In Eastern European countries, cases of complete loss of visual function in children due to increased intraocular pressure (IOP) have recently been detected, and their number is constantly growing. Glaucoma is an ophthalmic disease that is detected at birth or during the child's subsequent life, where the progression of the disease without treatment leads to significant complications, including blindness. For every 2,500 newborns, 1-3 cases of congenital vision problems are registered. The registration of this disease depends on the timely detection of intraocular pressure, which at birth is registered within the range of 9–14 mm Hg and with reduced tension of the eye shell (<100 kPa). The progress of glaucoma development leads to a sharp increase in tension (и>150 kPa) and an increase in intraocular pressure, reaching a maximum in the range of 14-45 mm Hg in adolescents and adults. The purpose of this study is to model pressure changes in children with detected glaucoma and to consider individual parameters and dimensions of the eye shell thickness for making a decision on surgical intervention. It is known that with age, during a child's development, the dimensions of the orbit and other eye parameters change, including the thickness of the eye shell and its elasticity, which significantly affect the distribution of tension, accelerate the development of glaucoma, and this process requires more precise modeling, the use of additional fluid drainage devices, and individual implant selection. The authors conducted modeling and calculations that allowed for establishing the optimal pressure range for children: 9 mm Hg – 14 mm Hg, and the eye shell thickness of 0.1–0.3 mm (normal), ensuring individual internal tensions less than 100 kPa. Furthermore, the authors proposed and described the operation of an original automated system for individual preoperative testing of valves before their use in critical cases of pediatric glaucoma. Therefore, solving the problems of treating pediatric glaucoma and detecting it in the early stages of eye disease is an extremely important issue that requires modeling the process of individual selection of drainage parameters (valves) before surgical intervention. This is especially important when impaired functioning of the trabecular meshwork and lack of regular preventive examination with intraocular pressure control, and changes in the eye shell thickness are detected.

In children's ophthalmology, there are not isolated cases of partial or complete loss of visual function in children, characterized by increased intraocular pressure (IOP), and due to changes in exposure conditions during eye diseases, this number is constantly growing in European countries [1, 2]. In glaucoma, vision impairment significantly reduces the level of information perception and exacerbates the pathological state with progressive death of ganglion cell axons, causing a complete loss of the visual field. Modern methods for treating glaucoma include: drug therapy, laser therapy, and surgical implantation of drainage devices that provide the necessary rate of intraocular fluid outflow (normally it is 2-2.5 μl/min). It is known that the implantation of drainage devices for glaucoma is performed after unsuccessful previous attempts at conservative treatment, and due to the reduction of the movement rate and insufficient outflow of intraocular fluid through the eye's trabecular meshwork [3-5].Normal IOP values for children are lower than for adults: the norm for newborns is approximately 9-11 mm Hg, and at the age of 4-5 years, this value increases to 14 mm Hg. Therefore, with a constant increase in IOP, which can often occur before planned surgery, it is necessary to perform an individual selection of implants with substantiated parameters for each patient. The main clinical sign of glaucoma in children is a significant increase in IOP (more than 14-22 mm Hg and higher), and in some cases, even low pressure in this range may be considered unacceptable. The detection of increased IOP leads to the effect of high pressure on the eye shell and consequently on the optic nerve [4-6]. This creates a force that changes the shape and stretches the thin eye shell. In these conditions, tension is defined as the ratio of pressure to the actual size of the shell upon which it acts. It should be noted that performing surgical intervention and installing a regulating valve, such as the Ahmed type, is a complex process that can be applied if drug therapy has not achieved results and further deterioration of the child's vision is observed. The decision to perform surgery as the only option to prevent a child's vision loss depends on many factors: the choice of the valve and the use of quality material for its components, checking the timely triggering modes (the values of its opening and closing pressures), the necessity of technological testing on special stands, etc. [7, 8]. A correct assessment of the eye's condition during functioning and the level of tension within it is also important. The purpose of this study is to model the tension of the child's eye shell at different pressure parameters and eye shell thickness dimensions with the goal of their further consideration in the preoperative period, which will subsequently increase the effectiveness of surgical intervention [9, 10].

Theoretical studies of modeling the distribution of tension in the shell of the child's eye tension

It is known that the size of a child's eye at birth is, on average, 16.2 mm. By the age of 1 year, it increases to 19.2 mm, and at the age of 15 years, it equals 23 mm, which is practically close to the average size of an adult's eye, namely 24 mm. Since the shape of the child's eye shell is not perfectly spherical (Figure.1), its radius of curvature is variable: it increases from the anterior to the posterior part. In the central part of the cornea, its radius of curvature is approximately 7 mm, while on the periphery of the cornea it is 9 mm, in the anterior part of the sclera it is 11 mm, and in the posterior part, it is 12 mm.

                                                                                                                  Figure 1: Human eye anatomy

The thickness of the sclera is also uneven in different areas: in the posterior part of the eye, it is almost 1 mm, and anteriorly near the corneal edge, it is 0.6 mm [5].

Considering the above eye parameters, we proceed to the modeling of tensions. Since the wall thickness of the spherical eye shell (Fig. 2) is much smaller than its radius of curvature, it is appropriate to use the Young-Laplace formula to calculate the tension per unit area of the eye shell cross-section TS, where all necessary values can be accounted for: the intraocular pressure range, and the parameters of the eye shell and cornea:

        (1)

where Р is intraocular pressure (IOP); rk – radius of curvature of the cornea of the eye; d – thickness of the eye conjunctiva.

                                                                                 Figure 2: Image of tension action in the spherical conjunctiva 

Since the shape of a child's eye is elliptical, to calculate the tension per unit of the cross-sectional area Tφ it is necessary to apply a more accurate formula (2) that uses clarifying coefficients, which provides more accurate

results:

      (2)

where: P is intraocular pressure (IOP); a – larger diameter of the conjunctiva; b – smaller diameter of the conjunctiva; d – thickness of the conjunctiva; r – coefficient determined from the ratio:

where a and b – are the larger and smaller radiuses of the conjunctiva, respectively.

Based on the above ratios (1-3), the authors have constructed graphs of the dependence of tensions on different conjunctiva thicknesses, taking into account the parameters of the child's eye at different IOPs. The distribution of tensions in the posterior segment of the conjunctiva on the conjunctiva thickness is given below (Figure. 3).

Figure 3: Dependence of the posterior conjunctiva tensions on its thickness, with a curvature radius of 12 mm for different IOP levels: 9 mm Hg; 14 mm Hg; 21 mm Hg; 40 mm Hg.

In the process of modelling, based on the calculations and results obtained, it can be stated that with IOP in the range of 9 mm Hg - 14 mm Hg (normal in children), optimal tension of less than 100 kPa is ensured. An increase in IOP values ​​significantly more than 21 mm Hg leads to a rapid increase in 

tension (˃150 kPa) and the creation of conditions for the development of glaucoma.

The graph of the dependence of tension on the radius of curvature and thickness of the eye shell is shown below:

                                                             Figure 4: Dependence of tension on the radius of curvature and thickness of the shell

The graph shows that the dimensions of the shell affect the magnitude of the tensions. Already at an IOP of 21 mm Hg and above, the tension increases almost 2 times or more, especially when the shell thickness decreases to less than 0.1 mm. In such a case, the process of glaucoma onset is diagnosed, which ultimately leads to damage to the optic nerve and, as a result, to loss of a child's vision.             

Technical support for preoperative testing of intraocular implants

As a result of the analysis of industrial drainage devices, it was established that in most cases, the real possibility of their individual selection, considering the developmental features of pediatric patients, is not utilized. Therefore, the authors [8, 10] developed an automated system for preoperative testing of individually selected drainage devices. The implementation of such a system provides the ability to consider specific patient data, automatically record pressure indicators, the duration of valve opening and cessation of operation, allows for predicting reliability and performance during long-term use, and records information on the testing process, allowing individually adapted intraocular fluid drainage devices to be selected with increased accuracy for each patient. The functional diagram of the automated selection system is shown in Figure. 5:

                                                                     Figure 5: Block diagram of the automated system for implant testing

It consists of a computer 1, a microcontroller 2 connected in series, a motor 3 with a worm gear 4, a reservoir with saline solution 5, a 3-way splitter 6 connected to an electromechanical manometer 7, a tube for pressure balancing 8, and an implant 9, to the output of which a fluid detector 10 and an ADC 11 are connected, which is connected to the input of the microcontroller 2, the second output of which is connected to the input of the computer 1.The principle of operation when testing implants for regulating intraocular pressure is as follows. First, the implant is connected to the cannula, then it is filled with saline solution through the pressure tube 8 and the system of connecting tubes and reservoir 5. The computer 1 is set to the mode for checking for air inclusions, and in the system, to the "zero setting mode," for which the microcontroller 2 generates a series of rotor rotation pulses for the stepper motor 3, which increases the pressure in the reservoir 5 and the connection system by 3-5 units of mm Hg. With the help of the worm gear 4, any remaining air is squeezed out through the pressure balancing tube 7. The "implant testing" mode is set, for which the pressure tube 7 is closed: the microcontroller 2 generates a test sequence of pulses for rotating the rotor of the stepper motor 3 through the worm gear 4 connected to the piston of the saline reservoir 5. The pressure in the connection system gradually increases and is continuously monitored by the microelectromechanical manometer 7. The pressure level is constantly read by the microcontroller 2 and recorded in the computer's operational memory as pressure readings. The pressure increases from zero to the activation value of the tested implant. Fluid exits the implant and enters the fluid detector 10. The signal from the detector 10 is converted into digital form through the ADC 11 and sent to the microcontroller 2, which stops the rotation process of the stepper motor 3. Information about the completion of the testing process and the measured pressure level value of the implant is transmitted from the microcontroller 2 and the electromechanical manometer 8 and recorded in the computer's memory. The STM32F103RET6 microchip is used as the microcontroller, and the ST Microelectronics LPS33HW microelectromechanical manometer is one of the functional blocks that provides the possibility of automating the measurement process. The microcontroller reads data from the meter via the SPI interface and provides communication with the computer. The pressure measurement error is 0.075 mm Hg or 0.25% at the maximum pressure value in the reservoir.  To reduce the error, an important task was to create a software algorithm for the automatic regulation system with feedback that would allow for accurate determination of the intraocular fluid outflow parameters by the implant and 

increase the effectiveness of operations by determining the suitability of the implants for use in medical surgical practice. Thus, the presented work obtained results that expand the possibilities for individual selection of implants for intraocular fluid drainage in the treatment of glaucoma in childhood.

1. Preventive control of intraocular pressure in childhood can prevent glaucoma with vision loss.

2. An increase in IOP to 11-14 mm Hg creates tension in the eye shell within the range of values up to 100 kPa, which is already a signal for the use of more effective treatment methods.

3. Further increase in IOP (>14-22 mm Hg) with ineffective treatment and reaching tensions greater than 100 kPa requires surgical intervention with the installation of an intraocular fluid drainage valve.

4. An automated system for testing and individual selection of implants has been proposed.

5. Therefore, exceeding the normal IOP value in the treatment of glaucoma in childhood requires intensified treatment or effective surgical intervention, as evidenced by publications of domestic and foreign authors and the calculation results with graphical representations presented above.