Mathematical Modeling of Eyeball Vitreous Cavity and Software Based Thereon for Automatic Calculation of Individual Doses of Antibiotics for Intravitreal Injection in Treating Bacterial Endophthalmitis

Purpose: Mathematical modeling of the eyeball vitreous cavity and analysis of the vitreous cavity volume vs. eyeball length correlation dependence; software for automatic calculation of individual doses of antibiotics for intravitreal injection in treating bacterial endophthalmitis.

Materials and methods: The study included three sequential stages: 1st stage — mathematical modeling of the vitreous cavity of human eye based on data of 77 phakic eyes, by the least square method. The data were obtained by Tomey UD-8000 ultrasonography (Japan) and VuMax Sonomed ultrasound biomicroscopy (USA). 2nd stage — study of the vitreous cavity residual volume, free from silicon oil, by measuring a volume of vitreous body substitute injected to 64 pseudophakic patients who underwent a vitrectomy on account of detached retina. 3d stage — development of a computer program based on the data of the vitreous cavity volume vs. eyeball length dependence, vitreous cavity residual volume, and anterior chamber volume, and description of an algorithm for diluting antibiotics for intravitreal injection, based on a required concentration.

Results. Vitreous cavity of eyeball was approximated by ellipsoid. Statistical analysis has shown a linear dependence of eyeball length vs. vitreous cavity volume; vitreous cavity calculation accuracy does not depend on the cavity size, and a relative error of volume calculations that were performed from the resulting data of a single determination of the cavity surface point coordinates, with a probability of 0.866, does not exceed 1 %. Average residual volume of the vitreous cavity subjected to silicon oil tamponade was 332.36 ± 0.02 mm3, and average anterior chamber volume, 246.36 ± 0.06 mm3. The resulting data were exported to the computer program kernel.

Conclusion. The developed original mathematical model of the eyeball made it possible to calculate a vitreous cavity volume vs. eyeball length dependence and whereby to plot calibration nomograms that allow individual doses of antibiotics for intravitreal injection to be precisely calculated, thus providing a desired concentration thereof to suppress bacterial microflora and preventing toxic effect on retinae.

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