CN106725468B - Multi-frequency electromagnetic tomography method for cerebral hemorrhage detection - Google Patents

Multi-frequency electromagnetic tomography method for cerebral hemorrhage detection Download PDF

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CN106725468B
CN106725468B CN201611031436.2A CN201611031436A CN106725468B CN 106725468 B CN106725468 B CN 106725468B CN 201611031436 A CN201611031436 A CN 201611031436A CN 106725468 B CN106725468 B CN 106725468B
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cerebral hemorrhage
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tissue
excitation current
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CN106725468A (en
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谭超
肖志利
董峰
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Tianjin University
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    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/05—Detecting, measuring or recording for diagnosis by means of electric currents or magnetic fields; Measuring using microwaves or radio waves 
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
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    • A61B5/7203—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal

Abstract

The invention discloses a multi-frequency electromagnetic chromatography for cerebral hemorrhage detectionThe imaging method comprises the following steps of distributing a plurality of coils on the periphery of a detected area, sequentially introducing alternating excitation currents with different frequencies to the excitation coils, sequentially generating induction voltages at different frequencies by detection coils positioned around the detected area, and realizing the reconstruction of a cerebral hemorrhage target image: and calculating the detection voltage difference caused by the brain containing the cerebral hemorrhage on the detection coil. Calculating at an excitation current frequency of fiIn time, the brain with cerebral hemorrhage causes a phase shift in the detected voltage on the detection coil. Solving the equation by using a Tikhonov regularization method to obtain the reference frequency f of the excitation current1The phase shift of the detected voltage on the detection coil caused by a single tissue j. Calculating the frequency f of the exciting current of the cerebral hemorrhage tissuenAnd f1The phase difference obtained at the detection coil. And (5) calculating the conductivity distribution of the cerebral hemorrhage tissues.

Description

Multi-frequency electromagnetic tomography method for cerebral hemorrhage detection
Technical Field
The invention belongs to the technical field of biological imaging, and relates to a multi-frequency electromagnetic tomography method.
Technical Field
Currently, the clinical medical imaging methods for detecting cerebral hemorrhage include CT, MRI, and the like. However, these imaging methods are expensive and contain radioactive sources, which are not conducive to long-term continuous monitoring. The electromagnetic tomography is an electrical tomography technology based on the electromagnetic induction principle, and as the electromagnetic field can penetrate through the skull with lower conductivity and has the characteristics of non-contact, no radiation, low price and the like, the long-term continuous monitoring of focus such as cerebral hemorrhage can be realized, and the electromagnetic tomography has great development prospect.
When the electromagnetic tomography technology is used for cerebral hemorrhage detection, two methods of time difference and frequency difference exist when boundary measurement values are solved through image reconstruction: the time difference method is characterized in that under the same frequency, a detection signal obtained by a brain with cerebral hemorrhage in a sensitive field is differentiated from a detection signal obtained by a brain without cerebral hemorrhage in the sensitive field to be used as a boundary measurement value during image reconstruction, and the method can be used for continuously monitoring cerebral hemorrhage, but is not beneficial to the initial detection of the cerebral hemorrhage because the brain scanning information of a patient before the cerebral hemorrhage occurs is difficult to obtain; the frequency difference method is based on the characteristic that dielectric characteristic parameters of biological tissues change along with frequency, when a sensitive field contains a brain with cerebral hemorrhage, detection signals obtained by the conductivity of the brain tissues under different frequencies are subjected to subtraction to be used as boundary measurement values to carry out image reconstruction, and object field information before the cerebral hemorrhage occurs is not needed in the method, so that the defect that the object field information before the cerebral hemorrhage occurs cannot be obtained by a time difference method is overcome.
Disclosure of Invention
The invention aims to solve the problem of artifact in a cerebral hemorrhage imaging result of the existing frequency difference method, and the cerebral hemorrhage information is separated from all tissue test information by using a multi-frequency sequential excitation method, so that the position and the size of cerebral hemorrhage are subjected to independent image reconstruction, and the resolution of cerebral hemorrhage imaging is improved. The technical scheme of the invention is as follows:
a multi-frequency electromagnetic tomography method for cerebral hemorrhage detection distributes a plurality of coils on the periphery of a detected area, alternating excitation currents with different frequencies are sequentially introduced to excitation coils, detection coils positioned around the detected area sequentially generate induction voltages under different frequencies, and the specific calculation method for realizing cerebral hemorrhage target image reconstruction is as follows:
(1) by using
Figure GDA0002551444850000011
Calculating the detection voltage difference caused by the brain containing the cerebral hemorrhage on the detection coil, wherein i is more than or equal to 1 and less than or equal to n, and n is the number of all brain tissues including the cerebral hemorrhage tissues;
Figure GDA0002551444850000012
at an excitation current frequency fiDetecting the detection voltage on the coil when a brain containing cerebral hemorrhage exists in the time sensitive field;
Figure GDA0002551444850000013
at an excitation current frequency fiAnd only air in the time sensitive field is distributed to detect the detection voltage on the coil.
(2) By using
Figure GDA0002551444850000014
Calculating at an excitation current frequency of fiIn time, detection of the coil of detection of cerebral hemorrhagePhase shift of voltage
Figure GDA0002551444850000015
(3) Setting f1For exciting a current reference frequency, using
Figure GDA0002551444850000021
Solving the equation by using a Tikhonov regularization method to obtain the reference frequency f of the excitation current1When a single tissue j causes a phase shift of the detection voltage on the detection coil
Figure GDA0002551444850000022
j is the label of the brain tissue to be tested; kσIs a square matrix relating the conductivity of the respective tissue at different excitation current frequencies, i.e.
Figure GDA0002551444850000023
Figure GDA0002551444850000024
Is an excitation current frequency of fiThe electrical conductivity of tissue j. Setting j to 1 as cerebral hemorrhage tissue,
Figure GDA0002551444850000025
that is, the cerebral hemorrhage tissue is at the excitation current reference frequency f1Detecting the phase shift of the detection voltage on the coil; the phase shift of the detection voltage on the detection coil when the cerebral hemorrhage tissue excites the current reference frequency can be obtained through simulation, and the phase shift is compared with the detection voltage
Figure GDA0002551444850000026
With the smallest error therebetween, the regularization parameters of the Tikhonov regularization method are selected.
(4) According to the formula
Figure GDA0002551444850000027
Calculating the frequency f of the exciting current of the cerebral hemorrhage tissuenAnd f1Phase difference between the detection coils
Figure GDA0002551444850000028
Wherein
Figure GDA0002551444850000029
Is the brain bleeding tissue at the excitation current reference frequency f1Electrical conductivity of the alloy;
Figure GDA00025514448500000210
is the frequency f of the cerebral hemorrhage tissue in the excitation current testnElectrical conductivity of the steel.
(5) By using
Figure GDA00025514448500000211
Solving the formula by using a Tikhonov regularization method to obtain the conductivity distribution delta sigma of the cerebral hemorrhage tissue, wherein S is at the excitation current reference frequency f1Dividing the sensitivity field into voxels with the same size by using a perturbation method, and circularly exciting the phase shift of detection voltage of the detection coil obtained by circular detection when the conductivity change of each voxel is 1S/m; the regularization parameters of the Tikhonov regularization method are selected by solving for the minimum error between the reconstructed conductivity distribution and the true conductivity distribution.
Based on the electromagnetic induction principle, according to the characteristic that the phase shift of the detection voltage obtained by the detection coil linearly changes along with the frequency and the conductivity, the phase shift of the cerebral hemorrhage tissue is separated by detecting the phase shift of all the cerebral tissues under multi-frequency excitation, a cerebral hemorrhage distribution image is reconstructed, and artifacts generated by other tissues on cerebral hemorrhage imaging are eliminated.
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The following drawings depict selected embodiments of the present invention, all by way of example and not by way of exhaustive or limiting example, and are presented in the figures of the accompanying drawings:
FIG. 1 is a schematic diagram of a distribution of a 2-dimensional 16-coil electromagnetic tomography coil sensor array used in a multi-frequency imaging method of the present invention;
FIG. 2 is a schematic diagram of a 2-dimensional coil sensor structure used in the multi-frequency imaging method of the present invention;
FIG. 3 is a schematic view of the tissue distribution of a 2-dimensional brain model for simulated image reconstruction used in the multi-frequency imaging method of the present invention;
figure 4 reconstruction of the conductivity change of cerebral hemorrhage by the multi-frequency imaging method of the present invention.
Detailed Description
The electromagnetic tomography multi-frequency imaging method is based on the characteristic that dielectric characteristic parameters of biological tissues change along with frequency, and can reconstruct the imaging result of a single cerebral hemorrhage tissue according to the characteristic that the phase shift of detection voltage changes along with the frequency and the linear change of conductivity, so that the defect that the object field information before the cerebral hemorrhage occurs cannot be acquired by a time difference method can be overcome, and artifacts in the cerebral hemorrhage imaging result obtained by a double-frequency difference method can be eliminated. The multi-frequency imaging method comprises the steps of separating detection voltage phase shifts generated by single tissues on a detection coil by acquiring the detection voltage phase shifts generated by brain tissues containing cerebral hemorrhage on the detection coil under different frequencies, and then acquiring the phase difference of the cerebral hemorrhage tissues under the test frequency and the reference frequency, so as to reconstruct the imaging result of the cerebral hemorrhage single tissues.
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1, an array of electromagnetic tomography coil sensors is a distributed form, which includes 16 coil sensors, a sensitive field and a shielding layer. The 16 coil sensors are completely the same, can be used as excitation coils to pass excitation current and can be used as detection coils to acquire detection voltage, and the structure of the sensor is shown in fig. 2. At different excitation current excitation frequencies fiThen, an excitation current is introduced into one coil, and all other coils are used as detection coils to respectively acquire detection voltage in the case of a null field
Figure GDA0002551444850000031
Voltage detection in cerebral hemorrhage
Figure GDA0002551444850000038
The tested brain model can be placed in the sensitive field. The shielding layer is used for shielding external magnetic field interference.
FIG. 3 is a simulation diagram for use with the multi-frequency imaging method of the present inventionLike a schematic representation of the tissue distribution of a reconstructed 2-dimensional real brain model. The figure contains seven tissues, respectively fat, skull, muscle, cerebrospinal fluid, grey brain matter, white brain matter and cerebral hemorrhage. The radius of the cerebral hemorrhage in the figure is 17mm, and the conductivity setting of the cerebral hemorrhage is the same as the blood conductivity. Conductivity of brain tissue at different frequencies
Figure GDA0002551444850000032
As shown in table 1.
Fig. 4 is a reconstruction result of cerebral hemorrhage obtained by the multi-frequency imaging method of the present invention, and the black solid line in the figure indicates the position and size of cerebral hemorrhage.
The multi-frequency imaging method of the present invention, which can be used for electromagnetic tomography of other biological tissues, is described below by taking the brain model of fig. 3 as an example.
The method for realizing the image reconstruction of the cerebral hemorrhage target by using the test data obtained by the electromagnetic tomography coil sensor array and the multi-frequency imaging method comprises the following steps:
step 1: in electromagnetic tomography, detection voltage can be directly obtained at a detection coil, and the voltage difference between an object field and a null field of a brain containing cerebral hemorrhage is as follows:
Figure GDA0002551444850000033
in the formula (f)i(i is more than or equal to 1 and less than or equal to n) represents the frequency of the excitation current, and n is the number of all brain tissues including the cerebral hemorrhage tissues;
Figure GDA0002551444850000034
at a frequency fiDetecting the detection voltage on the coil when a brain containing cerebral hemorrhage exists in the time sensitive field;
Figure GDA0002551444850000035
at a frequency fiAnd only air in the time sensitive field is distributed to detect the detection voltage on the coil.
Step 2: under the current excitation-phase detection strategy of electromagnetic tomographyDue to the fact that
Figure GDA0002551444850000036
The phase shift of the voltage difference between the object field and the null field of a brain containing a cerebral hemorrhage is:
Figure GDA0002551444850000037
and step 3: it is assumed that the phase shift of the detection voltage caused by all tissues is a linear superposition of the phase shifts of the detection voltages caused by the individual tissues, i.e.:
Figure GDA0002551444850000041
in the formula (f)iIs the excitation frequency; j is the label of the brain tissue to be tested;
Figure GDA0002551444850000042
is a single tissue j at a frequency fiThe phase shift of the resulting detection voltage.
And 4, step 4: under the current excitation-phase detection strategy of electromagnetic tomography, the phase shift of the detection voltage linearly changes with frequency for a fixed conductivity distribution. At excitation current test frequency fiPhase shift of the detected voltage
Figure GDA0002551444850000043
Can be equivalently converted into an excitation current reference frequency f1Phase shift of the detected voltage
Figure GDA0002551444850000044
Namely:
Figure GDA0002551444850000045
and
Figure GDA0002551444850000046
bringing into formula (3) to obtain:
Figure GDA0002551444850000047
and 5: under the current excitation-phase detection strategy of electromagnetic tomography, the phase shift of the detection voltage varies linearly with the conductivity of a tissue for a fixed tissue distribution and excitation frequency. For tissue j at excitation current reference frequency f1Phase shift of lower detection voltage
Figure GDA0002551444850000048
And
Figure GDA0002551444850000049
are equivalently transformed between, i.e.
Figure GDA00025514448500000410
Bringing into formula (4) to obtain:
Figure GDA00025514448500000411
in the formula (I), the compound is shown in the specification,
Figure GDA00025514448500000412
is at a frequency fiThe electrical conductivity of tissue j. Steps 1 to 3 can be simplified to the following formula:
Figure GDA00025514448500000413
in the formula, matrix KσThe number of rows is equal to the number of frequencies, and the number of columns is equal to the number of types of the tested brain tissues. The number of frequencies in the present invention is equal to the number of types of the brain tissue to be measured. Due to the matrix KσThe condition number of (2) is large, and the formula (6) is a disease state equation. For the brain model of FIG. 3, the number of frequencies is 7, between 1MHz and 10MHz, at 0.5MHz intervals, with matrix KσBased on the condition number of (1), selecting the frequency combination to make the matrix KσThe condition number of (2) is minimal. The selected frequencies are 1MHz, 1.5MHz, 2.5MHz, 4MHz, 6.5MHz, 7.5MHz and 10MHz, the matrix KσThis can be obtained from the electrical conductivity of each tissue in table 1 at different frequencies. Solving the equation of morbidity (by using Tikhonov regularization method6) The tissue j at the reference frequency f can be calculated1Phase shift of the lower induced sense voltage
Figure GDA0002551444850000051
Setting j to 1 as cerebral hemorrhage tissue,
Figure GDA0002551444850000052
is the cerebral hemorrhage tissue at the reference frequency f1The phase shift of the voltage is detected at 1 MHz. Detecting voltage phase shift and phase shift of cerebral hemorrhage tissue at reference frequency obtained by simulation
Figure GDA0002551444850000053
With the smallest error in between, to select the regularization parameter.
Figure GDA0002551444850000054
Is the cerebral hemorrhage tissue at the test frequency f7The phase shift of the voltage is detected at 10 MHz.
Step 6: cerebral hemorrhage tissue at test frequency f710MHz and reference frequency f1The phase difference between the detection voltages is 1 MHz:
Figure GDA0002551444850000055
solution formula
Figure GDA0002551444850000056
Solving this equation using a Tikhonov regularization method to reconstruct the conductivity distribution Δ σ of the cerebral hemorrhage tissue, where S is at the excitation current reference frequency f1Dividing the sensitive field into voxels with the same size by using a perturbation method, and circularly exciting the phase shift of detection voltage of the detection coil obtained by cyclic detection when the conductivity change of each voxel is 1S/m; the regularization parameters may be selected by solving for a minimum error between the reconstructed conductivity distribution and the true conductivity distribution.
The invention uses a multi-frequency excitation method to separate the phase shift of the detection voltage of the cerebral hemorrhage tissue under the reference frequency from the phase shift of the detection voltage generated by all tissues under the excitation of a plurality of frequencies, thereby reconstructing the image of the cerebral hemorrhage distribution. From the reconstruction result of fig. 4, it can be seen that the multi-frequency imaging method eliminates artifacts caused by frequency change of other tissues, and only obtains the conductivity change distribution of the cerebral hemorrhage tissue, thereby improving the reconstruction accuracy of the cerebral hemorrhage imaging.
Table 1 is the conductivity of a portion of brain tissue at different frequencies.
Frequency (MHz) 1 1.5 2.5 4 6.5 7.5 10
Fat (S/m) 0.044 0.044 0.045 0.047 0.049 0.050 0.053
Skull (S/m) 0.024 0.027 0.030 0.034 0.039 0.040 0.043
Muscle (S/m) 0.503 0.531 0.559 0.581 0.600 0.606 0.617
Cerebrospinal fluid (S/m) 2.000 2.000 2.000 2.000 2.001 2.001 2.002
Polio (S/m) 0.163 0.172 0.189 0.212 0.248 0.262 0.292
White matter of brain (S/m) 0.102 0.107 0.116 0.125 0.140 0.145 0.158
Cerebral hemorrhage (blood) (S/m) 0.822 0.822 0.958 1.017 1.064 1.075 1.097

Claims (1)

1. A multi-frequency electromagnetic tomography method for cerebral hemorrhage detection is used for simulating a 2-dimensional real brain model for image reconstruction, a plurality of coils are distributed on the periphery of a detected region, alternating excitation currents with different frequencies are sequentially introduced into the excitation coils, detection coils positioned around the detected region sequentially generate induction voltages under different frequencies, and the step of reconstructing a cerebral hemorrhage target image is as follows:
(1) by using
Figure FDA0002551444840000011
Calculating the detection voltage difference caused by the brain containing the cerebral hemorrhage on the detection coil, wherein i is more than or equal to 1 and less than or equal to n, and n is the number of all brain tissues including the cerebral hemorrhage tissues;
Figure FDA0002551444840000012
at an excitation current frequency fiDetecting coil when brain containing cerebral hemorrhage exists in time sensitive fieldThe detection voltage of (1);
Figure FDA0002551444840000013
at an excitation current frequency fiDetecting the detection voltage on the coil when only air is distributed in the time sensitive field;
(2) by using
Figure FDA0002551444840000014
Calculating at an excitation current frequency of fiIn time, the phase shift of the detection voltage on the detection coil caused by the brain with cerebral hemorrhage
Figure FDA0002551444840000015
(3) Setting f1For exciting a current reference frequency, using
Figure FDA0002551444840000016
Solving the equation by using a Tikhonov regularization method to obtain the reference frequency f of the excitation current1When a single tissue j causes a phase shift of the detection voltage on the detection coil
Figure FDA0002551444840000017
j is the label of the brain tissue to be tested; kσIs a square matrix relating the conductivity of the respective tissue at different excitation current frequencies, i.e.
Figure FDA0002551444840000018
Figure FDA0002551444840000019
Is an excitation current frequency of fiThe conductivity of tissue j; setting j to 1 as cerebral hemorrhage tissue,
Figure FDA00025514448400000110
that is, the cerebral hemorrhage tissue is at the excitation current reference frequency f1Detecting the phase shift of the detection voltage on the coil; the cerebral hemorrhage tissue can be obtained through simulationDetecting a phase shift of the detected voltage on the coil at the reference frequency of the excitation current, based on the detected voltage and the reference frequency
Figure FDA00025514448400000111
Selecting a regularization parameter of the Tikhonov regularization method by using the minimum error between the regularization parameters and the regularization parameter;
(4) according to the formula
Figure FDA00025514448400000112
Calculating the frequency f of the exciting current of the cerebral hemorrhage tissuenAnd f1Phase difference between the detection coils
Figure FDA00025514448400000113
Wherein
Figure FDA00025514448400000114
Is the brain bleeding tissue at the excitation current reference frequency f1Electrical conductivity of the alloy;
Figure FDA00025514448400000115
is the frequency f of the excitation current of the cerebral hemorrhage tissuenElectrical conductivity of the alloy;
(5) using the formula P.DELTA.sigma ═ DELTA.phi1Solving the equation by using a Tikhonov regularization method to obtain the conductivity distribution delta sigma of the cerebral hemorrhage tissue, wherein P is at the excitation current reference frequency f1Dividing the sensitivity field into voxels with the same size by using a perturbation method, and circularly exciting the phase shift of detection voltage of the detection coil obtained by circular detection when the conductivity change of each voxel is 1S/m; the regularization parameters of the Tikhonov regularization method are selected by solving for the minimum error between the reconstructed conductivity distribution and the true conductivity distribution.
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