CN106373194A - Human lung electric resistance tomography finite element model design method - Google Patents
Human lung electric resistance tomography finite element model design method Download PDFInfo
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Abstract
The present invention discloses a human lung electric resistance tomography finite element model design method. According to a human thorax CT scanning image, the whole finite element model is divided into a region 1 consisting of the lung, the heart and the vertebra and a region 2 consisting of adipose tissues; the advanced particle swarm algorithm is employed to determine the boundary curve equations of the region 1 and the region 2; on this basis, improving the direct problem calculation precision and improving the sensitivity matrix morbid degree are optimization targets, the ratios of the number of layers of the finite element model included by the region 1 and the region 2 and the finite element nodes of each layer in the region 1 and the region 2 with the polar radiuses of the finite element nodes corresponding to the same polar angles of each boundary are taken as variables, and the advanced particle swarm algorithm is employed to optimize the finite element model so as to obtain a finite element model which is suitable for human lung electric resistance tomography. The human lung electric resistance tomography finite element model design method not only improves the direct problem calculation precision and improves the sensitivity matrix and Hessian matrix morbid degree, but also improves the sensitivity distribution uniformity so as to effectively improve the image reconstruction precision.
Description
Technical field
The present invention relates to a kind of human lung's Electrical Resistance Tomography FEM (finite element) model method for designing, belong to Electrical Resistance Tomography
Technical field.
Background technology
Biomedical electrical impedance tomography (electrical impedance tomography, eit) technology is with life
Distribution that object internal resistance resists or become the biomedical detection of a kind of novel lossless wound turning to imageable target and imaging technique, it leads to
Cross and necessarily safe exciting current is applied in vitro, record organism surface voltage signal and divide come the impedance to reconstruct organism
Cloth, if ignoring imaginary impedance information, electrical impedance tomography technology is just reduced to Electrical Resistance Tomography.
In case of human, pulmonary disease is a kind of commonly encountered diseases and frequently-occurring disease, and pulmonary disease common at present has pneumonia, a gas
Guan Yan, pulmonary tuberculosis, bronchiectasis or lung tumors etc..When above-mentioned pulmonary disease occurs, the feature pathological changes of organ are often
Generation early than Organic pathological changes or other clinical symptoms.Medical diagnosiss at present and the imaging skill adopting usual in clinical practice
Art has ct, ultrasonic or magnetic resonance etc..Compared with these imaging techniques, the resolution of Electrical Resistance Tomography is relatively low, but conduct
A kind of new non-destructive testing technology, the Clinics and Practices being applied to human lung's disease early stage have the advantage that
1. Electrical Resistance Tomography adopts electrode as sensor, and detection means volume is little, structure simple, has cost
Cheap, portable superiority；
2. Electrical Resistance Tomography utilizes low-frequency current to be imaged, it is to avoid radioactive radiation, to human zero damage, can be right
Patient carry out for a long time, dynamic monitor；
3. Electrical Resistance Tomography can achieve functional imaging.
At present, in Electrical Resistance Tomography, multiple physical field is generally adopted to couple finite element analysis software comsol
Multiphysics calculates direct problem.Although comsol multiphysics has the advantages that powerful, highly versatile,
When being applied to human lung's Electrical Resistance Tomography, the shortcoming of existing for property difference, direct problem computational accuracy is relatively low.In order to just improve
Problem computational accuracy, the method typically adopting grid reconstruction, but the amount of calculation of the method very big it is impossible to meet right in practical application
The requirement of real-time.In addition, the pathosis of sensitivity matrix are also impact human lung's electricity with the inhomogeneities of sensitivity profile
The key factor of resistance tomographic image reconstruction precision.Therefore, it is badly in need of one kind and just can improve human lung's Electrical Resistance Tomography
The computational accuracy of problem, improves the Degree of Ill Condition of sensitivity matrix and hessian matrix, improves the uniformity of sensitivity profile,
And then improve the setting of human lung's Electrical Resistance Tomography FEM (finite element) model of human lung's Electrical Resistance Tomography image reconstruction accuracy
Meter method.
Content of the invention
The problem existing for above-mentioned prior art, the present invention provides a kind of human lung's Electrical Resistance Tomography finite element mould
Type method for designing, under same experimental conditions, not only can improve the computational accuracy of human lung's Electrical Resistance Tomography direct problem, change
Kind sensitivity matrix and the Degree of Ill Condition of hessian matrix, and the uniformity of sensitivity profile can be improved, and then improve human body
Pulmonary's Electrical Resistance Tomography image reconstruction accuracy.
To achieve these goals, a kind of human lung's Electrical Resistance Tomography FEM (finite element) model design side that the present invention adopts
Method, human lung's Electrical Resistance Tomography FEM (finite element) model refers to for this certain organs of human lung, is applied to human lung
The FEM (finite element) model of Electrical Resistance Tomography；
The comprising the concrete steps that of human lung's Electrical Resistance Tomography FEM (finite element) model method for designing:
Step one: according to human chest ct scanning figure, whole FEM (finite element) model is divided into and is made up of lung, heart, vertebra
Region one and the region two being made up of fatty tissue, determine the boundary curve side in region one, two using improvement particle cluster algorithm
Journey；
Step 2: according to pulmonary's priori, the model of setting reflection human lung's structure, have using based on grid reconstruction
Limit meta-model calculates Electrical Resistance Tomography direct problem, and using gained sensitivity field boundary voltage value of calculation as theoretical value；
Step 3: to improve direct problem computational accuracy and to improve sensitivity matrix Degree of Ill Condition as optimization aim, with region
First, two are comprised the FEM (finite element) model number of plies and region one, two each layers of finite element node polar angle identical with respective border are corresponding
The ratio of finite element node polar diameter is variable, using improving particle cluster algorithm optimized FEMs model, thus obtain being directed to human body
This certain organs of pulmonary, the FEM (finite element) model of human lung's Electrical Resistance Tomography of being applied to.
Preferably, the boundary curve equation in described region one, two takes polar form:Formula
In,For polar diameter, θ is polar angle, ai、bi、ci∈ [- 10,10], n are integer and meet 20≤n≤100.
Preferably, described using improve particle cluster algorithm determine the boundary curve equation in region one, two be withFor fitness function, in formula, x is ai、bi、ci(i=1,2 ... n) represented by variable, m be border section
Count out, ρ is boundary node polar diameter,With ρiPolar angle is identical, λi∈(0,+∞).
Preferably, described using improve particle cluster algorithm optimized FEMs model be withFor adapting to
Degree function, in formula, y is the FEM (finite element) model number of plies that comprised of region one, two and region one, two each layers of finite element node with respectively
From the variable represented by the ratio of the corresponding finite element node polar diameter of the identical polar angle in border, rms and s is based on pulmonary's priori mould
The corresponding root-mean-square value of type and sensitivity matrix, cond represents conditional number.
Under same experimental conditions, compared with prior art, the present invention not only increases human lung's Electrical Resistance Tomography
The computational accuracy of direct problem, improves the Degree of Ill Condition of sensitivity matrix and hessian matrix, and improves sensitivity profile
Uniformity, thus effectively increasing human lung's Electrical Resistance Tomography image reconstruction accuracy.
Brief description
Fig. 1 is the schematic diagram of actual boundary；
Fig. 2 is the schematic diagram determining border using improvement particle cluster algorithm；
Fig. 3 is the comparison schematic diagram that actual boundary and improvement particle cluster algorithm determine border；
Fig. 4 is the schematic diagram by traditional FEM (finite element) model of principle subdivision at equal intervals；
Fig. 5 be FEM (finite element) model a i.e. on the basis of by FEM (finite element) model knot adjustment in Fig. 4 to border one, with improve
Direct problem computational accuracy is optimization aim with improving sensitivity matrix Degree of Ill Condition, and using improving, particle cluster algorithm Optimized model is each
The schematic diagram of the FEM (finite element) model that the ratio of layer finite element node and the corresponding finite element node polar diameter in border two same pole angle is worth to；
Fig. 6 is region one, two respectively by the signal of traditional FEM (finite element) model of principle subdivision at equal intervals for FEM (finite element) model b
Figure；
The schematic diagram of the FEM (finite element) model that Fig. 7 is obtained using method for designing proposed by the present invention for FEM (finite element) model c；
Fig. 8 is the FEM (finite element) model d i.e. schematic diagram based on grid reconstruction FEM (finite element) model；
Fig. 9 is the schematic diagram of model according to set by pulmonary's priori；
Figure 10 is the corresponding difference of model according to set by pulmonary's priori FEM (finite element) model sensitivity field border electricity in Fig. 9
The comparison schematic diagram of pressure value of calculation；
Figure 11 is the schematic diagram that the corresponding model of pathological tissues in one group of pulmonary's diverse location；
Figure 12 is that different FEM (finite element) model are corresponding in improving Newton-Raphson image reconstruction algorithm iterative process
The comparison schematic diagram of hessian Matrix condition number；
Figure 13 is the schematic diagram of FEM (finite element) model a corresponding improved capacity spectrum method image reconstruction result；
Figure 14 is the schematic diagram of FEM (finite element) model b corresponding improved capacity spectrum method image reconstruction result；
Figure 15 is the schematic diagram of FEM (finite element) model c corresponding improved capacity spectrum method image reconstruction result；
In figure: 1, border one, 2, border two, 3, region one, 4, region two.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
As shown in Figures 1 to 7, human lung's Electrical Resistance Tomography FEM (finite element) model refers to that this is specific for human lung
Organ, it is applied to the FEM (finite element) model of human lung's Electrical Resistance Tomography；
The comprising the concrete steps that of the present invention a kind of human lung Electrical Resistance Tomography FEM (finite element) model method for designing:
Step one: as shown in Figures 1 to 7, according to human chest ct scanning figure, by whole FEM (finite element) model be divided into by lung,
Region 1 and the region 24 being made up of fatty tissue that heart, vertebra are constituted, determine region using improving particle cluster algorithm
First, two boundary curve equation；Wherein, the boundary curve equation in described region one, two takes polar form:In formula,For polar diameter, θ is polar angle, ai、bi、ci∈ [- 10,10], n be integer and meet 20≤n≤
100；And withFor fitness function, in formula, x is ai、bi、ci(i=1,2 ... n) represented by variable, m
For boundary node number, ρ is boundary node polar diameter,With ρiPolar angle is identical, λi∈(0,+∞)；
Step 2: as shown in figure 9, according to pulmonary's priori, the model of setting reflection human lung's structure, using as schemed
Shown in 5, Electrical Resistance Tomography direct problem is calculated based on grid reconstruction FEM (finite element) model, and gained sensitivity field boundary voltage is calculated
Value is as theoretical value；
Step 3: to improve direct problem computational accuracy and to improve sensitivity matrix Degree of Ill Condition as optimization aim, with region
First, two are comprised the FEM (finite element) model number of plies and region one, two each layers of finite element node polar angle identical with respective border are corresponding
The ratio of finite element node polar diameter is variable, using improving particle cluster algorithm optimized FEMs model, thus obtaining as shown in Figure 7
For this certain organs of human lung, FEM (finite element) model c that is applied to human lung's Electrical Resistance Tomography.Wherein, described
Using improve particle cluster algorithm optimized FEMs model be withFor fitness function, in formula, y is region
First, two are comprised the FEM (finite element) model number of plies and region one, two each layers of finite element node polar angle identical with respective border are corresponding
The variable represented by ratio of finite element node polar diameter, rms and s be based on the corresponding root-mean-square value of pulmonary's priori model with
Sensitivity matrix, cond represents conditional number.
As shown in Figure 1 to Figure 3, work as λi=1 (i=1,2 ... m) when, using improve particle cluster algorithm determine border and reality
Border border is substantially identical, can be by artificial adjustment λiValue, improves the degree of agreement of area-of-interest further.
As shown in Figure 10, calculate direct problem gained sensitivity field border electricity to be based on grid reconstruction FEM (finite element) model in step 2
Press value of calculation as theoretical value, using the finite model c in finite model b and Fig. 7 in finite model a, the Fig. 6 in Fig. 5
Calculate Electrical Resistance Tomography direct problem, rms value is respectively 5.2167%, 4.1566%, 1.4202%.It can be seen that, limited with Fig. 5
In meta-model a with Fig. 6, FEM (finite element) model is compared, and adopts the rms value point of FEM (finite element) model c of the design method acquisition in Fig. 7
Do not reduce 72.7759%, 65.8327%, effectively increase direct problem computational accuracy.
Empirical tests, based on the model set by pulmonary as shown in Figure 9 priori, have in FEM (finite element) model a, Fig. 6 in Fig. 5
In limit meta-model b and Fig. 7, the conditional number of the sensitivity matrix corresponding to FEM (finite element) model c is respectively 1.9500 × 107、1.3212
×107、8.4075×106, compared with FEM (finite element) model b in FEM (finite element) model a in Fig. 5 and Fig. 6, FEM (finite element) model c pair in Fig. 7
The sensitivity matrix conditional number answered reduces 56.8846%, 36.3647% respectively, effectively improves the morbid state of sensitivity matrix
Degree, thus be conducive to improving image reconstruction quality.
In addition, the uniformity of sensitivity profile has important shadow to human lung's Electrical Resistance Tomography image reconstruction accuracy
Ring, generally adopt index p to evaluate the uniformity of sensitivity profile, shown in expression formula such as formula (1):
In formula: k is the effective number of sensitivity field boundary voltage；pijShown in expression formula such as formula (2):
In formula: sijSensitivity for electrode pair i-j；It is respectively the spirit introducing triangular finite element area coefficient
The average of sensitive matrix and standard deviation.
P is less, and sensitivity profile uniformity is better, is more conducive to improving Electrical Resistance Tomography image reconstruction accuracy.Experience
Card, based on the model set by pulmonary as shown in Figure 9 priori, the finite model b in finite model a, Fig. 6 in Fig. 5 with
And the p value corresponding to finite model c in Fig. 7 be respectively 8.1635,8.8428, in 8.0233, with Fig. 5 FEM (finite element) model a and
In Fig. 6, FEM (finite element) model b is compared, and the p value corresponding to FEM (finite element) model c in Fig. 7 reduces 1.7174%, 9.2674% respectively,
Improve the uniformity of sensitivity profile.
In order to verify that in Fig. 7, FEM (finite element) model c is in terms of improving human lung's Electrical Resistance Tomography image reconstruction quality
Effectiveness, setting diverse location lung pathological tissues as shown in figure 11 correspond to model, (duo t8100cpu under same experimental conditions
3.00gb internal memory 2.10ghz matlab 7.0), by three kinds of different FEM (finite element) model (FEM (finite element) model a, b, c) and its corresponding
Sensitivity matrix is applied to improved capacity spectrum method image reconstruction.As shown in figure 12, improving Newton-Raphson image
In algorithm for reconstructing iterative process, compared with FEM (finite element) model b in FEM (finite element) model a in Fig. 5 and Fig. 6, FEM (finite element) model c in Fig. 7
Corresponding hessian Matrix condition number is minimum, effectively improves the Degree of Ill Condition of hessian matrix.
In Electrical Resistance Tomography, generally adopt correlation coefficient and image relative error evaluation algorithms image weight at present
Build quality, shown in expression formula such as formula (3), (4).Correlation coefficient is bigger, image relative error is less, shows that image reconstruction accuracy is got over
High.Three kinds of different FEM (finite element) model (FEM (finite element) model a, b, c) correlation coefficienies compare as shown in table 1,2 with image relative error,
Correspondence image reconstructed results are respectively as shown in Figure 13,14,15.
In formula: g is setting model；For reconstructed results；L is finite element number；WithBe respectively g withMeansigma methodss.
The different FEM (finite element) model correlation coefficient of 1 three kinds of table compares
| Setting model | FEM (finite element) model a | FEM (finite element) model b | FEM (finite element) model c |
| Model a | 0.8706 | 0.8760 | 0.9359 |
| Model b | 0.8859 | 0.8848 | 0.9357 |
| Model c | 0.8719 | 0.8758 | 0.9347 |
| Model d | 0.8818 | 0.8774 | 0.9344 |
| Model e | 0.8851 | 0.8755 | 0.9296 |
| Model f | 0.8848 | 0.8718 | 0.9346 |
| Model g | 0.8699 | 0.8843 | 0.9332 |
| Model h | 0.8787 | 0.8759 | 0.9322 |
The different FEM (finite element) model image relative error of 2 three kinds of table compares (%)
| Setting model | FEM (finite element) model a | FEM (finite element) model b | FEM (finite element) model c |
| Model a | 30.6102 | 29.9774 | 22.8635 |
| Model b | 28.8769 | 29.0497 | 23.0424 |
| Model c | 30.1741 | 29.8459 | 23.1085 |
| Model d | 29.2233 | 29.7355 | 23.0999 |
| Model e | 28.9367 | 30.1424 | 23.7060 |
| Model f | 29.0242 | 30.5022 | 23.0997 |
| Model g | 30.6630 | 29.0480 | 23.1877 |
| Model h | 29.4768 | 29.8878 | 23.2817 |
From table 1,2, under same experimental conditions, in terms of correlation coefficient, three kinds of FEM (finite element) model correlation coefficienies
Meansigma methodss are respectively 0.8786,0.8777,0.9338, compared with FEM (finite element) model b in FEM (finite element) model a in Fig. 5 and Fig. 6, Fig. 7
Middle FEM (finite element) model c correlation coefficient averagely improves 6.2827%, 6.3917%；In terms of image relative error, three kinds limited
Meta-model diagram is respectively 29.6231% as the meansigma methodss of relative error, 29.7736%, finite element mould in 23.1737%, with Fig. 5
Type a is compared with FEM (finite element) model b in Fig. 6, in Fig. 7 FEM (finite element) model c image relative error averagely reduce 21.7715%,
22.1670%, effectively increase human lung's Electrical Resistance Tomography image reconstruction accuracy.
In sum, human lung's Electrical Resistance Tomography FEM (finite element) model method for designing proposed by the present invention, in identical reality
Under the conditions of testing, not only increase the computational accuracy of direct problem, improve the Degree of Ill Condition of sensitivity matrix and hessian matrix,
And improve the uniformity of sensitivity profile, thus effectively increasing human lung's resistive layer image reconstruction precision.
Claims (4)
1. a kind of human lung's Electrical Resistance Tomography FEM (finite element) model method for designing is it is characterised in that human lung's resistance chromatographs
The finite element that imaging FEM (finite element) model refers to for this certain organs of human lung, is applied to human lung's Electrical Resistance Tomography
Model；
The comprising the concrete steps that of human lung's Electrical Resistance Tomography FEM (finite element) model method for designing:
Step one: according to human chest ct scanning figure, whole FEM (finite element) model is divided into the region being made up of lung, heart, vertebra
One and the region two that is made up of fatty tissue, using the boundary curve equation improving particle cluster algorithm and determining region one, two；
Step 2: according to pulmonary's priori, the model of setting reflection human lung's structure, using based on grid reconstruction finite element
Model calculates Electrical Resistance Tomography direct problem, and using gained sensitivity field boundary voltage value of calculation as theoretical value；
Step 3: to improve direct problem computational accuracy and to improve sensitivity matrix Degree of Ill Condition as optimization aim, with region one, two
The FEM (finite element) model number of plies being comprised and region one, the corresponding finite element of two each layers of finite element node polar angle identical with respective border
The ratio of node polar diameter be variable, using improve particle cluster algorithm optimized FEMs model, thus obtain for human lung this
One certain organs, the FEM (finite element) model of human lung's Electrical Resistance Tomography of being applied to.
2. a kind of human lung's Electrical Resistance Tomography FEM (finite element) model method for designing according to claim 1, its feature exists
Boundary curve equation in, described region one, two takes polar form:In formula,For polar diameter, θ
For polar angle, ai、bi、ci∈ [- 10,10], n are integer and meet 20≤n≤100.
3. a kind of human lung's Electrical Resistance Tomography FEM (finite element) model method for designing according to claim 1, its feature exists
In, described using improve particle cluster algorithm determine the boundary curve equation in region one, two be withIt is suitable
Response function, in formula, x is ai、bi、ci(i=1,2 ... n) represented by variable, m be boundary node number, ρ be boundary node pole
Footpath,With ρiPolar angle is identical, λi∈(0,+∞).
4. a kind of human lung's Electrical Resistance Tomography FEM (finite element) model method for designing according to claim 1, its feature exists
In, described using improve particle cluster algorithm optimized FEMs model be withFor fitness function, in formula,
The FEM (finite element) model number of plies and region one, two each layers of finite element node and respective border same pole that y is comprised by region one, two
The variable represented by ratio of the corresponding finite element node polar diameter in angle, rms is corresponding mean square based on pulmonary's priori model with s
Root and sensitivity matrix, cond represents conditional number.
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| CN111091605A (en) * | 2020-03-19 | 2020-05-01 | 南京安科医疗科技有限公司 | Rib visualization method, identification method and computer-readable storage medium |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110021068A (en) * | 2019-02-14 | 2019-07-16 | 清华大学 | A kind of 3 d medical images reconstructing method based on finite element |
| CN110021068B (en) * | 2019-02-14 | 2020-10-23 | 清华大学 | Three-dimensional medical image reconstruction method based on finite element |
| CN110991014A (en) * | 2019-11-18 | 2020-04-10 | 中国计量大学 | Multi-physical field analysis method of artificial heart wireless energy supply system |
| CN110991014B (en) * | 2019-11-18 | 2023-06-16 | 中国计量大学 | Multi-physical field analysis method of artificial heart wireless energy supply system |
| CN110955992A (en) * | 2019-11-21 | 2020-04-03 | 天津科技大学 | Method and system for constructing finite element model of six-year-old child passenger and method and system for evaluating child restraint system |
| CN111091605A (en) * | 2020-03-19 | 2020-05-01 | 南京安科医疗科技有限公司 | Rib visualization method, identification method and computer-readable storage medium |
| CN111091605B (en) * | 2020-03-19 | 2020-07-07 | 南京安科医疗科技有限公司 | Rib visualization method, identification method and computer-readable storage medium |
| CN113456959A (en) * | 2021-06-28 | 2021-10-01 | 东北大学 | Method and device for setting positive end expiratory pressure of respirator and storage medium |
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