RU2791204C1 - Method for determining the optical power of an intraocular lens using an artificial neural network - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: invention relates to medicine, namely, to ophthalmology, and can be used to calculate the optical power of an intraocular lens (IOL) using the capabilities of an artificial intelligence, namely, a mathematical model created by deep learning of an artificial neural network (ANN model). Initial empirical data are prepared on a server, compiling a table, followed by building a primary ANN model on the server and performing machine learning of the primary ANN model on the server. The parameters of the primary ANN model are then determined and tested for sensitivity. Significant input factors are determined, the table is transformed on the server with the columns thereof corresponding to insignificant input factors, as determined when setting the sensitivity threshold, being removed. A secondary ANN model is then built on the server, subjected to machine learning on the server, potentially followed by operating the ANN model by the user, entering the data of preoperative examination of patients on the computer display and obtaining the value of optical power of the IOL.

EFFECT: possibility of increasing the accuracy of calculating the optical power of the IOL due to the possibility of taking the additional input factors and the unsteadiness of input data into account.

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Description

The invention relates to medicine, namely to ophthalmology, and can be used to calculate the optical power of an intraocular lens (IOL) using the capabilities of artificial intelligence, namely, a mathematical model obtained as a result of deep learning of an artificial neural network (ANN model).

Accurate preoperative calculation of the optical power of the IOL, along with high-quality performance of the operation, ensures a high functional result of pathology treatment that meets the needs and desires of a particular patient, as well as the technical conditions for the operation. Currently, various formulas are used to determine the optical power of the IOL, the most famous of which are SRK II, SRK / T, Hoffer-Q, Holladay II, Haigis, Barrett (Balashevich L.I. Results of using the formula of S.N. Fedorov to calculate powers of posterior chamber intraocular lenses / L.I. Balashevich, E.V. Danilenko // Ophthalmosurgery. - 2011. - No. 1. - P. 34-38.; Sanders D.R. Comparision of the SRK-2 formula and other second-generation formulas / D.R. Sanders, J.A. Retzlaff, M.C. Kraff // J. Cataract Refract Surg.-1988.- Vol.14.- P. 136-141; Retzlaff, M.C. Kraff // J. Cataract Refract Surg - 1990 - Vol.16 - P. 333-340 Hoffer K. J. The Hoffer Q formula: a comparison of theoretic and regression formulas // J. Cataract Refract Surg -1993. - Vol. 19. - P. 700-712).

However, the percentage of the average relative error of IOL calculation for each of the formulas is quite high (Haigis formula - 15.6%, Holladay formula - 13.4%, SRK - 11.7%, SRK T - 12.5% (Arzamastsev A.A. Optimization of formulas for / A. A. Arzamastsev, O. L. Fabrikantov, N. A. Zenkova, N. K. Belousov // Bulletin of the Tambov University. Series Natural and technical sciences. - 2016. - V.21. - Issue 1. - S. 208-212)). All formulas work well for the "average patient", but are not adequate enough at the boundaries of the ranges of input variables. Their other disadvantages are the impossibility of taking into account the non-stationarity of the object and adjustment when new empirical data arrives, for example, in the case of their localization, as well as a small, clearly insufficient number of input factors taken into account. These circumstances give rise to a large number of local corrections to these formulas, their constant adaptation and correction (Pershin K.B. Algorithm for choosing a formula for calculating the optical power of the IOL in extreme myopia / K.B. Pershin, N.F. Pashinova, A.Yu. Tsygankov, S.L. Lungs // Point of view. East-West. - 2016. - No. 1. - P. 64-67).

At the same time, the use of artificial intelligence systems based on artificial neural networks is being actively developed, which, through deep learning using significant arrays of empirical data, make it possible to build adequate models in almost any subject area, including biology and medicine (Buduma N. Fundamentals of Deep Learning: Creating Algorithms for the Next Generation of Artificial Intelligence / N. Buduma, N. Lokasho, translated from English by A. Korobeynikova (Scientific ed. A. Sozykin) - Moscow: Mann, Ivanov and Ferber, 2020 - 304 p.). In addition, modern ophthalmological centers over the past decades have created patient data repositories, including tens and hundreds of thousands of records of digitized indicators.

A known method of machine learning for predicting refraction after cataract surgery (Yamauchi, T. Use of a machine learning method in predicting refraction after cataract surgery / T. Yamauchi, T. Tabuchi, K. Takase, H. Masumoto // Journal of Clinical Medicine.- 2021, 10, P. 1103.), including the use of machine learning to predict the occurrence of postoperative refraction after cataract removal and comparing the accuracy of the resulting model with formulas for calculating the optical power of the IOL. The occurrence of postoperative refraction is predicted using conventional formulas, SRK/T, Haigis, Holladay 1, Hoffer Q and Barrett Universal II formula (BU-II). However, when comparing the accuracy of the resulting model with the known formulas for calculating the IOL, no statistically significant difference was observed, since, perhaps, additional input parameters were not used in the method, and machine learning and the least squares method, usually used in the parametric identification of formulas, usually lead to comparable results.

The objective of the invention is to improve the calculation of the optical power of the IOL by constructing a mathematical model that takes into account, compared to the known formulas, a greater number of input parameters for the patient, and also has the ability to adapt to local empirical data (including new ones).

The technical result obtained by implementing the proposed invention is to increase the accuracy of calculating the optical power of the IOL due to the possibility of taking into account additional input factors and the non-stationarity of the incoming data.

The technical result is achieved by the fact that for the implementation of the mathematical model, an artificial neural network simulator is used with the ability to build its architecture (structure designer) and built-in algorithms for deep machine learning of the model (gradient and non-gradient methods of nonlinear programming) based on empirical data, allowing the user to perform an accurate calculation of the optical power IOL.

The method is carried out as follows.

1. Prepare the initial empirical data. Based on the results of previous successful calculations of the optical power of the IOL, a table (database) is compiled on the server, the columns are input factors of two types:

1) defined as the results of preoperative measurements and analyzes of the patient;

2) reflecting the patient's medical history and the output factor - the optical power of the IOL.

Successful IOL calculations mean such calculations of the IOL optical power, in which the calculated (preoperative) and desired (postoperative) refraction values coincided. The number of columns in the table can be several tens, the number of records (rows) of the table should be several hundred (significantly more than the number of links of the mathematical model). Otherwise, the model will not have generalizing and predictive properties.

2. Carry out the construction of the primary ANN model. Using any artificial neural network simulator (there are a significant number of online simulators or built-in tools, for example, Python, MatLab, etc.), an artificial neural network is created on the server of the following simple architecture: the number of network inputs must be equal to the number of input factors of the table, the output factor is only one is the optical power of the IOL; the only hidden layer of the ANN model contains only one linear neuron. Such a network (let's call it the primary ANN model) will not have a good predictive ability, but it is very easy to evaluate the significance of the input factors contained in the table.

3. Carry out machine learning of the primary ANN model. Using the built-in algorithms of deep machine learning (gradient and non-gradient methods of non-linear programming), the primary ANN model is trained on the server until the minimum value of the mean square error is reached, determined by the formula:

- табличное (точное) значение оптической силы ИОЛ в i-й стоке;

- значение оптической силы ИОЛ в i-й стоке, полученное расчетным путем по ИНС-модели при векторе ее параметров Р.where, N is the number of records in the table;

- tabular (exact) value of the optical power of the IOL in the i-th drain;

- the value of the optical power of the IOL in the i-th drain, obtained by calculation using the ANN model with the vector of its parameters Р.

4. Determine the parameters of the primary ANN model and evaluate their sensitivity. The parameters of the trained primary ANN model are determined, which are the sensitivity of the output variable (optical power of the IOL) to the input factors and corresponding to the minimum of expression (1). These parameters are determined by the formula:

For the ANN model, the vector of parameters P is the coefficients of synaptic connections of neurons. Further, according to these data, a graph of the sensitivity of the output value to the input parameters is built. An example of such a graph is shown in figure 1, where

x1 - floor,

x2 is the value of visual acuity without correction before surgery, diopters;

x3 - the value of the sphere (Sph) before the operation, diopters;

x4 - the value of the optical power of the cylinder (Cyl) before surgery, diopters;

x5 - the value of the axis of the cylindrical inclination (Ax) before the operation, deg;

x6 - the value of visual acuity with correction before surgery, diopters;

x7 - the value of the strong meridian before surgery, deg;

x8 - refraction value of the strong meridian before surgery, diopters;

x9 - the value of the weak meridian before the operation, deg;

x10 - refraction value of the weak meridian before surgery, diopters;

x11 - refraction value of the sphere (Sph) before surgery, diopters;

x12 - the refraction value of the optical power of the cylinder (Cyl) before surgery, diopters;

x13 - the refraction value of the axis of the cylindrical inclination (Ax) before surgery, diopters;

x14 - the value of the length of the optical eye, mm;

x15 - the value of visual acuity without correction after surgery, diopters;

x16 - the value of the sphere (Sph) after the operation, diopters;

x17 - the value of the optical power of the cylinder (Cyl) after surgery, diopters;

x18 - the value of the axis of the cylindrical inclination (Ax) after the operation, deg;

x19 - the value of visual acuity with correction after surgery, diopters;

x20 - the value of the strong meridian after, deg;

x21 - refraction value of the strong meridian after surgery, diopters;

x22 - the value of the weak meridian after the operation, deg;

x23 - refraction value of the weak meridian after surgery, diopters;

x24 - the value of the refraction of the sphere (Sph) after surgery, diopters;

x25 - the refraction value of the optical power of the cylinder (Cyl) after surgery, diopters;

x26 - the refraction value of the axis of the cylindrical inclination (Ax) after the operation, diopters.

5. Determine significant input factors. Given a certain acceptable level of sensitivity, significant input factors are separated, the values of which will later be used to build the secondary ANN model, and insignificant ones, the impact of which is background, and which will not participate in the construction of the secondary ANN model. By changing the allowable sensitivity level, it is possible to adjust the number of input factors used: this number will be the maximum possible with a decrease in the level and approach the number of input factors given by classical formulas with an increase in the level.

6. Transform on the server the table compiled in step 1. Delete from the table columns corresponding to insignificant input factors determined when setting the sensitivity threshold in step 5.

7. Perform the construction of a secondary ANN model on the server. The number of non-linear (for example, parabolic second, third, etc. order) neurons in the layer is increased, and, if necessary, the number of hidden layers, following an algorithm based on two learning phenomena of ANN models: 1st - when increasing the number of neurons in the layer, the model training error first decreases and then stabilizes at a certain level so that a further increase in their number is inappropriate; 2nd - with an increase in the number of hidden layers of the ANN model, the learning error also first decreases, but starting from a certain number of layers, its decrease becomes small, so that a further increase in the number of hidden layers is impractical. In this case, a fully coupled perceptron of direct signal propagation is used.

8. Perform deep machine learning of the secondary ANN model. Using the built-in algorithms of deep machine learning (gradient and non-gradient methods of nonlinear programming), a secondary ANN model is trained on the server until the minimum value of the root-mean-square error, defined by formula (1), is reached. In this case, if the value of this error exceeds the allowable (user-specified) level, then go to step 7. If the error is less than the allowable level, then the ANN model for preoperative calculation of the optical power of the IOL is considered built. However, this model can be retrained and refined any number of times as new data arrives and is added to the original table.

9. Operation of the ANN model. The ANN model obtained in the previous step is a mathematical model for determining the optical power of the IOL, implemented using artificial neural network deep machine learning methods. To calculate the optical power of the IOL using this ANN model, the patient undergoes a diagnostic ophthalmological examination, the results of which use the following parameters: gender, visual acuity value without correction before surgery, diopters; sphere value (Sph) before surgery, diopters; the value of the optical power of the cylinder (Cyl) before surgery, diopters; the value of the axis of the cylindrical inclination (Ax) before the operation, deg; the value of visual acuity with correction before surgery, diopters; the value of the strong meridian before surgery, deg; refraction value of the strong meridian before surgery, diopters; the value of the weak meridian before the operation, deg; refraction value of the weak meridian before surgery, diopters; sphere refraction value (Sph) before surgery, diopter; the refraction value of the optical power of the cylinder (Cyl) before surgery, diopters; the refraction value of the axis of the cylindrical inclination (Ax) before surgery, diopters; optical eye length value, mm.

By entering the obtained parameter values into the corresponding fields of the ANN-model on the computer display, the optical power of the IOL required for implantation is calculated in the preoperative period.

The invention is illustrated by the following clinical example.

Patient P., born in 1947, was admitted to the Tambov branch of the Federal State Autonomous Institution "NMITs" Eye Microsurgery "n.a. acad. S.N. diagnosed with complicated cataract OD. According to the results of the diagnostic examination, the following parameters were used to determine the optical power of the IOL:

Visual acuity OD at admission: 0.05 Sph-4.0=0.08

eye length 23.04 mm

anterior chamber depth 4.41 mm

Ophthalmometry: refraction of the strong meridian 43.75 diopters

refraction of the weak meridian 43.50 diopters

Planned refraction - emmetropia

The optical power of the IOL was calculated:

- according to the formula Holladay = 22.02 diopters

- according to the formula Haigis=23.18 diopters

Based on the results of the IOL calculation using the proposed method, the optical power of the IOL was 21.00 diopters.

The patient underwent PE with implantation of Acrisof Natural IOL by Alcon, USA 21.00 diopters

Visual acuity 1 month after the operation was 0.7 C - 0.25=1.0, which confirms the effectiveness of the proposed method. If a lens were placed according to the Holladay formula, the refraction would be -1.25 D, and according to the Haigis formula, the refraction would be -2.25 D, which would indicate that the patient did not get into emmetropia and obtain myopic refraction for the patient, would not provide functional outcome of treatment and would reduce patient satisfaction.

Claims (1)

A method for determining the optical power of an intraocular lens (IOL) using a mathematical model obtained as a result of deep learning of an artificial neural network (ANN model), including preparation of initial empirical data on a server with compilation of a table, building a primary ANN model on a server, machine learning on on the server of the primary ANN model, determining the parameters of the primary ANN model and assessing their sensitivity, determining significant input factors, transforming the table on the server with the removal of columns from it corresponding to insignificant input factors determined when setting the sensitivity threshold, building a secondary ANN model on the server , deep machine learning on the server of the secondary ANN model and operation of the ANN model by the user with the introduction of data from the preoperative examination of patients on the computer display and obtaining the value of the optical power of the IOL.

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