{-k_{i}t}}---\left(1\right)$

Wherein, n represents the room number of phases (enumerator is i, value 1,2,3 ...), A_iAnd k_iRepresent intercept and the phase of the i-th phase respectively Answer speed constantRepresent absorption phase during i=0, during i >=1, represent that distribution mutually and eliminates phase, V_CFor reative cell liquid Volume, V_AFor absorption chamber liquid volume, its value asks calculation according to following formula:

$V_A=V_C\·e^{T_{\max }\·k_a\·(\frac{V_A}{V_C}-1)}---\left(2\right)$

In above formula, k_aFor absorption rate constant, T_maxFor peak time, its numerical value meets formula (3):

$T_{max}=\frac{1}{k_a}\·ln\frac{k_a\·\underset{i=1}{\overset{n}{\Σ}}{A}_i}{\underset{i=1}{\overset{n}{\Σ}}{A}_i\·k_i\·e^{-k_i\·T_{max}}}---\left(3\right)$

Wherein, A_i、k_iThe same formula (1) with the implication of n.

In the present invention, described formula (1) is transcendental equation formula to formula (3), it is impossible to direct solution, applies Excel Programming evaluation instrument or goal seek instrument in software can realize parameter T successively_max、V_ACalculating with F.

In the equation of the present invention, a described oral compartment model is in-vitro simulated, flow rate F and V_ACalculate as the following formula:

F=k_e·V_C；V_A=k_e·V_C/k_a (4)

Wherein, k_eFor medicine elimination rate constant in vivo.

In the equation of the present invention, simulating outside described oral two chamber model body, flow rate F computing formula meets:

$\frac{\frac{F}{V_C}{e}^{-\frac{F}{V_C}t}-\frac{F}{V_A}{e}^{-\frac{F}{V_A}t}}{e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t}}=\frac{{\mathrm{Lk}}_a{e}^{-k_{a}t}+{\mathrm{M\αe}}^{-\mathrm{\α}t}+{\mathrm{N\βe}}^{-\mathrm{\β}t}}{{\mathrm{Le}}^{-k_{a}t}+{\mathrm{Me}}^{-\mathrm{\α}t}+{\mathrm{Ne}}^{-\mathrm{\β}t}}---\left(5\right)$

Wherein, L, M and N represent and absorb phase intercept, distribution phase intercept and eliminate phase intercept (L+M+N=0)；α and β represents point Cloth phase and elimination phase speed constant.

V is estimated by formula (2)_A, wherein T_maxCalculate according to formula (6):

$T_{max}=\frac{1}{k_a}\·ln\frac{k_a\·(M+N)}{{\mathrm{M\αe}}^{-{\mathrm{\αT}}_{\max }}+{\mathrm{N\βe}}^{-{\mathrm{\βT}}_{max}}}---\left(6\right);$

Described oral three compartment models are in-vitro simulated, and flow rate F computing formula meets:

$\frac{\frac{F}{V_C}{e}^{-\frac{F}{V_C}t}-\frac{F}{V_A}{e}^{-\frac{F}{V_A}t}}{e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t}}=\frac{{\mathrm{Lk}}_a{e}^{-k_{a}t}+{\mathrm{M\αe}}^{-\mathrm{\α}t}+N_1{\mathrm{\β}}_1{e}^{-{\mathrm{\β}}_{1}t}+N_2{\mathrm{\β}}_2{e}^{-{\mathrm{\β}}_{2}t}}{{\mathrm{Le}}^{-k_{a}t}+{\mathrm{Me}}^{-\mathrm{\α}t}+N_1{e}^{-{\mathrm{\β}}_{1}t}+N_2{e}^{-{\mathrm{\β}}_{2}t}}---\left(7\right)$

Wherein, N₁And N₂Represent the fast phase intercept that eliminates and eliminate phase intercept, the same formula of L and M implication (5) with slow, meet L+M+N₁ +N₂=0；β₁And β₂Phase speed constant and slow elimination phase speed constant, k is eliminated for fast_aFormula same with α implication (5)；

V is estimated by formula (2)_A, wherein T_maxCalculate according to formula (8):

$T_{max}=\frac{1}{k_a}\·ln\frac{k_a\·(M+N_1+N_2)}{{\mathrm{M\αe}}^{-{\mathrm{\αT}}_{max}}+N_1{\mathrm{\β}}_1{e}^{-{\mathrm{\β}}_1{T}_{max}}+N_2{\mathrm{\β}}_2{e}^{-{\mathrm{\β}}_2{T}_{max}}}---\left(8\right).$

(2) recurrence method

Described recurrence method is the side that different time points flow velocity carries out recursion based on concentration values m-during Internal pharmacokinetics Method, the i-th moment flow velocity (F_i) calculating formula as follows:

$-\frac{\frac{F_i}{V_C}{e}^{-\frac{F_i}{V_C}{t}_i}-\frac{F_i}{V_A}{e}^{-\frac{F_i}{V_A}{t}_i}}{e^{-\frac{F_i}{V_C}{t}_i}-e^{-\frac{F_i}{V_A}{t}_i}}=(\frac{c_{i+1}}{c_i}-1)\·\frac{1}{t_{i+1}-t_i}---\left(26\right)$

Wherein, c_i+1And c_iRepresent i+1 moment (t_i+1) and the i-th moment (t_i) internal central compartment drug level；V_CAnd V_A The same formula of implication (1), its value calculates according to formula (2) and (3)；Initial time flow velocity is according to k_aWith V_AProduct obtains；

Described formula (26) is transcendental equation, by calling the goal seek in Excel software or programming evaluation work Tool, it is achieved F_iAsk calculation.

The bulk concentration stepping type of a described oral Room pharmacokinetic model is as follows:

$c_i=\frac{k_a\·F_{BA}\·Dose}{V_d\·(k_a-k_e)}(e^{-k_e{t}_i}-e^{-k_a{t}_i})---\left(27\right)$

Wherein, Dose is vivo medicine-feeding dosage, F_BAIt is respectively bioavailability, V_dFor internal apparent volume of distribution；

Described oral two Room and the bulk concentration stepping type of three Room pharmacokinetic model are as follows:

$c_i={\mathrm{Le}}^{-k_a{t}_i}+{\mathrm{Me}}^{-{\mathrm{\αt}}_i}+{\mathrm{Ne}}^{-{\mathrm{\βt}}_i}---\left(28\right)$

$c_i={\mathrm{Le}}^{-k_a{t}_i}+{\mathrm{Me}}^{-{\mathrm{\αt}}_i}+N_1{e}^{-{\mathrm{\β}}_1{t}_i}+N_2{e}^{-{\mathrm{\β}}_2{t}_i}---\left(29\right)$

The most same formula of each pharmacokinetic parameters implication (5) and (7) in formula (28) and (29).t_iThe same formula of implication (26).

When oral pharmacokinetic does not meets linear kinetics feature, as long as its concentration shows as dullness over time First rise and decline afterwards, pharmaceutical concentration-time curve is subdivided into n segment, still can carry out flow relocity calculation with above-mentioned formula (26), Realize the in-vitro simulated of this oral pharmacokinetic.

In the present invention, deducing described equation and recurrence method, it includes step:

(1) equation

Realize external pharmacokinetic model and the accurately simulation of Internal pharmacokinetics curve need to be met following two conditions: be the most external Reative cell medicine initial concentration (C in model₀) and internal central compartment medicine initial concentration (c₀) equal, i.e. C₀=c₀；The most external mould In type, the supersession rate (dC/dt) of reative cell drug level is equal, i.e. with internal central compartment's drug level supersession rate (dc/dt) DC/dt=dc/dt；Therefore, following formula is set up:

$\frac{dC/dt}{C}=\frac{dc/dt}{c}---\left(9\right)$

Wherein, (dC/dt)/C and (dc/dt)/c represents the relative change rate of in vitro and in vivo drug concentration versus time, its Implication and elimination rate constant k in intravenous one-compartment model_eSimilar；For a compartment model, the relative change rate of concentration vs. time Keep constant；For two Room and above compartment model, relative change rate elapses in time and gradually decreases；By internal central compartment medicine Concentration-time equation and vitro reactions room drug concentration-versus-time equation substitute into above formula, can derive various in-vitro simulated situation Under flow relocity calculation formula.

In device as shown in Figure 1, the differential equation that absorption chamber is illustrated with the available formula (10) of dose change in reative cell Group describes:

$\left\{\begin{array}{c}\frac{{\mathrm{dX}}_A}{dt}=-\frac{F}{V_A}{X}_A\\ \frac{{\mathrm{dX}}_C}{dt}=\frac{F}{V_A}{X}_A-\frac{F}{V_C}{X}_C\end{array}\right.---\left(10\right)$

Wherein, X_AAnd X_CInitial value be respectively dose (D) and 0；Reative cell drug level C is according to X_CWith V_CRatio be worth to；

Above-mentioned differential equation group obtains the calculating formula of reative cell drug level through Induction Solved by Laplace Transformation solution:

$C=\frac{D}{V_C-V_A}(e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t})---\left(11\right)$

Above-mentioned (11) formula derivation can be obtained model reaction indoor drug level relative change rate in time:

$\frac{dC/dt}{C}=-\frac{\frac{F}{V_C}{e}^{-\frac{F}{V_C}t}-\frac{F}{V_A}{e}^{-\frac{F}{V_A}t}}{e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t}}---\left(12\right);$

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

The densitometer formula of oral one-compartment model is:

$c=\frac{k_a\·F_{BA}\·Dose}{V_d\·(k_a-k_e)}(e^{-k_{e}t}-e^{-k_{a}t})---\left(13\right)$

Drug level relative change rate's expression formula in time is obtained by derivation:

$\frac{dc/dt}{c}=-\frac{k_e{e}^{-k_{e}t}-k_a{e}^{-k_{a}t}}{e^{-k_{e}t}-e^{-k_{a}t}}---\left(14\right)$

Make formula (14) equal with formula (12), then have:

$\frac{\frac{F}{V_C}{e}^{-\frac{F}{V_C}t}-\frac{F}{V_A}{e}^{-\frac{F}{V_A}t}}{e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t}}=\frac{k_e{e}^{-k_{e}t}-k_a{e}^{-k_{a}t}}{e^{-k_{e}t}-e^{-k_{a}t}}---\left(15\right)$

From above formula, to keep equal sign the right and left equal, following formula need to be met:

$\frac{F}{V_C}=k_e;\frac{F}{V_A}=k_a---\left(16\right)$

Above-mentioned formula is made deformation process, available formula (4)；Can simulate in the device according to above-mentioned formula An oral compartment model pharmacokinetics process；

Additionally, for an oral Room pharmacokinetic model, following formula is set up:

$T_{max}=\frac{ln(k_a/k_e)}{k_a-k_e}---\left(17\right)$

Wherein, T_maxRepresent drug level peak time；

Formula (16) is substituted into above formula arranging, obtains external model has relationship below:

$ln\left(\frac{V_A}{V_C}\right)=T_{max}\·k_a\·(\frac{V_A}{V_C}-1)---\left(18\right)$

Above formula is made deformation further, available formula (2)；By T_max、k_aAnd V_CSubstitute into this formula, then can obtain V_ANumerical value, Realized by the goal seek in Excel software or programming evaluation instrument；Under oral two chambers and three compartment model situations, Close see oral two chambers and the absorption phase of three compartment models and initial elimination as an oral compartment model, then can be according to Described (2) formula approximation seeks V under oral two chambers of calculation and three compartment model situations_ANumerical value；

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

The densitometer formula of oral two-compartment model is:

$c={\mathrm{Le}}^{-k_{a}t}+{\mathrm{Me}}^{-\mathrm{\α}t}+{\mathrm{Ne}}^{-\mathrm{\β}t}---\left(19\right)$

Drug level relative change rate's expression formula in time is obtained by derivation:

$\frac{dc/dt}{c}=-\frac{{\mathrm{Lk}}_a+e^{-k_{a}t}+{\mathrm{M\αe}}^{-\mathrm{\α}t}+{\mathrm{N\βe}}^{-\mathrm{\β}t}}{{\mathrm{Le}}^{-k_{a}t}+{\mathrm{Me}}^{-\mathrm{\α}t}+{\mathrm{Ne}}^{-\mathrm{\β}t}}---\left(20\right)$

Make formula (20) equal with formula (12), available formula (5)；

Described V_ASeek calculation process: when time t value T_maxTime, meet dc/dt=0, formula (19) is substituted into:

${\mathrm{Lk}}_a{e}^{-k_a{T}_{\max }}+{\mathrm{M\αe}}^{-{\mathrm{\αT}}_{max}}+{\mathrm{N\βe}}^{-{\mathrm{\βT}}_{max}}=0---\left(22\right)$

L=-(M+N) substituted into above formula and arranges, obtaining formula (6)；By M, N, k_a, α and β substitute into this formula, pass through Call the goal seek instrument in Excel software or programming evaluation instrument, seek calculation T_max；Then by T_max、k_aAnd V_CSubstitute into formula (2), thus obtain V_A；Finally, by V_A、V_CSubstitute into formula (5) with Internal pharmacokinetics parameter, again call the list in Excel software Variable solves instrument or programming evaluation instrument, available F continuous value in time, thus simulates outlet in the device Take two Atrium Models；

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

The densitometer formula of oral two-compartment model is:

$c={\mathrm{Le}}^{-k_{a}t}+{\mathrm{Me}}^{-\mathrm{\α}t}+N_1{e}^{-{\mathrm{\β}}_{1}t}+N_2{e}^{-{\mathrm{\β}}_{2}t}---\left(23\right)$

Drug level relative change rate's expression formula in time is obtained by derivation:

$\frac{dc/dt}{c}=-\frac{{\mathrm{Lk}}_a{e}^{-k_{a}t}+{\mathrm{M\αe}}^{-\mathrm{\α}t}+N_1{\mathrm{\β}}_1{e}^{-{\mathrm{\β}}_{1}t}+N_2{\mathrm{\β}}_2{e}^{-{\mathrm{\β}}_{2}t}}{{\mathrm{Le}}^{-k_{a}t}+{\mathrm{Me}}^{-\mathrm{\α}t}+N_1{e}^{-{\mathrm{\β}}_{1}t}+N_2{e}^{-{\mathrm{\β}}_{2}t}}---\left(24\right)$

Make formula (24) equal with formula (12), obtain formula (7)；

Described V_ASeek calculation process: when time t value T_maxTime, meet dc/dt=0, formula (23) is substituted into:

${\mathrm{Lk}}_a{e}^{-k_a{T}_{max}}+{\mathrm{M\αe}}^{-{\mathrm{\αT}}_{max}}+N_1{\mathrm{\β}}_1{e}^{-{\mathrm{\β}}_1{T}_{max}}+N_2{\mathrm{\β}}_2{e}^{-{\mathrm{\β}}_2{T}_{max}}=0---\left(25\right)$

By L=-(M+N₁+N₂) substitute into above formula and arrange, obtain formula (8)；By M, N₁、N₂、k_a、α、β₁And β₂Substitute into This formula, by calling the goal seek instrument in Excel software or programming evaluation instrument, seeks calculation T_max；Then by T_max、k_aWith V_CSubstitute into formula (2), obtain V_A；Finally, by V_A、V_CSubstitute into formula (7) with Internal pharmacokinetics parameter, again call Excel software In goal seek instrument or programming evaluation instrument, obtain F continuous value in time, thus simulate in the device Go out oral three Atrium Models.

(2) recurrence method

When vitro reactions room drug level (C) is equal with internal central compartment's drug level (c), vitro reactions room medicine simultaneously Concentration changes with time rate (dC/dt) and internal central compartment drug level change over rate (dc/dt) identical time, body can be realized Interior pharmacokinetics the most in-vitro simulated, the most above-mentioned formula (9) is set up；

For drug concentrations in vitro relative change rate [(dC/dt)/C], formula (11) formula is substituted into, and took for the i-th moment (t_i) result of calculation, obtain:

$\frac{dC/dt}{C}{|}_{t=t_i}=-\frac{\frac{F_i}{V_C}{e}^{-\frac{F_i}{V_C}{t}_i}-\frac{F_i}{V_A}{e}^{-\frac{F_i}{V_A}{t}_i}}{e^{-\frac{F_i}{V_C}{t}_i}-e^{-\frac{F_i}{V_A}{t}_i}}---\left(30\right)$

Described vivo medicine concentration relative change rate [(dc/dt)/c], when dt → 0, dc/dt ≈ Δ c/ Δ t sets up, will This formula is launched by forward-difference method, obtains:

$\frac{dc/dt}{c}{|}_{dt\→0}=(\frac{c_{i+1}}{c_i}-1)\·\frac{1}{t_{i+1}-t_i}---\left(31\right)$

Make item on the right of above-mentioned two formulas equal, obtain formula (26)；

Wherein, V_AComputational methods and above-mentioned equation in V_AComputational methods are consistent；By the i-th moment and i+1 moment Central compartment's drug level and time substitute into above formula, can calculate the flow velocity (F in the i-th moment_i), thus obtain flow velocity and change over Dynamic adjustment curve.

In the present invention, described in-vitro simulated method, finally the assignment to flow velocity can be that consecutive variations value form is alternatively 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 oral administration pharmacokinetic model based on flow rate regulation of the present invention, can be used for external medicine and moves / pharmacodynamics model technology and relate to other technical field of similar principles, its application form is based on above-mentioned formula or identical The artificial of the Equivalent Form of reasoning thought calculates or computed in software.

The in-vitro simulated method of the oral administration pharmacokinetic model based on flow rate regulation of the present invention, it is adaptable to determine at body Outer device is accurately simulated a Room, two Room, the linear pharmacokinetics of three-compartment model and the absorption after oral administration or the process of elimination tool The flow velocity having the pharmacokinetic model of nonlinear characteristic sets up scheme；Described in-vitro simulated method considerably simplify body Outer oral pharmacokinetic model equipment, for improving the PK/PD of the external PK/PD investigative technique level particularly antibacterials of medicine Investigative technique is significant.

In order to make it easy to understand, below by the drawings and specific embodiments oral administration based on flow rate regulation to the present invention The in-vitro simulated method of pharmacokinetic model is described in detail.It is important to note that specific embodiments and the drawings are only In order to illustrate, it is clear that those skilled in the art can carry out various correction or change according to illustrating herein to the present invention, these Within the scope of correction and change also will include this patent in.

Accompanying drawing explanation

Fig. 1 is the structural representation of the in-vitro simulated device of the oral administration pharmacokinetic model in the present invention, wherein,

V_AAnd V_CIt is respectively absorption chamber liquid volume and reative cell liquid volume, X_AAnd X_CRepresent respective dose, F respectively Represent flow velocity.

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

A: constant coordinate diagram；B: semilog plot；

Conc is for 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 oral pharmacokinetic one-compartment model in-vitro simulated flow relocity calculation result of the present invention, its In, F-Equ is equation gained flow velocity, and F-Rec is recurrence method gained flow velocity.

Fig. 4 shows the in-vitro simulated ratio Analysis of oral pharmacokinetic one-compartment 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 Recurrence method gained simulated concentration and the ratio calculating concentration.

Fig. 5 be the present invention oral pharmacokinetic two chamber model body outside simulate design sketch, wherein,

A: constant coordinate diagram；B: semilog plot.

Fig. 6 shows the contrast situation of the oral pharmacokinetic two-compartment model in-vitro simulated flow relocity calculation result of the present invention.

Fig. 7 shows the in-vitro simulated ratio Analysis of oral pharmacokinetic two-compartment model of the present invention.

Fig. 8 is the oral pharmacokinetic three in-vitro simulated design sketch of compartment model of the present invention, wherein,

A: constant coordinate diagram；B: semilog plot.

Fig. 9 shows the contrast situation of the oral pharmacokinetic three-compartment model in-vitro simulated flow relocity calculation result of the present invention.

Figure 10 shows the in-vitro simulated ratio Analysis of oral pharmacokinetic three-compartment model of the present invention.

Figure 11 is the in-vitro simulated design sketch of oral non-linear pharmacokinetic model of the present invention, wherein,

A: constant coordinate diagram, B: semilog plot.

Figure 12 shows the oral non-linear pharmacokinetic model in-vitro simulated flow relocity calculation result of the present invention.

Figure 13 shows the in-vitro simulated ratio Analysis of oral non-linear pharmacokinetic model of the present invention.

Figure 14 is that the flow velocity that regulates of the present invention realizes the in-vitro simulated figure of oral pharmacokinetic.

In above-mentioned figure, same Fig. 2 of Conc, C-Equ and C-Rec implication of Fig. 5, Fig. 8, Figure 11.In Fig. 6, Fig. 9, F-Equ and Same Fig. 3 of implication of F-Rec.In Fig. 7, Figure 10 and Figure 13, the same Fig. 4 of R, R-Equ and R-Rec implication.

Detailed description of the invention

Embodiment 1 is administered orally the flow relocity calculation that one-compartment model is in-vitro simulated

If meeting a compartment model in vivo after certain medicine is oral, dosage (Dose) is 250mg, and internal apparent distribution is held Long-pending (V_d/F_BA) it is 63.9L, absorption rate constant (k_a) and elimination rate constant (k_e) it is respectively 0.429h^-1And 0.076h^-1.Body Outer reative cell liquid volume (V_C) it is set to 0.25L.

(1) calculation procedure:

1) internal ideal medicament concentration is calculated according to formula (13), as shown in dashed line in figure 2；

2) it is equal to treated in vitro amount and reative cell liquid capacity ratio according to dosage with internal apparent volume of distribution ratio Value principle, conversion treated in vitro amount (D), it may be assumed that D=Dose × F_BA×V_C/V_d, obtaining D is 0.978mg；

3) according to formula (4) V_A=k_e·V_C/k_aCalculate absorption chamber liquid capacity, obtain V_AFor 0.0443L；

4) calculating of flow rate F:

1. equation: according to formula (4) F=V_C·k_eCalculating F value, obtaining F is 0.019L/h；

2. recurrence method: make iterative computation according to formula (26), it is thus achieved that F value；

Flow rate versus time curve obtained by above two method as it is shown on figure 3, described equation gained flow velocity be constant directly Line, the recurrence method gained flow velocity stage in early days slightly fluctuates around central value (0.019L/h), the flow velocity of later stage and formula Method institute flow speed value overlaps.

(2) simulation effect analysis

1) calculating of in-vitro simulated concentration: using forward difference stepping type to calculate, respective formula is formula (32), during calculating Between gradient be set to 0.02h, respectively equation and recurrence method gained F value are substituted into, the in-vitro simulated concentration-time curve obtained Respectively as shown in the crunode (×××) in Fig. 2 and hollow dots (0 0 0), described equation and recurrence method gained are in-vitro simulated Concentration is completely superposed with internal central compartment drug level；

$\left\{\begin{array}{c}{X}_{C,i+1}=X_{C,i}\[1-\frac{F_i}{V_C}\left(t_{i+1}-t_i\right)\]+\frac{F_i}{V_A}{X}_{A,t}\left(t_{i+1}-t_i\right)\\ X_{A,i+1}=X_{A,i}\[1-\frac{F_i}{V_A}\left(T_{i+1}-t_i\right)\]\end{array}\right.---\left(32\right);$

2) external pharmacokinetics model accuracy and Precision Analyze: calculate the above two in-vitro simulated concentration of method gained with The ratio of internal central compartment drug level, draw ratio-time graph, result as shown in Figure 4, described equation and recurrence method institute Different, later stage must be had in the simulated concentration ratio stage in early days to tend to overlapping, and maximum deviation amplitude falls at ± 0.5% model In enclosing, result shows, the two method achieves the in-vitro simulated of oral pharmacokinetic one-compartment model the most well.

External drug simulated concentration v. time data is made model estimate, ask and calculate oral one-compartment model pharmacokinetic parameters, and with The pharmacokinetic parameters value set is made comparisons, and calculates mean relative deviation (ARD), mean error (ME) and root-mean-square error (RMSE), result is as shown in table 1, and the parameter value that described equation and recurrence method gained simulated concentration-time data obtain relatively connects Closely, wherein, the former parameters obtained value is the most identical with setting value, and ARD is less than 0.2%, ME and RMSE is less than 0.05%；Knot Fruit shows, the two method is used equally to the in-vitro simulated of oral pharmacokinetic one-compartment model.

Table 1. is administered orally the comparison of one-compartment model external pharmacokinetic parameters estimated value and Internal pharmacokinetics pre-set parameter

Note 1:k_eElimination rate constant, V_d/F_BAApparent volume of distribution and bioavailability ratio, k_aAbsorption rate constant；

Note 2:ARD mean relative deviation；ME mean 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' it is respectively setting value and estimated value, m data amount check.

Embodiment 2 is administered orally the flow relocity calculation that two-compartment model is in-vitro simulated

If meeting two compartment models in vivo after certain medicine is oral, dosage (Dose) is 250mg, and pharmacokinetic parameters L (is inhaled Receive phase intercept), M (distribution phase intercept) and N (eliminating phase intercept) respectively-4.59,3.55 and 1.03mg/L, absorption rate constant k_aFor 2.38h^-1, distribution phase speed constant (α) and elimination phase speed constant (β) are respectively 0.429 and 0.0761h^-1；Vitro reactions Room liquid capacity (V_C) it is set to 0.25L.

(1) calculation procedure

1) according to formula (19)Internal pharmacokinetics parameter is substituted into, calculates internal central authorities Room drug level, mapping result is as shown in broken line in fig. 5；

2) internal apparent volume of distribution (V is calculated_d/F_BA), corresponding computing formula is shown in (33), obtains V_d/F_BAEqual to 63.9L； Then convert external dose (D), and formula is: D=Dose × F_BA×V_C/V_d, obtaining D is 0.979mg；

$\frac{V_d}{F_{BA}}=\frac{x_0\·k_a(k_{21}-k_a)}{L(\mathrm{\α}-k_a)(\mathrm{\β}-k_a)}---\left(33\right)$

Wherein:

$k_{21}=\frac{k_a-\frac{L(k_a-\mathrm{\β})}{M(\mathrm{\β}-\mathrm{\α})}\·\mathrm{\α}}{1-\frac{L(k_a-\mathrm{\β})}{M(\mathrm{\β}-\mathrm{\α})}}---\left(34\right);$

3) T is calculated according to formula (6)_maxValue, obtains T_max=0.96h；Then V is calculated according to formula (2)_AValue, uses Excel Goal seek instrument in software realizes calculating, and obtains V_A=0.035L；

4) being respectively adopted equation and recurrence method calculates flow rate F, formula used is respectively formula (5) and formula (26), uses Excel Programming evaluation instrument in software realizes corresponding calculating, and as shown in Figure 6, F value versus time curve is approximately acquired results Reverse S type curve, is generally in plateau after 0-1h and 15h after administration, interlude descending grade is the most obvious；

In described equation and recurrence method gained flow speed value time started section upon administration, (0-1h) has slight extent Difference, later stage result of calculation is completely superposed.

(2) simulation effect analysis

1) calculating of in-vitro simulated concentration: F value be updated in concentration forward difference stepping type (formula (32)), calculates body Outer simulation concentration C (X_C,i+1With V_CRatio), dosing interval is set to 0.02h, obtained simulated concentration-time graph such as Fig. 5 Shown in, simulated concentration curve essentially coincides with vivo medicine concentration curve；

2) external pharmacokinetics model accuracy and Precision Analyze: calculate in-vitro simulated concentration dense with internal central compartment medicine The ratio of degree, draws ratio-time diagram, as it is shown in fig. 7, described equation and recurrence method gained simulated concentration ratio result have one Determining difference, the former is less than the latter with the difference of vivo medicine concentration；Result shows, the outer analogue value of described equation resultant bulk and body The deviation of interior drug level falls in the range of ± 3%, and the outer analogue value of recurrence method resultant bulk is big with the deviation of vivo medicine concentration Cause in the range of ± 5%.

According to simulated concentration-dynamic parameter of learning of the oral two chamber model drug of time data estimation, and make to compare with setup parameter value Relatively, calculating ARD, ME and RMSE, for weighing accuracy and the elaboration of the simulation of external pharmacokinetics, result is as shown in table 2, described The pharmacokinetic parameters tried to achieve by the in-vitro simulated concentration of equation gained is the most identical with setting value, and root-mean-square error RMSE is less than 0.1.With setting value relatively, wherein gap is relative for the pharmacokinetic parameters numerical value tried to achieve by the in-vitro simulated concentration of recurrence method gained It is significantly k_aAnd N, relative deviation is respectively 22.8% and-8.7%, overall ME and RMSE value be respectively-0.087 and 0.258, the least.

Table 2. is administered orally the comparison of two-compartment model external pharmacokinetic parameters estimated value and Internal pharmacokinetics pre-set parameter

Note 1:L absorbs phase intercept, k_aAbsorption rate constant, M is distributed phase intercept, and α is distributed phase speed constant, and N eliminates and cuts mutually Away from, β eliminates phase speed constant；

Note 2:ARD, ME and RMSE computational methods are with table 1.

Embodiment 3 is administered orally the flow relocity calculation that three-compartment model is in-vitro simulated

If pharmacokinetics process after certain medicine is oral in vivo meets three chamber linear models, dosage (Dose) is 250mg.Absorb phase intercept (L) and absorption rate constant (k_a) it is respectively-5.08mg/L and 2.38h^-1, distribution phase intercept (M) and Distribution rate constant (α) is respectively 3.55mg/L and 0.429h^-1, fast elimination phase intercept (N₁) eliminate phase intercept (N with slow₂) respectively It is 1.03 and 0.50mg/L, corresponding elimination rate constant β₁And β₂It is respectively 0.096 and 0.016h^-1.External pharmacokinetics device Reative cell liquid capacity (V_C) it is set to 0.25L.

(1) calculation procedure

1) according to formula (23)Calculating vivo medicine concentration, acquired results is such as Shown in dotted line in Fig. 8；

2) medicine apparent volume of distribution (V in vivo is calculated_d/F_BA), corresponding computing formula is shown in formula (38), obtains V_d/F_BA For 56.88L；Then, according to this formula conversion initial dose in Absorption in vitro room (D): D=Dose × F_BA×V_C/V_d, obtaining D is 1.099mg；

$\frac{V_d}{F_{BA}}=\frac{k_a\·Dose}{L}\·\frac{\left(k_{21}-k_a\right)\left(k_{31}-k_a\right)}{\left(\mathrm{\α}-k_a\right)\left({\mathrm{\β}}_1-k_a\right)\left({\mathrm{\β}}_2-k_a\right)}---\left(35\right)$

Wherein, k₂₁And k₃₁Calculate according to following formula, Excel software can pass through goal seek or programming evaluation instrument Realize；

$k_{21}=\mathrm{\α}+\frac{M}{N_1}\·\frac{({\mathrm{\β}}_1-\mathrm{\α})({\mathrm{\β}}_2-\mathrm{\α})(k_a-\mathrm{\α})(k_{21}-{\mathrm{\β}}_1)(k_{31}-{\mathrm{\β}}_1)}{(k_{31}-\mathrm{\α})(\mathrm{\α}-{\mathrm{\β}}_1)({\mathrm{\β}}_2-{\mathrm{\β}}_1)(k_a-{\mathrm{\β}}_1)}---\left(36\right)$

$k_{31}=\mathrm{\α}+\frac{M}{N_2}\·\frac{({\mathrm{\β}}_1-\mathrm{\α})({\mathrm{\β}}_2-\mathrm{\α})(k_a-\mathrm{\α})(k_{21}-{\mathrm{\β}}_2)(k_{31}-{\mathrm{\β}}_2)}{(k_{21}-\mathrm{\α})(\mathrm{\α}-{\mathrm{\β}}_2)({\mathrm{\β}}_1-{\mathrm{\β}}_2)(k_a-{\mathrm{\β}}_2)}---\left(37\right);$

3) seek calculation peak time according to formula (8), obtain T_maxValue is 1.014h；Then calculate Absorption in vitro room liquid to hold Long-pending (V_A), formula used is formula (2), obtains V_AFor 0.0299L；The calculating of above-mentioned two parameter is all asked with the planning of Excel software Solution instrument realizes；

4) being respectively adopted equation and recurrence method calculates flow rate F, formula used is respectively formula (7) and formula (26), uses Excel Programming evaluation instrument in software realizes calculating, and acquired results is respectively such as the crunode (×××) in Fig. 9 and hollow dots (0 0 Zero), shown in, described equation is the most identical with recurrence method gained flow speed value, at incipient stage (in 0-1h) recurrence method gained flow velocity Value slightly above equation, the flow relocity calculation result of both subsequent period of time essentially coincides.

(2) simulation effect analysis

1) calculating of in-vitro simulated concentration: F value be updated in concentration forward difference stepping type (see formula (32)), calculates In-vitro simulated concentration C (X_C,i+1With V_CRatio), dosing interval is set to 0.02h, obtained simulated concentration-time graph as figure Shown in crunode (×××) in 8 and hollow dots (0 0 0), equation and the in-vitro simulated concentration of recurrence method gained with internal in Room, centre drug level is the most close, is rising the phase stage, and recurrence method gained drug level is slightly above equation gained drug level； In the lowering of concentration stage, the two method resultant bulk extracellular concentration all has the tendency less than vivo medicine concentration；Result shows, on State two kinds of method resultant bulk extracellular concentrations and be still the most parallel with the variation tendency of bulk concentration；

2) external pharmacokinetics model accuracy and Precision Analyze: calculate in-vitro simulated concentration dense with internal central compartment medicine The ratio of degree, draws ratio-time diagram, and as shown in Figure 10, described equation concentration in-vitro simulated with recurrence method gained is with internal The ratio of drug level is close to 1, and fluctuating margin is in the range of ± 10%；In the range of 0-1h, above two method resultant bulk Outer simulated concentration is slightly above vivo medicine concentration, and in the time range after 2h, the in-vitro simulated concentration of above two method gained Slightly below vivo medicine concentration, wherein, recurrence method gained simulation ratio deviation amplitude is higher than equation；Result shows, described public affairs The concentration of analog average of relatives value of formula method and recurrence method is respectively 0.977 and 0.963, and average deviation's amplitude of concentration of analog is all controlled System is in the range of ± 5%.

According to simulated concentration-oral three compartment model pharmacokinetic parameters of time data estimation, and make to compare with setup parameter value Relatively, calculating ARD, ME and RMSE, for weighing accuracy and the elaboration of the simulation of external pharmacokinetics, result is as shown in table 3, described Equation and recurrence method parameters obtained estimated value are totally closer to setting value.Described equation parameters obtained reflection medicine eliminates Parameter such as β₁、N₂And β₂Estimated value and setting value have certain gap, average deviation's amplitude to reach 46%；For the latter, parameter Estimated value and setting value deviation amplitude are significantly k_a、N₁And β₂Etc. parameter, average deviation's amplitude is 27.2%.

Result shows, mean error (ME) and the root-mean-square error (RMSE) of described equation and recurrence method are the most relatively low, These two kinds of methods are used equally to the flow relocity calculation of oral three-compartment model external pharmacokinetics simulation.

Table 3. is administered orally the comparison of three-compartment model external pharmacokinetic parameters estimated value and Internal pharmacokinetics pre-set parameter

Note 1:L absorbs phase intercept, k_aAbsorption rate constant, M is distributed phase intercept, and α is distributed phase speed constant, N₁And N₂For soon Eliminate phase intercept and slow elimination phase intercept, β₁And β₂For respective rate constant；

Note 2:ARD, ME and RMSE computational methods are with table 1.

Embodiment 4 is administered orally the flow relocity calculation that non-linear pharmacokinetic model is in-vitro simulated

If certain medicine dosage (Dose) is 250mg, oral after process in vivo can describe with a compartment model, its suction Receipts process meets first order kinetics, absorption rate constant k_aFor 0.5h^-1；The elimination process of medicine meets a meter Man equation, maximum Supersession rate V_maxFor 10mg/h, Michaelis rate constants k_m(characterize medicine corresponding when supersession rate is 50% maximum supersession rate Amount) it is 5mg, apparent volume of distribution V_d/F_BAFor 60L.

The present embodiment by flow relocity calculation realize that this non-linear pharmacokinetics is administered orally in a Room experimental provision in vitro accurate Simulation, reative cell liquid capacity (V_C) it is set to 0.25L.

(1) calculation procedure

1) according to the Internal pharmacokinetics process of this medicine, the dose as shown in formula (38)-time diffusion equation can be listed:

$\frac{{\mathrm{dx}}_a}{dt}=-k_a{x}_a;\frac{{\mathrm{dx}}_c}{dt}=k_a{x}_a-\frac{V_{max}{x}_c}{k_m+x_c}---\left(38\right)$

Wherein, x_aAnd x_cBeing respectively absorption chamber and central compartment's dose, initial value is respectively Dose and 0；Described central compartment medicine is dense Degree c is according to x_c/V_dObtain；When dt → 0, dx/dt ≈ Δ x/ Δ t sets up, and is rewritten by forward-difference method by above formula and carries out whole Reason, available:

$\left\{\begin{array}{c}{x}_{a,i+1}=x_{a,i}\·\[1-k_a(t_{i+1}-t_i)\]\\ x_{c,i+1}=k_a\·x_{a,i}\·(t_{i+1}-t_i)+x_{c,i}\·\[1-\frac{V_{max}(t_{i+1}-t_i)}{k_m+x_{c,i}}\]\end{array}\right.---\left(39\right)$

Wherein, x_a,i+1And x_a,iRepresent i+1 moment (t_i+1) and the i-th moment (t_i) absorption chamber dose, x_c,i+1And x_c,iTable Show central compartment's dose in i+1 moment and the i-th moment；By x_c,iDivided by V_dThe drug level c in available i-th moment_i；According to above-mentioned Stepping type carries out data assignment in Excel worksheet, calculates the x of the point of each time successively_a、x_cAnd c_i, calculate time gradient (t_i+1-t_i) it is set to 0.02h, obtain central compartment's pharmaceutical concentration-time curve, result is as shown in the dotted line in Figure 11；

2) in the concentration v. time data table of arrangement, find the time point that peak concentration is corresponding, obtain T_maxFor 5.08h；According to Formula (2) calculates absorption chamber liquid capacity (V_A), obtain V_AFor 0.0256L；

According to this formula conversion initial dose in Absorption in vitro room (D): D=Dose × F_BA×V_C/V_d, obtaining D is 1.042mg；

3) using recurrence method to calculate flow rate F, formula used is formula (26), real with the programming evaluation instrument in Excel software Calculating the most accordingly, as shown in figure 12, flow velocity is kept low acquired results in the incipient stage, elapses over time, flow velocity It is gradually increasing, and the speed increased is increasingly faster, reduces at end with concentration-time curve in the semilog plot of Figure 11 B Speed is accelerated corresponding.(the present embodiment is the pharmacokinetic model of nonlinear characteristic, there is no the formula calculating flow rate F).

(2) simulation effect analysis

1) calculating of in-vitro simulated concentration: flow rate F value is updated in concentration forward difference stepping type (see formula (32)), Calculate in-vitro simulated concentration C (X_C,i+1With V_CRatio), dosing interval is still 0.02h, obtained simulated concentration-time graph As shown in the hollow dots (0 0 0) in Figure 11, simulated concentration is more parallel with vivo medicine concentration trend over time, knot Fruit shows, in-vitro simulated concentration is higher than vivo medicine concentration, second half section simulated concentration and vivo medicine concentration in the first half section time The most identical, population mean deviation is about 10%；

2) external pharmacokinetics model accuracy and Precision Analyze: calculate in-vitro simulated concentration C and internal central compartment medicine The ratio (R-Rec) of concentration c, draw ratio-time diagram, as shown in figure 13, within the first half section time (0-4h), simulated concentration with The ratio calculating concentration is higher, elapses over time, and concentration proportion reduces rapidly, protects in latter half (after 5h) always Hold in the state close to baseline；Result shows, recurrence method the drug concentrations in vitro simulation error produced is primarily generated at first half Section.

According to simulated concentration-oral non-linear pharmacokinetic model parameter of time data estimation, and make to compare with setup parameter value Relatively, calculating ARD, ME and RMSE, for weighing accuracy and the elaboration of the simulation of external pharmacokinetics, result is as shown in table 4, is estimating In four pharmacokinetic parameters calculated, simulation pharmacokinetic data available the k obtained_aValue is higher compared with setting value, and gap amplitude is 32.9%, remaining parameter estimation value is slightly below setting value, and deviation amplitude is 2%.

Result shows, ME and RMSE numerical value, still in reduced levels, still can preferably realize according to recurrence method regulation flow velocity Non-linear pharmacokinetics in-vitro simulated.

Table 4. is administered orally non-linear pharmacokinetic model external model parameter estimation value and the ratio of Internal pharmacokinetics pre-set parameter Relatively

Note 1:k_aAbsorption rate constant, V_maxMaximum supersession rate, k_m(50% maximum supersession rate is corresponding for Michaelis speed constant Dose), V_d/F_BAApparent volume of distribution；

Note 2:ARD, ME and RMSE computational methods are with table 1.

The result of above-described embodiment shows, the external mould of the oral administration pharmacokinetic model based on flow rate regulation of the present invention Plan method, it is adaptable to determine in device in vitro the Room after accurate simulation oral administration, two Room, the linear pharmacokinetics of three-compartment model And absorb or elimination process have nonlinear characteristic pharmacokinetic model flow velocity set up scheme；Described in-vitro simulated method Considerably simplify external oral pharmacokinetic model equipment, for improving the external PK/PD investigative technique level of medicine The particularly PK/PD investigative technique of antibacterials is significant.

Claims (7)

1. the in-vitro simulated method of an oral administration pharmacokinetic model based on flow rate regulation, it is characterised in that comprising:

Use equation and recurrence method；

In described equation, pharmacokinetic model linear for n chamber, the computing formula of flow rate F is as follows:

$\frac{\frac{F}{V_C}{e}^{-\frac{F}{V_C}t}-\frac{F}{V_A}{e}^{-\frac{F}{V_A}t}}{e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t}}=\frac{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{A}_i\·k_i\·e^{-k_{i}t}}{\underset{i=0}{\overset{n}{\mathrm{\Σ}}}{A}_i\·e^{-k_{i}t}}---\left(1\right)$

Wherein, n represents the room number of phases, i value 1,2,3 ...；A_iRepresent the i-th phase intercept, meetIt is zero；k_iRepresent the i-th phase speed Constant, V_CFor reative cell liquid volume, V_AFor absorption chamber liquid volume；E and t is respectively natural constant and time；

Described recurrence method is method different time points flow velocity being carried out recursion based on concentration values m-during Internal pharmacokinetics, I-th moment flow rate F_iCalculating formula as follows:

$-\frac{\frac{F_i}{V_C}{e}^{-\frac{F_i}{V_C}{t}_i}-\frac{F_i}{V_A}{e}^{-\frac{F_i}{V_A}{t}_i}}{e^{-\frac{F_i}{V_C}{t}_i}-e^{-\frac{F_i}{V_A}{t}_i}}=(\frac{c_{i+1}}{c_i}-1)\·\frac{1}{t_{i+1}-t_i}---\left(26\right)$

Wherein, c_i+1And c_iRepresent i+1 moment t_i+1With the i-th moment t_iInternal central compartment drug level；V_CAnd V_AImplication is with public Formula (1), its value calculates according to formula (2) and (3)；Initial time flow velocity is according to k_aWith V_AProduct obtains；

In described equation and recurrence method, V_AComputational methods are shown in formula (2), T_maxComputational methods are shown in formula (3):

$V_A=V_C\·e^{T_{\max }\·k_a\·\left(\frac{V_A}{V_C}-1\right)}---\left(2\right)$

$T_{max}=\frac{1}{k_a}\·\ln \frac{k_a\·\underset{i=1}{\overset{n}{\Σ}}{A}_i}{\underset{i=1}{\overset{n}{\Σ}}{A}_i\·k_i\·e^{-k_i\·T_{\max }}}---\left(3\right)$

Wherein, k_aFor absorption rate constant, T_maxFor peak time.A_i、k_i, the same formula of n and e implication (1).

2. the in-vitro simulated method as described in claim 1, it is characterised in that in described equation,

An oral compartment model is in-vitro simulated, flow rate F and absorption chamber liquid volume V_AComputing formula is as follows:

F=k_e·V_C；V_A=k_e·V_C/k_a (4)

Wherein, k_eFor elimination rate constant, k_aThe same formula of implication (3)；

Simulating outside oral two chamber model body, flow rate F computing formula meets:

$\frac{\frac{F}{V_C}{e}^{-\frac{F}{V_C}t}-\frac{F}{V_A}{e}^{-\frac{F}{V_A}t}}{e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t}}=\frac{{\mathrm{Lk}}_a{e}^{-k_{a}t}+{\mathrm{M\αe}}^{-\mathrm{\α}t}+{\mathrm{N\βe}}^{-\mathrm{\β}t}}{{\mathrm{Le}}^{-k_{a}t}+{\mathrm{Me}}^{-\mathrm{\α}t}+{\mathrm{Ne}}^{-\mathrm{\β}t}}---\left(5\right)$

Wherein, L, M and N represent and absorb phase intercept, distribution phase intercept and eliminate phase intercept, and meeting L, M and N sum is zero；α and β Represent distribution phase speed constant and eliminate phase speed constant；k_aThe same formula of implication (3), the same formula of remaining meaning of parameters (1)；

Oral three compartment models are in-vitro simulated, and flow rate F computing formula meets:

$\frac{\frac{F}{V_C}{e}^{-\frac{F}{V_C}t}-\frac{F}{V_A}{e}^{-\frac{F}{V_A}t}}{e^{-\frac{F}{V_C}t}-e^{-\frac{F}{V_A}t}}=\frac{{\mathrm{Lk}}_a{e}^{-k_{a}t}+{\mathrm{M\αe}}^{-\mathrm{\α}t}+N_1{\mathrm{\β}}_1{e}^{-{\mathrm{\β}}_{1}t}+N_2{\mathrm{\β}}_2{e}^{-{\mathrm{\β}}_{2}t}}{{\mathrm{Le}}^{-k_{a}t}+{\mathrm{Me}}^{-\mathrm{\α}t}+N_1{e}^{-{\mathrm{\β}}_{1}t}+N_2{e}^{-{\mathrm{\β}}_{2}t}}---\left(7\right)$

Wherein, N₁And N₂Represent fast eliminate phase intercept and eliminate phase intercept, the same formula of L and M implication (5) slowly, meet L, M, N₁And N₂ Sum is zero；β₁And β₂It is followed successively by the fast phase speed constant that eliminates and eliminates phase speed constant with slow；k_a, the same formula of α, e and t implication (5)。

3. the in-vitro simulated method as described in claim 1, it is characterised in that in described recurrence method,

The bulk concentration stepping type of an oral Room pharmacokinetic model is as follows:

$c_i=\frac{k_a\·F_{BA}\·Dose}{V_d\·(k_a-k_e)}(e^{-k_e{t}_i}-e^{-k_a{t}_i})---\left(27\right)$

Wherein, Dose is vivo medicine-feeding dosage, F_BAFor bioavailability, k_aAnd k_eThe same formula of implication (4), V_dFor internal apparent point Cloth volume, the same formula of e implication (1), t_iThe same formula of implication (26)；

The bulk concentration stepping type of oral two Room and three Room pharmacokinetic model is as follows:

$c_i={\mathrm{Le}}^{-k_a{t}_i}+{\mathrm{Me}}^{-{\mathrm{\αt}}_i}+{\mathrm{Ne}}^{-{\mathrm{\βt}}_i}---\left(28\right)$

$c_i={\mathrm{Le}}^{-k_a{t}_i}+{\mathrm{Me}}^{-{\mathrm{\αt}}_i}+N_1{e}^{-{\mathrm{\β}}_1{t}_i}+N_2{e}^{-{\mathrm{\β}}_2{t}_i}---\left(29\right)$

In formula (28), L, M, N, k_a, the same formula of α and β implication (5), the same formula of remaining meaning of parameters (27).In formula (29), L, M、N₁、N₂、k_a、α、β₁And β₂The same formula of implication (7), the same formula of remaining meaning of parameters (27).

4. the in-vitro simulated method as described in claim 1, it is characterised in that described flow velocity be entered as consecutive variations value shape Formula or multistage mean value formation.

5. the in-vitro simulated method as described in claim 1, it is characterised in that described flow velocity be calculated as single-dose or many Flow relocity calculation during secondary administration.

6. the in-vitro simulated method as described in claim 1, it is characterised in that described method is used for external pharmacokinetics or drug effect Learn model flow rate regulation.

7. the in-vitro simulated method as described in claim 6, it is characterised in that described in-vitro simulated method is moved for external medicine Learn or the application form of pharmacodynamics model flow rate regulation includes computing formula (1)～(4), (5), (7), (26)～(29) and corresponding The artificial of Equivalent Form calculates and computed in software.