A method and device for calculating corneal biomechanical properties based on spline theory

Abstract

The present application relates to a kind of corneal biomechanical property calculation method and device based on spline theory, comprising the following steps: step 1, sampling and analysis are carried out from the dynamic video of corneal stress deformation in historical database, and the profile of cornea is extracted;Step 2, the curve of profile change in the process of corneal deformation is fitted using spline theory, and the curve equation of corneal profile is obtained;Step 3, according to the curve equation of corneal profile in step 2, the zero point of its first derivative and second derivative is solved, to determine the first flattening state moment, the maximum indentation moment and the second flattening moment in the process of corneal deformation, so as to calculate the biomechanical property of cornea.The present application can accurately and objectively evaluate the biomechanical property of cornea.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of corneal biomechanical property analysis, and relates to a corneal biomechanical property calculation method and device, in particular to a corneal biomechanical property calculation method and device based on spline theory. BACKGROUND

[0002] The calculation method of the existing corneal biomechanical property calculation application device still belongs to a technical secret and has not been disclosed. The existing corneal biomechanical property calculation method still has defects such as strong subjectivity, dependence on experience judgment and lack of systematic theoretical support because it cannot accurately fit the corneal deformation process.

[0003] Therefore, the technical personnel in the field urgently need to develop a corneal biomechanical property calculation method and device based on spline theory which can accurately and objectively evaluate the corneal biomechanical property.

[0004] After searching, no existing technical patent literature identical or similar to the present application has been found. SUMMARY

[0005] The present application aims to overcome the lack of theoretical support system based on experience in the prior art and proposes a corneal biomechanical property calculation method and device based on spline theory which can accurately and objectively evaluate the corneal biomechanical property.

[0006] The present application solves its practical problems by adopting the following technical scheme:

[0007] A corneal biomechanical property calculation method based on spline theory comprises the following steps:

[0008] Step 1: sampling and analyzing the dynamic video of corneal stress deformation in the historical database to extract the corneal contour;

[0009] Step 2: fitting the curve of the contour change in the corneal deformation process by using spline theory to obtain the curve equation of the corneal contour;

[0010] Step 3: determining the first flattening state moment, the maximum indentation moment and the second flattening moment in the corneal deformation process according to the curve equation of the corneal contour in step 2 to calculate the corneal biomechanical property.

[0011] Moreover, the dynamic video of corneal stress deformation in the historical database in step 1 records the corneal stress deformation process at a sampling frequency greater than 5000 and the image resolution is greater than 570*200 pixels.

[0012] Moreover, the specific method of step 2 is:

[0013] Based on spline theory, the curve fitting is performed on the corneal profile points to obtain the curve equation of the corneal profile corresponding to the whole corneal deformation process, and the B-spline is used to generate the required curve at one time;

[0014] Let the curve order k=3, the number of control points n+1, P0P1,…,P n , the number of nodes m+1, the sampling time is defined as the spline parameter: t0t1,…,t m , the profile pixel points are defined as the type value points, and there are l+1 in total, and n=l+2, m=n+k+1,

[0015]

[0016] Where B i,k (t) is a k-order B-spline basis function, and satisfies the following recursive formula

[0017]

[0018]

[0019] That is, when t∈[t j ,t j+1 ], since the curve order K=3, the curve equation of the interval is obtained by expanding the above recursive formula:

[0020] B(t)=B 0,3 P0+B 1,3 P1+…+B n,3 P n

[0021] =B j-3,3 (t)P j-3 +B j-2,3 (t)P j-2 +B j-1,3 (t)P j-1 +B j,3 (t)P j

[0022] Where,

[0023]

[0024]

[0025]

[0026]

[0027] Moreover, the specific steps of step 3 include:

[0028] (1) According to the corneal profile curve equation, the zero points of the first and second derivatives are calculated;

[0029] The first derivative equation of the profile curve is:

[0030] B'(t) = B' j-3,3 (t)P j-3 +B' j-2,3 (t)P j-2 +B' j-1,3 (t)P j-1 +B' j,3 (t)P j

[0031] Wherein,

[0032]

[0033]

[0034]

[0035]

[0036] The second derivative equation of the profile curve is:

[0037] B''(t) = B'' j-3，3 (t)P j-3 +B'' j-2，3 (t)P j-2 +B'' j-1，3 (t)P j-1 +B'' j，3 (t)P j

[0038] Wherein,

[0039]

[0040]

[0041]

[0042]

[0043] (2) Substitute the corneal profile point coordinates into the above equation to obtain the zero points of the first and second derivatives of the curve equation, respectively calculate the first flattening time, the maximum indentation time and the second flattening time in the corneal deformation process, and further calculate the corneal biomechanical properties.

[0044] A corneal biomechanical property calculation device based on spline theory, comprising the following modules:

[0045] a corneal profile extraction module for sampling and analyzing the dynamic video of corneal stress deformation in the historical database to extract the corneal profile;

[0046] a curve equation calculation module of the corneal profile for fitting the curve of the profile change in the corneal deformation process by using the spline theory to obtain the curve equation of the corneal profile;

[0047] a biomechanical property calculation module of the cornea for determining the first flattening time, the maximum indentation time and the second flattening time in the corneal deformation process by calculating the zero points of the first derivative and the second derivative of the curve equation of the corneal profile obtained by the curve equation calculation module of the corneal profile, so as to calculate the biomechanical properties of the cornea.

[0048] Moreover, the dynamic video of corneal stress deformation in the historical database of the corneal profile extraction module records the corneal stress deformation process at a sampling frequency greater than 5000, and the image resolution is greater than 570*200 pixels.

[0049] Moreover, the curve equation calculation module of the corneal profile is used for:

[0050] based on the spline theory, the curve fitting is performed on the corneal profile points to obtain the curve equation of the corneal profile corresponding to the entire corneal deformation process, and the B-spline is used to generate the required curve at one time:

[0051] assuming that the curve order k=3, the number of control points n+1, P0P1,…,P n , the number of nodes m+1, the sampling time is defined as the spline parameter: t0t1,…,t m , the profile pixel points are defined as the type value points, and there are l+1 in total, and n=l+2, m=n+k+1,

[0052]

[0053] where B i,k (t) is the k-order B-spline basis function, and satisfies the following recursive formula

[0054]

[0055]

[0056] that is, when t∈[t j ,t j+1 ], since the curve order K=3, the curve equation of the interval is obtained by expanding the above recursive formula:

[0057] B(t)=B 0,3 P0+B 1,3 P1+…+B n,3 Pn

[0058] = B j-3,3 (t) P j-3 + B j-2,3 (t) P j-2 + B j-1,3 (t) P j-1 + B j,3 (t) P j

[0059] wherein,

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] Advantages and beneficial effects of the present application:

[0066] The present application proposes a pixel-level corneal biomechanical property calculation method and device based on spline theory from the dynamic video data of corneal stress deformation in historical data. In order to achieve this purpose, the present application is divided into the following steps in order to overcome the rough evaluation of corneal biomechanics in the past. First, the corneal contour points are extracted from the dynamic video of corneal stress deformation in historical data. Then, the spline theory is used to fit the curve of the contour change in the corneal deformation process to obtain the curve equation of the corneal contour. Finally, the biomechanical property parameters of the cornea are calculated according to the curve equation of the corneal contour. Due to the characteristics of the traditional image processing algorithm, the sawtooth shape of the corneal contour is easily caused, and the traditional discrete point calculation method is easily caused. The calculation of the mechanical properties is unstable. The present application can basically calculate the pixel-level corneal biomechanical parameters from the corneal dynamic video in historical data with the help of spline theory, which is more objective, complete, accurate and has the theoretical support of the calculation of corneal biomechanical property parameters. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 The present application is a process flowchart. DETAILED DESCRIPTION

[0068] The embodiments of the present application are further described in detail below with reference to the accompanying drawings:

[0069] A corneal biomechanical property calculation method based on spline theory, as shown in Figure 1 , includes the following steps:

[0070] Step 1, sampling and analyzing the dynamic video of corneal stress deformation in the historical database to extract the corneal profile;

[0071] The dynamic video of corneal stress deformation in the historical database of step 1 records the corneal stress deformation process at a sampling frequency greater than 5000, and the image resolution is greater than 570*200 pixels.

[0072] Step 2, using spline theory to fit the curve of profile change in the corneal deformation process to obtain the curve equation of the corneal profile;

[0073] The specific method of step 2 is:

[0074] Based on spline theory, the curve fitting of corneal profile points is performed to obtain the curve equation of the corneal profile corresponding to the entire corneal deformation process, and B-spline is used to generate the required curve at one time.

[0075] Let the curve degree k=3, the number of control points n+1, P0P1,…,P n , the number of nodes m+1, the sampling time is defined as the spline parameter: t0t1,…,t m , the profile pixel point is defined as the type value point l+1, and n=l+2, m=n+k+1,

[0076]

[0077] Where B i,k (t) is a k-order B-spline basis function, and satisfies the following recursive formula

[0078]

[0079]

[0080] That is, when t∈[t j ,t j+1 ], since the curve degree K=3, the curve equation of the interval is obtained by expanding the above recursive formula:

[0081] B(t)=B 0,3 P0+B 1,3 P1+…+B n,3 P n

[0082] =B j-3,3 (t)P j-3 +B j-2,3 (t)P j-2 +B j-1,3 (t)P j-1 +B j,3 (t)P j

[0083] wherein,

[0084]

[0085]

[0086]

[0087]

[0088] Step 3, according to the curve equation of the corneal profile in step 2, the zero points of the first derivative and the second derivative are determined, the first flattening state moment, the maximum indentation moment and the second flattening moment in the corneal deformation process are determined, and the biomechanical properties of the cornea are calculated.

[0089] The specific steps of step 3 include:

[0090] (1) According to the above-mentioned corneal profile curve equation, the zero points of the first derivative and the second derivative are obtained; wherein the first derivative equation of the profile curve is:

[0091] B'(t) = B'(t)P j-3,3 + B'(t)P j-3 + B'(t)P j-2,3 + B'(t)P j-2 + B'(t)P j-1,3 + B'(t)P j-1 + B'(t)P j,3 + B'(t)P j

[0092] wherein,

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] wherein, the second derivative equation of the profile curve is:

[0099] B''(t) = B''(t)P j-3，3 + B''(t)P j-3 + B''(t)P j-2，3 + B''(t)P j-2 + B''(t)P j-1，3 + B''(t)P j-1 + B''(t)P j，3 + B''(t)P j + B''(t)P

[0100] wherein,

[0101]

[0102]

[0103]

[0104]

[0105] (2) substituting the corneal profile point coordinates into the above equation to obtain the zero points of the first derivative and the second derivative of the curve equation, calculating the first flattening time, the maximum indentation time and the second flattening time in the corneal deformation process, and then calculating the corneal biomechanical properties according to the following calculation formula of the corneal biomechanical properties:

[0106]

[0107]

[0108]

[0109] A corneal biomechanical property calculation device based on spline theory, comprising the following modules:

[0110] A corneal profile extraction module for sampling and analyzing the dynamic video of corneal stress deformation in the historical database to extract the corneal profile;

[0111] A curve equation calculation module of the corneal profile for fitting the curve of the profile change in the corneal deformation process by using spline theory to obtain the curve equation of the corneal profile;

[0112] A corneal biomechanical property calculation module for calculating the first derivative and the second derivative of the curve equation of the corneal profile obtained by the curve equation calculation module of the corneal profile, determining the first flattening time, the maximum indentation time and the second flattening time in the corneal deformation process, and calculating the corneal biomechanical properties.

[0113] In this embodiment, the dynamic video of corneal stress deformation in the historical database of the corneal profile extraction module records the corneal stress deformation process at a sampling frequency greater than 5000, and the image resolution is greater than 570*200 pixels.

[0114] In this embodiment, the curve equation calculation module of the corneal profile is used to:

[0115] Based on spline theory, the curve fitting is performed on the corneal contour points to obtain the curve equation of the corneal contour corresponding to the whole corneal deformation process, and the B-spline is used to generate the required curve at one time:

[0116] Suppose the curve order k=3, the number of control points n+1, P0P1,…,P n , the number of nodes m+1, the sampling time is defined as the spline parameter: t0t1,…,t m , the contour pixel points are defined as the type value points, and there are l+1 in total, and n=l+2, m=n+k+1,

[0117]

[0118] Where B i,k (t) is a k-order B-spline basis function, and satisfies the following recursive formula

[0119]

[0120]

[0121] That is, when t∈[t j ,t j+1 ], since the curve order K=3, the curve equation of the interval is obtained by expanding the above recursive formula:

[0122] B(t)=B 0,3 P0+B 1,3 P1+…+B n,3 P n

[0123] =B j-3,3 (t)P j-3 +B j-2,3 (t)P j-2 +B j-1,3 (t)P j-1 +B j,3 (t)P j

[0124] Where,

[0125]

[0126]

[0127]

[0128]

[0129] The corneal biomechanical property calculation module is used for:

[0130] (1) According to the corneal profile curve equation, the zero points of the first and second derivatives are obtained; wherein the first derivative equation of the profile curve is:

[0131] B'(t) = B' j-3,3 (t)P j-3 +B' j-2,3 (t)P j-2 +B' j-1,3 (t)P j-1 +B' j,3 (t)P j

[0132] wherein,

[0133]

[0134]

[0135]

[0136]

[0137] wherein the second derivative equation of the profile curve is:

[0138] B''(t) = B'' j-3，3 (t)P j-3 +B'' j-2，3 (t)P j-2 +B'' j-1，3 (t)P j-1 +B'' j，3 (t)P j

[0139] wherein,

[0140]

[0141]

[0142]

[0143]

[0144] (2) Substitute the corneal profile point coordinates into the above equation to obtain the zero points of the first and second derivatives of the curve equation, respectively calculate the first flattening time, the maximum indentation time and the second flattening time in the corneal deformation process, and then calculate the corneal biomechanical properties according to the following corneal biomechanical property calculation formula:

[0145]

[0146]

[0147]

[0148] It should be emphasized that the embodiments of the present application are illustrative only and not restrictive, therefore the present application includes and is not limited to the embodiments described in the specific embodiments, any other embodiments derived by those skilled in the art according to the technical solutions of the present application also belong to the scope of protection of the present application.

Claims

1. A method for calculating corneal biomechanical properties based on spline theory, characterized by the following steps: Step 1: Sample and analyze dynamic videos of corneal stress deformation from the historical database to extract the corneal contour; Step 2: Fit the curve of the corneal contour change during the corneal deformation process using spline theory to obtain the curve equation of the corneal contour; Step 3: Based on the curve equation of the corneal contour obtained in Step 2, find the zero points of its first and second derivatives, determine the time of the first flattening state, the time of maximum indentation, and the time of the second flattening during the corneal deformation process, and thus calculate the biomechanical properties of the cornea.

2. The method for calculating corneal biomechanical properties based on spline theory according to claim 1, characterized in that: the dynamic video of corneal stress deformation in the historical database of step 1 records the corneal stress deformation process at a sampling frequency greater than 5000, and the image resolution is greater than 570*200 pixels.

3. The method for calculating corneal biomechanical properties based on spline theory according to claim 1, characterized in that: the specific method of step 2 is as follows: Based on spline theory, curve fitting is performed on corneal contour points to obtain the curve equation of the corneal contour corresponding to the entire corneal deformation process, and the required curve is generated in one go using B-splines; Let the curve degree be k = 3, the number of control points be n+1, and P0P1, ..., P n The number of nodes is m+1, and the sampling time is defined as the spline parameters: t0t1,…,t m The contour pixels are defined as having a total of l+1 shape value points, satisfying n=l+2, m=n+k+1. Among them B i,k (t) is a k-th degree B-spline basis function, and satisfies the following recurrence relation. That is, when t∈[t j ,t j+1 When the degree of the curve is K = 3, expanding the above recurrence relation yields the curve equation for that interval: B(t)=B 0,3 P0+B 1,3 P1+…+B n,3 P n =B j-3,3 (t)P j-3 +B j-2,3 (t)P j-2 +B j-1,3 (t)P j-1 +B j,3 (t)P j in, 4. The method for calculating corneal biomechanical properties based on spline theory according to claim 1, characterized in that: step 3 specifically includes: (1) Based on the above corneal contour curve equation, find the zero points of its first and second derivatives; The first derivative equation of the contour curve is: B′(t)=B′ j-3,3 (t)P j-3 +B′ j-2,3 (t)P j-2 +B′ j-1,3 (t)P j-1 +B′ j,3 (t)P j in, The second derivative equation of the contour curve is as follows: B″(t)=B″ j-3,3 (t)P j-3 +B″ j-2,3 (t)P j-2 +B″ j-1,3 (t)P j-1 +B″ j,3 (t)P j in, (2) Substitute the coordinates of the corneal contour points into the above equation to obtain the zero points of the first and second derivatives in the curve equation. Calculate the time of the first flattening state, the time of the maximum indentation and the time of the second flattening during the corneal deformation process, and then calculate the biomechanical properties of the cornea.

5. A device for calculating corneal biomechanical properties based on spline theory, characterized in that: Includes the following modules: The corneal contour extraction module is used to sample and analyze dynamic videos of corneal stress deformation from a historical database to extract the corneal contour. The corneal contour curve equation calculation module is used to fit the curve of contour change during corneal deformation using spline theory to obtain the corneal contour curve equation. The corneal biomechanical property calculation module is used to calculate the corneal contour curve equation obtained by the corneal contour curve equation calculation module, find the zero points of its first and second derivatives, determine the time of the first flattening state, the time of maximum indentation and the time of the second flattening during the corneal deformation process, and thus calculate the biomechanical properties of the cornea.

6. The corneal biomechanical property calculation device based on spline theory according to claim 5, characterized in that: The corneal contour extraction module's historical database records the dynamic video of corneal deformation under stress at a sampling frequency greater than 5000, and the image resolution is greater than 570*200 pixels.

7. The corneal biomechanical property calculation device based on spline theory according to claim 5, characterized in that: The corneal contour curve equation calculation module is used for: Based on spline theory, curve fitting is performed on corneal contour points to obtain the curve equation of the corneal contour corresponding to the entire corneal deformation process, and the required curve is generated in one go using B-splines; Let the curve degree be k = 3, the number of control points be n+1, and P0P1, ..., P n The number of nodes is m+1, and the sampling time is defined as the spline parameters: t0t1,…,t m The contour pixels are defined as having a total of l+1 shape value points, satisfying n=l+2, m=n+k+1. Among them B i,k (t) is a k-th degree B-spline basis function, and satisfies the following recurrence relation. That is, when t∈[t j ,t j+1 When the degree of the curve is K = 3, expanding the above recurrence relation yields the curve equation for that interval: B(t)=B 0,3 P0+B 1,3 P1+…+B n,3 P n = B j-3,3 (t)P j-3 + B j-2,3 (t)P j-2 + B j-1,3 (t)P j-1 + B j,3 (t)P j wherein,

Images