Method for obtaining start point and end point of QRS complex by using imaginary number

Abstract

Disclosed is a method for obtaining a start point and an end point of a QRS complex by using an imaginary number. The method of obtaining a start point and an end point of a QRS complex by using an imaginary number comprises: receiving, by a receiving unit, a measured electrocardiogram signal, performing, by a transform unit, Hilbert transform on the electrocardiogram signal, and obtaining, by a measurement unit, the amplitude of the electrocardiogram signal by creating a phase space map on the basis of the Hilbert transformed electrocardiogram signal, wherein a vertex of an imaginary part representing the start point and the end point of the QRS complex exists in the phase space map, and the vertex exists in a phase space region of the QRS complex.

Description

Method to find the start and end points of the QRS complex using imaginary numbers

[0001] The present invention relates to a method for finding the start and end points of a QRS complex using imaginary numbers.

[0002]

[0003] In diagnosis using medical imaging (ultrasound, MT, CT), not only image information but also electrocardiography (ECG) signals are utilized to extract images of specific points in time within the body.

[0004] The waveform of the electrocardiogram signal (1) can be represented as a curve centered on the baseline (BL), showing the current and potential difference generated by the contraction of the heart as illustrated in FIG. 1. Within one cycle of the electrocardiogram signal (1), the P wave, Q wave, R wave, S wave, and T wave generally occur in succession. The P wave represents the contraction of the atrium, a series of Q waves, R waves, and S waves (QRS complex) represent the contraction of the ventricle, and the T wave is a characteristic that appears during the relaxation of the ventricle.

[0005]

[0006] The present invention aims to provide a method for finding the start and end points of a QRS complex using imaginary numbers, wherein the value of the electrocardiogram signal is a real value, and the imaginary part (part) of the electrocardiogram signal is obtained by Hilbert transform or the like to construct a phase space, thereby finding the start and end points of the QRS complex.

[0007]

[0008] A method for determining the start and end points of a QRS complex using imaginary numbers according to one embodiment of the present invention comprises: a receiving unit receiving a measured electrocardiogram signal; a converting unit performing a Hilbert transform on the electrocardiogram signal; and a measuring unit creating a phase space diagram based on the Hilbert-transformed electrocardiogram signal to determine the magnitude of the electrocardiogram signal, wherein the phase space diagram may contain vertices of imaginary numbers representing the start and end points of a QRS complex that do not exist in the electrocardiogram, and said vertices exist in the phase space region of the QRS complex.

[0009] Here, if there are multiple peaks, boundary conditions are set using the phase space diagram to determine the start and end points of the QRS complex.

[0010] In addition, the graph representing the electrocardiogram signal and the phase space diagram are derived as polynomials using numerical analysis methods, and the vertex of the imaginary part is obtained from the polynomials.

[0011]

[0012] According to the present invention, by creating a phase space diagram in which the value of the electrocardiogram signal is a real value and the value of the Hilbert-transformed electrocardiogram signal is an imaginary value, the phase space diagram has a vertex of the imaginary part that does not appear in the electrocardiogram, and thus the start and end points of the QRS complex that do not appear in the electrocardiogram graph can be obtained.

[0013] According to the present invention, the reliability of electrocardiogram diagnosis can be dramatically improved by accurately identifying the start and end points of the QRS complex in phase space, which cannot be clearly identified in a standard electrocardiogram.

[0014]

[0015] Figure 1 is a diagram illustrating a typical electrocardiogram signal.

[0016] FIG. 2 is a block diagram of an electrocardiogram signal magnitude measurement device using Hilbert transform according to one embodiment of the present invention.

[0017] Figure 3 shows an electrocardiogram signal.

[0018] Figure 4 is a diagram comparing an electrocardiogram signal and a Hilbert-transformed electrocardiogram signal.

[0019] Figure 5 is a graph of the QRS complex.

[0020] Figure 6 shows a graph with a peak of the cubic function (left) and a graph without a peak of the cubic function (right).

[0021] Figure 7 is a graph for finding the Q point (left) and an XY graph with the imaginary part obtained from the Hilbert transform as the X-axis and the electrocardiogram as the Y-axis (right).

[0022] Figure 8 is an electrocardiogram graph for finding point J.

[0023] Figure 9 is a graph showing point J in phase space.

[0024] Figure 10 is an electrocardiogram graph with two peaks.

[0025] Figure 11 is a graph with boundary conditions applied that have two peaks in phase space.

[0026] Embodiments of the present invention may be modified into various other embodiments, and the scope of the present invention is not limited only to the embodiments described below. The shapes and sizes of elements in the drawings may be exaggerated for clearer explanation, and elements indicated by the same reference numerals in the drawings are the same elements.

[0027]

[0028] FIG. 2 is a block diagram of a device for measuring the magnitude of an electrocardiogram signal using Hilbert transform according to an embodiment of the present invention. FIG. 3 shows an electrocardiogram signal. FIG. 4 is a diagram comparing an electrocardiogram signal and a Hilbert transformed electrocardiogram signal.

[0029] First, as illustrated in FIG. 2, a device (200) for measuring the magnitude of an electrocardiogram signal using a Hilbert transform according to one embodiment of the present invention may include a receiving unit (210) for receiving a measured electrocardiogram signal, a transforming unit (220) for performing a Hilbert transform on the received electrocardiogram signal, and a measuring unit (230) for obtaining an electrocardiogram phase space based on the Hilbert transformed electrocardiogram signal.

[0030] Specifically, the receiver (210) can receive an electrocardiogram signal measured from the outside and transmit the received electrocardiogram signal to the converter (220).

[0031] The conversion unit (220) can perform a Hilbert transform on the electrocardiogram signal received from the receiving unit (210).

[0032] The aforementioned Hilbert transform preserves the amplitude of the electrocardiogram signal while shifting only its phase by +π / 2 at negative frequencies and -π / 2 at positive frequencies. This allows the real signal to be extended to the complex dimension, making the analysis of amplitude and phase easier. In other words, if a real signal is denoted as x(t) and the Hilbert-transformed signal as x^(t), then the signal x extended to the complex dimension p We can obtain (t)=x(t)+jx^(t).

[0033] FIG. 3 illustrates an electrocardiogram signal (300) as an example, and FIG. 4 illustrates a comparison between an electrocardiogram signal (301) and a Hilbert-transformed electrocardiogram signal (302).

[0034] Next, the measurement unit (230) can obtain a phase space based on the Hilbert transformed electrocardiogram signal. To this end, the measurement unit (230) may include a first module (231), a second module (232), and a third module (233).

[0035] The first module (231) can create a phase space diagram in which the values ​​of the electrocardiogram signals are real values ​​and the values ​​of the Hilbert-transformed electrocardiogram signals are imaginary values. The created phase space diagram can be transmitted to the second module (232).

[0036]

[0037] Figure 5 is a graph of the QRS complex, and Figure 6 is a graph showing the peak of the cubic function (left) and a graph showing the peak of the cubic function not (right).

[0038] Both graphs are cubic functions, and the peak not visible in the right graph exists in complex space. All signals are composed of complex numbers, and the sine function is expressed as a complex number as in Equation 1.

[0039]

[0040] All signals can be represented as a combination of simple signals, and such simple signals can be represented as a combination of sine functions as in Equation 1. Since a sine function is the result of projecting a complex sine function onto the real axis, an electrocardiogram graph is also the result of projecting from a complex coordinate system onto the real axis.

[0041] Meanwhile, it is necessary to consider how to find the imaginary part and construct the phase space. To this end, the imaginary part is obtained using the Hilbert transform.

[0042] In the graph on the right in Fig. 6, a polynomial can be obtained using numerical analysis methods, and the imaginary roots can be found using that polynomial. The Hilbert transform described later must include all methods for finding imaginary roots in cases like the graph on the right in Fig. 6 using imaginary numbers.

[0043] Figure 7 is a graph for finding the Q point (left) and an XY graph with the imaginary part obtained through the Hilbert transform as the X-axis and the electrocardiogram as the Y-axis (right).

[0044] In Fig. 7, the peak is the peak at the point where the PR segment ends. In reality, there are cases where the peak does not exist. In Fig. 7, point A protrudes unnaturally. Although it is easily visible to the viewer, electrocardiogram software must make a numerical judgment regarding the unnaturally protruding part because it must make a judgment based on the electrocardiogram data.

[0045] An easy way to think about this is to use inflection points. If the inflection point of the curve forming the left peak and Q in Fig. 7 is 1, the curve is a cubic function and the peak becomes the starting point of the QRS. However, if the inflection point is greater than 1, it is a quartic function or higher, and it becomes an unnaturally protruding shape.

[0046] The left figure of Fig. 7 is a fifth-order function (inflection point 3). Even after identifying the inflection point and confirming that there is an unnatural protrusion, a problem still remains. The starting point of the QRS is point B, which is known as the point where it descends toward Q. However, it is difficult to precisely define the descending point.

[0047] There is a claim that a line A is drawn on the left graph of Fig. 7, and the point furthest from that line is called point A, and that point A is the starting point of the QRS.

[0048] Looking at the graph on the right in Fig. 7, there is a vertex marked as point B on the curve moving clockwise from the peak. This vertex does not exist in the electrocardiogram graph but represents the vertex of the imaginary part existing in phase space. Vertices existing only in phase space may represent the start and end points of the QRS complex. One of the existing methods is to draw line A in Figs. 6 and 7 and find the point furthest from that line when there is no vertex.

[0049] Figure 8 is an electrocardiogram graph for finding point J, and Figure 9 is a graph showing point J in phase space.

[0050] In Fig. 8, point S represents the starting point of the QRS complex, and point J represents the ending point of the QRS complex. Point J is the end point of the S wave and represents the ending point of the QRS complex. Also, point J is the starting point of the ST segment.

[0051] The start and end points of the QRS complex represent the QRS interval (duration) and are important indicators in electrocardiogram diagnosis. Additionally, the start point of the QRS complex is the start point of the QT interval, and the QT interval is also an important indicator of cardiovascular health.

[0052] Figure 8 shows an example of finding the vertex of the imaginary part using phase space and locating the QRS endpoint when there is no peak at the end of the S wave. In this way, the start and end points of the QRS complex, which are unclear in the electrocardiogram graph, can be identified using the imaginary vertex in phase space as shown in Figure 9.

[0053] Figure 10 is an electrocardiogram graph with two peaks, and Figure 11 is a graph with boundary conditions applied that have two peaks in phase space.

[0054] When multiple peaks are observed in the electrocardiogram, boundary conditions can be applied within the phase space diagram to determine the start or end point of the QRS complex.

[0055] Figure 10 shows an example of an endpoint of a QRS complex. Multiple peaks exist near the endpoint of the QRS complex. Depending on the situation, an imaginary root appearing around peaks A and B or in phase space can be the endpoint of the QRS complex. In this case, boundary conditions can be used to limit the location of the peak that can be the endpoint of the QRS complex.

[0056] In Figure 11, excluding peak A which forms boundary condition A, the QRS complex in phase space that is closest to boundary condition A among peak B and the imaginary root in phase space is selected as the end point.

[0057]

[0058] The present invention is not limited by the embodiments described above and the attached drawings. The scope of rights is intended to be limited by the attached claims, and it will be obvious to those skilled in the art that various substitutions, modifications, and changes can be made within the scope of the technical concept of the present invention as described in the claims.

Claims

1. A receiving unit receives a measured electrocardiogram signal, a converting unit performs a Hilbert transform on the electrocardiogram signal, and a measuring unit creates a phase space map based on the Hilbert-transformed electrocardiogram signal to obtain the magnitude of the electrocardiogram signal, A method for finding the start and end points of a QRS complex using imaginary numbers, characterized in that the above-described phase space diagram has vertices of the imaginary part representing the start and end points of the QRS complex, and said vertices exist in the phase space region of the QRS complex.

2. In Paragraph 1, A method for determining the start and end points of a QRS complex using imaginary numbers, characterized by determining the start and end points of the QRS complex by setting boundary conditions using the phase space diagram when the above peaks are multiple.

3. In Paragraph 1, A method for determining the start and end points of a QRS complex, characterized by obtaining a polynomial from a graph representing the electrocardiogram signal and the phase space diagram using a numerical analysis method, and obtaining the vertex of the imaginary part from the polynomial.

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