Intelligent fitting auxiliary system and method for orthokeratology lens based on corneal topography map

Abstract

The invention discloses an intelligent fitting auxiliary system and method for an orthokeratology lens based on a corneal topography map, and the system comprises a detection module which is used for obtaining optometry parameters and cornea characteristic parameters of a patient; the cornea topography initial construction module is used for drawing a cornea initial construction topographic map according to the optometry parameters and the cornea characteristic parameters; the cornea topography optimization module is used for performing reconstruction, optimization adjustment and resampling according to the cornea initial topographic map to obtain a cornea optimized topographic map; the model building module is used for building an evaluation auxiliary model of the orthokeratology lens according to preset parameters of the orthokeratology lens in combination with the optometry parameters, the cornea characteristic parameters and the cornea optimized topographic map; and the model evaluation module is used for carrying out evaluation operation on the evaluation auxiliary model of the orthokeratology lens according to a preset evaluation index, and an evaluation operation method is to calculate the contact area of the lens and the cornea and output orthokeratology lens parameters which meet the evaluation module.

Description

Technical Field

[0001] This invention relates to an intelligent fitting assistance system and method for orthokeratology lenses based on corneal topography. Specifically, it provides an orthokeratology lens evaluation assistance model that calculates the contact area AZ of the lens positioning zone for orthokeratology lens parameters. The feasible range of the contact area AZ is between (DIA-C1) / 2 and (DIA-OZ-C2) / 2. The aforementioned formula is based on the patient's basic refraction parameters pre-set by ophthalmologists or optometrists in the fitting assistance system. This eliminates the human uncertainty of direct trial fitting assessments and multiple fitting attempts by ophthalmologists or optometrists. Through an approximation algorithm based on pre-set constraints and an objective function, ophthalmologists or optometrists can quickly obtain suitable orthokeratology lens parameters. Compared to existing manual fitting methods, more accurate orthokeratology lens parameters can be obtained in one go, resulting in better vision control outcomes. Background Technology

[0002] Orthokeratology lenses are mainly used for children, teenagers, or young adults whose vision is not yet fully developed before the age of eighteen. The structure of orthokeratology lenses is similar to that of rigid contact lenses and they are worn during sleep at night. The method of controlling vision is to first make the peripheral positioning area of ​​the orthokeratology lens fit against the eyeball, and then use the relatively flat area in the center of the orthokeratology lens to press against the center of the cornea. The inversion arc located on the outer edge of the center of the orthokeratology lens is used to receive the corneal epithelium that has migrated to the sides, thereby rearranging the corneal epithelium and making the center flatter and the periphery steeper to achieve the purpose of controlling vision.

[0003] Currently, orthokeratology lenses require ophthalmologists or optometrists to conduct trial fitting assessments and multiple trial wears to determine the optimal parameters for the lenses. The lenses are then custom-made for each patient. However, this process heavily relies on the ophthalmologist's or optometrist's skill and experience. If the ophthalmologist or optometrist lacks the necessary skills and experience, the patient may not receive suitable orthokeratology lenses, and the vision control results will not be achieved. The problems arising from the current technology require improvement and solutions from those working in the industry. Summary of the Invention

[0004] Therefore, in view of the above-mentioned problems and deficiencies, the purpose of this invention is to provide an intelligent fitting assistance system and method for orthokeratology lenses based on corneal topography.

[0005] This invention provides an intelligent fitting assistance system for orthokeratology lenses based on corneal topography, comprising: a detection module for acquiring a patient's refraction parameters and corneal characteristic parameters; a corneal topography initial construction module for drawing an initial corneal topography map based on the refraction parameters and corneal characteristic parameters; a corneal topography optimization module for reconstructing, optimizing, and resampling based on the initial corneal topography map to obtain an optimized corneal topography map; and a model construction module for obtaining an orthokeratology lens evaluation assistance model based on predetermined orthokeratology lens parameters combined with the refraction parameters, corneal characteristic parameters, and optimized corneal topography map; and the orthokeratology lens... An evaluation auxiliary model is used to calculate the contact area AZ of the lens positioning zone for the orthokeratology lens parameters. The feasible range of the contact area AZ is between (DIA-C1) / 2 and (DIA-OZ-C2) / 2; where: DIA is the lens diameter; OZ is the contact area of ​​the lens optical zone, provided by the orthokeratology lens parameters; C1 is the first calculation parameter; and C2 is the second calculation parameter. A model evaluation module evaluates the orthokeratology lens evaluation auxiliary model according to a predetermined evaluation index. The evaluation calculation method is to calculate the contact area between the lens and the cornea and output an evaluation result.

[0006] The contact area AZ of the lens positioning zone is calculated using the aforementioned corneal reshaping lens evaluation auxiliary model. The feasible range of the contact area AZ is between (DIA-C1) / 2 and (DIA-OZ-C2) / 2. The aforementioned formula is based on the patient's basic refraction parameters pre-set by ophthalmologists or optometrists in the fitting assistance system. This eliminates the human uncertainty of direct fitting evaluation and multiple trial fittings by ophthalmologists or optometrists. Through approximation algorithms based on pre-set constraints and objective functions, ophthalmologists or optometrists can quickly obtain suitable corneal reshaping lens parameters. Compared with the existing manual fitting methods, more accurate corneal reshaping lens parameters can be obtained in one go, and better vision control results are expected.

[0007] The optimization adjustment of the corneal topography optimization module of the present invention is achieved by establishing an optimization function, and the formula for obtaining the value of the optimization function is as follows:

[0008] ∫w1×OZ-w2×AZ;

[0009] Where w1 is the first weighting factor; w2 is the second weighting factor; OZ is the contact area of ​​the lens optical zone; and AZ is the contact area of ​​the lens positioning zone.

[0010] The optimization function value can be linear programming, mixed integer linear programming, quadratic programming, second-order cone programming, nonlinear programming, constrained linear least squares method, nonlinear least squares and nonlinear equations.

[0011] The parameter range of C1 is between 0.5mm and 1.5mm, and the initial value is 0.8mm.

[0012] The parameter C2 ranges from 1mm to 2mm, with an initial value of 1.2mm. The better computational method for this corneal reshaping lens evaluation auxiliary model is to obtain the satisfied constraints and the target parameters to be minimized or maximized through an approximation algorithm. The method for minimizing the target parameters is to find the point where the first derivative is zero (f'(x) = 0). If the second derivative at this point is positive (f'(x) > 0), then this point is a local minimum. Similarly, the method for maximizing the target parameters is to find the point where the first derivative is zero (f'(x) = 0). If the second derivative at this point is negative (f'(x) < 0), then this point is a local maximum.

[0013] This invention also provides an intelligent fitting assistance method for orthokeratology lenses based on corneal topography, comprising the following steps:

[0014] S1. Patient parameter reading: A detection module is provided to obtain a patient's refraction parameters and corneal characteristic parameters through detection.

[0015] S2. Corneal Topography Reconstruction and Analysis: A corneal topography initial reconstruction module is provided to draw a corneal initial topography map based on the refraction parameters and corneal characteristic parameters; a corneal topography optimization module is also provided to reconstruct, optimize and adjust the corneal topography map and resample it to obtain an optimized corneal topography map.

[0016] S3. Lens and corneal model construction: A model construction module is provided to obtain a corneal reshaping lens evaluation auxiliary model based on a predetermined corneal reshaping lens parameter combined with the refraction parameter, the corneal characteristic parameter, and the corneal optimized topography.

[0017] S4. Setting Constraints: Set the number of iterations for the orthokeratology lens evaluation auxiliary model, and calculate the contact area AZ of the lens positioning area in the orthokeratology lens parameters. The implementation range of the contact area AZ is between (DIA-C1) / 2 and (DIA-OZ-C2) / 2, where DIA is the lens diameter; OZ is the contact area of ​​the lens optical zone, provided by the orthokeratology lens parameters; C1 is the first calculation parameter; and C2 is the second calculation parameter.

[0018] S5. Optimize the function and provide a model evaluation module. Based on a predetermined evaluation index, evaluate the corneal reshaping lens evaluation auxiliary model. The evaluation calculation method is to calculate the contact area between the lens and the cornea and output an evaluation result.

[0019] S6, Approximation algorithm adjusts lens parameters; and

[0020] S7. Obtain the optimal lens parameters. Attached Figure Description

[0021] Figure 1 This is a functional block diagram of the intelligent fitting assistance system of the present invention.

[0022] Figure 2 This is a scale diagram of the initial corneal topography of the present invention.

[0023] Figure 3 This is a proportional map of the corneal optimized topography of the present invention.

[0024] Figure 4 This is a dimensional diagram of the lens-cornea interaction model of the present invention.

[0025] Figure 5 This is a size diagram of the fluorescent tear model of the present invention.

[0026] Figure 6 This is a flowchart of the steps of the intelligent fitting assistance method of the present invention.

[0027] Figure labeling: 1-Detection module; 2-Fitting assistance system; 21-Initial corneal topography construction module; 22-Corneal topography optimization module; 23-Model construction module; 24-Corneal reshaping lens evaluation assistance model; 25-Model evaluation module; 3-Corneal reshaping lens parameters; 31-Lens optical zone; 32-Lens reversal arc; 33-Lens positioning zone; 4-Corneal characteristic parameters; S1-Patient parameter reading; S2-Corneal topography reconstruction and analysis; S3-Lens and corneal model construction; S4-Constraint setting; S5-Optimization function establishment; S6-Approximation algorithm to adjust lens parameters; S7-Obtaining optimal lens parameters. Detailed Implementation

[0028] To achieve the above objectives and effects, the technical means and structure adopted by the present invention are described in detail below with reference to the preferred embodiments of the present invention, so as to facilitate a complete understanding.

[0029] Please see Figures 1-5The figures show the functional block diagram, initial corneal topography scale diagram, optimized corneal topography scale diagram, lens-corneal interaction model size diagram, and fluorescent tear film model size diagram of the intelligent fitting assistance system of the present invention. As can be clearly seen from the figures, the intelligent fitting assistance system of the present invention mainly includes: a detection module 1 and a fitting assistance system 2. The fitting assistance system 2 refers to a personal computer (PC), notebook computer, tablet PC, or smartphone. The fitting assistance system 2 has a storage device (not shown in the figures, such as: hard disk drive (HDD), solid-state drive (SDD), or non-volatile flash memory). Its main components and features are detailed below:

[0030] The detection module 1 is used to obtain a patient's refraction parameters and corneal characteristic parameters.

[0031] A corneal topography preliminary modeling module 21 is installed in the fitting assistance system 2 to draw a preliminary corneal topography map based on the refraction parameters and the corneal characteristic parameters (e.g., Figure 2 (As shown).

[0032] A corneal topography optimization module 22, located in the fitting assistance system 2, reconstructs, optimizes, and resamples the initial corneal topography map to obtain an optimized corneal topography map (e.g., ...). Figure 3 (As shown).

[0033] A model construction module 23 is provided in the fitting assistance system 2, based on a predetermined corneal reshaping lens parameter (such as...). Figure 4 (As shown) Combined with the refraction parameters and the corneal characteristic parameters (such as...) Figure 4 As shown in the figure, the corneal optimized topography is used to obtain a corneal reshaping lens evaluation auxiliary model 24.

[0034] The corneal reshaping lens evaluation auxiliary model 24 calculates the contact area AZ of the lens positioning area for the corneal reshaping lens parameters, and the feasible range of the contact area AZ of the lens positioning area is between (DIA-C1) / 2 and (DIA-OZ-C2) / 2.

[0035] Wherein: DIA is the lens diameter; OZ is the contact area of ​​the lens optical zone, provided by the parameters of the orthokeratology lens; C1 is the first calculation parameter; C2 is the second calculation parameter.

[0036] A model evaluation module 25 is provided in the fitting assistance system 2. It evaluates the corneal reshaping lens evaluation assistance model 24 according to a predetermined evaluation index. The evaluation calculation method is to calculate the contact area between the lens and the cornea and output an evaluation result.

[0037] The aforementioned corneal topography optimization module 21 is optimized by establishing an optimization function, and the formula for obtaining the value of this optimization function is:

[0038] ∫w1×OZ-w2×AZ;

[0039] Where w1 is the first weighting factor; w2 is the second weighting factor; OZ is the optical zone of the lens; and AZ is the alignment zone of the lens.

[0040] w1 and w2 are weighted and adjusted based on the material of the orthokeratology lens, ambient temperature, and ambient humidity.

[0041] The optimization function value can be linear programming (LP), mixed integer linear programming (MILP), quadratic programming (QP), second-order cone programming (SOCP), nonlinear programming (NLP), constrained linear least squares method, nonlinear least squares and nonlinear equations.

[0042] like Figure 4 , Figure 5 As shown, the corneal reshaping lens evaluation auxiliary model 24 includes a lens-corneal interaction model and a fluorescent tear film model. The corneal reshaping lens parameter 3 is obtained by selecting the parameter that is closest to the refraction parameter and the corneal characteristic parameter 4. The corneal reshaping lens parameter 3 further includes a lens optical zone 31, a lens reversal arc 32 and a lens positioning zone 33. The method of controlling vision is to first make the lens positioning zone 33 fit the corneal characteristic parameter 4, and then press the center of the corneal characteristic parameter 4 through the lens optical zone 31. The lens reversal arc 32, located on the outer edge of the lens optical zone 31, is used to collect the corneal epidermis and tear film that migrate to both sides, so that the corneal epidermis is rearranged and the center becomes flatter and the periphery becomes steeper, thereby achieving the purpose of controlling vision.

[0043] The parameter range of C1 is between 0.5mm and 1.5mm, and the initial value is 0.8mm; while the parameter range of C2 is between 1mm and 2mm, and the initial value is 1.2mm. C1 and C2 are adjusted according to the size of the lens optical zone 31, lens reversal arc 32 and lens positioning zone 33 of the orthokeratology lens parameter 3.

[0044] The better computation of the aforementioned corneal reshaping lens evaluation auxiliary model 24 is to obtain the satisfied constraints and the target parameters to be minimized or maximized through an approximation algorithm. The method for obtaining the minimized target parameters is to find the point where the first derivative is zero (f'(x) = 0). If the second derivative of the point is positive (f(x) > 0), then the point is a local minimum. The method for obtaining the maximized target parameters is to find the point where the first derivative is zero (f'(x) = 0). If the second derivative of the point is negative (f(x) < 0), then the point is a local maximum.

[0045] Please see Figure 6 The diagram shown is a flowchart of the steps of the intelligent fitting assistance method of the present invention, including:

[0046] Step S1: Patient parameter reading. A detection module is provided to obtain the patient's refraction parameters and corneal characteristic parameters through detection.

[0047] Step S2: Corneal topography reconstruction and analysis. A corneal topography initial reconstruction module is provided to draw a corneal initial topography map based on the refraction parameters and corneal characteristic parameters. A corneal topography optimization module is also provided to reconstruct, optimize and adjust, and resample based on the corneal initial topography map to obtain an optimized corneal topography map.

[0048] Step S3: Lens and corneal model construction. A model construction module is provided to obtain a corneal reshaping lens evaluation auxiliary model based on a predetermined corneal reshaping lens parameter combined with the refraction parameter, the corneal characteristic parameter, and the corneal optimized topography. The corneal reshaping lens parameter is obtained by selecting the parameter that is closest to the refraction parameter and the corneal characteristic parameter. The corneal reshaping lens evaluation auxiliary model includes a lens-corneal interaction model and a fluorescent tear model.

[0049] Step S4: Setting constraints. Set the number of iterations for the orthokeratology lens evaluation auxiliary model and calculate the contact area AZ of the lens positioning area of ​​the orthokeratology lens parameters. The feasible range of the contact area AZ of the lens positioning area is between (DIA-C1) / 2 and (DIA-OZ-C2) / 2, where DIA is the lens diameter; OZ is the contact area of ​​the lens optical zone, provided by the orthokeratology lens parameters; C1 is the first calculation parameter; C2 is the second calculation parameter; the parameter range of C1 is between 0.5mm and 1.5mm, and the initial value is 0.8mm; and the parameter range of C2 is between 1mm and 2mm, and the initial value is 1.2mm.

[0050] Step S5: Optimize the function and provide a model evaluation module. Based on a predetermined evaluation index, evaluate the corneal reshaping lens evaluation auxiliary model. The evaluation calculation method is to calculate the contact area between the lens and the cornea and output an evaluation result.

[0051] The optimization of this corneal topography module involves establishing an optimization function, and the formula for calculating the value of this optimization function is as follows:

[0052] ∫w1×OZ-w2×AZ;

[0053] Where w1 is the first weighting factor; w2 is the second weighting factor; OZ is the contact area of ​​the lens optical zone; and AZ is the contact area of ​​the lens positioning zone.

[0054] Step S6: The approximation algorithm adjusts the lens parameters. The approximation algorithm obtains the constraints and the target parameters to be minimized or maximized. The target parameters to be minimized are obtained by finding the point where the first derivative is zero (f'(x) = 0). If the second derivative of the point is positive (f'(x) > 0), then the point is a local minimum. The target parameters to be maximized are obtained by finding the point where the first derivative is zero (f'(x) = 0). If the second derivative of the point is negative (f'(x) < 0), then the point is a local maximum.

[0055] Step S7: Obtain the optimal lens parameters.

[0056] The main feature of this invention is that it provides an auxiliary model for evaluating orthokeratology lenses, which calculates the contact area AZ of the lens positioning zone for orthokeratology lens parameters. The feasible range of the contact area AZ is between (DIA-C1) / 2 and (DIA-OZ-C2) / 2. The aforementioned formula is based on the patient's basic refraction parameters pre-set in the fitting assistance system by ophthalmologists or optometrists. This eliminates the human uncertainty of direct fitting evaluation and multiple trial fittings by ophthalmologists or optometrists. Through an approximation algorithm based on the pre-set constraints and objective function, ophthalmologists or optometrists can quickly obtain suitable orthokeratology lens parameters. Compared with existing manual fitting methods, more accurate orthokeratology lens parameters can be obtained in one go, and better vision control results are expected.

[0057] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any simple modifications and equivalent structural changes made based on the description and drawings of the present invention should also be included within the protection scope of the present invention and are hereby stated.

[0058] In summary, the intelligent fitting assistance system and method for corneal orthokeratology lenses based on corneal topography described above in this invention can reliably achieve its efficacy and purpose when used, thus this invention is indeed a highly practical invention.

Claims

1. An intelligent fitting aid system for a corneal topography based orthokeratology lens, the system comprising: It comprises: a detection module for obtaining a refraction parameter and a corneal characteristic parameter of a patient; a corneal topography initial modeling module provided in a fitting auxiliary system, which draws a corneal initial topography map according to the refraction parameter and the corneal characteristic parameter; a corneal topography optimization module provided in the fitting auxiliary system, which reconstructs, optimally adjusts and resamples according to the corneal initial topography map to obtain a corneal optimized topography map; a model construction module provided in the fitting auxiliary system, which obtains a corneal molding lens evaluation auxiliary model according to a predetermined corneal molding lens parameter in combination with the refraction parameter, the corneal characteristic parameter and the corneal optimized topography map; the corneal molding lens evaluation auxiliary model calculates a lens positioning area contact area AZ of the corneal molding lens parameter, and the implementation range of the lens positioning area contact area AZ is between (DIA-C1) / 2 and (DIA-OZ-C2) / 2; wherein DIA is the lens diameter, OZ is the lens optical zone contact area provided by the corneal molding lens parameter, C1 is the first calculation parameter, C2 is the second calculation parameter, and a model evaluation module provided in the fitting auxiliary system, which performs evaluation operation on the corneal molding lens evaluation auxiliary model according to a predetermined evaluation index, and the evaluation operation method is to calculate the contact area of the lens and the cornea and output an evaluation result.

2. The corneal topography-based intelligent fitting assistant system for orthokeratology lenses of claim 1, wherein, The optimal adjustment of the corneal topography optimization module is to establish an optimization function, and the formula for obtaining the value of the optimization function is: ∫w1×OZ-w2×AZ; wherein w1 is the first weighting factor, w2 is the second weighting factor, OZ is the lens optical zone contact area, and AZ is the lens positioning area contact area; and the optimization function value is linear programming, mixed integer linear programming, quadratic programming, second-order cone programming, nonlinear programming, constrained linear least square method, nonlinear least square and / or nonlinear equation.

3. The intelligent fitting aid system for orthokeratology lenses based on corneal topography of claim 1, wherein, The corneal molding lens parameter is obtained by selecting the parameter closest to the refraction parameter and the corneal characteristic parameter.

4. The intelligent fitting aid system for orthokeratology lenses based on corneal topography of claim 1, wherein, The corneal molding lens evaluation auxiliary model comprises a lens and cornea interaction model and a fluorescein tear model.

5. The intelligent fitting aid system for orthokeratology lenses based on corneal topography of claim 1, wherein, The parameter range of C1 is between 0.5mm and 1.5mm, and the initial value is 0.8mm.

6. The corneal topography-based orthokeratology lens intelligent fitting aid system of claim 1, wherein, The parameter range of C2 is between 1mm and 2mm, and the initial value is 1.2mm.

7. The intelligent fitting aid system for orthokeratology lenses based on corneal topography of claim 1, wherein, The operation of the corneal molding lens evaluation auxiliary model is to obtain the constraint condition and the minimized or maximized target parameter by using the approximation algorithm, the minimized target parameter is obtained by making the first derivative zero (f'(x)=0), if the second derivative of the point is positive (f''(x)>0), the point is the local minimum value; and the maximized target parameter is obtained by making the first derivative zero (f'(x)=0), if the second derivative of the point is negative (f''(x)<0), the point is the local maximum value.

8. An intelligent fitting aid method for a corneal topography based orthokeratology lens, characterized in that, It comprises the following steps: S1, patient parameter reading, providing a detection module to obtain a refraction parameter and a corneal characteristic parameter of a patient through detection; S2, corneal topography reconstruction and analysis, providing a corneal topography initial modeling module, according to the refractive parameters and the corneal characteristic parameters to draw a corneal initial topography; further providing a corneal topography optimization module, according to the corneal initial topography to reconstruct, optimize adjustment and resample, to obtain a corneal optimization topography; S3, lens and corneal model construction, providing a model construction module, according to a predetermined corneal molding lens parameter combined with the refractive parameters, the corneal characteristic parameters, the corneal optimization topography to obtain a corneal molding lens evaluation auxiliary model; S4, constraint condition setting, setting the iteration number of the corneal molding lens evaluation auxiliary model, and calculating the lens positioning area contact area AZ of the corneal molding lens parameter, and the implementation range of the lens positioning area contact area AZ is between (DIA-C1) / 2~(DIA-OZ-C2) / 2, wherein, DIA is the lens diameter; OZ is the lens optical zone contact area, and is provided by the corneal molding lens parameter; C1 is the first calculation parameter; C2 is the second calculation parameter; S5, optimization function establishment, providing a model evaluation module, and according to a predetermined evaluation index to evaluate the operation of the corneal molding lens evaluation auxiliary model, the evaluation operation method is to calculate the contact area of the lens and the cornea, and output an evaluation result; S6, approximation algorithm adjusts lens parameters; And S7, the best lens parameter is obtained.

9. The intelligent fitting aid method for orthokeratology lenses based on corneal topography of claim 8, wherein, In step S5, the formula for calculating the optimization function value is: ∫w1×OZ-w2×AZ; Wherein, w1 is the first weighting factor; w2 is the second weighting factor; OZ is the lens optical zone contact area; AZ is the lens positioning area contact area; And the optimization function value is linear programming, mixed integer linear programming, quadratic programming, second order cone programming, nonlinear programming, constrained linear least square method, nonlinear least square and / or nonlinear equation.

10. The intelligent fitting aid method for orthokeratology lens based on corneal topography of claim 8, wherein, In step S3, the corneal molding lens parameter is obtained by selecting the parameter closest to the refractive parameter and the corneal characteristic parameter.

11. The intelligent fitting aid method for orthokeratology lenses based on corneal topography of claim 8, wherein, In step S3, the corneal molding lens evaluation auxiliary model includes a lens and cornea interaction model and a fluorescent tear model.

12. The corneal topography-based intelligent fitting aid method of customizing orthokeratology lenses as claimed in claim 8, wherein, In step S4, the parameter range of C1 is between 0.5mm and 1.5mm, and the initial value is 0.8mm.

13. The intelligent fitting aid method for orthokeratology lens based on corneal topography of claim 8, wherein, In step S4, the parameter range of C2 is between 1mm and 2mm, and the initial value is 1.2mm.

14. The intelligent fitting aid method for orthokeratology lens based on corneal topography of claim 8, wherein, In step S6, the approximation algorithm satisfies the constraint condition and minimizes or maximizes the target parameter, and the method for obtaining the minimized target parameter is to make the first derivative zero (f'(x)=0), if the second derivative of the point is positive (f''(x)>0), the point is the local minimum; and the method for obtaining the maximized target parameter is to make the first derivative zero (f'(x)=0), if the second derivative of the point is negative (f''(x)<0), the point is the local maximum.

Images