KR20230141425A - Method and apparatus for analysing biocurrent - Google Patents

Abstract

The biological current analysis method includes the following steps: an analysis device receives information about current conduction in a living body; allowing the analysis device to match a first unit tangent vector of the moving frame with the direction in which the current is conducted; allowing the analysis device to make a second unit tangent vector among the flow coordinates parallel to a wavefront through which current is conducted; calculating, by the analysis device, a relative acceleration based on the second unit tangent vector; determining, by the analysis device, whether the relative acceleration has a value greater than or equal to a preset threshold; identifying, by the analysis device, an area having a relative acceleration greater than the threshold value as an area where conduction is blocked; Includes.

Description

Biocurrent analysis method and device {METHOD AND APPARATUS FOR ANALYSING BIOCURRENT}

The technology described below relates to a method of analyzing current in vivo using relative acceleration.

Electrical currents flow in the heart and brain. Electrical currents give the heart a contraction sequence. Electrical currents in the brain are used to transmit and store information.

It is important to know when the electrical currents flowing in the heart and brain flow and when they stop. Electrophysiologically, this is called a conduction block condition. Conduction blockage within the heart has been linked to heart diseases such as cardiac fibrillation. Additionally, conduction block in the brain is related to the connectivity and interconnectedness of information.

U.S. Registered Patent Publication 10/070,799

Previously, there were only clinical observations or theoretical explanations of conduction block conditions. There has been no practical algorithm to computationally quantify conduction blocking conditions in strongly anisotropic media such as brain and heart cells.

The technology described below makes it possible to derive quantitative and qualitative results about where conduction blocking occurs using conduction diffusion distributions obtained through computer simulations or observation data. Additionally, by substituting simulation variables for given data, it can be shown under what conditions actual conduction blockage is recovered or its intensity is reduced.

The biological current analysis method includes the following steps: an analysis device receives information about current conduction in a living body; allowing the analysis device to match a first unit tangent vector of the moving frame with the direction in which the current is conducted; allowing the analysis device to make a second unit tangent vector among the flow coordinates parallel to a wavefront through which current is conducted; calculating, by the analysis device, a relative acceleration based on the second unit tangent vector; determining, by the analysis device, whether the relative acceleration has a value greater than or equal to a preset threshold; identifying, by the analysis device, an area having a relative acceleration greater than the threshold value as an area where conduction is blocked; Includes.

Using the technology described below, it is possible to determine when conduction of biological current is blocked.

Using the technology described below, it is possible to identify the area where spiral waves are generated when performing a spiral ablation procedure.

Using the technology described below, it is possible to identify areas where conduction is blocked more inexpensively than conventional technologies.

Using the technology described below, signals from the brain can be analyzed, providing information about the connectivity or directionality of each section of the brain.

Using the technology described below, brain diseases such as Alzheimer's or schizophrenia can be detected early by observing changes in brain fiber curvature and distribution in brain white matter.

Figure 1 shows the overall process by which an analysis device analyzes biological current.
Figure 2 shows the flow coordinates.
Figure 3 shows an algorithm for generating the first unit tangent vector of the first-order flow coordinates.
Figure 4 shows how electric current is conducted.
Figure 5 analyzes cardiac electrical signal conduction using relative acceleration.
Figure 6 analyzes cardiac electrical signal conduction when the atria are filled with cardiac fibers.
Figure 7 analyzes cardiac electrical signal conduction in the case of cardiac fibers made of variable conductivity fibers.
Figure 8 is an example of the configuration of an analysis device.

The technology described below may be subject to various changes and may have various embodiments. Specific embodiments of the technology described below may be depicted in the drawings of the specification. However, this is for explanation of the technology described below and is not intended to limit the technology described below to specific embodiments. Therefore, it should be understood that all changes, equivalents, and substitutes included in the spirit and scope of the technology described below are included in the technology described below.

Terms such as first, second, A, and B may be used to describe various components. However, the above term is only used to distinguish one component from other components and is not intended to limit the components to the above term. For example, a first component may be named a second component without departing from the scope of the technology described below, and similarly, the second component may also be named a first component. The term “and/or” includes any combination of a plurality of related stated items or any of a plurality of related stated items.

In the terms used below, singular expressions should be understood to include plural expressions, unless clearly interpreted differently from the context, and terms such as “including” refer to the described features, numbers, steps, operations, components, parts, or It should be understood that it means the existence of a combination of these, but does not exclude the possibility of the presence or addition of one or more other features, numbers, step operation components, parts, or combinations thereof.

Before providing a detailed description of the drawings, it would be clarified that the division of components in this specification is merely a division according to the main function each component is responsible for. That is, two or more components, which will be described below, may be combined into one component, or one component may be divided into two or more components for more detailed functions. In addition to the main functions it is responsible for, each of the component parts described below may additionally perform some or all of the functions of other components, and some of the main functions of each component may be performed by other components. Of course, it can also be carried out in full charge.

In addition, when performing a method or operation method, each process forming the method may occur in a different order from the specified order unless a specific order is clearly stated in the context. That is, each process may occur in the same order as specified, may be performed substantially simultaneously, or may be performed in the opposite order.

First, we will look at the overall process of analyzing biological current by a biological current analysis device (hereinafter referred to as an analysis device).

Figure 1 shows the overall process by which an analysis device analyzes biological current.

The analysis device can receive information about current conduction in the living body. The analysis device may make the first unit tangent vector among the flow coordinates coincide with the direction in which the current is conducted. The analysis device may make the second unit tangent vector among the flow coordinates coincide with the wavefront through which the current is conducted. The analysis device may calculate the relative acceleration based on the second unit vector. The analysis device can determine whether the relative acceleration has a value greater than or equal to a preset threshold. The analysis device can identify an area with a relative acceleration greater than a threshold value as an area where conduction is blocked.

The relative acceleration may be the second-order covariant differentiation of the second flow tangent vector according to the first unit tangent vector.

Below we will look at the moving frame.

Figure 2 shows the flow coordinates.

Figure 2(a) shows the zero-order flow coordinates. Figure 2(b) shows the primary flow coordinates.

In Figure 2, the dotted line shows the trajectory. In Figure 2 , e1 and e2 show the first and second tangent vectors.

Flow coordinates can be used to show the direction in which cardiac current is conducted.

Flow coordinates can be expressed as a hexahedron. Each edge of the hexahedron may be a tangent vector.

Flow coordinates can be expressed as e i. The flow coordinate e _i may be three unit tangent vectors. Each of the three unit tangent vectors can be { e1, e2, e3 }. Each tangent vector may be called a first unit tangent vector, a second unit tangent vector, and a third unit tangent vector.

Among the unit tangent vectors, { e1, e2 } can be located on the tangent plane of the curved surface.

The remaining one of the unit tangent vectors { e3 } may be a surface normal vector to the tangent plane. The surface normal vector can be expressed as k .

Each unit tangent vector of the flow coordinates may be orthonormal to each other. Therefore, Equation 1 below can be satisfied.

In Equation 1 may be Kronecker delta.

Among the unit tangent vectors, e3 may be fixed.

On the other hand, the direction of the first unit tangent vector e1 may not yet be determined on the tangent plane. In this case, the orthogonality of the flow coordinates can determine the direction of the remaining tangent vector.

Computationally, the direction of e1 can affect integration and differentiation in differential operators such as divergence, curl, and Laplacian operators.

Nevertheless, in the past, the direction of e1 was set arbitrarily. This type of conventional distribution can be called a moving frame of the zero order. This can be confirmed in Figure 2 (a).

In this case, the flow coordinates can be a simple set of orthonormal local references representing the tangent plane.

On the other hand, the direction of e1 may have a specific direction. This type of distribution can be called a moving frame of the first order. In other words, e1 of the primary flow coordinate may have a specific direction. This is different from the zero-order flow coordinates. This can be confirmed in Figure 2 (b).

Therefore, in the technology described below, e1 can be aligned in the conduction direction so that the conduction pattern can be identified. This can be viewed as a set of specifically connected and ordered coordinates (frames).

The conducting direction may be the same as the conducting direction for the trajectory. Alternatively, the direction of conduction may be the same as the gradient of potential with respect to the current. Then, in order to study the divergence and convergence of a bundle of trajectories, the pattern of trajectories can be expressed as a connected 1-form or a kind of second covariant derivative.

Below, we will look at the algorithm for sorting the first unit tangent vector of the flow coordinates.

Figure 3 shows an algorithm for generating the first unit tangent vector of the first-order flow coordinates. In other words, Figure 3 may be an algorithm for arranging flow coordinates in the gradient direction.

First, check the validity of the flow coordinates. To check validity, Equation 8 described later can be used. You can then select the location of the gradient. The location of the gradient may be one of WF or WB, which will be described later. Afterwards, you can extract the gradient (str, Int, Wint) through the selection. You can set this as the new flow coordinate.

Below, we will look at the process for deriving the algorithm of Figure 3.

First, the numerical scheme for a trajectory will be explained.

The trajectory in the diffusion-reaction model can be calculated and constructed using the gradient of the action potential.

The derived gradient can be the first tangent vector by orthogonal normalization in the first-order flow coordinates.

Accordingly, three numerical systems can be proposed. The three numerical systems can be Maximum gradient (Str), Integration gradient (Int), and Weighted Integration gradient (Wint).

First, for convenience in the three numerical systems, it can be assumed that one action potential is conducted along its domain.

In the three numerical systems, u can mean membrane potential. The membrane potential u may be u(x, t). The membrane potential is the tangent plane ( ) may vary depending on the location (x) and time (t).

In all three numerical systems, the first flow coordinate e1 can be derived from the tangent vector t1 to the trajectory. In other words, the first flow coordinate e1 can be calculated by dividing the tangent vector t1 by its own size.

Equation 2 is the equation used to calculate the flow coordinate e1 .

Below, the three numerical schemes are explained.

The first numerical scheme could be Maximum gradient (Str)

In the first numerical scheme, the gradient of the membrane potential can be in the direction of the first tangent vector. The gradient of the membrane potential may refer to the case where the gradient is maximum during conduction.

Equation 3 shows the tangent vector t1 .

The numerical system above can be simple and concise. However, continuity and differentiability of the first tangent vector are not supported.

The second numerical system could be Integration gradient (Int).

The second numerical system can be an alternative to the maximum gradient described above. The second numerical system can be created by integrating the smooth distribution of the gradient. This numerical system integrates the normalized gradient of u.

Equation 4 shows the tangent vector t1 .

The advantage of this numerical system is that the first tangent vector can be distributed more smoothly. As a result, it can provide continuity and differentiability of the first tangent vector.

However, the tangential vector of the trajectory is not proportional to the size of the action potential. Additionally, the cutoff times ta and t _ab are also uncertain.

A third numerical system could be Weighted Integration Gradient (Wint).

In the third numerical system, the following weighted integration method can be used by combining the maximum gradient (str) and integral gradient (int) methods described above.

Equation 5 shows the tangent vector t1 .

This numerical system does not require a cut-off time compared to the integral gradient (int). The direction of the trajectory may be proportional to the magnitude of the action potential gradient. However, this numerical system can be more expensive than other numerical systems.

Below, the position of gradient will be described.

When constructing a trajectory, it must be taken into account that an action potential can have two rapidly changing gradients.

The first is the wavefront. A wavefront may be a region where the membrane potential depolarizes. Alternatively, the fracture may be a region where the membrane potential (u) increases dramatically.

The second is the back waveback. The back wavefront may be a region where the membrane potential repolarizes. Alternatively, the waveback may be a region where the membrane potential (u) decreases dramatically.

The increasing or decreasing rates of the wavefront and waveback may be different. Therefore, it is necessary to determine whether the direction of the first tangent vector should be calculated from the gradient of the wavefront or the waveback.

The location of time integration can be determined in the following way.

A wavefront may be a place where the membrane potential increases with time (du/dt>0). In other words, ∇u may be the direction of the first tangent vector. From now on, it can be called WF.

The back waveback may be where the membrane potential decreases with time (du/dt<0). In other words, -∇u may be the direction of the first tangent vector. From now on, it can be called WB.

Below we will look at the validity of moving frames.

The reason for checking the validity of the flow coordinates may be to check whether the distribution of the flow coordinates is smoothly distributed.

Primary flow coordinates can be aligned according to the direction of conduction. However, the distribution of flow coordinates may not be smooth enough to provide sufficient accuracy for the numerical solution of partial derivative (PDEs) equations.

The zero-order flow coordinate ( e _i 0) can be configured to be sufficiently smooth for each element. The primary flow coordinate ( e _i ) can be configured to be equal to the direction of conduction. Since the zero-order flow coordinate and the first-order flow coordinate are normal orthogonal basis vectors, the expansion of vector v in one of the flow coordinates can be 0.

Equation 6 shows for v .

Similar conditions can be applied to differential operators, especially the Laplacian operator of the diffusion-reaction equation.

The diffusion-reaction equation is as equation 7.

In equation 7: may be a diffusion tensor. In equation 7: may be a reaction function.

The anisotropic gradient of Equation 7 can be expanded by using flow coordinates. However, the anisotropic gradient in Equation 7 may not be affected by the direction of the flow coordinate.

In other words, the choice of flow coordinates ( e _i ⁰ or e _i) does not affect the accuracy of the Laplacian operator.

If the distribution of the first-order flow coordinates is not smooth enough, the accuracy of the Laplacian operator may be seriously impaired.

Therefore, the following validity test can be proposed to ensure accurate scaling of the anisotropic gradient.

Definition 1

It can be assumed that the zero-order flow coordinate ( e ⁰ ) yields an accurate numerical solution of Equation 7. The primary flow coordinate ( e _i ) can be said to be valid if it satisfies Equation 8 below.

In equation 8, may be a sufficiently small tolerance. may be a validity parameter.

The derivative (∂u/∂ e _i ) shows that the numerical system of Equation 7 uses flow coordinates ( e _i ).

Equivalently, Equation 8 above can be expressed as Equation 9 below.

In Equation 9, Δu shows the difference in u at a certain time interval Δt.

It can be assumed that the error of Δu of the first flow coordinate ( e _i ) is sufficiently lower than the discretization error.

If so, even if the new flow coordinates above are used, the accuracy and stability of the numerical system may not be affected.

However, invalid flow coordinates can produce unstable and inaccurate calculations.

The condition in Equation 9 can eliminate non-differentiable conduction directions that occur due to numerical noise or discretization errors.

Non-differentiable directions may not be constructed in the diffusion-reaction process due to the dissipative and smooth nature of the Laplacian operator.

However, the condition of Equation 9 may also not be satisfied if the curvature of the flow is large. And in such areas, spatial resolution may not be sufficient.

This phenomenon may occur because the current numerical system for calculating covariant derivatives requires more grid points in more curved regions.

Therefore, the parameter δ should be adjusted according to all curvatures of the conduction except for the gradient of the conduction, which is non-realistic.

Below we will look at relative acceleration.

In conventional kinematic analysis, the equation for the linearized version of conduction velocity (V) is Equation 10.

In Equation 10, V ₀ can determine the conducting velocity in the heart. In Equation 10, D may mean diffusion constant. In Equation 10, k may be the wavefront curvature.

When the conduction properties of cardiac tissue are isotropic or homogeneous, wavefront curvature can play an important role in conduction velocity.

If the wavefront curvature exceeds a certain threshold, the conduction velocity can rapidly decrease. Furthermore, evangelism may stop. In other words, physiologically large wavefront curvature can be consistent with sink-source mismatch. This is also known as impedance mismatch.

A large wavefront curvature may correspond to an increase in the ratio of the number of sources and sinks. The source may be excited cells. Sinks can be excitable cells.

The maximum ratio between source and sink can be fixed. This is because the resources of excited cells may be limited.

If the wavefront curvature is large, the source-to-sink ratio can exceed a critical value. Therefore, conduction may stop in places where the wave front curvature is large.

Figure 2 shows conduction starting from a point in an isotropic medium.

In Figure 2, there may be two orbits. The first orbit may be ξ1. The second orbit may be ξ2.

When conduction begins at a point in the medium, the wavefront can be represented by a circular arc.

P(λ _i , ξ _i ) may be a point on a specific orbit ξ _i at a specific time λ _i .

The arc length of P(λ _j , ξ ₁ ) P(λ _j , ξ ₂ ) at a specific time (λ _i ) is It can be said that (λ _i ). This arc may be a wavefront.

Arc length at a specific time (λ _i ) can also show the number of excited cells.

Therefore, the ratio of the length of the added arc and the length of the excited arc can be calculated using Equation 11. In other words, Equation 11 may be an equation used to calculate the ratio between the sink and the source.

If the arc length at time λ ₂ and the arc length at time λ ₁ are the same, Equation 11 can be 0. If Equation 11 is 0, it may mean that there is a one-to-one correspondence between the source and sink.

If the ratio in Equation 11 is negative, it shows that there are more sources than sinks. In this case, conduction may be accelerated.

If the ratio in Equation 11 is a positive number, it shows that there are more sinks than sources. In this case, conduction may slow down.

If the ratio in Equation 11 is very large, it shows that the source is not sufficient compared to the sink. As a result, propagation may fail and be stopped.

Equation 12 is the differentiation of Equation 11.

By differentiating Equation 12 one more time, Equation 13 can be obtained.

Equation 13 shows the change in sink/source ratio according to the conduction direction.

Equation 13 can be calculated using wavefront curvature.

Geometrically, wavefront curvature may have an intrinsic relationship with the growth of the volume of metric balls.

Wavefront curvature can be mathematically defined as ∂ e ₂ /∂ℓ for wavelength ℓ.

However, calculating the arc length of a wavefront, like the wavefront curvature, can be difficult in a multidimensional anisotropic domain.

Relative acceleration can generally be defined as the second covariant derivative of e2 along the e1 direction.

Equation 14 shows the relative acceleration (R _A ).

Below we will look at the process of deriving relative acceleration.

The ratio of the length of the wavefront to conduction can correspond to how quickly the trajectories diverge or converge.

In the case of circular inversion starting from one point as shown in Figure 4, the orbit may be a straight line. Both orbits can be spread apart while maintaining a certain angle. The above propagation can be called propagation with linear trajectory.

Case 1: Linear trajectory

Consider the wavefront at times λ ₁ and λ ₂ . The tangent vector to the orbit at time λ _i can be called u(λ _j ) . The tangent vector to the wavefront at s _k can be called n(s _k ) . n(s _k ) may be a separation vector.

The sizes of u(λ _i ) and n(s _k ) may generally not be units.

Tangent vectors u and n can constitute the coordinate system of the domain. Therefore, Equation 15 can be obtained.

In polar coordinates, it is equivalent to Equation 16.

Accordingly, another covariant differentiation or ∇ _r ∇ _r θ in the r direction may be 0.

e _i (λ _j ) and e _i (λ _j+1 ) can be said to be the flow coordinates at λ _j and λ _j+1 , respectively.

The first unit tangent vectors e ₁ (λ _j ) and e ₁ (λ _j+1 ) can each be aligned along the conduction direction. The second unit tangent vector e ₂ (λ _j ) can be aligned along the wavefront.

For conduction starting from a point, the first tangent vector may be in the radial direction. Additionally, the second tangent tangent vector may be in a circular direction.

Equation 17 can show the first tangent vector and the second tangent vector.

Then along the e _r direction The covariant derivative of or its opposite can be derived as in Equation 18.

This ratio may be geometrically identical to the source-sink ratio shown in Equation 12. Relative acceleration can generally be defined as the second-order covariant derivative of e2 along the direction of e1 , as shown in Equation 19.

In Equation 18, the relative acceleration as another covariant derivative of ∇ _er e _θ according to e _r may be 0. (Equation 20)

Through this, when the relative acceleration is 0, it can mean that there is no force that deforms or stops conduction. Therefore, conduction blocking is not observed when the relative acceleration is zero. This is because conduction blocking usually occurs when the change in sink-source ratio accelerates. The phenomenon of conduction blocking can be expressed as a deviated orbit as shown in Figure 4.

In the case of biased trajectories, the trajectories may converge or diverge rapidly depending on the conduction.

Case 2: Deviating Trajectory

If the trajectory converges or diverges dramatically and deviates from the coordinate system, the covariant derivative of the unit separation vector along the direction of conduction may be non-trivial.

This phenomenon is known as geodesic deviation, as shown in Figure 4.

Geometrically, the covariant derivative of the conduction vector u with respect to the separation vector n can be negative if the orbits diverge (Equation 21). Conversely, the covariant derivative of the conduction vector u with respect to the separation vector n can be positive if the orbits converge. (Equation 21)

Then we can consider the following theorem.

First corollary.

It can be assumed that e1 and e2 are the unit tangent vectors of the trajectory u and the separation vector n , respectively.

Then the covariant derivative ∇ _n u can have the same sign as ∇ _e2 e1.

The proof is as follows. u = u e ¹ and n = n e ² . In this case, Equation 22 can be obtained.

By simplifying Equation 22, Equation 23 can be obtained.

Therefore, if the trajectory diverges, ∇ _n u can be negative and ∇ _u ·e ₂ can be positive. At this time, ∇ _e2 e ₁ can be negative. If the trajectory converges, ∇ _n u can be positive and ∇ _u ·e ₂ can be negative. At this time, ∇ _e2 e ₁ may be a positive number.

That is, ∇ _n u and ∇ _e2 e ₁ have the same sign.

This can be summarized as Equation 24.

This corollary theorem may be similar to the state of the formula in Equation 21.

Therefore, we can obtain the following proposition:

Proposition 1.

A domain of sufficiently smooth two-dimensional curves can be considered.

The first flow coordinate ( e _i ) can be constructed in the domain such that the first tangent vector e ₁ is aligned along the direction of conduction with the action potential gradient described in the domain algorithm.

It can be assumed that ∇ _e2 e ₁ ·e ₂ is a negative number (Equation 25). It can be assumed that the relative acceleration is a positive number (Equation 25). It can be assumed that the relative acceleration is sufficiently large for trajectory divergence (Equation 25).

If so, conduction may stop due to sink and source mismatch. Therefore, the likelihood of the area developing a conduction block may increase.

The proof is as follows.

The covariant derivative ∇ _e2 e ₁ may correspond to the sink-source ratio. Relative acceleration can indicate the rate of change of this rate along the direction of conduction.

If the number of excited cells is greater than the number of excitable cells, the covariant derivative ∇ _e2 e1 can be negative.

Therefore, changes in ∇ _e2 e1 along the relative acceleration or conduction direction can indicate changes in the rate of divergence or convergence.

Consider the covariant derivative of Equation 26.

By applying Equation 26 to the covariant derivative, Equation 27 can be obtained.

If the relative acceleration is positive, ∇ _e1 ∇ _e2 e1 can be negative. Therefore, ∇ _e2 e1 can become more negative as conduction progresses. As a result, wave conduction may diverge or even cease.

Below we will look at the numerical system for relative acceleration.

It can be assumed that the first flow coordinates are configured as in the algorithm of Figure 3. Flow coordinates can be expressed as a matrix as shown in Equation 28 below at all points in the domain.

In Equation 28, e and x may each be a new tensor using the tangent vector (x, y, z) of the Cartesian coordinate axis (x, y, z).

Matrix A can indicate the direction of the flow coordinates. Matrix A may be an attitude matrix or an orientation matrix.

The differential equation can be expressed as Equation 29.

can be a 1-form that takes a vector as input and outputs a scalar.

procession The nine components of can also be in 1-form. procession The components of can also be expressed as w _ij . This may be called a connection form.

For example, w _ij ( v ) can represent the amount of rotation of e _i with respect to e _j when moving in the direction of v.

Equation 30 can be obtained through the orthogonal normality of the flow coordinates.

thus can have only three independent components, as shown in Equation 31 below.

Therefore, Equation 29 can be expressed as Equation 32 below.

Vector v can be expanded to a two-dimensional curved surface in the flow coordinates as shown in Equation 33 below.

Then, the connection 1-form for vector v is linear, so it can be expressed as Equation 34.

Therefore, if 1 ≤ k ≤ 2, ω _ij ( e ^k ) can be calculated. Then, the connection form W can be obtained as shown in Equation 35.

The connection 1-form for the tangent vector e _k can be calculated as Equation 36.

When viewed in matrix form, it can be calculated as shown in Equation 37.

Here, the 3 × 3 matrix may be the Jacobian matrix for e _j . Then, the covariant derivative of vector u according to the tangent vector e _j can be equal to Equation 38.

In Equation 38, here u = u1 e ₁ + u ² e ₂ . Correspondingly, the relative acceleration as the second-order covariant derivative according to e ₁ can be calculated using Equation 38, as explained in detail in the following proposition.

Second corollary

Consider a sufficiently smooth two-dimensional curved domain. It can be assumed that the first-order flow coordinate ( e ₁ ) is constructed in this domain such that the first tangent vector can be aligned along the direction according to the action potential gradient given in the algorithm of Figure 3.

Then, the relative acceleration, which represents the ratio between sink and source in current conduction in the heart, can be derived as Equation 39.

In Equation 39, ω ₂₁₁ may be equal to ω ₂₁ ( e1 ). Also, in Equation 39, ω ₂₁₂ may be equal to ω ₂₁ ( e2 ).

∇ _e1 ω ₂₁₁ and ∇ _e1 ω ₂₁₂ may be the same directional derivative as ∇ω ₂₁₁ · e1 and ∇ω ₂₁₂ · e1 , respectively.

The proof is as follows.

The covariant derivative of ∇ _e1 e2 can be derived from Equation 38 as in Equation 40.

By introducing relative acceleration into Equation 40, Equation 41 can be obtained.

In Equation 41, ∇ _e1 e1 = 0.

Equation 39 can be obtained by substituting Equation 40 into Equation 41 and sorting for the same tangent vector.

Through proposition 1 and theorem 2, the following proposition 2 can be obtained.

second proposition

Any two-dimensional curved domain can be considered.

The first-order flow coordinates can be constructed so that the first tangential vector is aligned along the direction of conduction with the gradient of the action potential, as described in Algorithm 1.

In this case, it can be assumed that ω ₂₁₂ is a negative number and ω ² ₂₁₂ ∇ _e1 ω ₂₁₂ is a positive number as follows. Therefore, equation 42 can be obtained.

If so, the sink and source may become mismatched and conduction may be interrupted. Therefore, there is a high possibility that conduction blockage will occur in that area.

Hereinafter, we will look at an example in which cardiac signal conduction is analyzed using relative acceleration.

Figure 5 analyzes cardiac electrical signal conduction using relative acceleration.

In Figure 5, the heart may be isotropic. Therefore, conduction velocity does not vary depending on the direction of cardiac tissue.

The waves may originate near the right pulmonary vein.

Figure 5(a) is a time map showing the start of arrival of conduction. The direction of conduction was calculated using the algorithm in Figure 3 described above.

Figure 5(b) shows the connected 1-form component ω 212.

Figure 5(C) shows conduction block. Conduction block may refer to an area where conduction does not occur. A conduction block may be where the relative acceleration due to conduction is positive. In this case the conduction cutoff may be where ω 212 is negative.

Figure 5 shows that if the cardiac tissue is isotropic, conduction block is very likely to occur in the pulmonary veins.

Figure 6 analyzes cardiac electrical signal conduction when the atria are filled with cardiac fibers.

Figure 6(a) shows cardiac fibers. Figure 6(b) shows a time map. Figure 6(c) shows ω 212. Figure 6(d) shows conduction block.

The cardiac fibers in Figure 6 are roughly drawn based on open source cardiac fiber images. Therefore, it can only be used for example simulations. Therefore, the fibers may not always be continuous. Additionally, the fibers may be orthogonal to the surface normal vector. The conductivity of the fiber can be three times greater than that of the orthogonal component. As a result, it can be seen that there has been a change in the overall conduction and time map. In conclusion, cardiac tissue can modify the distribution of ω212. As a result, it can be seen that the conduction blocking has also changed. In other words, if the fibers are not continuous, conduction blocking may occur.

Figure 7 shows the case of cardiac fibers made of variable conductance fibers.

Figure 7 (a) shows the conductivity map.

If the conductivity is 1, it may correspond to normal conductivity. On the other hand, as conductivity decreases, the conduction speed may decrease. This low conductivity can mainly occur when a wound occurs.

Because conductivity is variable, the wavefront becomes more curved and complex.

The configuration of the analysis device will be described below.

Figure 8 is an example of the configuration of an analysis device.

The analysis device 800 of FIG. 8 may correspond to the analysis device 100 described in FIG. 1.

The analysis device 800 may be physically implemented in various forms, such as a PC, laptop, smart device, server, or data processing chipset.

The analysis device 800 may include an input device 810, a storage device 820, an arithmetic device 830, an output device 840, an interface device 850, and a communication device 860.

The input device 810 may include an interface device (keyboard, mouse, touch screen, etc.) that receives certain commands or data.

The input device 810 may include a component that receives information through a separate storage device (USB, CD, hard disk, etc.).

The input device 810 may receive input data through a separate measuring device or through a separate DB.

The input device 810 can receive data through wired or wireless communication.

The input device 810 can receive information about current conduction in a living body.

The storage device 820 can store information input through the input device 810.

The storage device 820 can store information generated during calculation by the computing device 830. That is, the storage device 820 may include memory.

The storage device 820 can store the results calculated by the arithmetic device 830.

The arithmetic unit 830 may set the first unit tangent vector of the moving frame to coincide with the direction in which the current is conducted.

The arithmetic unit 830 may make the second unit tangent vector among the flow coordinates coincide with the wavefront through which current is conducted.

The arithmetic unit 830 may calculate relative acceleration according to the direction of the second unit tangent vector to the first unit tangent vector.

The computing device 830 may determine whether the relative acceleration has a value greater than or equal to a preset threshold.

The calculation device 830 may identify an area with a relative acceleration greater than the threshold value as an area where conduction is blocked.

The calculation device 830 can perform calculations according to the mathematical equations described in the specification.

The computing device 830 can check whether the distribution of flow coordinates affects the accuracy of the Laplacian operator.

The computing device 830 can visualize and show the area where conduction is blocked.

The computing device 830 can set the direction in which the membrane potential increases in vivo as the direction in which the current is conducted.

The arithmetic device 830 can set the direction in which the current is conducted to be opposite to the direction in which the membrane potential decreases in vivo.

The output device 840 may be a device that outputs certain information.

The output device 840 may output interfaces, input data, analysis results, etc. required for data processing.

The output device 840 may be physically implemented in various forms, such as a display, a document output device, etc.

The interface device 850 may be a device that receives certain commands and data from the outside.

The interface device 850 can receive information through current conduction from a physically connected input device or an external storage device.

The interface device 850 can receive a control signal to control the analysis device 800.

The interface device 850 may output the results analyzed by the analysis device 800.

The communication device 860 may refer to a configuration that receives and transmits certain information through a wired or wireless network.

The communication device 860 can receive control signals necessary to control the analysis device.

The communication device 860 can transmit the results analyzed by the analysis device.

The above-described biological current analysis method may be implemented as a program (or application) including an executable algorithm that can be executed on a computer.

The program may be stored and provided in a temporary or non-transitory computer readable medium.

A non-transitory readable medium refers to a medium that stores data semi-permanently and can be read by a device, rather than a medium that stores data for a short period of time, such as registers, caches, and memories. Specifically, the various applications or programs described above include CD, DVD, hard disk, Blu-ray disk, USB, memory card, ROM (read-only memory), PROM (programmable read only memory), and EPROM (Erasable PROM, EPROM). Alternatively, it may be stored and provided in a non-transitory readable medium such as EEPROM (Electrically EPROM) or flash memory.

Temporarily readable media include Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDR SDRAM), and Enhanced SDRAM (Enhanced RAM). It refers to various types of RAM such as SDRAM, ESDRAM), synchronous DRAM (Synclink DRAM, SLDRAM), and Direct Rambus RAM (DRRAM).

This embodiment and the drawings attached to this specification only clearly show some of the technical ideas included in the above-described technology, and those skilled in the art can easily understand them within the scope of the technical ideas included in the specification and drawings of the above-described technology. It will be self-evident that all inferable modifications and specific embodiments are included in the scope of rights of the above-described technology.

Claims (10)

A step in which an analysis device receives information about current conduction in a living body;
allowing the analysis device to match a first unit tangent vector of the moving frame with the direction in which the current is conducted;
allowing the analysis device to match a second unit tangent vector among the flow coordinates with a wavefront through which current is conducted;
calculating, by the analysis device, a relative acceleration according to the direction of the second unit tangent vector to the first unit tangent vector;
determining, by the analysis device, whether the relative acceleration has a value greater than or equal to a preset threshold; and
identifying, by the analysis device, a zone having a relative acceleration equal to or greater than the threshold value as a zone where conduction is blocked; containing
Biocurrent analysis method. In paragraph 1
The biological current analysis method wherein the relative acceleration is calculated by second-order covariant differentiation of the second unit tangent vector according to the direction of the first unit tangent vector. In paragraph 1
The direction in which the current is conducted is a direction opposite to the direction in which the membrane potential increases or the membrane potential decreases in the living body. In paragraph 1
Checking, by the analysis device, whether the distribution of the flow coordinates affects the accuracy of the Laplacian operator; A biocurrent analysis method further comprising: In paragraph 1
A biological current analysis method further comprising the step of having the analysis device visualize and display the area where the conduction is blocked. An input device that receives information about current conduction in the living body; and
The first unit tangent vector of the moving frame is aligned with the direction in which the current is conducted, and the second unit tangent vector of the moving frame is aligned with the wavefront through which the current is conducted. And, the second unit tangent vector calculates a relative acceleration according to the direction of the first unit tangent vector, the analysis device determines whether the relative acceleration has a value greater than or equal to a preset threshold, and the relative acceleration exceeds the threshold. An arithmetic device that determines the area having a as the area where conduction is blocked; containing
Biocurrent analysis device. In paragraph 6
The biocurrent analysis device wherein the relative acceleration is calculated by performing second-order covariant differentiation of the second unit tangent vector along the direction of the first unit tangent vector. In paragraph 6
The direction in which the current is conducted is a direction in which the membrane potential increases or is opposite to the direction in which the membrane potential decreases in the living body. In paragraph 6
The calculation device is a biocurrent analysis device that checks whether the distribution of the flow coordinates affects the accuracy of the Laplacian operator. In paragraph 6
The calculation device is a biological current analysis device that visualizes and shows the area where the conduction is blocked.

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