A method for calculating blood flow and shear stress in an aorta having a bicuspid aortic valve, a recording medium storing the same, and a medical device using the same.

Abstract

This significantly reduces the processing speed, enabling rapid diagnosis. [Solution] A method for calculating blood flow and shear stress in an aorta having a bicuspid aortic valve, a recording medium storing the same, and a medical device utilizing the same are disclosed. Such a method for calculating blood flow and shear stress in an aorta includes the steps of a computer receiving characteristic values ​​of the bicuspid aortic valve as input, and using the characteristic values ​​of the bicuspid aortic valve to calculate the blood flow rate per unit area and the shear stress applied to the aorta in the bipolar coordinate system of the governing equations.

Description

Technical Field

[0001] The present invention relates to a method for calculating the blood flow in the aorta having a bicuspid aortic valve and the shear stress in the aorta, a recording medium storing the same, and a medical device using the same.

Background Art

[0002] There is a valve in the cardiovascular system to prevent blood backflow. Such a valve has a membrane structure. The tricuspid aortic valve (TAV) that normal people have has a membrane divided into three leaves in a "Y" shape in the cross-section of the blood vessel. However, in some congenital malformations, the blood vessel is split into an "I" shape, and as shown in FIG. 1, there are people who have a bicuspid aortic valve (BAV) formed by two leaves.

[0003] The bicuspid aortic valve (BAV) is the most common congenital heart disease affecting about 1-2% of the population. This means that there are only two leaves instead of three in the aortic valve, which may cause potential cardiovascular problems. The main problems include valve dysfunction that may lead to stenosis or regurgitation (leakage). In addition, BAV patients have an even higher risk of aortic dilation, which may lead to life-threatening aortic dissection and an increased risk of developing infective endocarditis. Such risks require careful monitoring and timely intervention due to the altered valve mechanics and increased aortic wall stress in BAV patients.

[0004] For this reason, conventionally, using the finite element method (F.E.M.), simulations based on the Navier-Stokes equation have been used to calculate the blood flow in the aorta with a bicuspid aortic valve and the shear stress applied to the inner wall of the aortic blood vessel, but such a method has the problem of taking a lot of time.

Summary of the Invention

Problems to be Solved by the Invention

[0005] Therefore, the problem that the present invention aims to solve is to provide a method for calculating blood flow in an aorta having a bicuspid aortic valve and shear stress in the aorta, which can dramatically reduce calculation time.

[0006] Another problem that the present invention aims to solve is to provide a medical device that utilizes a method for calculating blood flow in an aorta having such a bicuspid aortic valve and the shear stress of the aorta. [Means for solving the problem]

[0007] A method for calculating aortic blood flow and aortic shear stress according to an exemplary embodiment of the present invention for solving such problems includes the steps of: a computer receiving characteristic values ​​of a bicuspid aortic valve as input; and using the characteristic values ​​of the bicuspid aortic valve to calculate the blood flow per unit area and the shear stress applied to the aorta in the bipolar coordinate system of the governing equations.

[0008] As one embodiment, the characteristic values ​​of the bicuspid aortic valve can be the inter-pole distance (2a) and the qusi value corresponding to the valve end in the bipolar coordinate system.

[0009] As one embodiment, the governing equation is:

[0010] JPEG2026057410000002.jpg1452

[0011] This can be expressed as follows, where P is the pressure, u(x,y) is the velocity in the z-axis direction, and μ is the viscosity of the blood.

[0012] At this time, the solution of the governing equation in bipolar coordinates is,

[0013] JPEG2026057410000003.jpg983

[0014] Obtained through the boundary conditions, where ξ* is the Kusa value corresponding to the valve end portion.

[0015] On the other hand, the steady state solution obtained by the above boundary conditions is

[0016] JPEG2026057410000004.jpg1790

[0017] where, in this equation

[0018] JPEG2026057410000005.jpg9145

[0019] is as follows.

[0020] In addition, the solution involving the time t due to the contraction motion of the heart can be approximated by multiplying the solution in the normal state by e iωt value. [[ID=3]]

[0021] Note that the blood flow rate Q obtained by integrating the steady state solution is

[0022] JPEG2026057410000006.jpg10141

[0023] expressed by the formula of

[0024] Note that the shear stress τ(ξ, η) applied to the aorta obtained from the steady state solution is

[0025] JPEG2026057410000007.jpg27105

[0026] expressed as follows.

[0027] In addition, the shear stress at the end (ξ*j) of the mitral aortic valve is

[0028] JPEG2026057410000008.jpg1746

[0029] It is expressed as follows.

[0030] The computer-readable recording medium according to the present invention stores a program for executing the above-mentioned method for calculating the blood flow in the aorta and the shear stress in the aorta.

[0031] The medical device according to the present invention utilizes the above-described method for calculating aortic blood flow and aortic shear stress, and includes an input unit, a calculation unit, and an output unit. The input unit receives characteristic values ​​of the bicuspid aortic valve as input. The calculation unit uses the characteristic values ​​transmitted from the input unit to calculate the blood flow rate per unit area and the shear stress applied to the aorta in the bipolar coordinate system of the governing equations. The output unit outputs the results calculated by the calculation unit.

[0032] As one embodiment, the above characteristic values ​​can be input from the user.

[0033] In another embodiment, the above characteristic values ​​can be received as input from the measurement unit. [Effects of the Invention]

[0034] Thus, the method for calculating aortic blood flow and aortic shear stress according to the present invention significantly reduces the calculation speed and enables rapid diagnosis compared to conventional methods that utilize the finite element method (FEM) and simulations using the Navier-Stokes equations. This is achieved by approximating the bicuspid aortic valve with a similarly shaped bipolar coordinate system and using the directly obtained solution. [Brief explanation of the drawing]

[0035] [Figure 1] Figure 1 is a schematic diagram illustrating the bicuspid aortic valve. [Figure 2]Figure 2 is a sequential diagram illustrating the calculation method for blood flow in an aorta with a bicuspid aortic valve and the shear stress of the aorta. [Figure 3] Figure 3 illustrates a bipolar coordinate system for approximating the bicuspid aortic valve shown in Figure 1. [Figure 4] Figure 4 shows the normal flow through the bipolar holes, and for the bicuspid aortic valve, the wall boundaries are shown at positions (a)ξ*=2π / 3, (b)ξ*=3π / 4, (c)ξ*=4π / 5, and (d)ξ*=5π / 6, respectively. [Figure 5] Figure 5 shows (a) BAV, (b) TAV, and (c) a combined profile showing BAV (blue) and TAV (red) at the center, relative to the comparative velocity profile at the aortic ost. [Figure 6] Figure 6 shows the normalized shear stress distribution across the entire bipolar hole, highlighting the wall boundaries at (a) ξ* = 2π / 3, (b) ξ* = 3π / 4, (c) ξ* = 4π / 5, and (d) ξ* = 5π / 6. [Figure 7] Figure 7 shows the WSS of BAV normalized by the WSS of TAV. [Figure 8] Figure 8 is a block diagram illustrating a medical device according to one exemplary embodiment of the present invention. [Figure 9] Figure 9 is a block diagram illustrating a medical device according to another exemplary embodiment of the present invention. [Modes for carrying out the invention]

[0036] Because the present invention can be modified in various ways and take on various forms, specific embodiments are illustrated in the drawings and described in detail herein. However, this should not be understood as limiting the invention to specific embodiments, but rather as including all modifications, equivalents, or substitutions that fall within the spirit and technical scope of the invention. In the description of each drawing, similar components are given the same reference numerals. In the accompanying drawings, the dimensions of structures may be exaggerated to enhance clarity of the invention.

[0037] Terms such as "first," "second," etc., can be used to describe various components, but the components should not be limited by these terms. These terms are used solely for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be named the second component, and similarly, the second component may be named the first component.

[0038] The terminology used in this application is for the purpose of describing specific embodiments and is not intended to limit the invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, terms such as “contain” or “have” should be understood as intending to specify the presence of features, figures, steps, operations, components, parts, or combinations thereof as described in the specification, and not as preemptively excluding the possibility of the presence or addition of one or more other features, figures, steps, operations, components, parts, or combinations thereof. Furthermore, the meaning of A and B being 'connected' or 'joined' includes not only the direct connection or joining of A and B, but also the connection or joining of A and B by including another component C between A and B.

[0039] Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as generally understood by a person of ordinary skill in the art to which the invention pertains. Terms as defined in commonly used dictionaries should be interpreted as having the meaning consistent with their meaning in the context of the relevant art, and not as ideal or overly formal unless explicitly defined herein. Furthermore, in the claims of a method invention, unless the steps are explicitly bound to be in a specific order, the order of the steps may be changed.

[0040] Furthermore, the configurations described individually in each embodiment can also be applied to other embodiments.

[0041] Hereinafter, embodiments of the present invention will be described in more detail with reference to the drawings.

[0042] Figure 2 is a sequential diagram illustrating the calculation method for blood flow in an aorta with a bicuspid aortic valve and the shear stress of the aorta.

[0043] Referring to Figure 2, an exemplary embodiment of the present invention provides a method for calculating aortic blood flow and aortic shear stress, which includes the steps of: a computer receiving characteristic values ​​of a bicuspid aortic valve (S110); and using the characteristic values ​​of the bicuspid aortic valve to calculate the blood flow rate per unit area and the shear stress applied to the aorta in the bipolar coordinate system of the governing equations (S120).

[0044] As one embodiment, the characteristic values ​​of the bicuspid aortic valve described above can be the inter-pole distance (2a) and the qusi value corresponding to the valve end in the bipolar coordinate system.

[0045] The following provides a more detailed explanation.

[0046] When a pressure gradient k acts axially through a tube with a bipolar cross-section, the governing equation for normal flow is expressed as shown in mathematical equation 1 below.

[0047]

number

[0048] In this equation, P is the pressure, u(x, y) is the velocity in the z-axis direction, and μ is the viscosity of the blood. Here, x and y represent the axes of the Cartesian coordinate system, respectively.

[0049] On the other hand, the lateral components of velocity (particularly the x-axis and y-axis components) are identically zero. In the case of the problem addressed in this invention, solving the equations becomes much simpler when transformed into a bipolar coordinate system as shown in Figure 3. This is because the shape of the bicuspid aortic valve (BAV) shown in Figure 1 is similar to the shape of the bipolar coordinate system. This transformation adjusts the coordinate system to better accommodate the geometric complexities often encountered in non-circular cross-section scenarios, thereby improving the mathematical processing and solution accuracy of flow dynamics.

[0050] The axes ξ and η of the bipolar coordinate system and the axes x and y of the Cartesian coordinate system satisfy the following relationship, as shown in mathematical equation 2.

[0051]

number

[0052] Here, 2a is the distance between foci. Here, the ξ coordinate represents one of the two angular coordinates of the bipolar coordinate system. This measures the angle between the line connecting a point to one focus and the line perpendicular to the line connecting the two foci. Essentially, ξ can be considered to describe the angle around each focus. On the other hand, the η coordinate is the second angular coordinate system, which measures the algebraic distance ratio between a point and the two foci. Figure 3 shows the bipolar coordinate system. The coordinate ξ varies from ξ* to π at the upper wall of the BAV and from π to 2π-ξ* at the lower wall of the BAV. The steady-state solution u0 of mathematical equation 1 satisfies the no-slip boundary condition of mathematical equation 3 below.

[0053]

number

[0054] Here, ξ* is the csi value corresponding to the valve end described above.

[0055] On the other hand, the steady-state solution obtained through the above boundary conditions can be expressed as shown in mathematical equation 4 below.

[0056]

number

[0057] In this formula,

[0058] JPEG2026057410000013.jpg8145

[0059] That is the case.

[0060] Furthermore, solutions involving time t due to cardiac contraction are obtained by adding e to the steady-state solution. iωt It can be approximated by multiplying by the value.

[0061] Normal flow occurs when ξ*=π / 2, ξ=π, and η=0 in a circular cylindrical tube of equivalent diameter u circular It decreases to the following mathematical formula 5, which can be expressed as shown below.

[0062]

number

[0063] Furthermore, the blood flow rate Q obtained by integrating the above steady-state equation can be expressed as shown in mathematical equation 6 below.

[0064]

number

[0065] In this formula,

[0066] When ξ*=π / 2, the blood flow rate Q is equivalent to the flow in a circular cylindrical tube of the same diameter, and the following mathematical equation 7 is derived.

[0067]

number

[0068] Furthermore, the shear stress τ(ξ,η) applied to the aorta, obtained from the above steady-state equation, can be expressed as shown in mathematical equation 8 below.

[0069]

number

[0070] The shear stress (WSS: Wall Shear Stress) at the end (ξ*j) of the bicuspid aortic valve is expressed by the following mathematical formula 9.

[0071]

number

[0072] This can be compared to a circular cylindrical tube with an equivalent diameter, as expressed by the following mathematical formula 10.

[0073]

number

[0074] Figure 4 shows the normal flow through the bipolar holes, and for the bicuspid aortic valve, the wall boundaries are shown at positions (a)ξ*=2π / 3, (b)ξ*=3π / 4, (c)ξ*=4π / 5, and (d)ξ*=5π / 6, respectively.

[0075] The velocity profiles are normalized to the maximum velocity observed in TAVs with equivalent diameters. Through this normalization, the flow characteristics of BAVs and TAVs can be directly compared, and the differences in their respective velocity profiles are highlighted relative to a common reference point. The velocity profiles of BAVs are remarkably consistent with those obtained in previous studies using consistent multi-scale simulations. Such profiles consistently indicate the presence of jet-like flow structures within the fluid, which are not prominent in the TAV scenario. This jet formation exhibits a distinct hemodynamic pattern associated with BAVs and highlights the significant influence of valve morphology on flow dynamics.

[0076] Figure 5 shows comparative velocity profiles at the aortic inlet for (a) BAV, (b) TAV, and (c) a coupled profile showing BAV (blue) and TAV (red) at the center. The analysis showed that the velocity of the bicuspid aortic valve (BAV) was considerably higher than that of the tricuspid aortic valve (TAV) at the center of the inlet. However, the BAV velocity decreases even faster than that of the TAV as it moves toward the vessel wall. If the BAV velocity decreases rapidly, an even steeper velocity gradient perpendicular to the vessel wall is generated. Consequently, in the case of BAV, the wall shear stress increases. Increased wall shear stress has a significant impact on vascular health and may contribute to the development of BAV-related aortic diseases and complications. While conventional calculation times were several minutes per cell, similar results were obtained in seconds using the analytical model of the present invention. The significant reduction in calculation time highlights the efficiency and effectiveness of the approach of the present invention, providing rapid and reliable analysis that is advantageous for both research and clinical application programs.

[0077] Figure 6 shows the normalized shear stress distribution across the entire bipolar hole, highlighting the wall boundaries at (a)ξ*=2π / 3, (b)ξ*=3π / 4, (c)ξ*=4π / 5, and (d)ξ*=5π / 6. Derived from equation (7) and discussed in the explanation of Figure 5, the wall shear stress (WSS) reaches its maximum at the bicuspid aortic valve boundary. Analysis reveals that WSS increases considerably as the bicuspid valve shape narrows. This indicates that the geometry of the bicuspid valve significantly influences the shear stress experienced by the vessel wall, with narrower valve shapes resulting in higher shear stress. This finding is essential for understanding the hemodynamic stress associated with the bicuspid aortic valve and its potential impact on vascular health.

[0078] Figure 7 shows the WSS of the bicuspid aortic valve (BAV) normalized by the WSS of the tricuspid aortic valve (TAV). The normalized WSS is inversely proportional to sin(ξ*), which increases rapidly as the aortic valve hole becomes more asymmetrical. Figure 7 shows the wall shear stress (WSS) of the bicuspid aortic valve (BAV) normalized by the WSS of the tricuspid aortic valve (TAV). The normalized WSS is inversely proportional to sin(ξ*) of the aortic valve hole and increases rapidly as the hole becomes more asymmetrical. This indicates that the WSS increases significantly as the aortic valve deviates from its symmetrical shape, which can have a significant impact on the structural integrity and function of the valve.

[0079] Stable blood flow through compressed or defective vessels, i.e., poiseuille flow, is a crucial issue in hemodynamics, particularly in cardiovascular research. This invention investigates a tube with a bipolar cross-section to simulate the elliptical systolic opening of a bicuspid aortic valve (BAV). Unlike a normal tricuspid aortic valve (TAV), the BAV, with its two cusps, presents unique hemodynamic problems. As the most common congenital heart defect, BAV carries a risk of increased aortic dilation and dissection among patients.

[0080] Bipolar cross-sectional analysis provides a more accurate geometric approximation for modeling flows through such atypical valve shapes and is important for understanding specific fluid dynamics associated with barometric outlets (BAVs). In this invention, we derived precise solutions to the governing equations for Poiseuille flow in a tube with a bipolar cross-section. The results include a detailed analysis of the velocity field, flow rate, and wall shear stress (WSS).

[0081] The results of this invention demonstrate that the velocity profile of the BAV (Body-Aided Velocity) remarkably matches that obtained through previous multi-scale simulations. Such profiles consistently exhibit a jet-like flow structure within the fluid, which is not observed in the TAV (Transcatheter Aided Velocity) scenario. Analysis shows that the flow velocity of the BAV is considerably higher than that of the TAV at the inlet center. However, the flow velocity of the BAV decreases more rapidly toward the vessel wall, creating a steeper vertical velocity gradient. This results in even higher shear stresses on the BAV wall.

[0082] Furthermore, wall shear stress (WSS) is proportional to the reciprocal of sin(ξ_) by ξ, which represents the bipolar coordinate of the wall boundary, and is considerably higher than that found in cylindrical tubes of equivalent diameter. In cases of aortic stenosis where ξ approaches π, WSS increases very rapidly. Such elevated WSS is commonly observed in BAV patients and negatively affects the aortic wall, particularly in the ascending aorta, and can contribute to a higher frequency of aortic complications in these patients. Understanding these hemodynamic factors is essential for developing better diagnostic and therapeutic strategies for the management of BAV-related diseases.

[0083] Figure 8 is a block diagram illustrating a medical device according to one exemplary embodiment of the present invention.

[0084] Referring to Figure 8, the medical device (1000) according to the present invention utilizes the above-mentioned method for calculating aortic blood flow and aortic shear stress, and includes an input unit (1100), a calculation unit (1200), and an output unit (1300).

[0085] The above input unit (1100) receives input of characteristic values ​​of the bicuspid aortic valve. More specifically, in one embodiment, the above characteristic values ​​can be input by the user. In this case, the input unit can be implemented via a keyboard, mouse, touchscreen, etc. That is, the user can input the required characteristic values ​​to the medical device (1000) according to the present invention via the above input unit (1100) through equipment capable of projecting blood vessels, such as ultrasound, CT, or MRI.

[0086] The calculation unit (1200) uses the characteristic values ​​transmitted from the input unit (1100) to calculate the blood flow rate per unit area and the shear stress applied to the aorta in the bipolar coordinate system of the governing equations. Since such a detailed calculation process has been explained earlier, a redundant explanation will be omitted.

[0087] The output unit (1300) outputs the result calculated from the association unit. This output unit can be implemented using a device such as a display or printer.

[0088] Figure 9 is a block diagram illustrating a medical device according to another exemplary embodiment of the present invention. The medical device shown in Figure 9 is substantially identical to the medical device shown in Figure 8, except that it further includes a measuring unit and the input unit receives characteristic values ​​from the measuring unit. Therefore, identical or similar components are given the same reference numerals, and redundant descriptions are omitted.

[0089] Referring to Figure 9, the above characteristic values ​​are received from the measurement unit (1400). In this case, the measurement unit (1400) is equipped to project blood vessels, such as ultrasound, CT, and MRI, and the medical device (1000) according to the present invention is integrated with such conventional measurement devices and can immediately calculate and display the blood flow rate per unit area and the shear stress applied to the aorta.

[0090] Furthermore, the computer-readable recording medium according to the present invention stores a program for performing the above-mentioned method for calculating the blood flow and shear stress of the aorta. Such a recording medium can be recorded on a computer-readable medium, where the method according to the embodiment is embodied in the form of program instructions that can be performed through various computer means. The computer-readable medium may include program instructions, data files, data structures, etc., individually or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiment, or may be known and usable by those skilled in the art. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes; optical media such as CD-ROMs and DVDs; magneto-optical media such as floptical disks; and hardware devices specially configured to store and execute program instructions, such as ROMs, RAMs, and flash memory. Examples of program instructions include not only machine code, such as that produced by a compiler, but also advanced language code that can be executed by a computer using an interpreter or the like. The hardware devices described above can be configured to operate as one or more software modules to perform the operations of the embodiment, and vice versa.

[0091] Thus, the method for calculating aortic blood flow and aortic shear stress according to the present invention significantly reduces the computational speed and enables rapid diagnosis compared to conventional methods that utilize the finite element method (FEM) and simulations based on the Navier-Stokes equations. This is achieved by approximating the bicuspid aortic valve with a similarly shaped bipolar coordinate system and using the directly obtained solution.

[0092] While the detailed description of the present invention has been based on reference to preferred embodiments, a person skilled in the art or with ordinary knowledge in the art will understand that the present invention can be modified and altered in various ways, within the scope of the concept and technical domain of the invention as described in the claims below. [Explanation of Symbols]

[0093] 1000: Medical devices 1100: Input section 1200: Calculation section 1300: Output section 1400: Measurement section

Claims

1. Electronic computers, The stage of receiving input for characteristic values ​​of the bicuspid aortic valve; and A step of calculating the blood flow rate per unit area and the shear stress applied to the aorta in the bipolar coordinate system of the governing equations, using the characteristic values ​​of the bicuspid aortic valve; A method for calculating blood flow in an aorta having a bicuspid aortic valve and shear stress in the aorta.

2. The characteristic values ​​of the bicuspid aortic valve are, The method for calculating aortic blood flow and aortic shear stress according to claim 1, characterized in that the interpolar distance (2a) and the qusi value corresponding to the valve end are in a bipolar coordinate system.

3. The governing equations are, It is expressed as, and in this formula, The method for calculating the blood flow in the aorta and the shear stress in the aorta according to claim 1, characterized in that P is pressure, u(x,y) is velocity in the z-axis direction, and μ is blood viscosity.

4. The solution to the governing equations in bipolar coordinates is: A method for calculating aortic blood flow and aortic shear stress according to claim 3, wherein the aortic blood flow and aortic shear stress are determined through boundary conditions, where ξ* is the xi value corresponding to the valve end.

5. The steady-state solution obtained using the aforementioned boundary conditions is: And in this formula, The method for calculating the blood flow in the aorta and the shear stress in the aorta according to claim 4.

6. The solution involving time t due to the contraction of the heart is: The solution in the stationary state is e iωt The method for calculating the blood flow in the aorta and the shear stress in the aorta according to claim 5, characterized in that the values ​​are approximated by multiplication.

7. The blood flow rate Q obtained by integrating the steady-state solution is: The method for calculating the blood flow in the aorta and the shear stress in the aorta according to claim 5, characterized in that it is expressed by the formula.

8. The shear stress τ(ξ,η) applied to the aorta, obtained from the steady-state solution, The method for calculating the blood flow in the aorta and the shear stress in the aorta according to claim 5, characterized in that it is expressed as such.

9. The shear stress at the end (ξ*j) of the bicuspid aortic valve is The method for calculating the blood flow in the aorta and the shear stress in the aorta according to claim 8, characterized in that they are expressed as follows.

10. A computer-readable recording medium for performing a method for calculating aortic blood flow and aortic shear stress according to any one of paragraphs 1 through 9.

11. A medical device that uses a method for calculating aortic blood flow and aortic shear stress according to any one of paragraphs 1 through 9, An input unit that receives characteristic values ​​of the bicuspid aortic valve; A calculation unit that uses the characteristic values ​​transmitted from the input unit to calculate the blood flow rate per unit area and the shear stress applied to the aorta in the bipolar coordinate system of the governing equations; and An output unit that outputs the result calculated by the aforementioned calculation unit; Medical devices including those mentioned.

12. The medical device according to claim 11, characterized in that the aforementioned characteristic values ​​are input from the user.

13. The medical device according to claim 1, characterized in that the aforementioned characteristic value is input from the measurement unit.

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