Food Processing: Techniques and Technology Food Processing: Techniques and Technology Техника и технология пищевых производств 2074-9414 2313-1748 110938 10.21603/2074-9414-2025-4-2607 NHTAQK ОРИГИНАЛЬНАЯ СТАТЬЯ ORIGINAL ARTICLE ОРИГИНАЛЬНАЯ СТАТЬЯ Mathematical Assessment of Carbohydrate and Protein Profiles of Milk under Thermal Stress Математическая оценка изменения углеводного и белкового профилей молока при термической нагрузке https://orcid.org/0000-0003-4779-1076 Барковская Ирина Александровна Barkovskaya Irina A. i_barkovskaya@vnimi.org https://orcid.org/0009-0007-7848-4606 Ярышев Владислав Юрьевич Yaryshev Vladislav Yu. https://orcid.org/0000-0001-9300-3267 Блиадзе Владимир Геннадьевич Bliadze Vladimir G. v_bliadze@vnimi.org https://orcid.org/0000-0002-5875-9875 Туровская Светлана Николаевна Turovskaya Svetlana N. https://orcid.org/0000-0002-9399-0984 Илларионова Елена Евгеньевна Illarionova Elena E. e_illarionova@vnimi.org https://orcid.org/0000-0002-0913-5644 Кондратенко Владимир Владимирович Kondratenko Vladimir V. v_kondratenko@vnimi.org

кандидат технических наук;

candidate of technical sciences;

 https://orcid.org/0000-0002-0786-2055 Галстян Арам Генрихович Galstyan Aram G. Всероссийский научно-исследовательский институт молочной промышленности Москва Россия All-Russian Dairy Research Institute Moscow Russian Federation Всероссийский научно-исследовательский институт молочной промышленности Москва Россия All-Russian Dairy Research Institute Moscow Russian Federation Всероссийский научно-исследовательский институт молочной промышленности Москва Россия All-Russian Dairy Research Institute Moscow Russian Federation Всероссийский научно-исследовательский институт молочной промышленности Москва Россия All-Russian Dairy Research Institute Moscow Russian Federation Всероссийский научно-исследовательский институт молочной промышленности Москва Россия All-Russian Dairy Research Institute Moscow Russian Federation Всероссийский научно-исследовательский институт молочной промышленности Москва Россия All-Russian Dairy Research Institute Moscow Russian Federation Всероссийский научно-исследовательский институт молочной промышленности Москва Россия All-Russian Dairy Research Institute Moscow Russian Federation 25 12 2025 25 12 2025 55 4 794 806 05 06 2025 05 08 2025 https://fptt.ru/en/issues/24078/24095/

Вопрос разработки новых методов оценки и прослеживаемости качества пищевой продукции на всех этапах жизненного цикла остается актуальным для агропромышленного комплекса России, в том числе и для молочного сектора. Внедрение математических методов оценки в структуру контроля качества продукции является перспективным направлением для изучения. Цель исследования – разработать математический подход к оценке кинетики образования продуктов изменения белкового и углеводного профилей молока для дальнейшего прогнозирования и практических исследований их накопления в ходе технологического процесса и трансформации во время хранения сухих молочных консервов. Объект – молоко при разных температурных режимах обработки и продолжительности воздействия. Исследование основано на анализе концентраций соединений-маркеров изменения углеводного и белкового профилей молока при температурной обработке. Для этого проведен подбор научных работ на русском и английском языках за период 1985–2025 гг. с применением ресурсов электронных библиотек eLIBRARY.RU, Google Scholar, CyberLeninka, PubMed и ScienceDirect. Для математической оценки углеводов применяли уравнения псевдонулевого порядка и Аррениуса, для оценки изменения белковой составляющей – уравнение первого порядка. Алгоритм расчета реализован на языке Python. Установлены зависимости накопления лактулозы, гидроксиметилфурфурола и фурозина от интегральной тепловой нагрузки на молоко. Определены величины энергий активации, позволяющие получить максимальную линейность: 130 кДж/моль (для лактулозы и фурозина) и 85 кДж/моль (для гидроксиметилфурфурола). Выявлено, что предложенная модель расчетов не подходит для оценки накопления продуктов изменения углеводного профиля при длительном температурном воздействии ввиду более глубоких изменений продукта. β-лактоглобулин в большей степени подвержен влиянию температур, чем α-лактальбумин. Рассчитаны значения энергий активации для сывороточных белков: 72,1 и 85,1–85,7 кДж/моль соответственно. Разработанный подход позволяет количественно оценивать термическую нагрузку на молоко и прогнозировать качество продуктов его переработки. Результаты исследования могут быть использованы в пищевой промышленности для контроля качества пищевых продуктов и коррекции сроков годности, в том числе при производстве сухих молочных консервов.

The dairy industry needs new methods for food quality assessment at all stages of production and storage. Mathematical methods offer efficient tools of product quality control. This article introduces a mathematical approach to assessing the kinetics of protein and carbohydrate profiles of milk powder to predict their transformations throughout production and storage. The study featured milk at different processing temperatures and exposure times. The analysis focused on the concentrations of compounds that mark the changes in the carbohydrate and protein profiles of milk during heat treatment. The equation of pseudo-zero-order and the Arrhenius equation were applied to carbohydrates while a first-order equation made it possible to assess the changes in proteins. The calculation algorithm was processed in Python. The lactulose, hydroxymethylfurfural, and furosine accumulations proved to depend on the integral heat load. The activation energies that provided the linearity maximum were as follows: 130 kJ/mol for lactulose and furosine; 85 kJ/mol for hydroxymethylfurfural. The calculation model failed to assess the accumulation of carbohydrate profile products during prolonged thermal exposure due to more profound product changes. β-lactoglobulin appeared to be more susceptible to thermal effects than α-lactalbumin. The activation energies for whey proteins were 72.1 and 85.1–85.7 kJ/mol, respectively. The new mathematical approach provided a reliable quantitative assessment of thermal stress that can be used for food quality control and shelf-life adjustments, e.g., in milk powder production.

 Математическое моделирование качество молока сухое молоко маркеры термообработки Mathematical modeling milk quality milk powder heat treatment markers

Rosa E, Prudencio ES. A comprehensive approach about comparison between drying technologies and powdered dairy products. Food Research International. 2023;173(Part 1):113326. https://doi.org/10.1016/j.foodres.2023.113326 Rosa E, Prudencio ES. A comprehensive approach about comparison between drying technologies and powdered dairy products. Food Research International. 2023;173(Part 1):113326. https://doi.org/10.1016/j.foodres.2023.113326 Kourkouta L, Frantzana A, Koukourikos K, Iliadis C, Papathanasiou IV, et al. Milk nutritional composition and its role in human health. Journal of Pharmacy and Pharmacology. 2021;9(1):10–15. https://doi.org/10.17265/2328-2150/2021.01.002 Kourkouta L, Frantzana A, Koukourikos K, Iliadis C, Papathanasiou IV, et al. Milk nutritional composition and its role in human health. Journal of Pharmacy and Pharmacology. 2021;9(1):10–15. https://doi.org/10.17265/2328-2150/2021.01.002 McCarthy NA, Magan JB, Kelleher CM, Kelly AL, O’Mahony JA, et al. Heat treatment of milk: Effect on concentrate viscosity, powder manufacture and end-product functionality. International Dairy Journal. 2022;128:105289. https://doi.org/10.1016/j.idairyj.2021.105289 McCarthy NA, Magan JB, Kelleher CM, Kelly AL, O’Mahony JA, et al. Heat treatment of milk: Effect on concentrate viscosity, powder manufacture and end-product functionality. International Dairy Journal. 2022;128:105289. https://doi.org/10.1016/j.idairyj.2021.105289 Song X, Shen S, Dong G, Ding H, Xie Z, et al. A comprehensive review of direct, indirect, and AI-based detection methods for milk powder. Frontiers in Sustainable Food Systems. 2025;9:1571317. https://doi.org/10.3389/fsufs.2025.1571317 Song X, Shen S, Dong G, Ding H, Xie Z, et al. A comprehensive review of direct, indirect, and AI-based detection methods for milk powder. Frontiers in Sustainable Food Systems. 2025;9:1571317. https://doi.org/10.3389/fsufs.2025.1571317 Ryabova AE, Semipyatnyi VK, Galstyan AG. Effects of storage conditions on milk powder properties. Journal of Dairy Science. 2023;106(10):6741–6758. https://doi.org/10.3168/jds.2022-23094 Ryabova AE, Semipyatnyi VK, Galstyan AG. Effects of storage conditions on milk powder properties. Journal of Dairy Science. 2023;106(10):6741–6758. https://doi.org/10.3168/jds.2022-23094 Ding Y, Han F, Xie Z, Li G, Zhuang Y, et al. Dairy fortification as a good option for dietary nutrition status improvement of 676 preschool children in China: A simulation study based on a cross-sectional diet survey (2018–2019). Frontiers in Nutrition. 2022;9:1081495. https://doi.org/10.3389/fnut.2022.1081495 Ding Y, Han F, Xie Z, Li G, Zhuang Y, et al. Dairy fortification as a good option for dietary nutrition status improvement of 676 preschool children in China: A simulation study based on a cross-sectional diet survey (2018–2019). Frontiers in Nutrition. 2022;9:1081495. https://doi.org/10.3389/fnut.2022.1081495 Hamed AM, Galli B, Hogan SA, Abdel-Hamid M, Romeih E. Adaptive and predictive approaches to mitigate the impact of milk seasonality on composition, processing technologies and quality of milk powders. International Journal of Dairy Technology. 2025;78(1):e13148. https://doi.org/10.1111/1471-0307.13148 Hamed AM, Galli B, Hogan SA, Abdel-Hamid M, Romeih E. Adaptive and predictive approaches to mitigate the impact of milk seasonality on composition, processing technologies and quality of milk powders. International Journal of Dairy Technology. 2025;78(1):e13148. https://doi.org/10.1111/1471-0307.13148 Qin Y, Pillidge C, Harrison B, Adhikari B. Pathways in formulating foods for the elderly. Food Research International. 2024;186:114324. https://doi.org/10.1016/j.foodres.2024.114324 Qin Y, Pillidge C, Harrison B, Adhikari B. Pathways in formulating foods for the elderly. Food Research International. 2024;186:114324. https://doi.org/10.1016/j.foodres.2024.114324 Zanini B, Simonetto A, Zubani M, Castellano M, Gilioli G. The effects of cow-milk protein supplementation in elderly population: Systematic review and narrative synthesis. Nutrients. 2020;12(9):2548. https://doi.org/10.3390/nu12092548 Zanini B, Simonetto A, Zubani M, Castellano M, Gilioli G. The effects of cow-milk protein supplementation in elderly population: Systematic review and narrative synthesis. Nutrients. 2020;12(9):2548. https://doi.org/10.3390/nu12092548 Schons PF, Colet R, Pinto SS, Verruck S. Powdered milk. In: da Cruz AG, Pimentel TC, Esmerino EA, Verruck S, editors. Dairy Foods Processing. NY: Springer US; 2024. pp. 179–192. https://doi.org/10.1007/978-1-0716-4144-6_13 Schons PF, Colet R, Pinto SS, Verruck S. Powdered milk. In: da Cruz AG, Pimentel TC, Esmerino EA, Verruck S, editors. Dairy Foods Processing. NY: Springer US; 2024. pp. 179–192. https://doi.org/10.1007/978-1-0716-4144-6_13 Рябова А. Е. Влияние условий хранения на качество сухого молока. Молочная промышленность. 2021. № 7. С. 56–57. [Ryabova AE. Influence of storage conditions on the quality of powder milk. Dairy industry. 2021;(7):56–57. (In Russ.)] https://doi.org/10.31515/1019-8946-2021-07-56-57 Ryabova AE. Influence of storage conditions on the quality of powder milk. Dairy industry. 2021;(7):56–57. (In Russ.) https://doi.org/10.31515/1019-8946-2021-07-56-57 Duan J, Gao S, Diao Y, Zhang Q, Gu Y, et al. Effects of heat treatment on liquid milk quality and safety: Nutritional changes, hazardous substances and control strategies. Food Control. 2025;176:111377. https://doi.org/10.1016/j.foodcont.2025.111377 Duan J, Gao S, Diao Y, Zhang Q, Gu Y, et al. Effects of heat treatment on liquid milk quality and safety: Nutritional changes, hazardous substances and control strategies. Food Control. 2025;176:111377. https://doi.org/10.1016/j.foodcont.2025.111377 Рязанцева К. А., Шерстнева Н. Е. Традиционные и инновационные способы применения ультрафиолетового излучения в молочной промышленности. Техника и технология пищевых производств. 2022. Т. 52. № 2. С. 390–406. [Riazantseva KA, Sherstneva NE. Traditional and innovative uses of ultraviolet treatment in the dairy industry. Food Processing: Techniques and Technology. 2022;52(2):390–406. (In Russ.)] http s://doi.org/10.21603/2074-9414-2022-2-2372 Riazantseva KA, Sherstneva NE. Traditional and innovative uses of ultraviolet treatment in the dairy industry. Food Processing: Techniques and Technology. 2022;52(2):390–406. (In Russ.) https://doi.org/10.21603/2074-9414-2022-2-2372 Bista A, Murphy EG, O’Donnell CP, O’Shea N. The effect of heat treatment on physicochemical properties of skim milk concentrate and spray-dried skim milk powder. International Journal of Dairy Technology. 2022;75(3):690–700. https://doi.org/10.1111/1471-0307.12876 Bista A, Murphy EG, O’Donnell CP, O’Shea N. The effect of heat treatment on physicochemical properties of skim milk concentrate and spray-dried skim milk powder. International Journal of Dairy Technology. 2022;75(3):690–700. https://doi.org/10.1111/1471-0307.12876 Алькадур М. И., Пряничникова Н. С., Юрова Е. А., Петров А. Н. Влияние термической обработки и пастеризации на качество сухого молока. Техника и технология пищевых производств. 2024. Т. 54. № 2. С. 275–284. https://doi.org/10.21603/2074-9414-2024-2-2506 Alkadour MI, Pryanichnikova NS, Yurova EA, Petrov AN. Effect of thermal treatment and pasteurization on milk powder quality. Food Processing: Techniques and Technology. 2024;54(2):275–284. (In Russ.) https://doi.org/10.21603/2074-9414-2024-2-2506 Акадур М. И., Петров А. Н., Пряничникова Н. С. Влияние класса термической обработки сухого молока на структуру и свойства ферментированного сгустка. Пищевая промышленность. 2024. № 11. С. 82–89. https://doi.org/10.52653/PPI.2024.11.11.015 Alkadour MI, Petrov AN, Pryanichnikova NS. Influence of the class of thermal treatment of dry milk on the structure and properties of the fermented curd. Food industry. 2024;(11):82–89. (In Russ.) htt ps://doi.org/10.52653/PPI.2024.11.11.015 Калугина Д. Н., Юрова Е. А. Обоснование определения индекса азота сывороточного белка для оценки белкового состава сухого молока. Молочная промышленность. 2022. № 7. С. 35–37. https://doi.org/10.31515/1019-8946-2022-07-35-37 Kalugina DN, Yurova EA. Rationale for determining the nitrogen index of whey protein to assess the protein composition of milk powder. Dairy industry. 2022;(7):35–37. (In Russ.) https://doi.org/10.31515/1019-8946-2022-07-35-37 Мельденберг Д. Н., Полякова О. С., Семёнова Е. С., Юрова Е. А. Разработка комплексной оценки белкового состава молока сырья различных сельскохозяйственных животных для выработки продуктов функциональной направленности. Хранение и переработка сельхозсырья. 2020. № 3. С. 118–133. https://doi.org/10.36107/spfp.2020.352 Meldenberg DN, Polyakova OS, Semenova ES, Yurova EA. Development of a comprehensive milk protein composition assessment from raw materials of various farm animals for the functional products production. Storage and Processing of Farm Products. 2020;(3):118–133. (In Russ.) https://doi.org/10.36107/spfp.2020.352 Paul A, Martin F, Simard B, Scher J, Gaiani C, et al. Deciphering the segregation of proteins in high-protein dairy powders after spray-drying. Journal of Dairy Science. 2023;106(2):843–851. https://doi.org/10.3168/jds.2022-22133 Paul A, Martin F, Simard B, Scher J, Gaiani C, et al. Deciphering the segregation of proteins in high-protein dairy powders after spray-drying. Journal of Dairy Science. 2023;106(2):843–851. https://doi.org/10.3168/jds.2022-22133 Рябова А. Е., Кондратенко В. В. Моделирование процесса самопрессования сухого молока в процессе хранения. Пищевая промышленность. 2024. № 9. С. 65–69. https://doi.org/10.52653/PPI.2024.9.9.013 Ryabova AE, Kondratenko VV. Modeling of the self-pressing process of powdered milk during storage. Food industry. 2024;(9):65–69 (In Russ.) https://doi.org/10.52653/PPI.2024.9.9.013 Fan X, Wang C, Cheng M, Wei H, Gao X, et al. Markers and mechanisms of deterioration reactions in dairy products. Food Engineering Reviews. 2023;15:230–241. https://doi.org/10.1007/s12393-023-09331-9 Fan X, Wang C, Cheng M, Wei H, Gao X, et al. Markers and mechanisms of deterioration reactions in dairy products. Food Engineering Reviews. 2023;15:230–241. https://doi.org/10.1007/s12393-023-09331-9 Mahmood N, Muhoza B, Huang Y, Munir Z, Zhang Y, et al. Effects of emerging food pretreatment and drying techniques on protein structures, functional and nutritional properties: An updated review. Critical Reviews in Food Science and Nutrition. 2024;64(26):9365–9381. https://doi.org/10.1080/10408398.2023.2212302 Mahmood N, Muhoza B, Huang Y, Munir Z, Zhang Y, et al. Effects of emerging food pretreatment and drying techniques on protein structures, functional and nutritional properties: An updated review. Critical Reviews in Food Science and Nutrition. 2024;64(26):9365–9381. https://doi.org/10.1080/10408398.2023.2212302 Rauh V, Xiao Y. The shelf life of heat-treated dairy products. International Dairy Journal. 2022;125:105235. https://doi.org/10.1016/j.idairyj.2021.105235 Rauh V, Xiao Y. The shelf life of heat-treated dairy products. International Dairy Journal. 2022;125:105235. https://doi.org/10.1016/j.idairyj.2021.105235 Clarke HJ, McCarthy WP, O’Sullivan MG, Kerry JP, Kilcawley KN. Oxidative quality of dairy powders: Influencing factors and analysis. Foods. 2021;10(10):2315. https://doi.org/10.3390/foods10102315 Clarke HJ, McCarthy WP, O’Sullivan MG, Kerry JP, Kilcawley KN. Oxidative quality of dairy powders: Influencing factors and analysis. Foods. 2021;10(10):2315. https://doi.org/10.3390/foods10102315 Lu J, Zhu T, Dai Y, Xing L, Jinqi L, et al. The effect of heat treatment on the lactosylation of milk proteins. Journal of Dairy Science. 2023;106(12):8321–8330. https://doi.org/10.3168/jds.2023-23526 Lu J, Zhu T, Dai Y, Xing L, Jinqi L, et al. The effect of heat treatment on the lactosylation of milk proteins. Journal of Dairy Science. 2023;106(12):8321–8330. https://doi.org/10.3168/jds.2023-23526 Li Y, Quan W, Jia X, He Z, Wang Z, et al. Profiles of initial, intermediate, and advanced stages of harmful Maillard reaction products in whole-milk powders pre-treated with different heat loads during 18 months of storage. Food Chemistry. 2021;351:129361. https://doi.org/10.1016/j.foodchem.2021.129361 Li Y, Quan W, Jia X, He Z, Wang Z, et al. Profiles of initial, intermediate, and advanced stages of harmful Maillard reaction products in whole-milk powders pre-treated with different heat loads during 18 months of storage. Food Chemistry. 2021;351:129361. https://doi.org/10.1016/j.foodchem.2021.129361 Dong L, Yu Z, Zhao R, Peng B, Zhang Y, et al. The effect of lactulose thermal degradation products on β-lactoglobulin: Linear-, loop-, and cross-link structural modifications and reduced digestibility. Food Chemistry. 2023;403:134333. https://doi.org/10.1016/j.foodchem.2022.134333 Dong L, Yu Z, Zhao R, Peng B, Zhang Y, et al. The effect of lactulose thermal degradation products on β-lactoglobulin: Linear-, loop-, and cross-link structural modifications and reduced digestibility. Food Chemistry. 2023;403:134333. https://doi.org/10.1016/j.foodchem.2022.134333 Claeys WL, Ludikhuyze LR, Hendrickx ME. Formation kinetics of hydroxymethylfurfural, lactulose and furosine in milk heated under isothermal and non-isothermal conditions. Journal of Dairy Research. 2001;68(2):287–301. https://doi.org/10.1017/s0022029901004745 Claeys WL, Ludikhuyze LR, Hendrickx ME. Formation kinetics of hydroxymethylfurfural, lactulose and furosine in milk heated under isothermal and non-isothermal conditions. Journal of Dairy Research. 2001;68(2):287–301. https://doi.org/10.1017/s0022029901004745 Andrews GR. Determining the energy of activation for the formation of lactulose in heated milks. Journal of Dairy Research. 1985;52(2):275–280. https://doi.org/10.1017/S0022029900024146 Andrews GR. Determining the energy of activation for the formation of lactulose in heated milks. Journal of Dairy Research. 1985;52(2):275–280. https://doi.org/10.1017/S0022029900024146 Wang Y, Xiao R, Liu S, Wang P, Zhu Y, et al. The impact of thermal treatment intensity on proteins, fatty acids, macro/micro-nutrients, flavor, and heating markers of milk—A comprehensive review. International Journal of Molecular Sciences. 2024;25(16):8670. https://doi.org/10.3390/ijms25168670 Wang Y, Xiao R, Liu S, Wang P, Zhu Y, et al. The impact of thermal treatment intensity on proteins, fatty acids, macro/micro-nutrients, flavor, and heating markers of milk—A comprehensive review. International Journal of Molecular Sciences. 2024;25(16):8670. https://doi.org/10.3390/ijms25168670 Abdulhameed AF, Memon QA. An improved trapezoidal rule for numerical integration. Journal of Physics: Conference Series. 2021;2090(1):012104. https://doi.org/10.1088/1742-6596/2090/1/012104 Abdulhameed AF, Memon QA. An improved trapezoidal rule for numerical integration. Journal of Physics: Conference Series. 2021;2090(1):012104. https://doi.org/10.1088/1742-6596/2090/1/012104 Kessler HG. Food and bio process engineering. In: Kessler VA. Dairy Technology. 2002. 694 p. Kessler HG. Food and bio process engineering. In: Kessler VA. Dairy Technology. 2002. 694 p. Li M, Shen M, Lu J, Yang J, Huang Y, et al. Maillard reaction harmful products in dairy products: Formation, occurrence, analysis, and mitigation strategies. Food Research International. 2022;151:110839. https://elibrary.ru/UGUAWT Li M, Shen M, Lu J, Yang J, Huang Y, et al. Maillard reaction harmful products in dairy products: Formation, occurrence, analysis, and mitigation strategies. Food Research International. 2022;151:110839. https://elibrary.ru/UGUAWT Calvo MM, Olano A. Formation of galactose during heat treatment of milk and model systems. Journal of Dairy Research. 1989;56(5):737–740. https://doi.org/10.1017/S0022029900029307 Calvo MM, Olano A. Formation of galactose during heat treatment of milk and model systems. Journal of Dairy Research. 1989;56(5):737–740. https://doi.org/10.1017/S0022029900029307 Lan XY, Wang JQ, Bu DP, Shen JS, Zheng N, et al. Effects of heating temperatures and addition of reconstituted milk on the heat indicators in milk. Journal of Food Science. 2010;75(8):C653–C658. https://doi.org/10.1111/j.1750-3841.2010.01802.x Lan XY, Wang JQ, Bu DP, Shen JS, Zheng N, et al. Effects of heating temperatures and addition of reconstituted milk on the heat indicators in milk. Journal of Food Science. 2010;75(8):C653–C658. https://doi.org/10.1111/j.1750-3841.2010.01802.x Marconi E, Messia MC, Amine A, Moscone D, Vernazza F, et al. Heat-treated milk differentiation by a sensitive lactulose assay. Food Chemistry. 2004;84(3):447–450. https://doi.org/10.1016/s0308-8146(03)00268-1 Marconi E, Messia MC, Amine A, Moscone D, Vernazza F, et al. Heat-treated milk differentiation by a sensitive lactulose assay. Food Chemistry. 2004;84(3):447–450. https://doi.org/10.1016/s0308-8146(03)00268-1 Olano A, Calvo MM. Kinetics of lactulose, galactose and epilactose formation during heat-treatment of milk. Food Chemistry. 1989;34(4):239–248. https://doi.org/10.1016/0308-8146(89)90101-5 Olano A, Calvo MM. Kinetics of lactulose, galactose and epilactose formation during heat-treatment of milk. Food Chemistry. 1989;34(4):239–248. https://doi.org/10.1016/0308-8146(89)90101-5 Топникова Е. В., Мягконосов Д. С., Абрамов Д. В., Кашникова О. Г. Колориметрический метод оценки интенсивности тепловой нагрузки при пастеризации молока. Пищевые системы. 2024. Т. 7. № 3. С. 481–490. https://doi.org/10.21323/2618-9771-2024-7-3-481-490 Topnikova EV, Myagkonosov DS, Abramov DV, Kashnikova OG. Colorimetric method for estimating the intensity of heat load during milk pasteurization. Food Systems. 2024;7(3):481–490. (In Russ.) ht tps://doi.org/10.21323/2618-9771-2024-7-3-481-490 Chen Z, Yan X. Simultaneous determination of melamine and 5-hydroxymethylfurfural in milk by capillary electrophoresis with diode array detection. Journal of Agricultural and Food Chemistry. 2009;57(19):8742–8747. https://doi.org/10.1021/jf9021916 Chen Z, Yan X. Simultaneous determination of melamine and 5-hydroxymethylfurfural in milk by capillary electrophoresis with diode array detection. Journal of Agricultural and Food Chemistry. 2009;57(19):8742–8747. https://doi.org/10.1021/jf9021916 Morales FJ, Jiménez-Pérez S. HMF formation during heat-treatment of milk-type products as related to milkfat content. Journal of Food Science. 1999;64(5):855–859. https://doi.org/10.1111/j.1365-2621.199+9.tb15927.x Morales FJ, Jiménez-Pérez S. HMF formation during heat-treatment of milk-type products as related to milkfat content. Journal of Food Science. 1999;64(5):855–859. https://doi.org/10.1111/j.1365-2621.199+9.tb15927.x Morales FJ, Romero C, Jiménez-Pérez S. Characterization of industrial processed milk by analysis of heat-induced changes. International Journal of Food Science and Technology. 2000;35(2):193–200. https://doi.org/10.1046/j.1365-2621.2000.00334.x Morales FJ, Romero C, Jiménez-Pérez S. Characterization of industrial processed milk by analysis of heat-induced changes. International Journal of Food Science and Technology. 2000;35(2):193–200. https://doi.org/10.1046/j.1365-2621.2000.00334.x Morales FJ, Romero C, Jiménez-Pérez S. Chromatographic determination of bound hydroxymethylfurfural as an index of milk protein glycosylation. Journal of Agricultural and Food Chemistry. 1997;45(5):1570–1573. https://doi.org/10.1021/jf960930v Morales FJ, Romero C, Jiménez-Pérez S. Chromatographic determination of bound hydroxymethylfurfural as an index of milk protein glycosylation. Journal of Agricultural and Food Chemistry. 1997;45(5):1570–1573. https://doi.org/10.1021/jf960930v Morales FJ, Romero C, Jiménez-Pérez S. Evaluation of heat-induced changes in Spanish commercial milk: Hydroxymethylfurfural and available lysine content. International Journal of Food Science and Technology. 2003;31(5):411–418. https://doi.org/10.1046/j.1365-2621.1996.00357.x Morales FJ, Romero C, Jiménez-Pérez S. Evaluation of heat-induced changes in Spanish commercial milk: Hydroxymethylfurfural and available lysine content. International Journal of Food Science and Technology. 2003;31(5):411–418. https://doi.org/10.1046/j.1365-2621.1996.00357.x Xing Q, Fu X, Liu Z, Cao Q, You C, et al. Contents and evolution of potential furfural compounds in milk-based formula, ultra-high temperature milk and pasteurised yoghurt. International Dairy Journal. 2021;120:105086. https://doi.org/10.1016/j.idairyj.2021.105086 Xing Q, Fu X, Liu Z, Cao Q, You C, et al. Contents and evolution of potential furfural compounds in milk-based formula, ultra-high temperature milk and pasteurised yoghurt. International Dairy Journal. 2021;120:105086. https://doi.org/10.1016/j.idairyj.2021.105086 Birlouez-Aragon I, Sabat P, Gouti N. A new method for discriminating milk heat treatment. International Dairy Journal. 2002;12(1):59–67. https://doi.org/10.1016/S0958-6946(01)00131-5 Birlouez-Aragon I, Sabat P, Gouti N. A new method for discriminating milk heat treatment. International Dairy Journal. 2002;12(1):59–67. https://doi.org/10.1016/S0958-6946(01)00131-5 Sakkas L, Moutafi A, Moschopoulou E, Moatsou G. Assessment of heat treatment of various types of milk. Food Chemistry. 2014;159:293–301. https://doi.org/10.1016/j.foodchem.2014.03.020 Sakkas L, Moutafi A, Moschopoulou E, Moatsou G. Assessment of heat treatment of various types of milk. Food Chemistry. 2014;159:293–301. https://doi.org/10.1016/j.foodchem.2014.03.020 Алкадур М. И., Илларионова Е. Е. Влияние класса термообработки сухого молока на переход белка в сыворотку. Пищевая промышленность. 2025. № 3. С. 96–99. https://doi.org/10.52653/PPI.2025.3.3.018 Alkadour MI, Illarionova EE. Effect of heat treatment class of dry milk on protein transfer to whey. Food industry. 2025;(3):9 6–99. (In Russ.) https://doi.org/10.52653/PPI.2025.3.3.018 Рязанцева К. А., Шерстнева Н. Е., Агаркова Е. Ю., Жижин Н. А. Влияние модифицированных ультрафиолетом сывороточных белков на стабильность кисломолочного сгустка. Известия высших учебных заведений. Пищевая технология. 2023. Т. 392. № 2–3.С. 83–92. https://doi.org/10.26297/0579-3009.2023.2-3.14 Ryazantseva KA, Sherstneva NE, Agarkova EYu, Zhizhin NA. Influence of ultraviolet modified whey proteins on the stability of the stability of the stabilized milk cloud. Izvestiya vuzov. Food technology. 2023;392(2–3):83–92. (In Russ.) https://doi.org/10.26297/0579-3009.2023.2-3.14 Калугина Д. Н., Юрова Е. А. Характеристики белкового состава в формировании сроков годности молока ультрапастеризованного. Вестник КрасГАУ. 2021. № 10. С. 165–172. https://doi.org/10.36718/1819-4036-2021-10-165-172 Kalugina DN, Yurova EA. The protein composition characteristics in the formation of ultra pasteurized milk shelf life. Bulletin of KSAU. 2021;(10):165–172. (In Russ.) https://doi.org/10.36718/1819-4036-2021-10-165-172 Wu J, Chen S, Van der Meeren P. Heat stability assessment of milk: A review of traditional and innovative methods. Foods. 2024;13(14):2236. https://doi.org/10.3390/foods13142236 Wu J, Chen S, Van der Meeren P. Heat stability assessment of milk: A review of traditional and innovative methods. Foods. 2024;13(14):2236. https://doi.org/10.3390/foods13142236 Wu Y, Wu S, Sun M, Nie L, Zhang Y, et al. Reduction of the levels of 5-hydroxymethylfurfural and advanced glycation end products in milk by the combination of high pressure and moderate heat pre-incubation. European Food Research and Technology. 2023;249:923–937. https://doi.org/10.1007/s00217-022-04184-8 Wu Y, Wu S, Sun M, Nie L, Zhang Y, et al. Reduction of the levels of 5-hydroxymethylfurfural and advanced glycation end products in milk by the combination of high pressure and moderate heat pre-incubation. European Food Research and Technology. 2023;249:923–937. https://doi.org/10.1007/s00217-022-04184-8 Zhang Y, Yi S, Lu J, Pang X, Xu X, et al. Effect of different heat treatments on the Maillard reaction products, volatile compounds and glycation level of milk. International Dairy Journal. 2021;123:105182. https://doi.org/10.1016/j.idairyj.2021.105182 Zhang Y, Yi S, Lu J, Pang X, Xu X, et al. Effect of different heat treatments on the Maillard reaction products, volatile compounds and glycation level of milk. International Dairy Journal. 2021;123:105182. https://doi.org/10.1016/j.idairyj.2021.105182 Большакова Е. И., Стрижко М. Н. Влияние белкового профиля на технологические свойства молочных консервов с сахаром. Известия высших учебных заведений. Пищевая технология. 2023. Т. 391. № 1. С. 107–113. https://doi.org/10 .26297/0579-3009.2023.1.17 Bolshakova EI, Strizhko MN. Influence of the protein profile on the technological properties of canned milk with sugar. Izvestiya vuzov. Food technology. 2023;391(1):107–113. (In Russ.) https://doi.org/10 .26297/0579-3009.2023.1.17 Mayer HK, Raba B, Meier J, Schmid A. RP-HPLC analysis of furosine and acid-soluble β-lactoglobulin to assess the heat load of extended shelf life milk samples in Austria. Dairy Science & Technology. 2010;90(4):413–428. https://doi.org/10.1051/dst/2009058 Mayer HK, Raba B, Meier J, Schmid A. RP-HPLC analysis of furosine and acid-soluble β-lactoglobulin to assess the heat load of extended shelf life milk samples in Austria. Dairy Science & Technology. 2010;90(4):413–428. https://doi.org/10.1051/dst/2009058 Гралевская И. В., Ионова Л. В., Хавров И. В., Барсукова Л. С. Мониторинг технологических особенностей мягких кислотно-сычужных сыров. Техника и технология пищевых производств. 2012. Т. 25. № 2. Gralevskaya IV, Ionova LV, Havrov IV, Barsukova LS. Monitoring of technological characteristics of soft acid-rennet cheese. Food Processing: Techniques and Technology. 2012;25(2). (In Russ.) Рязанцева К. А., Шерстнева Н. Е. Подходы к повышению термической стабильности сывороточных белков. Пищевая промышленность. 2021. № 8. С. 25–28. https://doi.org/10.52653/PPI.2021.8.8.006 Riazantseva KA, Sherstneva NE. Approaches to increasing the heat stability of whey proteins. Food industry. 2021;(8):25–28. (In Russ.) https://doi.org/10.52653/PPI.2021.8.8.006 Čurlej J, Zajác P, Čapla J, Golian J, Benešová L, et al. The effect of heat treatment on cow’s milk protein profiles. Foods. 2022;11(7):1023. https://doi.org/10.3390/foods11071023 Čurlej J, Zajác P, Čapla J, Golian J, Benešová L, et al. The effect of heat treatment on cow’s milk protein profiles. Foods. 2022;11(7):1023. https://doi.org/10.3390/foods11071023