CN112957027A - Electrical impedance tomography method for intracranial hemorrhage image reconstruction - Google Patents

Abstract

The invention discloses an electrical impedance tomography method for reconstructing an intracranial hemorrhage image, which is characterized in that a spiral computer tomography is adopted to scan a cranium, a cranium CT image is segmented and three-dimensional surface reconstructed, and a standardized normal three-dimensional cranium model is constructed on a computer by combining electrical impedance information of the cranium. Based on the constructed three-dimensional craniocerebral model, 16 groups of craniocerebral field potential values and a group of reference time boundary voltage measurement values are obtained in a relative current excitation mode, and 16 groups of craniocerebral field potential values are obtained in an adjacent current excitation mode. The method can reconstruct the images of the conductivity distribution of the cranium and the brain when the cranium and the brain bleed, and has good effects on reducing the artifact of the reconstructed images, improving the accuracy of the reconstructed images, accelerating the imaging speed and the like.

Description

Electrical impedance tomography method for intracranial hemorrhage image reconstruction

Technical Field

The invention belongs to the field of bioelectrical impedance tomography, and particularly relates to an electrical impedance tomography method for reconstructing an intracranial hemorrhage image.

Background

Intracranial hemorrhage is one of the most common acute cerebrovascular diseases in neurosurgery, and is generally caused by sudden rupture of cerebral vessels. If the patient cannot take timely and effective treatment, the temporary or permanent damage to the brain function will be caused. When intracranial hemorrhage occurs, the course of disease of a patient changes rapidly and evolves complicatedly, and the medicine has the characteristics of high morbidity, high mortality, high disability rate and high recurrence rate.

At present, the diagnosis and treatment of patients with cerebral hemorrhage are mainly performed clinically by methods such as Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Although in most cases, physicians can relatively accurately understand the basic condition of patients with cerebral hemorrhage according to the images generated by these devices, these devices have certain limitations: the operation and control are complex, the cost is high, the imaging time is long, and the CT has radioactivity, so that the CT can not be used for performing real-time craniocerebral imaging, early diagnosis and long-time continuous monitoring on a stroke patient, clinical medical care personnel can not know the development of the illness state of the patient in real time, and the treatment of the patient is influenced. Therefore, there is an urgent need for rapid, real-time imaging methods for intracranial hemorrhage for clinical treatment.

Electrical Impedance Tomography (EIT) is an imaging method for reconstructing the internal electrical characteristics of an object, which applies safe current excitation to a target under a certain excitation and measurement mode, then measures boundary voltage, and images the distribution information of the electrical characteristics by analyzing and processing measurement data. Compared with CT and MRI, electrical impedance tomography has the advantages of short time consumption, low cost, no radiation, portability and the like, and is widely applied to medical imaging. Current research shows that electrical impedance tomography can effectively image intracranial hemorrhage. However, the inverse problem of electrical impedance tomography is inherently ill-conditioned, i.e., the number of boundary voltage measurements is much smaller than the number of pixels that need to be reconstructed, so the solution to the inverse problem is not unique and the measurement voltage is sensitive to noise, making it difficult to obtain a stable solution. Currently, many algorithms are proposed to solve the ill-posed nature of the inverse problem, and in order to obtain an optimal solution and improve the stability of the solution, these algorithms usually need to perform iterative solution, but the computation amount is greatly increased during the iterative solution, so that the instantaneity of the EIT is reduced. In addition, in the electrical impedance imaging of the cranium and the brain, the conductivity of the skull of a human body is very low relative to the brain skin and the intracranial tissues, which can cause that the intracranial sensitivity is too low when an image is reconstructed, the boundary voltage is not sensitive to the change of the conductivity of the intracranial tissues, the reconstructed image is easy to generate artifacts, and the reconstructed target is not accurate.

Aiming at the problems of long imaging time consumption caused by large operation amount of the traditional brain electrical impedance tomography method and low imaging quality caused by low intracranial sensitivity, the invention needs to provide a simplified imaging method capable of improving the conductivity sensitivity degree of intracranial tissues. The method not only can effectively reduce the calculation amount of the algorithm iteration process, but also can improve the sensitivity degree of the boundary voltage to the conductivity of the intracranial tissues by updating the standardized sensitivity matrix in real time.

Disclosure of Invention

The invention solves the technical problem of providing an electrical impedance tomography method for intracranial hemorrhage. The method reduces modeling errors and obtains the sensitivity of the whole field of the cranium by constructing a standardized normal human cranium model. The sensitivity of the cranium is subjected to initial standardization processing, so that the sensitivity distribution is more uniform, and meanwhile, in the iterative solution process, the sensitivity of a target field is iteratively updated by adopting a self-adaptive sensitivity standardization method, so that the imaging quality is improved. In the inverse problem of EIT, a constraint sparse minimization model is provided to obtain an optimal solution for image reconstruction, and in the solving process, an improved fast gradient method is used for solving the conductivity distribution, so that the complexity of the algorithm is reduced, and the iterative computation speed is increased. The method can reconstruct the images of the conductivity distribution of the cranium and the brain when the cranium and the brain bleed, and has good effects on reducing the artifact of the reconstructed images, improving the accuracy of the reconstructed images, accelerating the imaging speed and the like.

The technical scheme adopted by the invention for solving the technical problems is as follows: scanning the cranium by adopting spiral computed tomography, segmenting and reconstructing a three-dimensional surface of a cranium CT image, and constructing a standardized normal three-dimensional cranium model on a computer by combining electrical impedance information of the cranium. Based on the constructed three-dimensional craniocerebral model, under a relative current excitation mode, 16 groups of craniocerebral field potential values and a group of reference time boundary voltage measured values u (sigma)₀) Under the adjacent current excitation mode, 16 groups of craniocerebral field potential values are obtained. And calculating a sensitivity matrix S by using the obtained field potential values, and initially standardizing the sensitivity matrix to ensure that the sensitivity distribution of the craniocerebra is more uniform. The initial normalization method was:

in the formula, S_m,nIs the sensitivity at m rows and n columns of the sensitivity matrix,

is the sensitivity after normalization.

At time t, applying safe relative current excitation to craniocerebral surface electrodes of real craniocerebral hemorrhage patients to obtain a group of boundary voltage measurement values u (sigma)_t). Linearizing a non-linear EIT problem to u (σ)_t)-u(σ₀)＝S·(σ_t-σ₀). Where S is the sensitivity matrix, σ_tThe conductivity of the cranium and brain at time t, sigma₀Is the craniocerebral conductivity at the reference moment. The inverse problem constraint sparse minimization model designed by the invention is as follows:

in the formula, | | represents an absolute value; sigma is the variation of conductivity of cranium and sigma is_t-σ₀And σ_nE is sigma; n is the number of units divided by the field during image reconstruction; u is a boundary voltage variation value, and U-U (sigma)_t)-u(σ₀) (ii) a And S sigma is a constraint condition U. Since the minimum model with absolute value is not easy to solve, an auxiliary variable g is introduced into the model, and g is made to be sigma, and then the model provided by the invention is converted into a form of an augmented Lagrangian function:

in the formula, T represents transposition, β₁As penalty term parameters I, beta₂For the penalty parameter II, gamma is an augmented Lagrange multiplier I, and delta is an augmented Lagrange multiplier II.

The model is decomposed into two subproblems using the augmented lagrange function:

in the formula, P_kAs a function of g, Q_kAs a function of σ, P_k、Q_kThe definition is as follows:

by a function P_k、Q_kAnd (5) iteratively solving the auxiliary variable g and the conductivity change amount sigma. The iterative solution process is as follows:

(1) initializing gamma⁰、δ⁰、β₁、β₂、g⁰、σ⁰The superscript 0 represents the initial value, the iteration number k is set, and the maximum iteration number k is_max；

(2) Setting P, C^k＝L_A(σ^k,g^k；γ^k,δ^k) C represents a function average value, P is a function average value parameter, and then internal iteration is carried out for solving;

(3) updating the auxiliary variable g:

in the formula, sgn represents a sign function, max represents a maximum function, and the superscript k is the kth iteration;

(4) in order to improve the calculation speed and avoid a large number of operations such as matrix transposition, inversion and the like, the conductivity variation is solved by using an improved fast gradient method. The modified fast gradient method is as follows:

update step size α:

in the formula, A^k＝σ^k-σ^k-1，y^k＝d^k(σ^k)-d^k(σ^k-1) D is the gradient direction of the objective function;

judging whether alpha meets the condition I: q_k(σ^k-α^kd^k)≤C^k-ωα^k(d^k)^Td_k，

In the formula, ω is a weight parameter i. If the step length alpha does not satisfy the condition, let alpha^k＝ρα^kAnd ρ is a shrinkage parameter.

Updating to obtain the craniocerebral conductivity variation sigma: sigma^k+1＝σ^k-α^kd^k；

(5) Update function mean C:

where eta is the weight parameter II, P^k+1＝ηP^k+1；

(6) The brain sensitivity matrix is standardized by using a self-adaptive standardization method, the sensitivity of a target region is improved, and the influence of a soft field effect is reduced. The self-adaptive standardization method comprises the following steps:

wherein W is a normalized diagonal matrix, W_n,nAs a normalization factor, S^*Is the normalized sensitivity matrix.

Adaptive normalization factor w_n,nIn the formula, w is a normalization parameter, and exp is an exponential function with a natural constant e as a base.

(7) If it is

Ending the internal iteration process, otherwise going to (3);

(8) updating and augmenting Lagrange multipliers I and II, wherein the iteration times k are k + 1;

(9) if k is less than the maximum number of iterations k_maxGo to (2), otherwise stop iteration.

(10) The variation sigma of the conductivity of the cranium and the brain is obtained by updating^kmax：

And then, according to the coordinate information corresponding to the conductivity variation of the craniocerebral, the reconstruction of the intracranial hemorrhage image is completed.

The invention has the beneficial effects that: the invention provides an electrical impedance tomography method for reconstructing an intracranial hemorrhage image. In the process of model construction, the shape of the real human cranium is determined by segmenting the cranium CT data and reconstructing the three-dimensional surface, and a three-dimensional cranium model is constructed by combining the electrical impedance characteristics of different tissues, so that the influence caused by modeling errors is reduced. The sensitivity matrix obtained by calculation is subjected to standardization processing by adopting an initial sensitivity standardization method, so that the sensitivity distribution of the cranium is more uniform, the imaging quality is improved, the sensitivity of a target field is continuously updated by a self-adaptive standardization method in the iterative calculation process of the algorithm, and the influence of a soft field effect on imaging is reduced. In the iterative solution process of the algorithm, the conductivity distribution is solved by using an improved rapid gradient descent method, so that the complexity of the algorithm is reduced, and the iterative computation speed is increased. The method can reconstruct the images of the conductivity distribution of the craniocerebral when the craniocerebral hemorrhage occurs, the reconstructed images of the craniocerebral hemorrhage have clear background and almost no artifacts, and the reconstructed position and the reconstructed size of the craniocerebral hemorrhage are accurate.

Drawings

FIG. 1 is an overall flow diagram of the present invention;

FIG. 2 is a diagram of an electrode arrangement during intracranial hemorrhage;

FIG. 3 is a schematic diagram of electrical resistance tomography of the cranium;

FIG. 4 is a block diagram of an iterative solution process for conductivity variations;

FIG. 5 is a diagram of the reconstruction results of a Tikhonov regularization method and a craniocerebral hemorrhage image obtained by the method of the present invention under four models;

fig. 6 shows the fuzzy radius (BR) and the Structural Similarity (SSIM) of the reconstruction results under the four models in fig. 5.

Detailed Description

The invention will be further explained with reference to the drawings.

The invention is illustrated with reference to fig. 1:

(1) the method comprises the steps of scanning the cranium by adopting spiral computed tomography, segmenting a cranium CT image, reconstructing a three-dimensional surface, analyzing and processing the shape of the cranium, and completing the construction of a three-dimensional cranium model on a computer by combining electrical impedance information of the cranium.

(2) Fig. 2 is a diagram showing an arrangement of electrodes in intracranial hemorrhage. The human body is assumed to stand on the ground vertically, the head is vertically upward, a detection plane parallel to the ground is established, and the detection plane is intersected with the bleeding position central point of the three-dimensional craniocerebral model. The 16 electrodes are attached around a closed curve intersecting the detection plane and the surface of the scalp at equal intervals, and the area of the plane surrounded by the closed curve is a measurement field.

(3) Fig. 3 shows a schematic diagram of a craniocerebral electrical resistance tomography system. Sequentially taking the opposite electrode pairs (1-9, 2-10, 3-11 … 15-7 and 16-8) as excitation electrode pairs, applying safe current, and measuring 16 groups of potential values in the field and a group of reference time boundary voltage values u (sigma)₀) (ii) a And sequentially taking adjacent electrode pairs (1-2, 2-3, 3-4 … 15-16 and 16-1) as excitation electrode pairs, applying safe current and measuring potential values in 16 groups of fields.

(4) Attaching 16 electrodes to the surface of the cranium of a real craniocerebral hemorrhage patient, wherein the attaching positions are the same as those in the attaching position (2), and obtaining a group of boundary voltage measured values u (sigma) at time t in a relative current excitation mode_t)。

(5) Calculating a sensitivity matrix using the potential values in the field obtained in (3). The sensitivity matrix comprises M rows and N columns, wherein M represents the sum of the number of boundary voltage measurement values obtained when all the electrode pairs are sequentially excited, and N is the number of divided field area units. The sensitivity vector calculation formula for the mth row is:

in the formula, superscripts 1 and 2 respectively represent a relative excitation pattern and an adjacent excitation pattern,

respectively the potential values of the N field units under the ith relative excitation and the jth adjacent excitation,

and

is the excitation current under the conditions of relative excitation and adjacent excitation, i is more than or equal to 1 and less than or equal to 16, and j is more than or equal to 1 and less than or equal to 16.

(6) Performing initial standardization on the sensitivity matrix obtained in (5), wherein the adopted sensitivity standardization method is as follows:

in the formula, S_m,nIs the sensitivity at m rows and n columns of the sensitivity matrix,

is the sensitivity after normalization.

(7) The EIT reconstruction algorithm provided by the invention is used for iteratively solving the conductivity variation.

The process of iteratively solving for the conductivity change is described with reference to fig. 4. The invention relates to an electrical impedance tomography method for reconstructing intracranial hemorrhage images, and a mathematical model of the electrical impedance tomography method can be linearized intou(σ_t)-u(σ₀)＝S·(σ_t-σ₀) Where S is the sensitivity matrix, σ_tThe conductivity of the cranium and brain at time t, sigma₀Is the craniocerebral conductivity at the reference moment. The established image reconstruction model is as follows:

in the formula, | | represents an absolute value; sigma is the variation of conductivity of cranium and sigma is_t-σ₀And σ_nE is sigma; u is a boundary voltage variation value, and U-U (sigma)_t)-u(σ₀) (ii) a And S sigma is a constraint condition U.

(1) Introducing an auxiliary variable g into the minimized norm model, wherein the related augmented Lagrangian function is expressed as:

in the formula, T represents transposition, β₁As penalty term parameters I, beta₂For the penalty term parameter II, gamma is an augmented Lagrange multiplier I, delta is an augmented Lagrange multiplier II, and the updating method of gamma and delta is as follows:

(2) and (3) carrying out minimum solving on the auxiliary variable g and the craniocerebral conductivity variation sigma:

in the formula, P_kAs a function of g, Q_kAs a function of σ, P_k、Q_kThe definition is as follows:

(3) initializing gamma⁰、δ⁰、β₁、β₂、g⁰、σ⁰The superscript 0 represents the initial value, the iteration number k is set, and the maximum iteration number k is_max；

(4) Setting P, C^k＝L_A(σ^k,g^k；γ^k,δ^k) C represents a function average value, P is a function average value parameter, and then internal iteration is carried out for solving;

(5) updating the auxiliary variable g:

in the formula, sgn represents a sign function, max represents a maximum function, and the superscript k is the kth iteration;

(6) update step size α:

in the formula, A^k＝σ^k-σ^k-1，y^k＝d^k(σ^k)-d^k(σ^k-1) D is the gradient direction of the objective function;

(7) judging whether alpha meets the condition I:

Q_k(σ^k-α^kd^k)≤C^k-ωα^k(d^k)^Td_k

in the formula, ω is a weight parameter i. If alpha does not satisfy the condition, let alpha^k＝ρα^kRho is a contraction parameter, and then the step (8) is carried out; if alpha satisfies the condition, directly go to (8);

(8) updating the craniocerebral conductivity change quantity sigma: sigma^k+1＝σ^k-α^kd^k；

(9) Updating a function meanC：

Where eta is the weight parameter II, P^k+1＝ηP^k+1；

(10) The craniocerebral sensitivity matrix is normalized by the proposed adaptive normalization method:

wherein W is a normalized diagonal matrix, W_n,nAs a normalization factor, S^*Is the normalized sensitivity matrix.

Adaptive normalization factor w_n,nIn the formula, w is a normalization parameter, and exp is an exponential function with a natural constant e as a base.

(11) If it is

Ending the internal iteration process, otherwise going to (5);

(12) updating and augmenting Lagrange multipliers I and II, wherein the iteration times k are k + 1;

(13) if k is less than the maximum number of iterations k_maxGo to (4), otherwise stop iteration.

(14) Updated to obtain the craniocerebral conductivity variation

And then, according to the coordinate information corresponding to the conductivity variation of the craniocerebral, the reconstruction of the intracranial hemorrhage image is completed.

Fig. 5 compares the reconstructed images of craniocerebral hemorrhage with different sizes and different positions by using the Tikhonov algorithm and the proposed algorithm. It can be seen that the image reconstructed by the method has clear background and basically no artifact, the reconstructed craniocerebral hemorrhage image is close to a real model, and the reconstructed image by the traditional Tikhonov algorithm has more artifact and inaccurate reconstructed target.

Meanwhile, in order to quantitatively analyze the reconstructed images of the cerebral hemorrhage, the images were compared using a Blur Radius (BR) and a Structural Similarity Index (SSIM). The closer the blur radius of an image is to 0, the better, the closer the structural similarity is to 1, the better. Fig. 6 shows the blur radius and structural similarity of the reconstructed images of cranial hemorrhage as described above. It can be seen that the fuzzy radius of the reconstructed image by the method provided by the invention is far smaller than that of the reconstructed image by the Tikhonov algorithm, and the structural similarity of the reconstructed image by the method provided by the invention is larger than that of the reconstructed image by the Tikhonov algorithm. The superiority of the electrical impedance tomography method for reconstructing the intracranial hemorrhage image provided by the invention is verified.

The above description is only exemplary of the present invention and should not be taken as limiting the invention, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. An electrical impedance tomography method for intracranial hemorrhage image reconstruction, which is characterized in that: the electrical impedance tomography technology is utilized to reconstruct images of the craniocerebral hemorrhage under the nonuniform conductivity, and the mathematical model of the images can be linearized into u (sigma)_t)-u(σ₀)＝S·(σ_t-σ₀) Where S is the sensitivity matrix, u (σ)_t) A set of boundary voltage measurements, u (σ), at time t₀) Is a set of boundary voltage measurements, σ, at a reference time_tThe conductivity of the cranium and brain at time t, sigma₀For the craniocerebral conductivity at the reference moment, the established image reconstruction model is as follows:

in the formula, | | represents an absolute value; sigma is the variation of conductivity of cranium and sigma is_t-σ₀And σ_nE is sigma; n is the number of units divided by the measurement field during image reconstruction; u is a boundary voltage variation value, and U-U (sigma)_t)-u(σ₀) (ii) a S sigma is U as a constraint condition;

the electrical impedance tomography method for reconstructing the intracranial hemorrhage image comprises the following specific steps:

the method comprises the following steps: scanning the cranium by adopting spiral computed tomography, segmenting and reconstructing a three-dimensional surface of a cranium CT image, and completing the construction of a standard normal three-dimensional cranium model on a computer by analyzing and processing the cranium shape data and combining with the electrical impedance information of the normal cranium;

step two: in a three-dimensional craniocerebral model, 16 electrodes are equidistantly attached around a closed curve intersected by a detection plane and the surface of the scalp in the model, a plane area surrounded by the closed curve is a measurement field, and 16 groups of field potential values and a group of reference time boundary voltage measurement values u (sigma) are obtained in a relative current excitation mode₀) (ii) a Under the adjacent current excitation mode, obtaining 16 groups of field potential values;

step three: attaching 16 electrodes to the surface of the cranium of a patient with craniocerebral hemorrhage, wherein the attaching positions are the same as those in the second step, and obtaining a group of boundary voltage measured values u (sigma) at the time t in a relative current excitation mode_t)；

Step four: calculating a sensitivity matrix by using the field potential values obtained in the step two, wherein the sensitivity matrix comprises M rows and N columns, M represents the sum of the number of the measured values obtained when all the electrode pairs are sequentially excited, and the sensitivity vector calculation formula of the mth row is as follows:

in the formula, superscripts 1 and 2 denote the relative excitation mode and the adjacent excitation mode, respectively, phi_i ¹、

Respectively the potential values of the N field units in the ith relative excitation and the jth adjacent excitation modes,

and

is the excitation current under the relative excitation and the adjacent excitation modes, i is more than or equal to 1 and less than or equal to 16, and j is more than or equal to 1 and less than or equal to 16;

step five: and (3) standardizing the sensitivity matrix obtained by calculation in the fourth step to reduce the influence of the soft field effect, wherein the initial standardization method comprises the following steps:

in the formula, S_m,nIs the sensitivity at m rows and n columns of the sensitivity matrix,

is the sensitivity after normalization;

step six: introducing an auxiliary variable g into an image reconstruction model, wherein the related augmented Lagrange function is expressed as:

in the formula, T represents transposition, β₁As penalty term parameters I, beta₂For the penalty term parameter II, gamma is an augmented Lagrange multiplier I, delta is an augmented Lagrange multiplier II, and the updating method of gamma and delta is as follows:

step seven: solving the auxiliary variable g and the craniocerebral conductivity variation sigma:

in the formula, P_kAs a function of g, Q_kAs a function of σ, P_k、Q_kThe definition is as follows:

step eight: respectively solving the auxiliary variable g and the craniocerebral conductivity variation sigma, wherein the iterative solving process is as follows:

(1) initializing gamma⁰、δ⁰、β₁、β₂、g⁰、σ⁰The superscript 0 represents the initial value, the iteration number k is set, and the maximum iteration number k is_max；

(2) Setting P, C^k＝L_A(σ^k,g^k；γ^k,δ^k) C represents a function average value, P is a function average value parameter, and then internal iteration is carried out for solving;

(3) updating the auxiliary variable g:

in the formula, sgn represents a sign function, max represents a maximum function, and the superscript k is the kth iteration;

(4) update step size α:

in the formula, A^k＝σ^k-σ^k-1，y^k＝d^k(σ^k)-d^k(σ^k-1) D is the gradient direction of the objective function;

(5) judging whether alpha meets the condition I:

Q_k(σ^k-α^kd^k)≤C^k-ωα^k(d^k)^Td_k

in the formula, omega is a weight parameter I, if alpha does not satisfy the condition, let alpha^k＝ρα^kRho is a contraction parameter, and then the step (6) is carried out; if alpha satisfies the condition, directly go to (6);

(6) updating the craniocerebral conductivity change quantity sigma: sigma^k+1＝σ^k-α^kd^k；

(7) Update function mean C:

where eta is the weight parameter II, P^k+1＝ηP^k+1；

(8) In the process of iteratively solving the craniocerebral conductivity variation, the sensitivity matrix is subjected to self-adaptive standardization:

wherein W is a normalized diagonal matrix, W_n,nAs a normalization factor, S^*Is the normalized sensitivity matrix;

adaptive normalization factor w_n,nExpressed as follows, where w is the normalization parameter and exp represents an exponential function with the natural constant e as the base:

(9) if it is

End internal iterative processOtherwise go to (3);

(10) updating and augmenting Lagrange multipliers I and II, wherein the iteration times k are k + 1;

(11) if k is less than the maximum number of iterations k_maxGo to (2), otherwise stop iteration;

step nine: updated to obtain the craniocerebral conductivity variation

And then, according to the coordinate information corresponding to the conductivity variation of the craniocerebral, the reconstruction of the intracranial hemorrhage image is completed.

Images