METHOD FOR CALCULATING BLOOD FLOW AND SHEAR STRESS OF AORTA HAVING A BICUSPID AORTIC VALVE, READABLE MEDIUM STORING THE SAME AND MEDICAL DEVICE USING THE SAME

Abstract

It can significantly reduce the calculation speed and enable quick diagnosis. [Solution] A method for calculating blood flow and shear stress in an aorta having a bicuspid aortic valve, a recording medium storing the method, and a medical device using the method are disclosed. The method for calculating blood flow and shear stress in an aorta includes the steps of receiving, by an electronic computer, characteristic values ​​of a bicuspid aortic valve as input, and calculating the blood flow per unit area and the shear stress applied to the aorta in a bipolar coordinate system of governing equations using the characteristic values ​​of the bicuspid aortic valve.

Description

[Technical Field]

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

[0002] The cardiovascular system contains valves that prevent blood from flowing backward. These valves are membrane-like structures, and the tricuspid aortic valve (TAV) found in normal individuals has a membrane that splits into a "Y" shape on the cross section of the blood vessel, forming three leaflets. However, some people with congenital malformations have an "I"-shaped split in the blood vessel, resulting in a bicuspid aortic valve (BAV) with two leaflets, as shown in Figure 1.

[0003] Bicuspid aortic valve (BAV) is the most common congenital heart defect, affecting approximately 1-2% of the population. This condition results in the presence of only two leaflets in the aortic valve, rather than three, potentially leading to cardiovascular problems. The primary problem is valve dysfunction, which can lead to stenosis or regurgitation (leakage). Patients with BAV are also at increased risk for aortic dilation, which can lead to life-threatening aortic dissection, and an increased likelihood of developing infective endocarditis. These risks, due to altered valve mechanics and increased aortic wall stress in BAV patients, require careful monitoring and timely intervention.

[0004] For this purpose, the conventional finite element method (FEM) is used to calculate the blood flow in an aorta with a bicuspid aortic valve and the shear stress applied to the inner wall of the aortic vessel through simulation using the Navier-Stokes equations, but this method has the problem of being time-consuming. Summary of the Invention [Problem to be solved by the invention]

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

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

[0007] To solve the above problems, a method for calculating aortic blood flow and aortic shear stress according to an exemplary embodiment of the present invention includes a step of receiving, by an electronic computer, characteristic values ​​of a bicuspid aortic valve as input, and a step of calculating, using the characteristic values ​​of the bicuspid aortic valve, the blood flow rate per unit area and the shear stress applied to the aorta in a bipolar coordinate system of governing equations.

[0008] As an example, the characteristic values ​​of the bicuspid aortic valve may be the pole-to-pole distance (2a) in the bipolar coordinate system and the corresponding xi values ​​of the valve ends.

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

[0010] JPEG0007794489000002.jpg1452

[0011] In this equation, P is pressure, u(x, y) is velocity in the z-axis direction, and μ is viscosity of blood.

[0012] In this case, the solution of the governing equation in the bipolar coordinate system is

[0013] JPEG0007794489000003.jpg983

[0014] where ξ* is the ξ value corresponding to the valve end.

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

[0016] JPEG0007794489000004.jpg1790

[0017] So, in this formula,

[0018] JPEG0007794489000005.jpg9145

[0019] is.

[0020] In addition, the solution involving time t due to the contraction of the heart is the solution for the normal state, e iωt It can be approximated by multiplying the values.

[0021] The blood flow rate Q obtained by integrating the steady-state solution is

[0022] JPEG0007794489000006.jpg10141

[0023] It is expressed by the formula:

[0024] The shear stress τ(ξ, η) applied to the aorta obtained from the steady-state solution is given by

[0025] JPEG0007794489000007.jpg27105

[0026] It is expressed as follows.

[0027] Also, the shear stress at the end (ξ*j) of the bicuspid aortic valve is

[0028] JPEG0007794489000008.jpg1746

[0029] It is expressed as follows.

[0030] A computer-readable recording medium according to the present invention stores a program for executing the above-described method for calculating aortic blood flow and aortic shear stress.

[0031] A 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 input of characteristic values ​​of a bicuspid aortic valve. 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] In one embodiment, the characteristic value may be input by a user.

[0033] As another example, the characteristic value can be input from a measurement unit. [Effects of the Invention]

[0034] As described above, the method for calculating the aortic blood flow and aortic shear stress according to the present invention uses a finite element method (FEM) and a simulation based on the Navier-Stokes equations. By approximating the bicuspid aortic valve using a bipolar coordinate system, which has a similar shape, and using a solution that is directly obtained, the calculation speed can be significantly reduced, enabling a quick diagnosis. [Brief explanation of the drawings]

[0035] [Figure 1] FIG. 1 is a schematic diagram illustrating a bicuspid aortic valve. [Figure 2]FIG. 2 is a flow chart illustrating a method for calculating blood flow and shear stress in an aorta having a bicuspid aortic valve. [Figure 3] FIG. 3 illustrates a bipolar coordinate system for approximating the bicuspid aortic valve illustrated in FIG. [Figure 4] Figure 4 shows normal flow through bipolar holes and indicates the wall boundaries at (a) ξ*=2π / 3, (b) ξ*=3π / 4, (c) ξ*=4π / 5, and (d) ξ*=5π / 6 for a bicuspid aortic valve. [Figure 5] Figure 5 shows comparative velocity profiles at the aortic inlet for (a) the BAV, (b) the TAV, and (c) the combined profile showing the BAV (blue) and TAV (red) at the center. [Figure 6] Figure 6 shows the normalized shear stress distribution across the bipolar hole, highlighting the wall boundaries at (a) ξ* = 2π / 3, (b) ξ* = 3π / 4, (c) ξ* = 4π / 5, and (d) ξ* = 5π / 6 locations. [Figure 7] Figure 7 shows the WSS of the BAV normalized with the WSS of the TAV. [Figure 8] FIG. 8 is a block diagram illustrating a medical device according to an exemplary embodiment of the present invention. [Figure 9] FIG. 9 is a block diagram illustrating a medical device according to another exemplary embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0036] Because the present invention can be modified in various ways and can have various forms, specific embodiments are illustrated in the drawings and described in detail herein. However, this does not limit the present invention to the specific embodiments, and it should be understood that the present invention includes all modifications, equivalents, and alternatives within the spirit and technical scope of the present invention. In the description of each drawing, similar reference numerals are used for similar components. In the accompanying drawings, the dimensions of structures may be exaggerated to enhance clarity of the present invention.

[0037] Terms such as "first," "second," and the like may be used to describe various components, but the components should not be limited by these terms. These terms are used only to distinguish one component from another. For example, a first component may be designated a "second component," and similarly, a second component may be designated a "first component," without departing from the scope of the present invention.

[0038] The terms used in this application are used to describe specific embodiments and are not intended to limit the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, terms such as "comprise" or "have" are intended to specify the presence of a feature, numeral, step, operation, component, or combination thereof described in the specification, but should be understood not to preclude the presence or addition of one or more other features, numerals, step, operation, component, or combination thereof. Furthermore, the meaning of "connected" or "coupled" between A and B includes not only direct connection or coupling between A and B, but also the connection or coupling between 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 commonly understood by a person of ordinary skill in the art to which this invention pertains. Terms defined in commonly used dictionaries should be interpreted to have a meaning consistent with the meaning they have in the context of the relevant art, and should not be interpreted in an idealized or overly formal sense unless expressly defined in this application. In addition, in claims of method inventions, unless expressly bound to a specific order, the order of the steps may be reversed.

[0040] Furthermore, the configurations individually explained 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] FIG. 2 is a flow chart illustrating a method for calculating blood flow and shear stress in an aorta having a bicuspid aortic valve.

[0043] Referring to FIG. 2, a method for calculating aortic blood flow and aortic shear stress according to an exemplary embodiment of the present invention includes a step (S110) in which an electronic computer receives input of characteristic values ​​of a bicuspid aortic valve, and a step (S120) in which the electronic computer uses 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.

[0044] As an example, the characteristic values ​​of the bicuspid aortic valve can be the pole-to-pole distance (2a) in the bipolar coordinate system and the corresponding xi values ​​of the valve ends.

[0045] This will be explained in more detail below.

[0046] When a pressure gradient k acts in the axial direction of the tube at both polar cross sections, the governing equation for normal flow is expressed as Equation 1 below.

[0047]

number

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

[0049] On the other hand, the transverse components of velocity (specifically, the x-axis and y-axis components) are identically zero. For the problems addressed in this invention, solving the equations is much easier if transformed into a bipolar coordinate system, as shown in FIG. 3. This is due to the similarity between the geometry of the bicuspid aortic valve (BAV) illustrated in FIG. 1 and the geometry of the bipolar coordinate system. This transformation improves the mathematical treatment of flow dynamics and solution accuracy by adjusting the coordinate system to better fit the geometric complexities often encountered in non-circular cross-section scenarios.

[0050] The axes ξ and η of the bipolar coordinate system and the axes x and y of the Cartesian coordinate system satisfy the relationship of the following mathematical formula 2.

[0051]

number

[0052] where 2a is the distance between the foci. Here, the ξ coordinate represents one of the two angular coordinates in the bipolar coordinate system. It measures the angle between a line connecting a point to one focus and a line perpendicular to the line connecting the two foci. Essentially, ξ can be thought of as describing the angle around each focus. Meanwhile, the η coordinate is the second angular coordinate and measures the algebraic distance ratio between the point and the two foci. Figure 3 shows the bipolar coordinate system. The coordinate ξ varies from ξ* to π at the top wall of the BAV and from π to 2π-ξ* at the bottom wall of the BAV. The steady-state solution u0 of Equation 1 satisfies the no-slip boundary condition of Equation 3 below.

[0053]

number

[0054] where ξ* is the ksi value corresponding to the valve end.

[0055] Meanwhile, the steady state solution obtained through the above boundary conditions is expressed as Equation 4 below.

[0056]

number

[0057] In this formula,

[0058] JPEG0007794489000013.jpg8145

[0059] is.

[0060] In addition, the solution involving time t due to the contraction of the heart is a steady-state solution with e iωt It can be approximated by multiplying the values.

[0061] Normal flow is when ξ*=π / 2, ξ=π and η=0, in a circular cylindrical tube of equivalent diameter u circular and is expressed as the following mathematical formula 5.

[0062]

number

[0063] Furthermore, the blood flow rate Q obtained by integrating the above steady-state equation is expressed as in the following mathematical formula 6.

[0064]

number

[0065] In this formula,

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

[0067]

number

[0068] In addition, the shear stress τ(ξ, η) applied to the aorta calculated from the above steady-state equation is expressed as the following mathematical formula 8:

[0069]

number

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

[0071]

number

[0072] This can be compared to a circular cylindrical tube of equivalent diameter, which is expressed by Equation 10 below.

[0073]

number

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

[0075] Velocity profiles are normalized by the maximum velocity observed in a TAV of comparable diameter. This normalization allows direct comparison of BAV and TAV flow characteristics, highlighting differences in their respective velocity profiles relative to a common reference point. The BAV velocity profiles are remarkably consistent with those obtained in previous studies using consistent multiscale simulations. Such profiles consistently demonstrate the presence of jet-like flow structures within the fluid, which are less prominent in the TAV scenario. This jet formation demonstrates a distinct hemodynamic pattern associated with the BAV and highlights the considerable influence of valve morphology on flow dynamics.

[0076] Figure 5 shows comparative velocity profiles at the aortic inlet for (a) the BAV, (b) the TAV, and (c) a combined profile showing the BAV (blue) and TAV (red) at the center. Analysis revealed significantly higher velocities at the bicuspid aortic valve (BAV) compared with the tricuspid aortic valve (TAV) at the center of the inlet. However, BAV velocity decreases more rapidly than TAV as it moves toward the vessel wall. The rapid decrease in BAV velocity creates a steeper velocity gradient perpendicular to the vessel wall. Consequently, the BAV experiences higher wall shear stress. Increased wall shear stress can have a significant impact on vascular health and potentially contribute to the pathogenesis of BAV-related aortic disease and complications. While previous computational methods required several minutes per cell, our analytical model achieved similar results in a matter of seconds. This significant reduction in computational time highlights the efficiency and effectiveness of our approach, 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 bipolar opening, highlighting the wall boundaries at (a) ξ* = 2π / 3, (b) ξ* = 3π / 4, (c) ξ* = 4π / 5, and (d) ξ* = 5π / 6. As derived from equation (7) and discussed in the legend to Figure 5, wall shear stress (WSS) reaches a maximum at the bicuspid aortic valve boundary. Analysis reveals that WSS increases significantly as the bicuspid valve shape becomes narrower. This indicates that bicuspid valve geometry has a significant impact on the shear stress experienced at the vessel wall, with narrower valve shapes resulting in higher shear stress. This finding is essential for understanding the hemodynamic stresses associated with the bicuspid aortic valve and its potential impact on vascular health.

[0078] Figure 7 shows the wall shear stress (WSS) of the bicuspid aortic valve (BAV) normalized by the WSS of the TAV. The normalized WSS is inversely proportional to sin(ξ*), which increases rapidly as the aortic valve orifice becomes more asymmetric. Figure 7 displays 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 orifice, which increases rapidly as the orifice becomes more asymmetric. This indicates that the WSS increases significantly as the aortic valve deviates from a symmetrical shape, which may have important implications for the structural integrity and function of the valve.

[0079] Steady blood flow through compressed or defective blood vessels, i.e., Poiseuille flow, is an important issue in hemodynamics, especially in cardiovascular research. This invention investigates tubes with bipolar cross sections to simulate the elliptical systolic opening of a bicuspid aortic valve (BAV). Unlike a normal tricuspid aortic valve (TAV), a BAV with two cusps presents unique hemodynamic challenges. BAV, the most common congenital heart defect, places patients at increased risk for aortic dilatation and dissection.

[0080] Bipolar cross-section analysis provides a more accurate geometric approximation for modeling flow through such atypical valve geometries and is important for understanding the specific fluid dynamics associated with BAVs. In this study, we derived accurate solutions to the governing equations for Poiseuille flow in tubes with bipolar cross-sections. Results include detailed analysis of the velocity field, flow rate, and wall shear stress (WSS).

[0081] Our results show that the velocity profiles of the BAV are remarkably consistent with those obtained through previous multiscale simulations. These profiles consistently exhibit jet-like flow structures within the fluid that are not observed in the TAV scenario. Our analysis reveals that the flow velocity of the BAV is significantly 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 higher shear stress at the wall of the BAV.

[0082] Furthermore, wall shear stress (WSS), proportional to the inverse of sin(ξ_), where ξ represents the bipolar coordinate of the wall boundary, is significantly higher than that found in a cylindrical tube of equivalent diameter. In the case of aortic stenosis, where ξ approaches π, WSS increases very rapidly. Such elevated WSS is commonly observed in patients with BAV and may negatively impact the aortic wall, particularly within the ascending aorta, contributing to the higher incidence 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 disease.

[0083] FIG. 8 is a block diagram illustrating a medical device according to an 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 the aortic blood flow and aortic shear stress, and includes an input unit (1100), a calculation unit (1200), and an output unit (1300).

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

[0086] The calculation unit 1200 calculates 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 ​​transmitted from the input unit 1100. The detailed calculation process has been described above, so a duplicated description will be omitted.

[0087] The output unit (1300) outputs the results of the calculations performed by the associative unit, and can be realized by a device such as a display or a printer.

[0088] Figure 9 is a block diagram illustrating a medical device according to another exemplary embodiment of the present invention. The medical device illustrated in Figure 9 is substantially the same as the medical device illustrated in Figure 8, except that it further includes a measurement unit and an input unit that receives input of characteristic values ​​from the measurement unit. Therefore, the same or similar components are denoted by the same reference numerals, and redundant description will be omitted.

[0089] 9, the characteristic values ​​are input from a measuring unit 1400. At this time, the measuring unit 1400 is equipment capable of projecting blood vessels such as ultrasound, CT, MRI, etc., and the medical device 1000 according to the present invention is integrated with such conventional measuring devices to immediately calculate and display the blood flow rate per unit area and the shear stress applied to the aorta.

[0090] Furthermore, a computer-readable recording medium according to the present invention stores a program for performing the above-described method for calculating aortic blood flow and aortic shear stress. Such a recording medium may be embodied in the form of program instructions that can be executed by various computer means and recorded on the computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions recorded on the medium may be specially designed and constructed for the embodiments, or may be known and available to 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 memories. Examples of program instructions include not only machine language code, such as that produced by a compiler, but also high-level language code that can be executed by a computer using an interpreter, etc. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of an embodiment, and vice versa.

[0091] Thus, the method of calculating the aortic blood flow and aortic shear stress according to the present invention, compared to conventional methods that use simulations based on the Navier-Stokes equations using the finite element method (FEM), approximates the bicuspid aortic valve using a bipolar coordinate system with a similar shape and uses a solution that is directly obtained, thereby significantly reducing the calculation speed and enabling faster diagnosis.

[0092] The above detailed description of the present invention has been given with reference to preferred embodiments of the present invention, but it will be understood by those skilled in the art or those with ordinary knowledge in the art that the present invention can be modified and changed in various ways without departing from the spirit and technical scope of the present invention as set forth 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. 1. A method for calculating blood flow and shear stress in an aorta having a bicuspid aortic valve, the method comprising: The calculation method comprises: an input stage for receiving input of a characteristic value of a bicuspid aortic valve; A calculation step of calculating a blood flow rate per unit area and a shear stress applied to the aorta based on a solution of a governing equation in a bipolar coordinate system using characteristic values ​​of the bicuspid aortic valve, The governing equation is: In this formula, P is pressure, u(x, y) is velocity in the z-axis direction, μ is viscosity of blood, The solution of the above governing equations in bipolar coordinates is where ξ* is the ksi value corresponding to the valve end, The steady state solution obtained by the boundary conditions is given by In this formula, and The blood flow rate is calculated by integrating the steady-state solution: The blood flow rate Q is calculated using The shear stress is given by the formula obtained from the steady-state solution: the calculation step is performed by calculating the shear stress τ(ξ,η) applied to the aorta using A method for calculating blood flow and shear stress in an aorta having a bicuspid aortic valve, comprising:

2. The characteristic values ​​of the bicuspid aortic valve are:

2. The method for calculating the blood flow in the aorta and the shear stress in the aorta according to claim 1, characterized in that the values ​​are the distance between poles (2a) in the bipolar coordinate system and the Ksi values ​​corresponding to the valve end portions.

3. The solution involving time t due to the contraction of the heart is The steady-state solution e ｉωｔ 2. The method for calculating the aortic blood flow and the aortic shear stress according to claim 1, wherein the aortic blood flow and the aortic shear stress are approximated by multiplying the aortic blood flow and the aortic shear stress by a value.

4. The shear stress at the edge of the bicuspid aortic valve (ξ*j) is Using τ|ξ ＊ｊ 2. The method for calculating the aortic blood flow and the aortic shear stress according to claim 1, wherein the aortic blood flow and the aortic shear stress are calculated by:

5. A recording medium readable by an electronic computer, storing a program for causing the electronic computer to execute the method for calculating aortic blood flow and aortic shear stress according to any one of claims 1 to 4.

6. A medical device using the method for calculating aortic blood flow and aortic shear stress according to any one of claims 1 to 4, an input unit for executing the input step; a calculation unit that performs the calculation step; an output unit that outputs the calculation result from the calculation unit; Medical devices, including:

7. The medical device according to claim 6 , wherein the characteristic value is input by a user.

8. The medical device according to claim 6, wherein the characteristic value is input from a measurement unit.

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