Fast sar estimation method based on plane wave electric field reconstruction

Abstract

The application relates to the field of bioelectromagnetics, in particular to a fast SAR (Specific Absorption Rate) estimation method based on plane wave electric field reconstruction. rec The application comprises the following steps: establishing a plurality of reconstruction planes in the electric field measurement space of a fast SAR measurement system, calculating the electric field E of any reconstruction plane based on a plane wave expansion method, calculating the electric fields of the plurality of reconstruction planes and obtaining the specific absorption rate (SAR) value of the measurement space. In the reconstruction plane electric field calculation, the stability of the field reconstruction algorithm is enhanced based on the plane wave expansion method combined with Tikhonov regularization, the accuracy of the field reconstruction is improved, the SAR value calculation error is effectively reduced, and the ill-conditioned problem existing in the fast SAR measurement method based on field reconstruction is overcome.

Description

Technical Field

[0001] This invention relates to the field of bioelectromagnetics, and more particularly to a rapid measurement method for SAR. Background Technology

[0002] SAR is an abbreviation for Specific Absorption Rate, which is a measure of how much electromagnetic radiation energy the body actually absorbs. It is expressed in watts per kilogram (W / kg) or milliwatts per gram (mW / g). Traditional SAR electromagnetic wave absorption ratio or specific absorption rate measurement systems estimate the energy absorbed from the device by measuring the electric field with a single probe. This is time-consuming and requires complex setup. Therefore, there is a need to develop a rapid measurement system that can accurately measure SAR in a very short time.

[0003] Regarding SAR measurement systems, the paper titled "EU Standards and Measurement Methods for Human Exposure to Radio Frequency Electromagnetic Fields," provided by inventors Jiang Ke et al., introduces the applicable scope, environmental requirements, measurement methods, measurement processes, and result interpretation of traditional SAR measurement systems, but does not cover rapid measurement systems. To develop rapid measurement systems, the paper titled "Discrepancies of Measured SAR between Traditional and Fast Measuring Systems," provided by Liu Zicheng et al., uses a probe array to measure the amplitude and phase of the electric field on a single plane, and then estimates the SAR value based on the reconstructed field of the region of interest. Because the reconstruction algorithm runs quickly and avoids the mechanical scanning steps of traditional SAR measurement equipment, it has become the main direction for the development of SAR measurement equipment.

[0004] The human body simulation fluid is a lossy medium, and the electromagnetic field loses energy during propagation within the fluid. Therefore, the maximum SAR value exists in the region close to the inner wall of the human body model. However, the size of the electric field probe itself and the coupling between the probe and the inner wall mean that the probe can only measure the electric field at a location far from the inner wall of the human body model. Therefore, it is necessary to reconstruct the near field based on the far-field measurements.

[0005] However, near-field reconstruction based on far-field measurements suffers from ill-posed problems and cannot accurately reconstruct the target field. The propagation attenuation of radio waves within the human body model reduces near-field differences in far-field measurements. Since near-field reconstruction based on far-field measurements is the inverse problem of propagation attenuation, far-field measurement errors are amplified in the near-field reconstruction results, leading to insufficient stability of fast SAR measurement methods based on field reconstruction. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art by providing a fast SAR estimation method based on plane wave electric field reconstruction, which enhances the stability of the field reconstruction algorithm and improves the accuracy of near-field reconstruction by combining the plane wave expansion method with Tikhonov regularization, thereby achieving fast and stable SAR estimation.

[0007] To achieve the above objectives, the technical solution adopted by this invention is as follows: a fast SAR estimation method based on plane wave electric field reconstruction, comprising the following steps:

[0008] Step 1: Establishing multiple reconstruction planes in the electric field measurement space of the fast SAR measurement system: The electric field propagating from the radiation source to the measurement plane of the measurement system is taken as the electric field E of the measurement plane. mea The measurement plane is a probe array used for electric field measurement within the simulated human tissue fluid of the measurement system. The simulated human tissue fluid is contained in a measurement tank, and the space enclosed by the measurement plane and the measurement tank is the electric field measurement space. Multiple reconstruction planes parallel to the measurement plane are established within the electric field measurement space, and the electric field of any of the reconstruction planes is the reconstruction plane electric field E. rec ;

[0009] Step 2: Calculate the electric field E of any reconstructed plane based on the plane wave expansion method. rec Steps: Establish any of the reconstructed plane electric fields E rec And measuring the plane electric field E mea The equation is:

[0010] E mea =AE rec ,

[0011] In the formula, A represents the mapping matrix from the measured plane electric field to the reconstructed plane electric field. The following minimization problem is then solved:

[0012]

[0013] In the formula, β is the regularization parameter, which is used to balance the proportion of data difference terms and regularization terms in the total value of the cost function; It is a norm 2 operator;

[0014] Furthermore, the electric field E of any reconstructed plane is obtained. rec The expression is:

[0015] E rec =(A H *A+βI) -1 *A H *E mea ,

[0016] Where I is the identity matrix and the superscript H is the conjugate transpose operator;

[0017] Step 3: Calculate multiple reconstructed plane electric fields The step of obtaining the measured spatial specific absorptivity (SAR) value is as follows: The electric field E of any reconstructed plane obtained in step two is used cyclically. rec The electric field of the multiple reconstructed planes is obtained from the expression. Where l is the distance from the bottom surface of the measurement slot to any reconstruction plane within the measurement space, then the specific absorption rate (SAR) at any position r in the measurement space is:

[0018]

[0019] Where |E rec (r)| represents the root mean square of the reconstructed planar electric field at position r, where σ and ρ represent the conductivity and mass density, respectively.

[0020] Furthermore, in step two, the reconstructed plane electric field E is established based on the plane wave expansion calculation method. rec And measuring the plane electric field E mea The process of obtaining the equation is as follows:

[0021] The reconstructed planar electric field E rec The measured planar electric field E is obtained after amplitude attenuation and phase change during propagation in space. mea The specific propagation process is represented as follows:

[0022] E mea =invF*[P.*(F*E rec )],

[0023] Where F is the two-dimensional Fourier transform matrix, and E is the reconstructed plane electric field. rec Multiplying the components yields the spectrum of the reconstructed plane electric field, where P is the propagation factor, used to measure the amplitude and phase changes of each spectral component as it transforms from the measured plane electric field to the reconstructed plane electric field. Therefore, P is multiplied by F*E. rec Multiplying them yields the spectrum of the electric field in the measured plane; invF is the two-dimensional inverse Fourier transform matrix, and invF is related to P.*(F*E). rec Multiplying these yields the measured plane electric field E. mea ;

[0024] Let A = invF * P * F, then the reconstructed planar electric field E is obtained. rec And measuring the plane electric field E mea The equation.

[0025] Furthermore, in step two, the reconstructed planar electric field E is obtained by solving a minimization problem. rec The specific process is as follows:

[0026] Due to the aforementioned reconstructed plane electric field Erec And measuring the plane electric field E mea Satisfying the equation:

[0027] E mea =A*E rec ,

[0028] To ensure that the difference between the two sides of the equation is minimized, let:

[0029]

[0030] Therefore, we get:

[0031]

[0032] However, since the mapping matrix A is ill-conditioned, the reconstructed planar electric field E... rec The optimal solution for measuring the plane electric field E mea The interference present in the middle is very sensitive, causing the reconstructed plane electric field E rec If the solution is unstable, then Tikhonov regularization is used to obtain the reconstructed plane electric field E. rec The solution formula is:

[0033]

[0034] Since the minimization problem is a convex problem, the reconstructed planar electric field E rec If the optimal solution is the extreme point, then taking the derivative of the cost function yields:

[0035]

[0036] And setting it equal to 0, we obtain any of the reconstructed planar electric fields E. rec The expression.

[0037] Furthermore, the multiple reconstructed planar electric fields obtained in step three... Used to estimate the maximum electric field value radiated from the radiation source into the simulated human tissue fluid of the fast SAR measurement system.

[0038] Furthermore, the height from the bottom of the measuring groove to the measuring plane within the measuring space is z. mea , and z mea ∈[1, 20] mm, the distance from any of the reconstructed planes to the bottom surface of the measuring slot in the measuring space is in

[0039] Furthermore, the rapid SAR measurement system includes a probe array, a measurement tank filled with human body simulation fluid, and a radiation source. The radiation source is placed on a support frame below the measurement tank. The human body simulation fluid is a simulated liquid of human tissue. The probe array is an array of probes immersed in the human body simulation fluid and is used to measure the electric field amplitude and phase in the measurement tank.

[0040] Furthermore, the probe array is as follows:

[0041] (2M+1)×(2M+1),

[0042] The array position is:

[0043] (mΔd, nΔd, Z) mea ),

[0044] m, n=-M, -M+1,...,M,

[0045] Wherein, the probe spacing Δd∈(2,20)mm, M∈[10,30], and M is the number of probes.

[0046] Furthermore, the probe array is a 29×29 probe array, which is uniformly distributed on the measurement plane within the measurement slot defined by x and y, where -10cm≤x≤10cm and -10cm≤y≤10cm. The radiation source is placed on a support frame 2-5mm from the bottom of the measurement slot, and the vector probe array is on the plane with z = 19.25mm. The probe spacing is 7mm.

[0047] Furthermore, the radiation source is an electronic device with electromagnetic wave emission capabilities, such as mobile phones, computers, wireless network cards, and other electronic products.

[0048] The beneficial effects of this invention are: the method provided by this invention overcomes the ill-conditioned problems of fast SAR measurement methods based on field reconstruction. In the process of obtaining the reconstructed plane electric field, this invention can process the measured plane electric field data to obtain an accurate reconstructed plane electric field, effectively reducing the SAR value calculation error. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the probe array of the present invention measuring the amplitude and phase of the electric field on a single plane;

[0050] Figure 2 This is a schematic diagram of the ill-conditioned problem of electromagnetic field reconstruction in this invention;

[0051] Figure 3 This is the x-component diagram of the reconstructed planar electric field obtained in the experiment of this invention;

[0052] Figure 4This is a diagram of the y-axis component of the reconstructed planar electric field obtained in the experiment of this invention;

[0053] Figure 5 This is a diagram of the z-axis component of the reconstructed planar electric field obtained in the experiment of this invention;

[0054] Figure 6 This is the x-axis component diagram of the reconstructed true value of the planar electric field in the experiment of this invention;

[0055] Figure 7 This is the y-axis component diagram of the reconstructed true value of the planar electric field in the experiment of this invention;

[0056] Figure 8 This is the z-axis component diagram of the reconstructed true value of the planar electric field in the experiment of this invention;

[0057] Figure 9 This is a graph showing the error between the x-axis component of the reconstructed planar electric field obtained in the experiment of this invention and the true value.

[0058] Figure 10 This is a diagram showing the error between the y-axis component of the reconstructed planar electric field obtained in the experiment of this invention and the true value.

[0059] Figure 11 This is a diagram showing the error between the z-axis component of the reconstructed planar electric field obtained and the true value in the experiment of this invention.

[0060] Figure 12 This is a SAR value map calculated from the reconstructed plane electric field in the experiment of this invention;

[0061] Figure 13 This is a SAR value map calculated from the true value of the reconstructed planar electric field in the experiment of this invention;

[0062] Figure 14 This is an error diagram between the SAR value calculated from the reconstructed plane electric field and the SAR value calculated from the actual value of the reconstructed plane electric field in the experiment of this invention. Detailed Implementation

[0063] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0064] To achieve the above objectives, the present invention provides the following specific embodiments:

[0065] Example 1: As Figure 1 As shown, a fast SAR estimation method based on plane wave electric field reconstruction includes the following steps:

[0066] Step 1: Establishing multiple reconstruction planes in the electric field measurement space of the fast SAR measurement system: The electric field E propagating from radiation source 2 to measurement plane 1 of the measurement system is taken as the measurement plane electric field. mea The measurement plane 1 is a probe array used for electric field measurement within the simulated human tissue fluid of the measurement system. The simulated human tissue fluid is contained in the measurement tank 5. The space enclosed by the measurement plane 1 and the measurement tank 5 is the electric field measurement space. Multiple reconstruction planes parallel to the measurement plane 1 are established within the electric field measurement space. The electric field of any one of the reconstruction planes is the reconstruction plane electric field E. rec ;

[0067] Step 2: Calculate the electric field E of any reconstructed plane based on the plane wave expansion method. rec Steps: Establish any of the reconstructed plane electric fields E rec And measuring the plane electric field E nea The equation is:

[0068] E mea =AE rec ,

[0069] In the formula, A represents the mapping matrix from the measured plane electric field to the reconstructed plane electric field. The following minimization problem is then solved:

[0070]

[0071] In the formula, 13 is the regularization parameter, which is used to balance the proportion of data difference terms and regularization terms in the total value of the cost function; It is a norm 2 operator;

[0072] Furthermore, the electric field E of any reconstructed plane is obtained. rec The expression is:

[0073] E rec =(A H *A+βI) -1 *A H *E mea ,

[0074] Where I is the identity matrix and the superscript H is the conjugate transpose operator;

[0075] Among them, the plane electric field E is reconstructed based on the plane wave expansion calculation method. rec And measuring the plane electric field E mea The process of obtaining the equation is as follows:

[0076] The reconstructed planar electric field E rec The measured planar electric field E is obtained after amplitude attenuation and phase change during propagation in space. nmea The specific propagation process is represented as follows:

[0077] E mea =invF*[P.*(F*E rec )],

[0078] Where F is the two-dimensional Fourier transform matrix, and E is the reconstructed plane electric field. rec Multiplying the components yields the spectrum of the reconstructed plane electric field, where P is the propagation factor, used to measure the amplitude and phase changes of each spectral component as it transforms from the measured plane electric field to the reconstructed plane electric field. Therefore, P is multiplied by F*E. rec Multiplying them yields the spectrum of the electric field in the measured plane; invF is the two-dimensional inverse Fourier transform matrix, and invF is related to P.*(F*E). rec Multiplying these yields the measured plane electric field E. mea ;

[0079] Let A = invF * P * F, then the reconstructed planar electric field E is obtained. rec And measuring the plane electric field E mea The equation.

[0080] Simultaneously, the reconstructed planar electric field E is obtained by solving a minimization problem. rec The specific process is as follows:

[0081] Due to the aforementioned reconstructed plane electric field E rec And measuring the plane electric field E mea Satisfying the equation:

[0082] E mea =A*E rec ,

[0083] To ensure that the difference between the two sides of the equation is minimized, let:

[0084]

[0085] Therefore, we get:

[0086]

[0087] However, since the mapping matrix A is ill-conditioned, the reconstructed planar electric field E... rec The optimal solution for measuring the plane electric field E mea The interference present in the middle is very sensitive, causing the reconstructed plane electric field E rec If the solution is unstable, then Tikhonov regularization is used to obtain the reconstructed plane electric field E. rec The solution formula is:

[0088]

[0089] Since the minimization problem is a convex problem, the reconstructed planar electric field Erec If the optimal solution is the extreme point, then taking the derivative of the cost function yields:

[0090]

[0091] And setting it equal to 0, we obtain any of the reconstructed planar electric fields E. rec The expression.

[0092] Step 3: Calculate multiple reconstructed plane electric fields The step of obtaining the measured spatial specific absorptivity (SAR) value is as follows: The electric field E of any reconstructed plane obtained in step two is used iteratively. rec The electric field of the multiple reconstructed planes is obtained from the expression. Where l is the distance from the bottom surface of the measurement slot 5 in the measurement space to any reconstruction plane, then the specific absorption rate (SAR) at any position r in the measurement space is:

[0093]

[0094] Where |E rec (r)| represents the root mean square of the reconstructed planar electric field at position r, where σ and ρ represent the conductivity and mass density, respectively.

[0095] The aforementioned method for obtaining multiple reconstructed planar electric fields This is used to estimate the maximum electric field value radiated from radiation source 2 into the simulated human tissue fluid of the fast SAR measurement system. The height from the bottom of the measurement tank 5 to the measurement plane 1 within the measurement space is z. mea , and z mea ∈[1, 20] mm, the distance from any of the reconstructed planes to the bottom surface of the measuring slot 5 in the measuring space is Where l = 1, 2, ..., L,

[0096] like Figure 1 As shown, the fast SAR measurement system includes a probe array 1, a measurement tank 5 containing human body simulation liquid 3, and a radiation source 2. The radiation source 2 is placed on a support frame 4 below the measurement tank 5. The human body simulation liquid 3 is a simulated liquid of human tissue. The probe array 1 is a probe array immersed in the human body simulation liquid 3 and is used to measure the electric field amplitude and phase in the measurement tank.

[0097] The probe array is as follows:

[0098] (2M+1)×(2M+1),

[0099] The array position is:

[0100] (mΔd, nΔd, Z) mea ),

[0101] m, n=-M, -M+1,...,M,

[0102] Wherein, the probe spacing Δd∈(2,20)mm, M∈[10,30], and M is the number of probes.

[0103] The radiation source 2 is an electronic device with electromagnetic wave emission capabilities.

[0104] Experimental Example: The advantages of this invention can be further illustrated by the following simulation experiment: The fast SAR measurement system includes a measurement plane 1 of a probe array and a radiation source 2, the positional relationship of which is as follows: Figure 1 As shown, the fast SAR measurement system uses a probe array distributed on the measurement plane 1 instead of a single probe. The human body simulation fluid 3 is a simulated liquid of human tissue, which is contained in the measurement tank 5. The radiation source 2 is placed on the support frame 4. The probe array measures the amplitude and phase of the vector electric field propagating from the radiation source 2 to multiple reconstruction planes, thus obtaining the electric field E of any reconstruction plane. mea .

[0105] The electric field probe array is uniformly distributed within the measurement groove 5 defined by the x-axis and y-axis. To verify the effectiveness of the algorithm, the experiment was conducted with the following configuration: the probe array was configured as a 29×29 probe array, i.e., a square with 29 probes in both the x-axis and y-axis directions, where -10cm≤x≤10cm, -10cm≤y≤10cm, and the spacing between any two adjacent probes was 7mm. The radiation source 2 was placed on a support frame 4 5mm away from the simulated liquid, and the vector probe array was positioned on the measurement plane 1 at z = 19.25mm.

[0106] 1. Simulation parameters

[0107] The probe array is configured with 29×29 probes, -10cm≤x≤10cm, -10cm≤y≤10cm, and the spacing between adjacent probes Δd=7mm. mea =19.25mm. The reconstructed field is set as follows: -10cm≤x, y≤10cm, 0cm≤z rec ≤3cm.

[0108] 2. Simulation Results

[0109] Complete two tasks:

[0110] 2.1 Comparison and analysis of the obtained values ​​and the true values ​​of the reconstructed planar electric field;

[0111] 2.2 Comparative analysis of SAR values ​​calculated based on the reconstructed plane electric field and the true value;

[0112] 3. Results Analysis

[0113] Conclusion 1: Figures 3 to 5 The x, y, and z components of the reconstructed plane electric field are obtained respectively. Figures 6 to 8 These represent the x, y, and z components of the reconstructed true value of the planar electric field. Figures 9 to 11 The values ​​are the differences between the reconstructed plane electric field values ​​and the actual values ​​in the x, y, and z directions, respectively, which are the error values. The total error value is 0.4006.

[0114] Conclusion 2: Figure 12 The SAR value is calculated from the reconstructed plane electric field. Figure 13 The SAR value is calculated from the true value of the reconstructed plane electric field. Figure 14 The error value is the difference between the SAR value calculated from the reconstructed plane electric field and the SAR value calculated from the true value. The total error value is 0.0014.

[0115] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A fast SAR estimation method based on plane wave electric field reconstruction, characterized in that, Includes the following steps: Step 1: Establish multiple reconstruction planes in the electric field measurement space of the fast SAR measurement system: the electric field propagated from the radiation source (2) to the measurement plane (1) of the measurement system is taken as the electric field of the measurement plane. The measurement plane (1) is a measurement plane composed of a probe array used for electric field measurement in the human tissue simulation fluid of the measurement system; the human tissue simulation fluid is contained in the measurement tank (5), and the space enclosed by the measurement plane (1) and the measurement tank (5) is the electric field measurement space; multiple reconstruction planes parallel to the measurement plane (1) are established in the electric field measurement space, and the electric field of any reconstruction plane is the electric field of the reconstruction plane. ; Step 2: Calculate the electric field of any reconstructed plane based on the plane wave expansion method. Establish any of the reconstructed planar electric fields described above. and measuring plane electric field The equation is: ， In the formula The mapping matrix from the measured plane electric field to the reconstructed plane electric field is represented by the following minimization problem: In the formula, This is a regularization parameter used to balance the weight of data variance terms and regularization terms in the total cost function. It is a norm 2 operator; Since the minimization problem is a convex problem, reconstructing the planar electric field... If the optimal solution is the extreme point, then taking the derivative of the cost function yields: ， Setting it to 0, we obtain any of the reconstructed planar electric fields. The expression: ， in For an identity matrix, the superscript H is the conjugate transpose operator; Step 3: Calculate multiple reconstructed plane electric fields The measured spatial specific absorptivity (SAR) value is obtained by iteratively applying any reconstructed plane electric field obtained in step two. The electric field of the multiple reconstructed planes is obtained from the expression. ,in The distance from the bottom surface of the measuring groove (5) within the measuring space to any reconstructed plane is the distance at any position within the measuring space. The specific absorption SAR value at this location is: ， in To reconstruct the complex modulus of the plane electric field at position r, and These represent electrical conductivity and mass density, respectively.

2. The fast SAR estimation method based on plane wave electric field reconstruction as described in claim 1, characterized in that, Step two describes the establishment of a reconstructed plane electric field based on the plane wave expansion calculation method. and measuring plane electric field The process of obtaining the equation is as follows: The reconstructed planar electric field The electric field of the plane is obtained after amplitude attenuation and phase change during propagation in space. The specific propagation process is represented as follows: ， in The matrix is ​​a two-dimensional Fourier transform matrix, and it is related to the reconstructed plane electric field. Multiplying them yields the spectrum of the reconstructed planar electric field. The propagation factor measures the amplitude and phase changes of each spectral component as it is transformed from the measured plane electric field to the reconstructed plane electric field, thereby employing... and Multiplying them yields the electric field spectrum of the measured plane; It is a two-dimensional inverse Fourier transform matrix. and Multiplication yields the measured plane electric field ; make Then the reconstructed planar electric field is obtained. and measuring plane electric field The equation.

3. The fast SAR estimation method based on plane wave electric field reconstruction as described in claim 1, characterized in that, The multiple reconstructed planar electric fields mentioned in step three , used to estimate the maximum electric field value of the radiation source (2) radiated into the human tissue simulation fluid of the fast SAR measurement system.

4. The fast SAR estimation method based on plane wave electric field reconstruction as described in claim 1, characterized in that, The height from the bottom of the measuring groove (5) in the measuring space to the measuring plane (1) is z. mea ,and The distance from any of the reconstructed planes to the bottom surface of the measuring groove (5) in the measuring space is Where l = 1, 2, ..., L, 5. The fast SAR estimation method based on plane wave electric field reconstruction as described in claim 4, characterized in that, The fast SAR measurement system includes a measurement plane (1), a measurement tank (5) containing human body simulation liquid (3), and a radiation source (2). The radiation source (2) is placed on a support frame (4) below the measurement tank (5). The human body simulation liquid (3) is a simulated liquid of human tissue. The measurement plane (1) is a probe array immersed in the human body simulation liquid (3) for measuring the electric field amplitude and phase in the measurement tank.

6. The fast SAR estimation method based on plane wave electric field reconstruction as described in claim 5, characterized in that, The probe array is as follows: ， The array position is: ， ， Among them, probe spacing , .

7. The fast SAR estimation method based on plane wave electric field reconstruction as described in claim 6, characterized in that, The probe array is a 29×29 probe array, which is uniformly distributed on the measurement plane (1) within the measurement groove (5) defined by x and y, and −10cm≤x≤10 cm, −10cm≤y≤10 cm. The radiation source (2) is placed on the support frame (4) 2-5 mm away from the bottom of the measurement groove (5). The vector probe array (1) is on the plane z=19.25 mm. The probe spacing is 7 mm.

8. The fast SAR estimation method based on plane wave electric field reconstruction as described in claim 6, characterized in that, The radiation source (2) is an electronic device with electromagnetic wave emission function.

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