A kind of human lung's electrical resistance tomography finite element model design method
Technical field
The present invention relates to a kind of human lung's electrical resistance tomography finite element model design methods, belong to electrical resistance tomography
Technical field.
Background technique
Biomedical electrical impedance tomography (Electrical Impedance Tomography, EIT) technology is with life
The distribution or variation of electrical impedance are a kind of biomedical detection of novel lossless wound and the imaging technique of imageable target in object, it is logical
It crosses and certain safe exciting current is applied in vitro, measure organism surface voltage signal to reconstruct the impedance of organism point
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 common disease and frequently-occurring disease, and pulmonary disease common at present has pneumonia, branch gas
Guan Yan, pulmonary tuberculosis, bronchiectasis or lung tumors etc..When above-mentioned pulmonary disease occurs, the functional lesion of organ is often
Earlier than the generation of Organic lesion or other clinical symptoms.The imaging skill generallyd use in medical diagnosis at present and clinical application
Art has CT, ultrasound or magnetic resonance etc..Compared with these imaging techniques, the resolution ratio of Electrical Resistance Tomography is lower, but conduct
A kind of new non-destructive testing technology, the Clinics and Practices for being applied to human lung's disease early stage have the advantage that
1. Electrical Resistance Tomography is using electrode as sensor, detection device volume is small, structure is simple, has cost
Cheap, portable superiority;
2. Electrical Resistance Tomography is imaged using low-frequency current, radioactive radiation is avoided, it, can be right to human zero damage
Patient carries out long-time, dynamic monitor;
3. Electrical Resistance Tomography can realize functional imaging.
Currently, generalling use multiple physical field coupling finite element analysis software COMSOL in Electrical Resistance Tomography
Multiphysics calculates direct problem.Although COMSOLMultiphysics has the advantages that powerful, versatile, answer
When for human lung's electrical resistance tomography, have the shortcomings that specific aim is poor, direct problem computational accuracy is lower.It is just asked to improve
Computational accuracy, the general method for using grid reconstruction are inscribed, but the calculation amount of this method is very big, is unable to satisfy in practical application to reality
The requirement of when property.In addition, the pathosis of sensitivity matrix and the inhomogeneities of sensitivity profile are also to influence human lung's resistance
An important factor for tomographic image reconstruction precision.Therefore, it is badly in need of one kind human lung's electrical resistance tomography can be improved just asking
The computational accuracy of topic improves the Degree of Ill Condition of sensitivity matrix and Hessian matrix, improves the uniformity of sensitivity profile, into
And improve the design of human lung's electrical resistance tomography finite element model of human lung's electrical resistance tomography image reconstruction accuracy
Method.
Summary of the invention
In view of the above existing problems in the prior art, the present invention provides a kind of human lung's electrical resistance tomography finite element moulds
Type design method not only can be improved the computational accuracy of human lung's electrical resistance tomography direct problem, change under same experimental conditions
The Degree of Ill Condition of kind sensitivity matrix and Hessian matrix, and the uniformity of sensitivity profile can be improved, and then improve human body
Lung's electrical resistance tomography image reconstruction accuracy.
To achieve the goals above, a kind of human lung's electrical resistance tomography finite element model design side that the present invention uses
Method, human lung's electrical resistance tomography finite element model refer to for human lung this certain organs, are suitable for human lung
The finite element model of electrical resistance tomography;
Human lung's electrical resistance tomography finite element model design method comprises the concrete steps that:
Step 1: according to human chest CT scan figure, entire finite element model is divided into and is made of lung, heart, vertebra
Region one and the region two being made of adipose tissue determine the boundary curve side in region one, two using improvement particle swarm algorithm
Journey;
Step 2: according to lung's priori knowledge, the model of setting reflection human lung's structure is had using based on grid reconstruction
It limits meta-model and calculates electrical resistance tomography direct problem, and using gained sensitivity field boundary voltage calculated value as theoretical value;
Step 3: to improve direct problem computational accuracy and improve sensitivity matrix Degree of Ill Condition as optimization aim, with region
One, the two finite element model numbers of plies for being included and region one, two each layers of finite element node polar angle identical as respective boundary are corresponding
The ratio of finite element node polar diameter is variable, using particle swarm algorithm optimized FEMs model is improved, is directed to human body to obtain
This certain organs of lung, suitable for the finite element model of human lung's electrical resistance tomography.
Preferably, the boundary curve equation in the 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, it is described using improve particle swarm algorithm determine region one, two boundary curve equation be withFor fitness function, in formula, X ai、bi、ci(i=1,2 ... n) represented by variable, m be boundary section
Point number, ρ are boundary node polar diameter,With ρiPolar angle is identical, λi∈(0,+∞)。
Preferably, it is described using improve particle swarm algorithm optimized FEMs model be withTo adapt to
Spend function, in formula, the finite element model number of plies that Y includes for region one, two and region one, two each layers of finite element node with respectively
From boundary, identical polar angle is corresponding with variable represented by the ratio for limiting first node polar diameter, and RMS and S are based on lung's priori knowledge mould
The corresponding root-mean-square value of type and sensitivity matrix, cond indicate 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 Yu Hessian matrix, and improves sensitivity profile
Uniformity, to effectively increase human lung's electrical resistance tomography image reconstruction accuracy.
Detailed description of the invention
Fig. 1 is the schematic diagram of actual boundary;
Fig. 2 is the schematic diagram that boundary is determined using improvement particle swarm algorithm;
Fig. 3 is the comparison schematic diagram that actual boundary and improvement particle swarm algorithm determine boundary;
Fig. 4 is the schematic diagram by traditional finite element model of principle subdivision at equal intervals;
Fig. 5 is finite element model a i.e. on the basis of adjusting finite element model node in Fig. 4 to boundary one, to improve
Direct problem computational accuracy and improvement sensitivity matrix Degree of Ill Condition are optimization aim, and using improving, particle swarm algorithm Optimized model is each
The schematic diagram for the finite element model that the ratio of layer finite element node finite element node polar diameter corresponding with two same pole angle of boundary obtains;
Fig. 6 is finite element model b, that is, region one, two respectively by the signal of traditional finite element model of principle subdivision at equal intervals
Figure;
Fig. 7 is the schematic diagram that finite element model c is the finite element model obtained using design method proposed by the present invention;
Fig. 8 is that finite element model d is the schematic diagram based on grid reconstruction finite element model;
Fig. 9 is the schematic diagram of the model according to set by lung's priori knowledge;
Figure 10 is the corresponding different finite element model sensitivity field border electricity of the model according to set by lung's priori knowledge in Fig. 9
Press the comparison schematic diagram of calculated value;
Figure 11 is that one group of lung's different location the schematic diagram that pathological tissues correspond to model occurs;
Figure 12 is that different finite element models 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 the corresponding improved capacity spectrum method image reconstruction result of finite element model a;
Figure 14 is the schematic diagram of the corresponding improved capacity spectrum method image reconstruction result of finite element model b;
Figure 15 is the schematic diagram of the corresponding improved capacity spectrum method image reconstruction result of finite element model c;
In figure: 1, boundary one, 2, boundary two, 3, region one, 4, region two.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings.
As shown in Figures 1 to 7, human lung's electrical resistance tomography finite element model refers to that this is specific for human lung
Organ, suitable for the finite element model of human lung's electrical resistance tomography;
A kind of human lung's electrical resistance tomography finite element model design method of the invention comprises the concrete steps that:
Step 1: as shown in Figures 1 to 7, according to human chest CT scan figure, by entire finite element model be divided by lung,
Heart, the region 1 that vertebra is constituted and the region 24 being made of adipose tissue determine region using particle swarm algorithm is improved
One, two boundary curve equation;Wherein, the boundary curve equation in the 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 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 lung's priori knowledge, the model of setting reflection human lung's structure utilizes such as figure
Electrical resistance tomography direct problem is calculated based on grid reconstruction finite element model shown in 5, and gained sensitivity field boundary voltage is calculated
Value is used as theoretical value;
Step 3: to improve direct problem computational accuracy and improve sensitivity matrix Degree of Ill Condition as optimization aim, with region
One, the two finite element model numbers of plies for being included and region one, two each layers of finite element node polar angle identical as respective boundary are corresponding
The ratio of finite element node polar diameter is variable, using particle swarm algorithm optimized FEMs model is improved, to obtain as shown in Figure 7
Be directed to this certain organs of human lung, the finite element model c suitable for human lung's electrical resistance tomography.Wherein, described
Using improve particle swarm algorithm optimized FEMs model be withFor fitness function, in formula, Y is region
One, the two finite element model numbers of plies for being included and region one, two each layers of finite element node polar angle identical as respective boundary are corresponding
Variable represented by the ratio of finite element node polar diameter, RMS and S be based on the corresponding root-mean-square value of lung's priori knowledge model with
Sensitivity matrix, cond indicate conditional number.
As shown in Figure 1 to Figure 3, work as λi=1 (i=1,2 ... m) when, utilize improve particle swarm algorithm determine boundary and reality
Border boundary coincide substantially, can be by artificially adjusting λiValue, further increases the degree of agreement of area-of-interest.
As shown in Figure 10, sensitive field border electricity obtained by direct problem is calculated to be based on grid reconstruction finite element model in step 2
Press calculated value as theoretical value, using the finite model c in the finite model b and Fig. 7 in finite model a, Fig. 6 in Fig. 5
Electrical resistance tomography direct problem is calculated, RMS value is respectively 5.2167%, 4.1566%, 1.4202%.As it can be seen that with limited in Fig. 5
Meta-model a is compared with finite element model b in Fig. 6, the RMS value difference of the finite element model c obtained in Fig. 7 using the design method
72.7759%, 65.8327% is reduced, direct problem computational accuracy is effectively increased.
It is verified, based on model set by lung's priori knowledge as shown in Figure 9, have in finite element model a, Fig. 6 in Fig. 5
The conditional number for limiting sensitivity matrix corresponding to finite element model c in meta-model b and Fig. 7 is respectively 1.9500 × 107、1.3212
×107、8.4075×106, in Fig. 5 in finite element model a and Fig. 6 compared with finite element model b, c pairs of finite element model in Fig. 7
The sensitivity matrix conditional number answered reduces 56.8846%, 36.3647% respectively, effectively improves the morbid state of sensitivity matrix
Degree, to be conducive to improve image reconstruction quality.
In addition, the uniformity of sensitivity profile has important shadow to human lung's electrical resistance tomography image reconstruction accuracy
It rings, generallys use the uniformity of index P evaluation 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 to i-j;Respectively introduce the spirit of triangular finite element area coefficient
The mean value and standard deviation of sensitive matrix.
P is smaller, and sensitivity profile uniformity is better, is more conducive to improve electrical resistance tomography image reconstruction accuracy.Experience
Card, based on model set by lung's priori knowledge as shown in Figure 9, the finite model b in finite model a, Fig. 6 in Fig. 5 with
And P value corresponding to the finite model c in Fig. 7 is respectively 8.1635,8.8428, in 8.0233, with Fig. 5 finite element model a and
Finite element model b is compared in Fig. 6, and P value corresponding to finite element model c reduces 1.7174%, 9.2674% respectively in Fig. 7,
Improve the uniformity of sensitivity profile.
In order in proof diagram 7 finite element model c in terms of improving human lung's electrical resistance tomography image reconstruction quality
Validity is arranged different location lung pathological tissues as shown in figure 11 and corresponds to model, (the Duo T8100 under same experimental conditions
CPU 3.00GB memory 2.10GHz MATLAB 7.0), by three kinds of different finite element models (finite element model a, b, c) and its right
The sensitivity matrix answered is applied to improved capacity spectrum method image reconstruction.As shown in figure 12, Newton-Raphson is being improved
In image reconstruction algorithm iterative process, in Fig. 5 in finite element model a and Fig. 6 compared with finite element model b, finite element mould in Fig. 7
The corresponding Hessian Matrix condition number of type c is minimum, effectively improves the Degree of Ill Condition of Hessian matrix.
In Electrical Resistance Tomography, related coefficient and image relative error evaluation algorithms image weight are generallyd use at present
Quality is built, shown in expression formula such as formula (3), (4).Related coefficient is bigger, image relative error is smaller, shows that image reconstruction accuracy is got over
It is high.Three kinds of different finite element model (finite element model a, b, c) related coefficients compared with image relative error as shown in table 1,2,
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;WithRespectively g withAverage value.
1 three kinds of table different finite element model related coefficients compare
Model is set |
Finite element model a |
Finite element model b |
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 |
2 three kinds of table different finite element model image relative errors compare (%)
Model is set |
Finite element model a |
Finite element model b |
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 |
By table 1,2 it is found that under same experimental conditions, in terms of related coefficient, three kinds of finite element model related coefficients
Average value is respectively 0.8786,0.8777,0.9338, in Fig. 5 in finite element model a and Fig. 6 compared with finite element model b, Fig. 7
Middle finite element model c related coefficient averagely improves 6.2827%, 6.3917%;In terms of image relative error, three kinds limited
Meta-model diagram is as the average value of relative error is respectively 29.6231%, 29.7736%, finite element mould in 23.1737%, with Fig. 5
Type a is compared with finite element model b in Fig. 6, in Fig. 7 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 conclusion human lung's electrical resistance tomography finite element model design method proposed by the present invention, in identical reality
Under the conditions of testing, the computational accuracy of direct problem is not only increased, improves the Degree of Ill Condition of sensitivity matrix Yu Hessian matrix,
And the uniformity of sensitivity profile is improved, to effectively increase human lung's resistive layer image reconstruction precision.