CN109241680B - Finite element-based human eye biomechanics simulation method in weightless state - Google Patents
Finite element-based human eye biomechanics simulation method in weightless state Download PDFInfo
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Abstract
The invention discloses a human eye biomechanics simulation method under a weightless state based on finite elements, which comprises the following steps: 1) simplifying and assuming eyeballs, and establishing a three-dimensional geometric model of the eyes; 2) determining the biomechanical characteristics of human eyes; 3) determining the properties of the material and setting the parameters in a weightless state; 4) carrying out finite element mesh division on the human eye three-dimensional geometric model, and setting boundary conditions of the finite element model; 5) and setting the mode and the numerical value of the action of human eyes under weightlessness, and judging the visual quality by using a wavefront theory. The method can solve the problem that the biomechanics data of the human eyes cannot be accurately measured, and the accurate biomechanics data of the human eyes in the weightless state can be obtained, so that the method can help people to better research the biomechanics characteristics of the eye tissues, provides an effective auxiliary research method for the biomechanics research of the eye tissues, and has important significance.
Description
Technical Field
The invention relates to a finite element analysis technology of eyeballs in biomedicine, in particular to a finite element-based human eye biomechanical simulation method in a weightless state.
Background
Finite element analysis is widely applied in the field of ophthalmology, and a finite element model can help people to better research the biomechanical characteristics of eye tissues. Therefore, by establishing a relatively perfect ideal eyeball model and a relatively perfect complex eyeball and accurately analyzing ocular biomechanics, the repeatability and the accuracy of related ophthalmic experiments can be remarkably improved, the research cost is reduced, and the method has important significance for diagnosis, treatment and research of ocular diseases.
The eye is the visual organ, one of the most important sensory organs. Human beings can perceive and acquire rich information from a complex external environment through eyes. The ground ophthalmological diseases such as cataract, glaucoma and the like seriously affect the quality of life of people, and the damage of the space microgravity eye not only causes serious harm to the bodies of astronauts, but also seriously threatens the completion of the space missions. In 2011 or so, NASA started a related study named "eye injury and Intracranial Pressure" (VIIP), aiming at studying the changes of eye structures, far Vision and near Vision of astronauts before and after arriving at the earth after long-term exposure to microgravity space environment. Researches show that under the condition of space microgravity, the structural and functional changes of eyes comprise optic nerve head edema, eyeball flattening, choroid pucker, retinal cotton wool exudation points, optic nerve sheath swelling, near point distancing and the like, and permanent damage to eyes can be caused under severe conditions. The research on the eye injury in the microgravity environment is mainly developed by an experimental method, the experimental cost is high and is limited by factors such as a small number of samples of astronauts, obvious individual difference, high space testing cost and the like, and related research data is not universal and progresses slowly, so that related research is limited.
Disclosure of Invention
The invention provides a finite element-based human eye biomechanical simulation method in a weightless state, aiming at solving the problem that accurate measurement cannot be carried out and human eye biomechanical data in the weightless state cannot be obtained.
The purpose of the invention is realized by the following technical scheme. A human eye biomechanics simulation method under a weightless state based on finite elements is characterized by comprising the following steps:
1) simplifying and assuming eyeballs, and establishing a three-dimensional geometric model of the eyes;
2) determining the biomechanical characteristics of human eyes;
3) determining the properties of the material and setting the parameters in a weightless state; the process is as follows:
(1) after data processing, a good linear correlation exists between the intracranial pressure and the intraocular pressure, and a linear regression equation is calculated:
IOP＝0.934*ICP+3.705；
in the formula: ICP is intracranial pressure, IOP is intraocular pressure;
(2) according to the linear regression equation, applying pressure of 14.91-31.73 mmHg to the human eyes, and restraining the outer surfaces of the human eyes;
4) carrying out finite element mesh division on the human eye three-dimensional geometric model, and setting boundary conditions of the finite element model; the process is as follows:
(1) inputting a human eye biomechanics geometric model into finite element analysis software, selecting a unit type, setting unit density, and dividing a grid, wherein the size of the grid is less than or equal to 0.20 mm;
(2) setting the intraocular pressure initial test value to be 15mmHg, then carrying out eye internal pressure increment simulation on the corneal model, correspondingly setting time sequences, carrying out eye internal pressure increment simulation on the corneal model, analyzing and processing the calculation result obtained after simulation, wherein the intraocular pressure difference between adjacent time sequences is 1 mmHg; selecting the back surface of the cornea and the inner surface of the sclera as action surfaces for loading, and constraining the outer surface of the human eye finite element model;
5) setting the acting mode and the acting numerical value of human eyes under weightlessness, carrying out finite element solution in the human eyes, and obtaining a stress-strain-displacement distribution diagram of the human eye internal organization units according to the stress-strain-displacement calculation result obtained by each node of the human eye internal organization units; quantitatively analyzing the result of the displacement change of the front and back surfaces of the cornea of human eye tissues in a weightless state, and obtaining the change of the wavefront aberration and the change of the visual quality, wherein the process comprises the following steps: carrying out finite element solution on internal tissues of the human eyes, inserting function synthesis stress-strain-displacement graphs by using analysis result data of finite element software, leading out data on the stress-strain-displacement graphs, comparing related data with normal data, analyzing the change of corneal displacement, causing the change of corneal wavefront aberration and influencing the quantity and the characteristics of the ocular aberration, and judging the visual quality by using a wavefront theory, namely completing the human eye biomechanics simulation method under the weightlessness state based on the finite elements;
further, the specific process of establishing the three-dimensional geometric model of the human eye in the step 1) is as follows:
(1) programming three-dimensional coordinate data corresponding to the upper surface and the lower surface of the cornea in MATLAB software to obtain cornea three-dimensional information data; clinically measuring a corneal topography by using a Pentacam comprehensive anterior segment analysis system to obtain height difference data of the front and back surfaces of a cornea; establishing a geometric model of an individual human cornea by utilizing the three-dimensional information data of the cornea and the height difference data of the front surface and the back surface of the cornea and combining a reference curved surface and the thickness of the cornea; wherein the eyeball of the human eye is an axisymmetric ellipsoid, and the inner surface and the outer surface of the cornea of the human eye are ellipsoidal surfaces;
wherein the anterior corneal surface function is:
the corneal posterior surface function is:
in the formula: r ' is the curvature radius of the fitting spherical surface of the front surface of the cornea, R ' is the curvature radius of the fitting spherical surface of the rear surface of the cornea, X and Y are coordinates of spherical points, Ci ' is a Zernike coefficient, and Zi is a Zernike polynomial;
(2) setting the sclera thickness to be uniform, the inner wall and the outer wall to be ellipsoidal, and establishing a human eye shape model according to the size of the measured axial length data determined clinically;
(3) carrying out parametric modeling by using known lens diameter, thickness, nuclear diameter, nuclear thickness and nuclear offset characteristic parameters, and fusing the parameters with actually measured geometric and physical characteristic parameters to obtain an entity morphological model;
(4) analyzing and integrating the entity form model, and establishing a complete individual human eye biomechanical model in modeling software;
determining the biomechanical characteristics of the human eyes in the step 2) as follows:
the cornea is treated as an isotropic material, the eyeball tissue is approximated to an isotropic elastic body which conforms to linear change under weightlessness conditions, and the density, elastic modulus and poisson ratio of the cornea are set on the basis of an assumption of continuity of a substance in the eyeball tissue, an assumption of uniformity of a substance in the eyeball tissue, an assumption of isotropy of mechanical properties of a substance in the eyeball tissue, an assumption of linear elasticity and an assumption of small deformation.
Further, the specific process of establishing the three-dimensional geometric model of the human eye in the step 1) is as follows:
(1) programming three-dimensional coordinate data corresponding to the upper surface and the lower surface of the cornea in MATLAB software to obtain cornea three-dimensional information data; clinically measuring a corneal topography by using a Pentacam comprehensive anterior segment analysis system to obtain height difference data of the front and back surfaces of a cornea; establishing a geometric model of an individual human cornea by utilizing the three-dimensional information data of the cornea and the height difference data of the front surface and the back surface of the cornea and combining a reference curved surface and the thickness of the cornea; wherein the eyeball of the human eye is an axisymmetric ellipsoid, and the inner surface and the outer surface of the cornea of the human eye are ellipsoidal surfaces;
wherein the anterior corneal surface function is:
the corneal posterior surface function is:
in the formula: r ' is the curvature radius of the fitting spherical surface of the front surface of the cornea, R ' is the curvature radius of the fitting spherical surface of the rear surface of the cornea, X and Y are coordinates of spherical points, Ci ' is a Zernike coefficient, and Zi is a Zernike polynomial;
(2) setting the sclera thickness to be uniform, the inner wall and the outer wall to be ellipsoidal, and establishing a human eye shape model according to the size of the measured axial length data determined clinically;
(3) carrying out parametric modeling by using characteristic parameters of known lens diameter, thickness, nuclear diameter, nuclear thickness and nuclear offset, and fusing the parameters with actually measured geometric and physical characteristic parameters to obtain an entity morphological model;
(4) analyzing and integrating the entity form model, and establishing a complete individual human eye biomechanical model in modeling software;
determining the biomechanical characteristics of the human eyes in the step 2) as follows:
(1) treating the cornea as a heterogeneous, anisotropic, nonlinear, and viscoelastic complex biomechanical material; the nonlinear stress-strain relationship of the cornea obeys the following equation:
σ＝A(e^αε-1)；
wherein: sigma is stress, epsilon is strain, A and alpha are material constants;
the viscoelastic characteristics of the cornea are obtained from the stress relaxation curve, and an empirical formula is calculated:
y＝-0.0157ln(t)+0.9785；
wherein: y is the normalized cumulative modulus at an elongation ratio of 1.5, and t is time;
(2) the density of each human eye tissue including cornea, iris, sclera, crystalline lens and zonules is determined, and the biomechanical properties of the human eye tissue are determined from the above formula.
Further, the specific process of establishing the three-dimensional geometric model of the human eye in the step 1) is as follows:
(1) constructing a human eye three-dimensional geometric model for recovering normal after operation by using clinically measured data related to the eyes of a patient subjected to corneal laser operation; programming three-dimensional coordinate data corresponding to the upper surface and the lower surface of the cornea in MATLAB software to obtain cornea three-dimensional information data; clinically measuring a corneal topography by using a Pentacam comprehensive anterior segment analysis system to obtain height difference data of the front and back surfaces of a cornea; establishing a geometric model of an individual human cornea by utilizing three-dimensional information data of the cornea and height difference data of the front surface and the rear surface in combination with a reference curved surface and the thickness of the cornea; wherein the eyeball of the human eye is an axisymmetric ellipsoid, and the inner surface and the outer surface of the cornea of the human eye are ellipsoidal surfaces;
wherein the anterior corneal surface function is:
posterior surface of cornea:
in the formula: r ' is the curvature radius of the fitting spherical surface of the front surface of the cornea, R ' is the curvature radius of the fitting spherical surface of the rear surface of the cornea, X and Y are coordinates of spherical points, Ci ' is a Zernike coefficient, and Zi is a Zernike polynomial;
(2) setting the sclera thickness to be uniform, the inner wall and the outer wall to be ellipsoidal, and establishing a human eye shape model according to the size of the measured axial length data determined clinically;
(3) with the characteristic parameters of the known lens: carrying out parametric modeling on five parameters of the diameter, the thickness, the nuclear diameter, the nuclear thickness and the nuclear offset of the crystalline lens, and fusing the parameters with actually measured geometric and physical characteristic parameters to obtain an entity morphological model;
(4) analyzing and integrating the model, and establishing a complete individual human eye biomechanical model in modeling software;
determining the biomechanical characteristics of the human eyes in the step 2) as follows:
the cornea is treated as an isotropic material, the eyeball tissue is approximated to an isotropic elastic body which conforms to linear change under weightlessness conditions, and the density, elastic modulus and poisson ratio of the cornea are set according to assumption of continuity of substances in the eyeball tissue, assumption of uniformity of substances in the eyeball tissue, assumption of isotropy of mechanical properties of the substances in the eyeball tissue, assumption of linear elasticity and assumption of small deformation.
The specific process of establishing the three-dimensional geometric model of the human eye in the step 1) is as follows:
(1) constructing a human eye three-dimensional geometric model for recovering normal after operation by using clinically measured data related to the eyes of a patient subjected to corneal laser operation; programming three-dimensional coordinate data corresponding to the upper surface and the lower surface of the cornea in MATLAB software to obtain cornea three-dimensional information data; clinically measuring a corneal topography by using a Pentacam comprehensive anterior segment analysis system to obtain height difference data of the front and back surfaces of a cornea; establishing a geometric model of an individual human cornea by utilizing three-dimensional information data of the cornea and height difference data of the front surface and the rear surface in combination with a reference curved surface and the thickness of the cornea; wherein the eyeball of the human eye is an axisymmetric ellipsoid, and the inner surface and the outer surface of the cornea of the human eye are ellipsoidal surfaces;
wherein the anterior corneal surface function is:
the corneal posterior surface function is:
in the formula: r ' is the curvature radius of the fitting spherical surface of the front surface of the cornea, R ' is the curvature radius of the fitting spherical surface of the rear surface of the cornea, X and Y are coordinates of spherical points, Ci ' is a Zernike coefficient, and Zi is a Zernike polynomial;
(2) setting the sclera thickness to be uniform, the inner wall and the outer wall to be ellipsoidal, and establishing a human eye shape model according to the size of the measured axial length data determined clinically;
(3) carrying out parametric modeling by using characteristic parameters of known lens diameter, thickness, nuclear diameter, nuclear thickness and nuclear offset, and fusing the parameters with actually measured geometric and physical characteristic parameters to obtain an entity morphological model;
(4) analyzing and integrating the model, and establishing a complete individual human eye biomechanical model in modeling software;
the specific process of determining the biomechanical characteristics of the human eyes in the step 2) is as follows:
(1) treating the cornea as a heterogeneous, anisotropic, nonlinear and viscoelastic complex biomechanical material; the nonlinear stress-strain relationship of the cornea obeys the following equation:
σ＝A(e^αε-1)；
wherein: sigma is stress, epsilon is strain, A and alpha are material constants;
the viscoelastic characteristics of the cornea are obtained from the stress relaxation curve, and an empirical formula is calculated:
y＝-0.0157ln(t)+0.9785；
wherein: y is the normalized cumulative modulus at an elongation ratio of 1.5, and t is time;
(2) the density of each human eye tissue including cornea, iris, sclera, crystalline lens and zonules is determined, and the biomechanical properties of the human eye tissue are determined by the above formula.
The invention can solve the problem that the biomechanics data of human eyes can not be accurately measured, and can obtain the accurate biomechanics data of the human eyes in a weightless state, thereby helping people to better research the biomechanics characteristics of eye tissues. The method comprises the steps of carrying out finite element solution on human eye internal tissues, and obtaining a stress-strain-displacement distribution diagram of the human eye internal tissues according to stress-strain-displacement calculation results obtained by nodes of the human eye tissue units; according to the distribution result of stress-strain-displacement, the change of aberration caused by the change of displacement is quantitatively analyzed and further used for predicting the visual quality of human eyes, so that the method provides an effective auxiliary research method for the biomechanical research of eye tissues and has important significance.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a three-dimensional geometric model of a human eye according to the present invention;
FIG. 3 is a finite element mesh partition of the eye model of the present invention;
fig. 4 is a front view of the displacement distribution of the human eye in the present invention.
Detailed Description
The invention is further illustrated by the following figures and examples. See fig. 1-4.
Example 1: a human eye biomechanics simulation method under a weightless state based on finite elements is specifically prepared according to the following steps:
the method comprises the following steps: simplifying and assuming eyeballs, and establishing a three-dimensional geometric model of the eyes;
step two: determining the biomechanical characteristics of human eyes;
step three: determining the properties of the material and setting the parameters in a weightless state;
step four: carrying out finite element meshing on the human eye three-dimensional geometric model (shown in figure 2) (shown in figure 3), and setting boundary conditions of the finite element model;
step five: setting the acting mode and the acting numerical value of the human eyes under weightlessness, carrying out finite element solution in the human eyes, and obtaining a stress-strain-displacement distribution diagram (as shown in figure 4) of the human eye internal organization units according to the stress-strain-displacement calculation result obtained by each node of the human eye internal organization units; quantitatively analyzing the result of the displacement change of the front and back surfaces of the cornea of human eye tissues in a weightless state, and obtaining the change of wavefront aberration and the change of visual quality caused by the displacement change; namely, the human eye biomechanics simulation method under the weightless state based on the finite element is completed.
The effect of the embodiment is as follows: the finite element-based human eye biomechanical simulation method under the weightless state can obtain accurate data of human eye biomechanics under the weightless state, thereby helping people to better research the biomechanical characteristics of eye tissues. The method carries out finite element solution on the internal tissue of the human eye, and obtains the stress-strain-displacement distribution of the internal tissue unit of the human eye according to the stress-strain-displacement calculation result obtained by each node of the tissue unit of the human eye; according to the distribution result of stress-strain-displacement, the change of aberration caused by the change of displacement is quantitatively analyzed and further used for predicting the visual quality of human eyes, so that the method provides an effective auxiliary research method for the biomechanical research of eye tissues and has important significance.
Example 2: the difference from example 1 is: simplifying and assuming the eyeball in the first step, and establishing a three-dimensional geometric model of the human eye comprises the following steps:
(1) and constructing a human eye three-dimensional geometric model for recovering normal after the operation by utilizing clinically measured data related to the eyes of the patient subjected to the corneal laser operation. The influence of tissues such as optic nerve bundles on the overall shape of the eyeball is not considered, the micro asymmetry at the part of the eyeball is ignored, and the eyeball is considered to be an axisymmetric ellipsoid; approximately considering that the inner and outer surfaces of the cornea are ellipsoid surfaces; the geometric parameters adopted by the establishment of the human eye geometric model are based on the human eye clinical classical geometric parameters and on reasonable simplification and assumption, and the simplification and the assumption are established on the basis of ensuring the result analysis to be correct.
(2) Programming three-dimensional coordinate data corresponding to the upper surface and the lower surface of the cornea in MATLAB software to obtain cornea three-dimensional information data; clinically measuring a corneal topography by using a Pentacam comprehensive anterior segment analysis system to obtain height difference data of the front and back surfaces of a cornea; the method comprises the steps of establishing a geometric model of an individual human cornea by utilizing three-dimensional information data of the cornea and height difference data of front and back surfaces and combining a reference curved surface and the thickness of the cornea. Wherein the eyeball of the human eye is an axisymmetric ellipsoid, and the inner surface and the outer surface of the cornea of the human eye are ellipsoidal surfaces;
wherein, the functions of the anterior and posterior surfaces of the cornea are respectively:
anterior surface of cornea:
posterior surface of cornea:
in the formula: r ' is the curvature radius of the fitting spherical surface of the front surface of the cornea, R ' is the curvature radius of the fitting spherical surface of the rear surface of the cornea, X and Y are coordinates of spherical points, Ci ' is a Zernike coefficient, and Zi is a Zernike polynomial.
(3) The thickness of the sclera is set to be uniform, the inner wall and the outer wall are ellipsoidal surfaces, and the size of the measured axial length data is determined clinically to establish a human eye shape model.
(4) With the characteristic parameters of the known lens: and carrying out parametric modeling on five parameters including the diameter, the thickness, the nuclear diameter, the nuclear thickness and the nuclear offset of the crystalline lens, and fusing the parameters with actually measured geometric and physical characteristic parameters to obtain a solid morphological model with stronger authenticity.
(5) Analyzing and integrating the model, and establishing a complete individual human eye biomechanical model in modeling software; the other steps and parameters were the same as in example 1.
Example 3: the differences from the examples 1 and 2 are: defining the biomechanical characteristics of the human eyes in the second step as follows: the cornea has complex biomechanical properties of heterogeneity, anisotropy, nonlinearity and viscoelasticity. The ocular tissues contain cells with different shapes, fibers with different properties, flowing intercellular substance and the like, and the distribution of the cells in different positions and directions causes different mechanical properties of the ocular tissues in different directions, which is the anisotropy of the ocular tissues. The cornea has typical anisotropic biomechanical behavior, exhibiting different stress and deformation characteristics in the long and short axis directions of the cornea. The cornea has higher viscoelasticity and viscoplasticity along the minor axis direction, the extensibility of the cornea is larger than that of the cornea along the major axis direction, and the cornea has higher elastic modulus and tensile ultimate strength along the major axis soft tissue fiber direction; the "stress-strain" of various ocular tissues under experimental conditions does not conform to a strict linear relationship, so that the ocular tissues cannot adopt a fixed elastic modulus in a large internal pressure range. The nonlinear stress-strain relationship of the cornea obeys the following formula sigma ═ A (e ^ alpha epsilon-1), wherein sigma is stress, epsilon is strain, and A and alpha are material constants; the eyeball tissue consists of various cells and intercellular substance, and the substance in the eyeball tissue can be considered to be continuous; the space within the corneal tissue is completely filled with liquid and can be considered an incompressible material. The viscoelastic characteristics of the cornea are given by a stress relaxation curve, satisfying the empirical formula y ═ 0.0157ln (t) +0.9785, where y is the normalized cumulative modulus at an elongation ratio of 1.5 and t is time. Other steps and parameters were the same as in examples 1 and 2.
Example 4: a human eye biomechanics simulation method under a weightless state based on finite elements is specifically prepared according to the following steps:
the method comprises the following steps: simplifying and assuming eyeballs, and establishing a three-dimensional geometric model of the eyes;
(1) the influence of tissues such as optic nerve bundles on the overall shape of the eyeball is not considered, the micro asymmetry at the part of the eyeball is ignored, and the eyeball is considered to be an axisymmetric ellipsoid; the inner and outer surfaces of the cornea of the eye are considered to be ellipsoidal; the geometric parameters adopted by the establishment of the human eye geometric model are based on the human eye clinical classical geometric parameters and on reasonable simplification and assumption, and the simplification and the assumption are established on the basis of ensuring the result analysis to be correct.
(2) Programming three-dimensional coordinate data corresponding to the upper surface and the lower surface of the cornea in MATLAB software to obtain data with cornea three-dimensional information (adopting A load ('cloud3d.dat');% read-in data:% X, Y, Z-axis coordinate X ═ A (: 1);, Y;, 2);% Z ═ A (;, 3) Figure, surf (X, Y, Z);% three-dimensional coordinate); the method comprises the following steps of utilizing a Pentacam comprehensive anterior segment analysis system to measure a corneal topography clinically, and obtaining height difference data of the front surface and the back surface of a cornea (in less than 2 seconds, the Pentacam can measure and analyze 25000/138000 data points of the anterior segment of the cornea, and rotation measurement can obtain more data in the center of the cornea, so that the measurement data result of the center of the cornea is more accurate); the method comprises the steps of establishing a geometric model of an individual human cornea by utilizing three-dimensional information data of the cornea and height difference data of front and back surfaces and combining a reference curved surface and the thickness of the cornea. Wherein the eyeball of the human eye is an axisymmetric ellipsoid, and the inner surface and the outer surface of the cornea of the human eye are ellipsoidal surfaces;
wherein, the functions of the anterior and posterior surfaces of the cornea are respectively:
anterior surface of cornea:
posterior surface of cornea:
wherein R ' is the curvature radius of the fitting spherical surface of the front surface of the cornea, R ' is the curvature radius of the fitting spherical surface of the rear surface of the cornea, X and Y are coordinates of spherical points, Ci ' is a Zernike coefficient, and Zi is a Zernike polynomial.
(3) The thickness of the sclera is set to be uniform, the inner wall and the outer wall are ellipsoidal surfaces, and the size of the measured axial length data is determined clinically to establish a human eye shape model.
(4) With the characteristic parameters of the known lens: and carrying out parametric modeling on five parameters including the diameter, the thickness, the nuclear diameter, the nuclear thickness and the nuclear offset of the crystalline lens, and fusing the parameters with actually measured geometric and physical characteristic parameters to obtain a solid morphological model with stronger authenticity.
(5) Analyzing and integrating the model, and establishing a complete individual human eye biomechanical model in modeling software;
step two: determining the biomechanical characteristics of human eyes as follows:
when the simulation calculation is carried out, the human eye tissues need to be accurately calculated, and the curve characteristic expression of the stress-strain curve is not obvious and an obvious linear relation is presented in a valuable intraocular pressure range; meanwhile, the composition of eyeball tissue has strong regularity, and the eyeball tissue can be considered to be isotropic. The cornea is essentially a orthotropic material, which has three elastic principal directions in three orthogonal directions, and the stress-strain characteristics in the X, Y and Z directions, or three elastic modulus principal values, need to be input for accurate calculation. However, due to the limitations of the current experimental conditions and experimental techniques, there is only one direction of stress-strain curve and one direction of elastic modulus. And it was found in the study that the elastic modulus in the other directions is not greatly different. Therefore, we treat the cornea here as an isotropic material. In summary, the eyeball tissue can be considered to be a linearly changing, isotropic elastomer under a certain pressure range, i.e. under the condition of weightlessness. I.e. it obeys five basic assumptions: assumption of continuity of material in eyeball tissue; presuming the uniformity of substances in eyeball tissues; isotropic assumption of mechanical properties of materials in eyeball tissues; linear elastic assumption; small deformation assumptions.
| Material properties | Human eye tissue |
| Mechanical characteristics | Anisotropy of linear elastomer |
| Density (Kg/m)3) | 1030 |
| Young's modulus (MPa) | 1.8 |
| Poisson ratio | 0.49 |
Step three: determining the properties of the material and setting the parameters in a weightless state as follows;
(1) under the condition of weightlessness, the hydrostatic pressure disappears, the body fluid pressure is about 100mmHg at all positions of the human body because the hydrostatic pressure disappears and the head of the body fluid moves upwards. The head pressure is elevated by 30mmHg compared with the normal environmental state (normal intraocular pressure value is 11-21 mmHg).
(2) Intraocular pressure (IOP) was considered to be 15mmHg and intracranial pressure (ICP) was approximately 12mmHg under normal gravity conditions at the time of study; the intracranial pressure (ICP) is increased to 30mmHg under the weightless environment, and a good linear correlation exists between the intracranial pressure and the intraocular pressure, and a linear regression equation is obtained through data processing, calculation and analysis: IOP is 0.934 × ICP + 3.705.
Step four: importing the accurate three-dimensional geometric model of the human eye into finite element software, carrying out finite element meshing (as shown in figure 3), and setting boundary conditions of the finite element model to be constructed according to actual conditions;
the human eye biomechanical geometric model is input into finite element analysis software, the type of the unit is selected, the density of the unit is set, free grid division is adopted, and considering that the thickness of the shell is only 0.62mm, and the spatial distribution and the spatial layout have large difference, therefore, in order to avoid generating deformed grids, the size of the grids is less than or equal to 0.20mm, and a 'free orientation unit' is selected so as to be beneficial to more reasonably and more conveniently obtaining qualified grids. It was confirmed in the calculation that the selection of such a division condition can achieve satisfactory results in mesh division. The initial intraocular pressure value was set at 15mmHg, which is a normal intraocular pressure, and then intraocular pressure increase simulation was performed on the corneal model, and the intraocular pressure was increased by 1mmHg per time series over fifteen time series, and then analysis processing was performed using finite element software to obtain the calculated results after simulation. The pressure is applied on the geometric model, the pressure value of the inner surface of the cornea is the same in all aspects because the intraocular pressure on the cornea is uniform liquid pressure transmitted by aqueous humor, the back surface of the cornea is selected as an acting surface for loading, and the value of the intraocular pressure is in the range of 10-22mmHg (1mmHg is 133.322pa) under normal conditions. The finite element mesh partition diagram of the model of the human eye is shown in figure 3.
Step five: setting the acting mode and the acting numerical value of human eyes under weightlessness, carrying out finite element solution in the human eyes, and obtaining a stress-strain-displacement distribution diagram of the human eye internal organization units according to the stress-strain-displacement calculation result obtained by each node of the human eye internal organization units; quantitatively analyzing the result of the displacement change of the front and back surfaces of the cornea of human eye tissues in a weightless state, and obtaining the change of wavefront aberration and the change of visual quality caused by the displacement change;
finite element solving is carried out on internal tissues of human eyes, analysis result data of finite element software is utilized, a function is inserted to synthesize a stress-strain-displacement diagram, data are derived from the stress-strain-displacement diagram, relevant data are compared with normal data, the change of corneal displacement is analyzed to cause the change of corneal wavefront aberration and influence the quantity and the characteristics of ocular aberration, the high-level irregular aberration caused influences the visibility range of large pupils, the resolution and the imaging quality of retinas are reduced, and further the vision quality is changed. Therefore, the visual quality can be judged according to the wavefront theory.
Claims (3)
1. A human eye biomechanics simulation method under a weightless state based on finite elements is characterized by comprising the following steps:
1) simplifying and assuming eyeballs, and establishing a three-dimensional geometric model of the eyes;
(1) constructing a human eye three-dimensional geometric model for recovering normal after operation by using clinically measured data related to the eyes of a patient subjected to corneal laser operation; programming three-dimensional coordinate data corresponding to the upper surface and the lower surface of the cornea in MATLAB software to obtain cornea three-dimensional information data; clinically measuring a corneal topography by using a Pentacam comprehensive anterior segment analysis system to obtain height difference data of the front and back surfaces of a cornea; establishing a geometric model of an individual human cornea by utilizing three-dimensional information data of the cornea and height difference data of the front surface and the rear surface in combination with a reference curved surface and the thickness of the cornea; wherein the eyeball of the human eye is an axisymmetric ellipsoid, and the inner surface and the outer surface of the cornea of the human eye are ellipsoidal surfaces;
wherein the anterior corneal surface function is:
posterior surface of cornea:
in the formula: r ' is the curvature radius of the fitting spherical surface of the front surface of the cornea, R ' is the curvature radius of the fitting spherical surface of the rear surface of the cornea, X and Y are coordinates of spherical points, Ci ' is a Zernike coefficient, and Zi is a Zernike polynomial;
(2) setting the sclera thickness to be uniform, the inner wall and the outer wall to be ellipsoidal, and establishing a human eye shape model according to the size of the measured axial length data determined clinically;
(3) with the characteristic parameters of the known lens: carrying out parametric modeling on five parameters of the diameter, the thickness, the nuclear diameter, the nuclear thickness and the nuclear offset of the crystalline lens, and fusing the parameters with actually measured geometric and physical characteristic parameters to obtain an entity morphological model;
(4) analyzing and integrating the model, and establishing a complete individual human eye biomechanical model in modeling software;
2) determining the biomechanical characteristics of human eyes;
3) determining the properties of the material and setting the parameters in a weightless state; the process is as follows:
(1) after data processing, a good linear correlation exists between the intracranial pressure and the intraocular pressure, and a linear regression equation is calculated:
IOP＝0.934*ICP+3.705；
in the formula: ICP is intracranial pressure, IOP is intraocular pressure;
(2) according to the linear regression equation, applying pressure of 14.91-31.73 mmHg to the human eyes, and restraining the outer surfaces of the human eyes;
4) carrying out finite element mesh division on the human eye three-dimensional geometric model, and setting boundary conditions of the finite element model; the process is as follows:
(1) inputting a human eye biomechanics geometric model into finite element analysis software, selecting a unit type, setting unit density, and dividing a grid, wherein the size of the grid is less than or equal to 0.20 mm;
(2) setting the intraocular pressure initial test value to be 15mmHg, then carrying out eye internal pressure increment simulation on the corneal model, correspondingly setting time sequences, carrying out eye internal pressure increment simulation on the corneal model, analyzing and processing the calculation result obtained after simulation, wherein the intraocular pressure difference between adjacent time sequences is 1 mmHg; selecting the back surface of the cornea and the inner surface of the sclera as action surfaces for loading, and constraining the outer surface of the human eye finite element model;
5) setting the acting mode and the acting numerical value of human eyes under weightlessness, carrying out finite element solution in the human eyes, and obtaining a stress-strain-displacement distribution diagram of the human eye internal organization units according to the stress-strain-displacement calculation result obtained by each node of the human eye internal organization units; quantitatively analyzing the result of the displacement change of the front and back surfaces of the cornea of human eye tissues in a weightless state, and obtaining the change of the wavefront aberration and the change of the visual quality, wherein the process comprises the following steps: finite element solving is carried out on internal tissues of the human eyes, analysis result data of finite element software is utilized, a function is inserted to synthesize a stress-strain-displacement diagram, data are derived from the stress-strain-displacement diagram, relevant data are compared with normal data, the change of corneal displacement is analyzed to cause the change of corneal wavefront aberration and influence the quantity and the characteristics of the ocular aberration, visual quality is judged by using a wavefront theory, and then the human eye biomechanics simulation method based on the finite element under the weightless state is completed.
2. The finite element-based biomechanical simulation method of human eyes in weight loss state of claim 1, wherein: determining the biomechanical characteristics of the human eyes in the step 2) as follows:
the cornea is treated as an isotropic material, the eyeball tissue is approximated to an isotropic elastic body which conforms to linear change under weightlessness conditions, and the density, elastic modulus and poisson ratio of the cornea are set on the basis of an assumption of continuity of a substance in the eyeball tissue, an assumption of uniformity of a substance in the eyeball tissue, an assumption of isotropy of mechanical properties of a substance in the eyeball tissue, an assumption of linear elasticity and an assumption of small deformation.
3. The finite element-based biomechanical simulation method of human eyes in weight loss state of claim 1, wherein:
determining the biomechanical characteristics of the human eyes in the step 2) as follows:
(1) treating the cornea as a heterogeneous, anisotropic, nonlinear, and viscoelastic complex biomechanical material; the nonlinear stress-strain relationship of the cornea obeys the following equation:
σ＝A(e^αε-1)；
wherein: sigma is stress, epsilon is strain, A and alpha are material constants;
the viscoelastic characteristics of the cornea are obtained from the stress relaxation curve, and an empirical formula is calculated:
y＝-0.0157ln(t)+0.9785；
wherein: y is the normalized cumulative modulus at an elongation ratio of 1.5, and t is time;
(2) the density of each human eye tissue including cornea, iris, sclera, crystalline lens and zonules is determined, and the biomechanical properties of the human eye tissue are determined from the above formula.
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