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Mathematical notes of NEFU, 2025, Volume 32, Issue 4, Pages 113–131 (Mi svfu498)

Mathematical modeling

A multicontinuous approach to modeling ozone infiltration into bone tissue

Nikolaeva Nadezhda A.a, V. V. Rozanovb, A. P. Chernyaevb, Matveychuk Igor V., S. P. Stepanova, Gavrilova Svetlana A.b, Khutsistova Alana Otarievnab

a North-Eastern Federal University named after M. K. Ammosov, Yakutsk
b Lomonosov Moscow State University

Abstract: This study aims to develop and optimize a combined method for sterilizing ancient animal bone tissue using ozone and radiation for biomaterial preservation. The research focuses on the mathematical modeling of ozone infiltration into the porous bone structure and the analysis of collagen structural changes under various irradiation conditions. The results can be applied in medical sterilization. A multicontinuum approach based on multicontinuum homogenization and the solution of conjugate flow and transport equations was used to model ozone infiltration. The mathematical model made it possible to determine the optimal parameters for the infiltration process and reduce the need for numerous real-world experiments. The combined sterilization method (ozone and radiation) demonstrated high efficiency in treating ancient bone tissue. It ensures the destruction of pathogenic microflora while reducing the radiation dose and preserving the structural properties of the bone. The use of multicontinuum mathematical modeling allows optimization of the treatment process and improves the accuracy of predicting its results.

Keywords: bone tissue, multicontinuum model, porous media, ozone, infiltration, intraosseous space system, multicontinuum, bone tissue sterilization, radiation, radiation sterilization, radiation biotechnology

UDC: 519.6

Received: 26.09.2025
Accepted: 01.12.2025

DOI: 10.25587/2411-9326-2025-4-112-131



© Steklov Math. Inst. of RAS, 2026