CN105717087B - The discrete scan-type fluorescer pharmacokinetic parameter direct imaging method of spiral - Google Patents
The discrete scan-type fluorescer pharmacokinetic parameter direct imaging method of spiral Download PDFInfo
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Abstract
The invention discloses a kind of discrete scan-type fluorescer pharmacokinetic parameter direct imaging methods of spiral, step is: obtaining fluorescer scan data according to the discrete scan pattern of three-dimensional spiral, establish multi-chamber's fluorescer kinetic model, pharmacokinetic parameter direct imaging state equation, pharmacokinetic parameter image is obtained based on adaptive extended kalman filtering, final estimated value by obtained state vector finally obtains permeability and excretion rate to obtain compartment concentration and intermediate vector.This method advantage: each step of algorithm does not need partial data, obtains instant measurement data using the discrete scanning mode of spiral, reduces the requirement to data acquisition equipment high time resolution；Multi-chamber's kinetic model more accurately describes organizer, has corresponding physiological significance；Avoid the intermediate concentration reconstruction error of indirect method；Adaptive extended kalman filtering, which is compensated for, lacks brought influence to system initial state priori knowledge.
Description
Technical field
The present invention relates to pharmacokinetic parameters to analyze imaging field, especially for glimmering used in near-infrared spectroscopy
The pharmacokinetic parameter imaging method of photo etching, and in particular to the direct imaging of helical scan type fluorescer pharmacokinetic parameter
Method.
Background technique
Tumour has become the maximum killer of human health at present, early diagnoses most important for the life for saving patient.
Near-infrared fluorescent diffusion chromatography at imaging method (Diffuse fluorescence tomography, DFT) due to its is noninvasive,
The advantages that radiationless damage and high specific, is increasingly closed extensively in the related research field such as the diagnosis of tumour
Note[1].Recent studies indicate that whole features of disease cannot be represented for the diagnosis of a set time point, it is quiet in tradition
The Dynamic Fluorescence imaging method developed on the basis of state DFT imaging is more and more widely paid close attention to.Tumor tissues are due to its blood vessel
Newborn effect produces a large amount of " osmosis type " blood vessel, fluorescer wherein dynamic process and normal tissue different from.
" osmosis type " blood vessel has higher permeability, the image of permeability to fluorescer compared to " compact type " blood vessel of normal tissue
With to potentiality such as neoplasm staging, Treatment monitoring and anticancer drug research assessments[2,3]。
The method of fluorescence pharmacokinetics imaging at present can be divided into indirect method and direct method.In indirect method, base first
Multiframe concentration image (a series of images obtained by sample time order) is reconstructed in static DFT method for reconstructing, and then is obtained
The curve of position concentration changes with time in imaging region, and curve is fitted or non-linear based on biexponential model
Filtering mode is analyzed to obtain attenuation constant or pharmacokinetics Permeability Parameters[4,5].Presently, there are two problems for indirect method.The
One, pilot process static state DFT reconstructed results are influenced by the pathosis etc. of its inverse problem, are often shown the inaccuracy rebuild, are led
Cause the estimation inaccuracy finally for pharmacokinetic parameter.For each frame concentration 3-D image, static DFT method for reconstructing is needed
Complete three-dimensional scanning measurement data are wanted, and ignore the concentration variation during data acquisition.Therefore, indirect method requires data acquisition
Equipment realizes the acquisition of whole three-dimensional datas with high time resolution, to guarantee the standard of the concentration image reconstructed results of each frame
Really, the multidate information in fluorescer metabolic process is not lost, makes indirect method in pharmacokinetic parameter imaging practical application
It is restricted.
In existing direct method, the first is the inverse problem for rebuilding biexponential model insertion DFT, directly reconstructs decaying
Constant[6,7].However, biexponential model, as a kind of empirical model, attenuation constant can not represent the life with practical significance
Parameter is managed, there are drawbacks for application aspects such as diagnosing tumors for this.Another direct method is then that the imaging equation of DFT is incorporated
Into the conventional Extension Kalman filtering based on two compartment model[8], but its there is still a need for the complete measurement data of each frame in the short time
It is inside measured, very high, higher cost is required for the temporal resolution of system.In addition, its conventional Extension Kalman filtering
As a result the setting of its initial value is depended on, this also affects the estimation of pharmacokinetic parameter.
[bibliography]
[1]V.Ntziachristos,C.-H.Tung,C.Bremer,and R.Weissleder,"Fluorescence
molecular tomography resolves protease activity in vivo,"Nature Med.8(2002)
757–760.
[2]L.A.Bauer,Applied Clinical Pharmacokinetics,McGraw-Hill,New York
(2008).
[3]K.M Tichauer,Y.Wang,B.W Pogue and J.T.C.Liu,“Quantitative in vivo
cell-surface receptor imaging in oncology:kinetic modeling and paired-agent
principles from nuclear medicine and optical imaging,”Phys.Med.Biol.60,R239-
R269(2015).
[4]B.Alacam,B.Yazici,X.Intes,and B.Chance,“Extended Kalman filtering
for the modeling and analysis of ICG pharmacokinetics in cancerous tumors
using NIR optical methods,” IEEE Trans.Biomed.Eng.53(2006)1861–1871.
[5]X.Intes,J.Ripoll,Y.Chen,et al,"In vivo continuous-wave optical
breast imaging enhanced with Indocyanine Green,"Med.Phys.30(2003)1039-1047.
[6]A.B.Milstein,K.J.Webb,and C.A.Bouman,"Estimation of kinetic model
parameters in fluorescence optical diffusion tomography,"J.Opt.Soc.Am.A 7
(2005)1357-1368.
[7]G.Zhang,F.Liu,H.Pu,W.He,J.Luo and J.Bai,“A direct method with
structural priors for imaging pharmacokinetic parameters in dynamic
fluorescence molecular tomography,” IEEE Trans.Biomed.Eng.61,986–990(2014).
[8]B.Alacam and B.Yazici,"Direct reconstruction of pharmcokinetix-
rate images of optical fluorophores from NIR measurement,"IEEE
Trans.Med.Imag.28(2009)1337-1353.
Summary of the invention
The present invention is directed to overcome the shortcomings of existing methods, existing imaging method is solved for the time point of data acquisition equipment
The requirement of resolution and the defect of kinetic model accuracy etc. develop the discrete scan-type fluorescer pharmacokinetics of spiral
Parameter three-dimensional straight connects imaging method.Mentioned in the present invention to the mode measurement of multiplexing refer to: in detecting location quantity
More than or equal to detector quantity when, detector in chronological order successively measurement obtain the data of each detecting location.
In order to solve the above-mentioned technical problem, the discrete scan-type fluorescer pharmacokinetics ginseng of a kind of spiral proposed by the present invention
Number direct imaging method, wherein the organizer for being injected intravenously fluorescer is placed in the imaging chamber of a cylinder, which is characterized in that
The following steps are included:
Step 1: obtaining fluorescer scan data according to the discrete scan pattern of three-dimensional spiral:
Step 1-1, light source by collimation after be incident on imaging chamber surface, imaging chamber peripheral surface and with the same water of light source
Uniformly distributed D detecting location in the height of planeNdA detector measures in a multiplexed manner,
Nd≤ D, sampling interval are Δ T；L parallel measurement obtains the data for projection of all detecting locations under the light source, L=D/Nd；
Then, it is Δ Angle that imaging chamber, which rotates an angle, while rising a height is Δ Z, and so on, until completing complete three
The scanning survey of dimension forms S light source position r in the scanning survey processs(s=1,2 ..., S)；
Step 1-2 repeats the scanning survey of full three-dimensional described in P step 1-1, obtains required scan data M, sweeps for P times
The metabolism time for retouching the covered fluorescer of measurement is P × S × L × Δ T,
In formula (1), Γ (p, s)=[Inb(p,s,1),Inb(p,s,2),...,Inb(p,s,L)]TWherein,S=1,2 ..., S, l=1,2 ..., L, p are the serial number of 3 d scan data, and s is light source position serial number, l
Indicate that sampling sequence number, Γ (p, s) indicate the s group data for projection in pth group 3 d scan data and by boundary survey luminous fluxes
Berne than composition,
In formula (2), Ix(rd,rs, t) and Im(rd,rs, t) be respectively exciting light and fluorescence boundary survey luminous flux, if Inb
(p, s, l) is Inb(k), i.e. parallel measurement data when t=k Δ T, k=1,2 ..., K, K=P × S × L；
Step 2: establishing multi-chamber's fluorescer kinetic model:
N is divided by the organizer for being imaged intracavitary is conceptualcA compartment is retouched using multi-chamber's fluorescer kinetic model
It states interpenetrating between different compartments and the process outside organizer, multi-chamber's fluorescer power is discharged by metabolic system
It is as follows to learn model:
In formula (3),Ci(r, k) indicates i-th of compartment in moment k
Compartment concentration when Δ T, i=1,2 ..., Nc；K (θ (r, k)) is sytem matrix relevant to pharmacokinetics permeability,
In formula (4), ω (r, k) andIt is independent from each other white Gaussian noise, θ (r, k) indicates to seep with pharmacokinetics
The relevant intermediate vector of saturating rate,KijIt indicates from the i-th compartment between jth
The permeability of room, KjiIt indicates from jth compartment to the permeability of the i-th compartment, KiIt indicates that body is discharged by metabolic system by the i-th compartment
Outer excretion rate, i=1,2 ..., Nc；J=1,2 ..., Nc；
Step 3: pharmacokinetic parameter direct imaging state equation:
In conjunction with finite element fission node r all in universenThe compartment fluorescer concentration at place and indirect pharmacokinetic parameter,
N=1,2 ..., N define state vector X=[C to be estimatedT(r1),θT(r1),…,CT(rN),θT(rN)]T；Introduce fluorescent chromatographic
Imaging equation obtains direct imaging state equation,
In formula (6), A=diag [K (r1),I,K(r2),I,…,K(rN), I], K (rn) calculated by formula (4), I is unit square
Battle array, Λ (k)=ε η ln (10) W (k) E are calculation matrix, and η and ε are the quantum efficiency and extinction coefficient of fluorescer respectively, and E is N
RowX is transformed into total concentration C by the matrix of columnT=C1+C2+L+CN, Ci=[Ci(r1),…,Ci(rN)]T, W (k)
It is NdThe weight matrix of the fluorescence tomography equation of row N column, δ (k) and γ (k) are independent white Gaussian noise, covariance
Matrix is Q and R；
Step 4: adaptive extended kalman filtering is to make up to know system initial state priori by using forgetting factor
Knowing influences brought by missing, obtains pharmacokinetic parameter image based on adaptive extended kalman filtering:
DefinitionIt is respectively the state vector and mistake that the kth step of estimated value prediction is walked according to k-1 with P (k | k-1)
Poor covariance matrix,It is respectively the estimated value of state vector and error co-variance matrix that k-1 is walked with P (k-1),It is respectively the state vector of k step and the estimated value of error co-variance matrix with P (k)；
Specific step is as follows:
Prediction steps: the state vector estimated according to previous stepWith error co-variance matrix P (k-1), prediction is worked as
The state vector of preceding stepWith error co-variance matrix P (k | k-1),
In formula (8), λ (k) is forgetting factor, and J (k-1) is the system Jacobin matrix of -1 step of kth；
Kalman gain step: Kalman gain G (k) is currently walked according to above-mentioned predictor calculation, and according to current pacing
Measure Berne ratio Inb(k) new breath d (k) is calculated,
It updates step: the state vector currently walked is updated according to current step predicted value and new breath valueError covariance
The Jacobin matrix J (k) of matrix P (k) and system,
Above-mentioned prediction-Kalman gain-renewal process is repeated, until obtaining the final estimated value of state vector X
Utilize X=[CT(r1),θT(r1),…,CT(rN),θT(rN)]TCompartment concentration and intermediate vector theta (r, k) are obtained, is utilized formula (4)
Obtain permeability Kij, permeability KjiWith excretion rate Ki。
Compared with prior art, the beneficial effects of the present invention are:
(1) each step estimation for directly reconstructing method of the method for the present invention does not need Complete three-dimensional data, but uses spiral shell
Whiz dissipates scanning mode and obtains instant parallel measurement data, reduces the requirement to the high time resolution of data acquisition equipment,
The lower measurement pattern of cost of implementation；
(2) multi-chamber's kinetic model that the method for the present invention is established can more precisely describe organizer, parameter tool
There is corresponding practical physiological significance, there are larger potentiality to cancer diagnosis；
(3) the intermediate concentration reconstruction process for directly reconstructing state equation and eliminating indirect method that the method for the present invention uses, keeps away
Exempt from intermediate conventional fluorescent tomography due to its inverse problem pathosis bring error.
(4) the method for the present invention uses adaptive extended kalman filtering, makes up by using forgetting factor initial to system
It is influenced brought by state priori knowledge missing, realizes more preferably reconstructed results compared to conventional Extension Kalman filtering.
Detailed description of the invention
Fig. 1 is multiplexing detection plane schematic diagram of the present invention；
Fig. 2 is the discrete scan data composition schematic diagram of spiral in the present invention；
Fig. 3 is helical scanning imaging chamber and light source position schematic diagram in the present invention；
Fig. 4 is two compartment model schematic diagram of the embodiment of the present invention.
Specific embodiment
Technical solution of the present invention is described in further detail in the following with reference to the drawings and specific embodiments, it is described specific
Embodiment is only explained the present invention, is not intended to limit the invention.
A kind of discrete scan-type fluorescer pharmacokinetic parameter direct imaging method of spiral proposed by the present invention, wherein
The organizer of intravenous injection fluorescer is placed in the imaging chamber of a cylinder, comprising the following steps:
Step 1: obtaining fluorescer scan data according to the discrete scan pattern of three-dimensional spiral:
Step 1-1, light source by collimation after be incident on imaging chamber surface, imaging chamber peripheral surface and with the same water of light source
(Fig. 1, which is shown, assumes that light source is 0 °, is located at 101.25 ° to 258.75 ° of light source same level (X/Y plane) in the height of plane
Position) uniformly distributed D detecting locationNdA detector measures in a multiplexed manner, Nd≤
D, sampling interval are Δ T；Using configuration as described above, L parallel measurement obtains the throwing of all detecting locations under the light source
Shadow data, L=D/Nd；Then, it is Δ Angle that imaging chamber, which rotates an angle, while rising a height is Δ Z, with such
It pushes away, until completing complete three-dimensional scanning survey, forms S light source position r in the scanning survey processs(s=1,2 ...,
S)；The imaging chamber radius that Fig. 3 is shown is 15mm, a height of 40mm, scans the Z-direction step pitch from Z1=36mm to Z2=5mm
Δ Z=1mm rotates Angle=22.5 ° of angle delta, light source position number S=32.
Step 1-2 repeat P step 1-1 described in full three-dimensional scanning survey, obtain required scan data M (how
The conventional techniques that scan data M belongs to the art are obtained, details are not described herein), what P scanning survey was covered
The metabolism time of fluorescer is P × S × L × Δ T, as shown in Fig. 2,
In formula (1),Wherein,S=
1,2 ..., S, l=1,2 ..., L, p are the serial number of 3 d scan data, and s is light source position serial number, and l indicates sampling sequence number, Γ
(p, s) indicates the s group data for projection in pth group 3 d scan data and is made of the Berne of boundary survey luminous flux ratio,
In formula (2), Ix(rd,rs, t) and Im(rd,rs, t) be respectively exciting light and fluorescence boundary survey luminous flux, if Inb
(p, s, l) is Inb(k), i.e. parallel measurement data when t=k Δ T, k=1,2 ..., K, K=P × S × L；
Step 2: establishing multi-chamber's fluorescer kinetic model:
N is divided by the organizer for being imaged intracavitary is conceptualcA compartment is retouched using multi-chamber's fluorescer kinetic model
It states interpenetrating between different compartments and the process outside organizer, multi-chamber's fluorescer power is discharged by metabolic system
It is as follows to learn model:
In formula (3),Ci(r, k) indicates i-th of compartment in moment k
Compartment concentration when Δ T, i=1,2 ..., Nc；K (θ (r, k)) is sytem matrix relevant to pharmacokinetics permeability,
In formula (4), ω (r, k) andIt is independent from each other white Gaussian noise, θ (r, k) indicates to seep with pharmacokinetics
The relevant intermediate vector of saturating rate,KijIt indicates from the i-th compartment between jth
The permeability of room, KjiIt indicates from jth compartment to the permeability of the i-th compartment, KiIt indicates that body is discharged by metabolic system by the i-th compartment
Outer excretion rate, i=1,2 ..., Nc；J=1,2 ..., Nc；Organizer is divided into outside vasculature part and blood vessel by common two compartment model
Part, and think that only vasculature part can excrete fluorescer by body processes system, as shown in figure 4, its system square
Battle array be
Wherein, Kpe(r) and Kep(r) it respectively indicates and is penetrated into extravascular point by vasculature part and seeped by extravascular point
The permeability of saturating blood back tube portion, KpTo be expelled directly out external excretion rate by vasculature part；
Step 3: pharmacokinetic parameter direct imaging state equation:
In conjunction with finite element fission node r all in universenThe compartment fluorescer concentration at place and indirect pharmacokinetic parameter,
N=1,2 ..., N define state vector X=[C to be estimatedT(r1),θT(r1),…,CT(rN),θT(rN)]T；Introduce fluorescent chromatographic
DFT imaging equation obtains direct imaging state equation,
In formula (6), A=diag [K (r1),I,K(r2),I,…,K(rN), I], K (rn) calculated by formula (4), I is unit square
Battle array, Λ (k)=ε η ln (10) W (k) E are calculation matrix, and η and ε are the quantum efficiency and extinction coefficient of fluorescer respectively, and E is N
RowX is transformed into total concentration C by the matrix of columnT=C1+C2+L+CN, Ci=[Ci(r1),…,Ci(rN)]T, W (k)
It is NdThe weight matrix of the fluorescence tomography equation of row N column, δ (k) and γ (k) are independent white Gaussian noise, covariance
Matrix is Q and R；(N when based on two compartment modelc=2), then I is 4 rank unit matrixs, E=diag [E ', E ' ..., E '] E ' herein
=[1 1000 0]) it is N row 6N column transition matrix, each element calculation method of W (k) is as follows,
Wherein,It is the excitation r at rdLocate the unit volume elements domain Ω of detectioneGreen's letter of interior diffusion equation
Number average value,It is in rsThe unit volume elements domain Ω detected at place's excitation reInterior exciting light photon density is averaged
Value, Ix(rd,rs) it is in rsPlace's excitation rdLocate the excitation light flow of detection, c is the light velocity, unIt (r) is finite element fission grid
The shape function of interior n-th of node；
Step 4: adaptive extended kalman filtering is to make up to know system initial state priori by using forgetting factor
Knowing influences brought by missing, obtains pharmacokinetic parameter image based on adaptive extended kalman filtering:
DefinitionIt is respectively the state vector and mistake that the kth step of estimated value prediction is walked according to k-1 with P (k | k-1)
Poor covariance matrix,It is respectively the estimated value of state vector and error co-variance matrix that k-1 is walked with P (k-1),It is respectively the state vector of k step and the estimated value of error co-variance matrix with P (k)；
Specific step is as follows:
Prediction steps: the state vector estimated according to previous stepWith error co-variance matrix P (k-1), prediction is worked as
The state vector of preceding stepWith error co-variance matrix P (k | k-1),
In formula (8), λ (k) is forgetting factor, and J (k-1) is the system Jacobin matrix of -1 step of kth；
λ (k) is that its calculation method of forgetting factor is as follows,
Wherein,It is respectively innovation sequence with D (k)Estimate covariance square
Battle array and calculating covariance matrix, calculation method is as follows,
D (k)=Λ P (k | k-1) ΛT+R (11)
Wherein, W is length of window；
Kalman gain step: Kalman gain G (k) is currently walked according to above-mentioned predictor calculation, and according to current pacing
Measure Berne ratio Inb(k) new breath d (k) is calculated,
It updates step: the state vector currently walked is updated according to current step predicted value and new breath valueError covariance
The Jacobin matrix J (k) of matrix P (k) and system,
Above-mentioned prediction-Kalman gain-renewal process is repeated, until obtaining the final estimated value of state vector X
Utilize X=[CT(r1),θT(r1),…,CT(rN),θT(rN)]TCompartment concentration and intermediate vector theta (r, k) are obtained, is utilized formula (4)
Obtain permeability Kij, permeability KjiWith excretion rate Ki。
Although above in conjunction with attached drawing, invention has been described, and the invention is not limited to above-mentioned specific implementations
Mode, the above mentioned embodiment is only schematical, rather than restrictive, and those skilled in the art are at this
Under the enlightenment of invention, without deviating from the spirit of the invention, many variations can also be made, these belong to of the invention
Within protection.
Claims (1)
1. a kind of discrete scan-type fluorescer pharmacokinetic parameter direct imaging method of spiral, wherein intravenous injection fluorescer
Organizer be placed in the imaging chamber of a cylinder, which comprises the following steps:
Step 1: obtaining fluorescer scan data according to the discrete scan pattern of three-dimensional spiral:
Step 1-1, light source by collimation after be incident on imaging chamber surface, imaging chamber peripheral surface and with light source same level face
Height on uniformly distributed D detecting locationNdA detector measures in a multiplexed manner, Nd≤ D,
Sampling interval is △ T；L parallel measurement obtains the data for projection of all detecting locations under the light source, L=D/Nd；Then, at
It is △ Angle as chamber rotates an angle, while rising a height is △ Z, and so on, until completing complete three-dimensional scanning
Measurement, forms S light source position r in the scanning survey processs, s=1,2 ..., S；
Step 1-2 repeats the scanning survey of full three-dimensional described in P step 1-1, obtains required scan data M, and P scanning is surveyed
The metabolism time for measuring covered fluorescer is P × S × L × △ T,
In formula (1), Γ (p, s)=[Inb(p,s,1),Inb(p,s,2),...,Inb(p,s,L)]T, wherein p=1,2 ..., P, s
=1,2 ..., S, l=1,2 ..., L, p are the serial number of 3 d scan data, and s is light source position serial number, and l indicates sampling sequence number, Γ
(p, s) indicates the s group data for projection in pth group 3 d scan data and is made of the Berne of boundary survey luminous flux ratio,
In formula (2), Ix(rd,rs, t) and Im(rd,rs, t) be respectively exciting light and fluorescence boundary survey luminous flux, if Inb(p,
S, l) it is Inb(k), i.e. parallel measurement data when t=k △ T, k=1,2 ..., K, K=P × S × L；
Step 2: establishing multi-chamber's fluorescer kinetic model:
N is divided by the organizer for being imaged intracavitary is conceptualcA compartment, not using the description of multi-chamber's fluorescer kinetic model
The process outside organizer, multi-chamber's fluorescer kinetic simulation is discharged with interpenetrating between compartment and by metabolic system
Type is as follows:
In formula (3),Ci(r, k) indicates i-th of compartment in moment k △ T
Compartment concentration, i=1,2 ..., Nc；K (θ (r, k)) is sytem matrix relevant to pharmacokinetics permeability,
In formula (4), ω (r, k) andIt is independent from each other white Gaussian noise, θ (r, k) is indicated and pharmacokinetics permeability
Relevant intermediate vector,KijIt indicates from the i-th compartment to jth compartment
Permeability, KjiIt indicates from jth compartment to the permeability of the i-th compartment, KiWhat expression was excreted by the i-th compartment by metabolic system
Excretion rate, i=1,2 ..., Nc；J=1,2 ..., Nc；
Step 3: pharmacokinetic parameter direct imaging state equation:
In conjunction with finite element fission node r all in universenThe compartment fluorescer concentration at place and indirect pharmacokinetic parameter, n=1,
2 ..., N define state vector X=[C to be estimatedT(r1),θT(r1),…,CT(rN),θT(rN)]T；Introduce fluorescence tomography side
Journey obtains direct imaging state equation,
In formula (6), A=diag [K (r1),I,K(r2),I,…,K(rN), I], K (rn) calculated by formula (4), I is unit matrix, Λ
(k)=ε η ln (10) W (k) E is calculation matrix, and η and ε are the quantum efficiency and extinction coefficient of fluorescer respectively, and E is N rowX is transformed into total concentration C by the matrix of columnT=C1+C2+L+CN, Ci=[Ci(r1),…,Ci(rN)]T, W (k) is Nd
The weight matrix of the fluorescence tomography equation of row N column, δ (k) and γ (k) are independent white Gaussian noise, covariance matrix
For Q and R；
Step 4: adaptive extended kalman filtering is to make up to lack system initial state priori knowledge by using forgetting factor
Bring of becoming homeless influences, and obtains pharmacokinetic parameter image based on adaptive extended kalman filtering:
DefinitionWith P (k | k-1) be respectively according to k-1 walk estimated value prediction kth step state vector and error assist
Variance matrix,It is respectively the estimated value of state vector and error co-variance matrix that k-1 is walked with P (k-1),And P
(k) be respectively k step state vector and error co-variance matrix estimated value；
Specific step is as follows:
Prediction steps: the state vector estimated according to previous stepWith error co-variance matrix P (k-1), current step is predicted
State vectorWith error co-variance matrix P (k | k-1),
In formula (8), λ (k) is forgetting factor, and J (k-1) is the system Jacobin matrix of -1 step of kth；
Kalman gain step: Kalman gain G (k) is currently walked according to above-mentioned predictor calculation, and according to current pacing amount primary
Grace ratio Inb(k) new breath d (k) is calculated,
It updates step: the state vector currently walked is updated according to current step predicted value and new breath valueError co-variance matrix P
(k) and the Jacobin matrix J (k) of system,
Above-mentioned prediction-Kalman gain-renewal process is repeated, until obtaining the final estimated value of state vector XUtilize X
=[CT(r1),θT(r1),…,CT(rN),θT(rN)]TCompartment concentration and intermediate vector theta (r, k) are obtained, is seeped using formula (4)
Saturating rate Kij, permeability KjiWith excretion rate Ki。
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