Mathematical modeling of quality parameters of fermented milk products

The scientific topic related to the modeling of optimal quality  parameters of fermented milk products does not lose its relevance and is in the plane of existing state programs and national projects to provide the population with affordable high-quality products that meet the body's needs for nutrients. Computational methods based on digital systems of computer mathematics play a special role in modeling recipes, which makes it possible to approach the process of producing fermented dairy products for specialized and mass nutrition as reasonably as possible. This scientific article reflects the results of mathematical modeling of the formulation and quality indicators of fermented dairy products based on camel milk using probiotic starter cultures. The simulation was performed using the concept of a «black box», which is often used to create a mathematical model of the process under study. The study planning matrix included 30 repetitions, which covered all the variable parameters for fermentation of 100 liters of milk (the amount of probiotic starter culture (0.1-0.3 kg), time (4-12 hours) and temperature (30-34°C) of fermentation, acidity (104121°T). Taking into account the input data, the response surface and lines of equal level for the fermented milk product were determined, regression equations for individual indicators were compiled. As a result of the scientific work carried out, the optimal quality parameters for the production of fermented dairy products based on camel milk were determined: the fermentation time – 12 hours, the temperature –32 °C, the shelf life – 45 days, while the achieved acidity – 116 °T, as a result, the best organoleptic parameters of the fermented milk product have been preserved, which were estimated at 4.8 points out of a possible 5. Thus, this modeling method is the most effective tool for researching and implementing the results of scientific research into the production of food products with specified properties.

1. Tasturganova E., Dikhanbaeva F., Prosekov A., Zhunusova G., Dzhetpisbaeva B., Matibaeva A. “Research of Fatty Acid Composition of Samples of Bio-Drink Made of Camel Milk”. Current Research in Nutrition and Food Science 6 (2), (2018): 491-499. doi: http://dx.doi.org/10.12944/CRNFSJ.6.2.23

2. Dikhanbayeva, F., Zhaxybayeva, E., Dimitrov, Z., Baiysbayeva, M., Yessirkep, G., & Bansal, N. “Studying the effect of the developed technology on the chemical composition of yogurt made from camel milk”. Eastern-European Journal of Enterprise Technologies3(11 (111), (2021): 36–48. https://doi.org/10.15587/1729-4061.2021.235831

3. Aralbayev, N., Dikhanbayeva, F., Yusof, Y. A. B., Tayeva, A., Smailova, Z. “Devising optimal technological parameters for spray drying to produce whole camel milk powder”. Eastern-European Journal of Enterprise Technologies 4(11(112), (2021):82–91. https://doi.org/10.15587/1729-4061.2021.238686

4. Subbaiyan, R., Ganesan, A., Varadharajan, V. et al. “Formulation and validation of probioticated foxtail millet laddu as a source of antioxidant for biological system using response surface methodology”. Brazilian Journal of Microbiology (2023). https://doi.org/10.1007/s42770-023-01188-8

5. Rashid, A.A., Saeed, S., Ahmad, I. et al. “Development of ricotta cheese from concentrated buffalo cheese whey by optimization of processing conditions using RSM”. Food Measure 17, (2023): 4739–4746. https://doi.org/10.1007/s11694-023-02004-5

6. Shojaeimeher, S., Babashahi, M., Shokri, S. et al. “Optimizing the Production of Probiotic Yogurt as a New Functional Food for Diabetics with Favorable Sensory Properties Using the Response Surface Methodology”. Probiotics and Antimicrobial Proteins (2023). https://doi.org/10.1007/s12602-023-10051-z

7. Tahmasebi, M., Mofid, V. “Innovative synbiotic fat-free yogurts enriched with bioactive extracts of the red macroalgae Laurencia caspica: formulation optimization, probiotic viability, and critical quality characteristics”. Food Measure 15, (2021): 4876–4887. https://doi.org/10.1007/s11694-021-01061-y

8. Khodashenas, M., Jouki, M. “Optimization of stabilized probiotic Doogh formulation by edible gums and response surface methodology: assessment of stability, viability and organoleptic attributes”. Journal of Food Science and Technology 57, (2020): 3201–3210. https://doi.org/10.1007/s13197-020-04351-3

9. Muzyka M.Yu., Blagoveshchensky I.G., Blagoveshchensky V.G., Mokrushin S.A., Blagoveshchenskaya M.M. “Ispol'zovanie metodov imitacionnogo modelirovaniya dlya analiza funkcionirovaniya processov proizvodstva kefira [Using simulation modeling methods to analyze the functioning of kefir production processes]”. Bulletin of the Voronezh State University of Engineering Technologies, 83(4) (2021): 17-24 – (In Russian). https://doi.org/10.20914/2310-1202-2021-4-17-24

10. Yurk N.A., Diener Yu.A. “Modelirovanie sostava kislomolochnogo produkta [Modeling of the composition of a fermented milk product]”. Technologies of the food and processing industry of the agro–industrial complex-healthy food products4, 2021: 32-37.– (In Russian). doi:10.24412/2311-6447-2021-4-32-37

11. Vukić, D.V., Vukić, V.R., Milanović, S.D. etal. “Modeling of rheological characteristics of the fermented dairy products obtained by novel and traditional starter cultures”. Journal of Food Science and Technology 55, (2018): 2180–2188. https://doi.org/10.1007/s13197-018-3135-9

12. Koh, W.Y., Utra, U., Rosma, A. et al. “Development of a novel fermented pumpkin-based beverage inoculated with water kefir grains: a response surface methodology approach”. Food Science and Biotechnology 27, (2018): 525–535. https://doi.org/10.1007/s10068-017-0245-5

13. Dorota, Z., Danuta, KK., Antoni, G. et al. “Predictive modelling of Lactobacillus casei KN291 survival in fermented soy beverage”. Journal of Microbiology 52, (2014): 169–178. https://doi.org/10.1007/s12275-014-3045-0

14. Habibi Najafi, M.B., Pourfarzad, A., Zahedi, H. et al. “Development of sourdough fermented date seed for improving the quality and shelf life of flat bread: study with univariate and multivariate analyses”. Journal of Food Science and Technology 53, (2016): 209–220. https://doi.org/10.1007/s13197-015-1956-3

15. Vukolov E., Osnovy statisticheskogo analiza. Praktikum po statisticheskim metodami issledovaniyu operacij s ispol'zovaniempaketov STATISTICA i Excel: uchebnoe posobie [Fundamentals of statistical analysis. Workshop on statistical methods and operations research using STATISTICA and Excel packages: a textbook]. Moscow: FORUM: INFRA-M, 2008. – 464p. – (In Russian).

16. Krasulya O. N., Nikolaeva S. V., Tokarev A.V., Krasnov A. E., Panin I. G.,Modelirovanie receptur pishchevyh produktov i tekhnologij ih proizvodstva: teoriya i praktika: uchebnoe posobie[Modeling of food formulations and production technologies: theory and practice: textbook]. St. Petersburg.: GIORD, 2015. – 320 p.– (In Russian).