A method for measuring skull thickness based on bioelectrical impedance

Abstract

This invention discloses a method for measuring cranial thickness based on bioelectrical impedance analysis (BIA), comprising: dividing the target region into subdivisions using the finite element method (FEM) to establish a finite element model; acquiring surface voltage signals of the skull using a four-electrode method on a brain electrical impedance imaging platform; obtaining the conductivity distribution of each node of the triangular element by solving the inverse voltage problem; inputting the conductivity distribution into the finite element model and calculating the distance between the node with the largest resistivity change and the corresponding boundary voltage node by solving the forward problem, thus obtaining the skull width at a set of signal locations; measuring the node voltages and calculating the corresponding skull thickness using a sixteen-electrode cyclic excitation method; and finally, assembling all node voltages and skull thicknesses into a plane to obtain the overall skull thickness. This invention designs a method for measuring cranial thickness based on bioelectrical impedance analysis (BIA), providing an accurate method for calculating cranial thickness.

Description

Technical Field

[0001] This invention relates to the field of EIT imaging in biomedical engineering, specifically to a study on the influence of high resistivity skull thickness on excitation signals in brain tissues during brain imaging. Background Technology

[0002] Brain imaging is a challenging problem in EIT research, and therefore, research in this area is of great significance. The main reason for the difficulty in brain EIT imaging is that conventional EIT studies targets with relatively uniform resistivity distribution, while the resistivity distribution in the brain is extremely non-uniform.

[0003] When performing brain electrical impedance tomography (EIT), we need to consider the influence of skull tissue on imaging. Skull tissue has extremely high resistivity, thus significantly impeding current flow, resulting in a much lower current density flowing into the brain tissue compared to imaging other sites. Furthermore, the cerebrospinal fluid beneath the skull has extremely low resistivity, allowing current to shunt around it, further reducing the current density in the brain tissue. Therefore, the boundary voltage for brain EIT imaging varies much less with internal resistivity perturbations than in other sites. We need to consider these factors to develop the optimal brain EIT imaging protocol.

[0004] The purpose of this invention is to provide a method for measuring brain skull thickness based on bioelectrical impedance analysis (BIA), aiming to address current problems, namely, how to select measurement points to minimize the influence of high-impedance skull on the excitation current, and how to select different excitation currents at different measurement points so that the boundary voltage signal can reflect intracranial impedance changes to a similar degree. This method focuses on the impedance thickness characteristics of different skulls and improves the ability to identify boundary voltage variations at different brain test points as a function of internal resistivity perturbations. Through this method, we can measure brain skull thickness more accurately, thereby improving the precision of brain electrical impedance imaging. Summary of the Invention

[0005] To achieve the above objectives, the present invention provides a method for measuring skull thickness based on bioelectrical impedance, comprising the following steps:

[0006] The target is divided into a finite number of triangular elements by finite element analysis to construct a finite element subdivision model;

[0007] Two sets of skull boundary voltage signals were measured using a ring-shaped sixteen-electrode device and a four-electrode method.

[0008] By solving the inverse problem using the collected voltage signal information, the distribution of conductivity in the finite element model is obtained;

[0009] Based on the theoretical basis that the conductivity of the skull is significantly lower than that of other intracranial tissues and the conductivity distribution in the finite element model, the boundary point of the triangular element with the largest conductivity difference in the finite element model is identified, and then the corresponding boundary triangular element node is obtained by solving the forward problem.

[0010] The distance between the triangular element at the boundary line and the edge of the finite element model is the skull thickness between these two sets of voltage points.

[0011] By changing the excitation electrode pair, measuring the voltage, and solving for the skull thickness corresponding to the new voltage point, the process continues until all sixteen electrodes are cycled through. The inner ring formed by connecting the calculated skull thicknesses at all voltage points and the edge of the finite element model represents the overall skull thickness.

[0012] Step 2 describes the construction of the finite element mesh model:

[0013] Includes the following steps:

[0014] Step 1.1: Transform the boundary value problem into a variational problem;

[0015] Step 1.2: Decompose the sensitive field;

[0016] Step 1.3: Linear interpolation;

[0017] The brain electrical impedance imaging detection platform described in step 2 mainly includes three modules: 1) an excitation module; 2) an electrode interface subsystem module; and 3) a detection module. The main working principle is as follows: Through main control, a sinusoidal signal synthesized using DDS technology drives a voltage-controlled constant current source to output an excitation alternating current (1mA / 50kHz) of a specific magnitude and frequency. Through the selectivity of an analog switch, electrode pairs fixed to the human skin are selected to excite human tissue. Simultaneously, different electrode pairs are selected to measure the boundary voltage of the human tissue. The acquired boundary voltage is filtered and amplified, and finally acquired by an AD converter and demodulated by the main controller. The data obtained after processing the voltage signal by the main controller is transmitted to a PC via a serial port for further calculation of the perturbation impedance change in the sensitive area. The electrode interface subsystem module includes sixteen Ag / AgCl electrodes, numbered 1 to 16.

[0018] Step 2 of the four-electrode method includes the following steps:

[0019] Step 2.1: Select electrodes 1 and 2 as the excitation current input and output electrodes, respectively;

[0020] Step 2.2: Select electrodes 16 and 3 as boundary voltage acquisition electrodes, and acquire the first set of boundary voltage values;

[0021] Step 2.3: Select electrodes 15 and 4 as boundary voltage acquisition electrodes, and acquire the second set of boundary voltage values;

[0022] Step 3 describes applying I to the field Ω from electrodes 1 and 2. ψ Then a potential Ψ will be formed on the field Ω and its boundary S, and the surface integral is equal to the following equation:

[0023]

[0024] If we assume the applied current is a unit current, i.e., I Ψ =I Φ =1, then the relationship between the boundary voltage of measuring electrode 16.3 and the field conductivity distribution is:

[0025] If the field is divided into a finite number of discrete elements (such as triangular elements), and the conductivity of each element is constant, then each triangular element can be viewed as a linear equation:

[0026]

[0027] Represented in matrix form as follows:

[0028]

[0029] In the formula, V p It is the boundary voltage change vector, c p Let S be a discrete conductivity vector, and let S be the sensitivity matrix, whose matrix elements are as follows: ;

[0030] Here, i represents the measured voltage under the i-th injection, and j represents the j-th cell. Therefore, by measuring the boundary voltage V... p The perturbation conductivity c can then be calculated. p Distribution;

[0031] Step 4, based on the premise that the conductivity of the skull is much lower than that of other intracranial tissues, involves inputting a perturbation conductivity c. p By solving the forward problem, the maximum change in boundary voltage of the finite element model can be obtained from the distribution of the voltage, and the boundary point of the triangular element with the largest difference in conductivity can be obtained accordingly.

[0032] Step 5 includes solving for the centroid coordinates of the triangular element at the boundary line, and solving for the centroid coordinates of the triangular element at the measurement electrode point. The magnitude between the two centroid coordinates is the skull thickness corresponding to this boundary voltage. The centroid coordinates of the triangular element follow the following formula:

[0033]

[0034]

[0035] The centroid coordinates of the triangular element at the boundary node of electrode 16 are G( , The centroid coordinates of the boundary node triangular element are M( , If the modulus is 0, then the modulus is 0. This is the thickness of the skull at this location; similarly, the thickness of the skull at electrode number 3 can be calculated.

[0036] Step 6 involves changing the excitation electrode pair, measuring the voltage, and calculating the skull thickness corresponding to the new voltage point. This process is repeated until all sixteen electrodes have been cyclically excited, and the skull thickness (i.e., the modulus |GM|) at all nodal electrodes is calculated. Finally, the plane formed by the moduli corresponding to all boundary nodes is the skull planar thickness. Attached Figure Description

[0037] Figure 1 A flowchart of a method for measuring brain and skull thickness based on bioelectrical impedance provided in an embodiment of the present invention.

[0038] Figure 2 This is a schematic diagram of the four-electrode method for measuring boundary node voltage based on the finite element model, provided for an embodiment of the present invention.

[0039] Figure 3 The flowchart of the finite element model creation program provided for the embodiments of the present invention is shown.

[0040] Figure 4 This is a schematic diagram of the brain electrical impedance tomography detection platform provided in an embodiment of the present invention.

[0041] Figure 5 This is a triangular element mesh diagram of a finite element model provided in an embodiment of the present invention.

[0042] Figure 6 This is a schematic diagram of single-point skull thickness measurement based on a finite element model, provided for an embodiment of the present invention.

[0043] Figure 7 This is a schematic diagram of the skull thickness plane based on the finite element model provided for an embodiment of the present invention. Detailed Implementation

[0044] The following specific examples illustrate the implementation of the present invention, providing a clear and complete description of the technical solutions in these embodiments. Obviously, the described embodiments are only a part of, and not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0045] Please see Figures 1 to 7This invention provides a technical solution: a method for measuring skull thickness based on bioelectrical impedance, the method comprising the following steps:

[0046] Step S1: Construct a finite element mesh model, including the following steps:

[0047] Step 1.1: Transform the boundary value problem into a variational problem;

[0048] Step 1.2: Decompose the sensitive field;

[0049] Step 1.3: Linear interpolation;

[0050] Step 1.1 includes: mathematical calculation model based on the sensitive field of electrical resistance tomography. , boundary potential The problem is transformed into an equivalent variational problem:

[0051]

[0052] In the formula: V and S represent the measured object field and its boundary, respectively;

[0053] Step 1.2 uses a three-node triangular finite element method to divide the sensitive field, and assumes that the conductivity σ within each triangular finite element is constant, i.e. =0, then the equivalent variational problem can be further written as:

[0054]

[0055] In the formula: m is the number of triangular finite elements in the measured field, determined according to the required calculation accuracy;

[0056] After dividing the measured field into three nodes using the three-node triangular finite element method in step 1.3, a linear interpolation polynomial is used as the interpolation function, as shown below:

[0057]

[0058] In the formula: α, β, and γ are determined by the coordinate values ​​and potentials of the three vertices of the three-node triangular finite element.

[0059] Step S2: The brain electrical impedance imaging detection platform mainly includes three modules: 1) excitation module; 2) electrode interface subsystem module; 3) detection module. The main working principle is as follows: Through main control, a sinusoidal signal is synthesized using DDS technology to drive a voltage-controlled constant current source to output an excitation alternating current (1mA / 50kHz) of a specific magnitude and frequency. Through the selectivity of an analog switch, electrode pairs fixed to the human skin are selected to excite human tissue. Simultaneously, different electrode pairs are selected to measure the boundary voltage of the human tissue. The acquired boundary voltage is filtered and amplified, and finally acquired by an AD converter and demodulated by the main controller. The data obtained after processing the voltage signal by the main controller is transmitted to the PC via a serial port for further calculation of the perturbation impedance change in the sensitive area. The electrode interface subsystem module includes sixteen Ag / AgCl electrodes, numbered 1 to 16.

[0060] The four-electrode method includes the following steps:

[0061] Step 2.1: Select electrodes 1 and 2 as the excitation current input and output electrodes, respectively;

[0062] Step 2.2: Select electrodes 16 and 3 as boundary voltage acquisition electrodes, and acquire the first set of boundary voltage values;

[0063] Step 2.3: Select electrodes 15 and 4 as boundary voltage acquisition electrodes, and acquire the second set of boundary voltage values;

[0064] Step S3: For the measured field, when I is applied from electrodes 1 and 2 into the field Ω... ψ Then a potential Ψ will be formed on the field Ω and its boundary S, and the surface integral is equal to the following equation:

[0065]

[0066] If we assume the applied current is a unit current, i.e., I Ψ =I Φ =1, then the relationship between the boundary voltage of measuring electrode 16.3 and the field conductivity distribution is:

[0067]

[0068] If the field is divided into a finite number of discrete elements (such as triangular elements), and the conductivity of each element is constant, then each triangular element can be viewed as a linear equation:

[0069]

[0070] Represented in matrix form as follows:

[0071]

[0072] In the formula: It is the boundary voltage change vector. Let S be a discrete conductivity vector, and let S be the sensitivity matrix, whose matrix elements are as follows:

[0073]

[0074] Here, i represents the measured voltage under the i-th injection, and j represents the j-th cell. Therefore, by measuring the boundary voltage... The perturbation conductivity can then be calculated. Distribution;

[0075] Step S4: Based on the premise that the conductivity of the skull is much lower than that of other intracranial tissues, the perturbation conductivity c is input. p By determining the distribution of voltage across the finite element model and solving the forward problem, we can obtain the maximum change in boundary voltage of the finite element model. This leads to the triangular element boundary point with the largest conductivity difference. The specific steps are as follows:

[0076] The vertex coordinates of the triangular unit e , , The linear interpolation polynomial interpolation function represents the relationship between the potential at any point in a triangular element and the potential values ​​at each vertex of that element:

[0077]

[0078]

[0079] In the formula, Δ represents the area of ​​a three-node triangle finite element, and the element at node e is taken as a triangular element:

[0080]

[0081] The finite element functional can then be expressed as:

[0082]

[0083] In the formula: , The expressions are respectively

[0084]

[0085]

[0086] In the formula: The expression is:

[0087]

[0088] The overall functional of the measured field can be obtained. The expression is:

[0089]

[0090] Where: total coefficient matrix K, and The expression is:

[0091]

[0092]

[0093]

[0094] In the formula: n is the sensitive field The total number of nodes in the finite element method for an interior three-node triangle is given by: Finite element nodal potential values (k=1, 2, The first-order partial derivative of (n) is zero, as shown below:

[0095]

[0096] The finite element equation for the forward problem of resistive tomography can be obtained as follows:

[0097]

[0098] Finally, the sensitive field can be obtained by using Gaussian elimination. Internal finite element node potential values .

[0099] Step S5: This includes solving for the centroid coordinates of the triangular element at the boundary line, solving for the centroid coordinates of the triangular element at the measurement electrode point, and determining the modulus between the two centroid coordinates, which corresponds to the skull thickness at this boundary voltage. The centroid coordinates of the triangular element follow the following formula:

[0100]

[0101]

[0102] The centroid coordinates of the triangular element at the boundary node of electrode 16 are G( , The centroid coordinates of the boundary node triangular element are M( , If the modulus is 0, then the modulus is 0. This is the thickness of the skull at this location; similarly, the thickness of the skull at electrode number 3 can be calculated.

[0103] Step S6: This involves changing the excitation electrode pair, measuring the voltage, and calculating the skull thickness corresponding to the new voltage point. This process is repeated until all sixteen electrodes have been cyclically excited, and the skull thickness (i.e., the modulus |GM|) at all node electrodes is calculated. Finally, the plane formed by the moduli corresponding to all boundary nodes is the skull plane thickness.

Claims

1. A bioelectrical impedance based method of measuring skull thickness of the brain, characterized in that, It includes the following six main steps: Step 1: Use the finite element method to divide the target region into a finite number of triangular elements to construct a finite element model; Step 2: Using a brain electrical impedance imaging platform, two sets of skull boundary voltage signals were measured using the four-electrode method. Step 3: Solve the inverse problem using the acquired voltage signal to obtain the conductivity distribution in the finite element model; Step 4: Based on the theoretical basis that the conductivity of the skull is significantly lower than that of other intracranial tissues and the conductivity distribution in the finite element model, identify the boundary point of the triangular element with the largest conductivity difference in the finite element model, and find the corresponding boundary triangular element node by solving the forward problem; Step 5: Solve for the centroid coordinates of the nodal triangular elements at the boundary point of the finite element model. Use these as the boundary point between the skull and intracranial tissue. Then, by solving for the centroid coordinates of the nodal triangular elements at the measuring electrode, the boundary point between the skull and extracranial skin tissue can be obtained. The modulus between the centroid coordinates of these two nodal triangular elements is the skull thickness corresponding to this boundary voltage. Step 6: By changing the combination of excitation electrode pairs, measure the corresponding boundary voltage, and then solve for the skull thickness corresponding to each new voltage point. The area formed by the inner circle of the line connecting the skull thicknesses corresponding to all voltage points and the outer edge of the finite element model is the overall skull thickness.

2. The method of claim 1, wherein, The four-electrode method in step 2 includes the following: Electrodes 1 and 2 are selected as the positive and negative electrodes of the excitation current, respectively. The boundary voltages of electrodes 16 and 3 are measured as the first set of boundary voltage values, and the boundary voltages of electrodes 15 and 4 are measured as the second set of boundary voltage values.

3. The method of claim 2, wherein the method is a bioelectrical impedance based method of measuring brain skull thickness. In step 3, for the field under test, when an excitation current is applied into the field from electrodes 1 and 2, the boundary voltage change vector is obtained by solving the linear equation corresponding to each triangular unit. Based on the measured voltage injected each time and the coordinate position of the triangular unit, the conductivity distribution in the field is derived and calculated.

4. The method of claim 3, wherein the method is a bioelectrical impedance based method of measuring brain skull thickness. In step 4, based on the premise that the conductivity of the skull is much lower than that of other intracranial tissues, the distribution of conductivity is input, and the boundary point of the triangular element with the largest conductivity difference is obtained by iteratively polling. Then, the finite element equation of the resistance tomography forward problem is solved to obtain the node with the largest change in boundary potential of the finite element model, that is, the boundary triangular element node corresponding to the node with the largest conductivity difference. Finally, the potential value of each finite element node in the field can be obtained by using the Gaussian elimination method.

5. The method of claim 1, wherein the method is a bioelectrical impedance based method of measuring brain skull thickness. In step 6, by changing the excitation electrode pair, the corresponding boundary voltage is measured, and the corresponding single-point skull thickness is solved. The skull thickness of the sixteen electrode points is solved respectively, and the skull thickness modulus of each electrode point forms a plane, which is the skull plane thickness.

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