MODELING COMPONENTS OF BIOREGENERATIVE LIFE SUPPORT SYSTEM INTENDED FOR SPACE PURPOSES

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Introduction. It is known that a space diet was calcu- lated by the method of one-criterion optimization using AMPL environment [1]. In that study we assigned the masses of dishes as independent variables. The balance of ingredient masses in the dishes remained constant, whereas the use of ingredient masses as independent vari- ables may enhance the efficiency of diet optimization. Minimizing equivalent system mass (ESM) of foods was the objective function of optimization z = min å c jmd j , (1) jÎF where cj is the “cost” of 1 gram of the j-th dish in terms of ESM units; mdj is the mass of the j-th dish; F - a set of dishes. Nowadays, ESM calculation can be carried out on the basis of terrestrial test-beds [2]. In space conditions, To fulfill the norm of the content of animal protein in the diet for cosmonauts [7], we also added to our list the ingredients of animal origin that were considered as can- didates for cultivation in BLSS: quail meat [8], quail eggs and pork [9], tilapia [10], milk [11], as well as table salt, water, sugar and safflower oil. Thus, the list of ingredients included 31 names. Model Description. We conducted simulations in the Excel environment using the COIN-OR-CBC solver in the OpenSolver add-in [12]. We used the following objec- tive functions: minimizing the daily food mass and maximizing its antioxidant activity. We assigned the masses of dish ingredients as independent variables. We considered the daily food mass as sum of dish masses. Our linear model was based on the matrix A: the results of the calculation may not be relevant. There- fore, as an objective function, it is advisable to use the minimization of the daily food mass. This objective func- æ x11 x12 L x1 j x x L x ç ç 21 22 2 j L x1v ö L x ÷ 2v ÷ ç M M M M M M ÷ tion is a variant of ESM minimizing, if in the equation (1) A = ç x x L x L x ÷ , (2) the coefficients cj = 1. ç i1 i 2 ij iv ÷ Space radiation induces oxidative stress in cosmo- ç M M M M M M ÷ nauts' bodies after a long space flight on the International Space Station [3; 4]. Partial solution to the problem of ç x x è u1 u 2 L xuj L xuv ÷ ø oxidative stress is in the selection of ingredients that have antioxidant properties. Dietary countermeasures are food products and preparations that, when ingested into a cos- monaut’s body, may have the potential to reduce the ef- fects of ionizing radiation [5]. It is of interest to calculate the antioxidant potential of a diet. The purpose of this work was to develop a computer model using masses of dish ingredients as independent where u is the number of dish ingredients in the dishes; v - number of dishes in the daily diet; xij - mass of i-th ingredient in the j-th dish. The rows in the matrix A represented the distribution of dish ingredients along the dishes and the columns rep- resented the masses of dish ingredients in the dishes. The total masses of ingredients in the daily menu were represented by a column vector: variables for minimizing the daily food mass consumed in BLSS and maximizing food’s antioxidant potential. Selecting dish ingredients. When compiling the list uuuuur [ VTM = X1 v X 2 L Xi L Xu ]¢ , (3) of ingredients for diet modeling, the following conditions were met: a) data on the biochemical composition of the ingredients should be publicly available; b) the ingrediwhere diet. Xi = å xij j =1 - mass of i-th ingredient in the daily ents were used previously in experimental or theoretical studies of BLSS. Ingredients obtained from plants [6] partially meet these conditions; these ingredients are: wheat, rice, oats, quinoa, millet, sweet potato, potatoes, beets, lettuce, carrots, oyster mushrooms, Pinto beans, soybeans, chickpeas, lentils, cow peas, strawberries, to- matoes, cantaloupe, onions, garlic and chili. We calculated the mass of the j-th dish using the following formula: Подпись: u md j = å xij. (4) i=1 We represented the content of nutrients per 100 g of ingredients as a matrix B: æ n11 n12 L n1 j L n1p ö Table 2 ç n n L n L n ÷ Specific menu plan Eating 1 2 3 4 Chicken with rice Morning sausages Fresh-soup Nut Bread Soy milk Roast Goat milk Water Tofu Candied nuts Bread Cocktail ç 21 22 2 j 2 p ÷ ç M M M M M M ÷ B = ç n n L n L n ÷ , (5) ç i1 i 2 ij ip ÷ ç M M M M M M ÷ ç n n L n L n ÷ è u1 u 2 uj up ø where p is the number of monitored nutrients; u is the number of ingredients in the dishes. The rows in matrix B represented the nutrient content of the ingredients, and the columns showed the nutrient distribution along ingredients. Data on the content of nu- trients in 100 g of ingredients was taken from open data- bases [13-15]. We recorded the distribution of the j-th nutrient along ingredients as a column vector: uuur = é ù¢ Some constraints were imposed on the masses of vari- ables and dishes. The daily intakes of nutrients were re- stricted by NASA standards [7]. The calorie value of the daily menu was accepted to be 2800 kcal in accordance N j ënj1 nj 2 L nji L nju û . (6) with the daily energy consumption of the explorer in the We calculated the mass of the j-th nutrient in the daily menu as the scalar product of the vectors: uuur uuuuur mn j = N j ´VTM / 100 . (7) BIOS 3 complex [18] and the estimated energy consump- tion of the lunar base inhabitant [19]. We carried out the calculation of caloric content of the daily menu according to the Atwater formula: We carried out the minimization of the daily food mass using the formula: E = 4[ protein] + 9[ fat] + 4[carbohydrate], (10) Подпись: v TM = min å md j . (8) j =1 To maximize the antioxidant potential of the daily food mass, the following formula was used: Подпись: u AP = max å ai Xi / (100 ´1000) , (9) i=1 where AP - antioxidant potential of the daily food mass, expressed in mmol Trolox-equivalent; ai - antioxidant efficacy, expressed in µmol Trolox-equivalent [16] per 100 g of i-th ingredient [17]. Planning the daily menu: an example. We planned four meals that included soup, main courses, snacks, des- sert, bread and drinks. We arranged the dishes according to the plan (tab. 1). We chose a list of dishes and the composition of the ingredients in the dishes, taking into account the fact that the ingredients were included in the list given in the sec- tion “Selecting dish ingredients”. The specificity of the menu plan (tab. 1) is shown in tab. 2. Table 1 Menu plan Meals 1 2 3 4 Main course Snack First course Snack Bread Drink Main course Drink Drink Snack Dessert Bread Drink where [protein], [fat], [carbohydrate] - masses of proteins, fats and carbohydrates in the daily menu. These 12 dishes (tab. 2, 3) include 24 ingredients (tab. 3). The data in tab. 3 were obtained as a result of optimization of the daily menu with the use of minimizing the total mass of the daily diet as an objective function. The minimum weight of the daily diet was 2641 g, and its maximum antioxidant activity was 14 mmol Trolox equivalent. Currently, the norm on the antioxidant activity of the daily diet is not established [7]. It should be noted that the antioxidant activity of the products is de- termined in vitro [16], whereas in vivo the properties of the products are likely to vary. The calculated diet was not balanced for four nutri- ents: iron, phosphorus, pantothenic acid and saturated fat. The values of daily intake of iron, phosphorus and satu- rated fats exceeded NASA standards, while the diet was deficient in pantothenic acid. It is known that excessive intake of iron and its accu- mulation in the body can provoke cancer and heart dis- ease [20-22]. In this regard, the installation of low iron consumption seems justified. Nevertheless, the range of both Russian and American products used on board the ISS to complete joint diets did not allow to maintain a low daily iron intake rate (8-10 mg) in accordance with the desire of the American side. In Russian-American joint diets actually used in the 1st-7th expeditions, iron intake was 21 mg/day. Metabolic parameters did not exceed the limits of permissible physiological fluctuations and did not indicate violations of the nutritional status of crew members. The data obtained show that the joint Russian- American diets adequately ensured the energy and con- structive metabolism of the crew members during the seven long-term expeditions to the ISS and contributed to the maintenance of the operability sufficient to carry out the flight programs [23]. Table 3 Calculated masses of ingredients in dishes and masses of dishes Ingredients Dishes Fresh soup Chicken Roast Sausages Tofu Chickpeas Candied nuts Bread Goat milk Soy milk Cocktail Water Table salt 2 0,1 0,1 0,1 0,1 0,1 0 0,1 0 0 0 0 Water 238 20 40 30 200 30 0 0 0 241 100 100 Wheat grains 0 0 0 0 0 0 0 218 0 0 0 0 Rice 0 40 0 0 0 0 100 0 0 0 0 0 Quinoa 0 5 5 5 0 0 0 0 0 0 0 0 Millet 5 0 0 0 0 0 0 0 0 0 0 0 Sweet potato 0 50 60 0 0 0 0 0 0 0 0 0 White potato 70 0 0 0 0 0 0 0 0 0 0 0 Carrot 0 5 0 0 0 0 0 0 0 0 0 0 Safflower oil 3 4 10 18 0 0 0 0 0 0 0 0 Soybeans 0 5 0 2 17 0 0 0 0 80 0 0 Chickpeas 0 0 0 0 0 10 0 0 0 0 0 0 Lentils 5 0 0 0 0 0 0 0 0 0 0 0 Vigna 0 0 5 0 0 0 0 0 0 0 0 0 Strawberries 0 0 0 0 0 0 0 0 0 0 30 0 Tomatoes 0 5 5 0 0 5 0 0 0 0 0 0 Onion 10 0 10 0 0 0 0 0 0 0 0 0 Garlic 0 5 0 0 0 0 0 0 0 0 0 0 Chili pepper 2 2 2 0 0 0 0 0 0 0 0 0 Quail 0 60 0 0 0 0 0 0 0 0 0 0 Pork 0 0 5 85 0 0 0 0 0 0 0 0 Tilapia 65 0 0 0 0 0 0 0 0 0 0 0 Goat’s milk 0 0 0 0 0 0 0 0 600 0 0 0 Sugar 0 0 0 0 2 5 7 0 0 7 7 0 Masses of dishes, g 400 201 142 139 219 50 107 218 600 328 137 100 Thus, the daily iron intake (23 mg) calculated in this model is probably not critical. If we consider the con- sumption of iron in relation to its available form, the NASA requirement looks more realistic. The upper permissible level of daily intake of phos- phorus is not established. Therefore, it is likely that the daily consumption of phosphorus calculated in this work (2685 mg against the normative 1800 mg) can be consid- ered unacceptable after setting an upper limit on the daily intake of phosphorus. To prevent the excess of phosphorus and saturated fat in the diets, we can recommend the selection of ingredi- ents with the reduced content of these nutrients. Defi- ciency of pantothenic acid can be overcome through the use of vitamin products and / or vitamin preparations. Conclusion. We described the algorithm for calculat- ing the daily diet in BLSS intended for space purposes using the masses of ingredients in dishes as independent variables. We simulated the menu in the Excel environ- ment using the public OpenSolver add-in. The distinctive features of the model are: - the use of the free-for-all add-in of OpenSolver; - the ability to vary the masses of components in dishes. The calculation of the daily diet presented in this study is demonstrative in nature, since it does not take into account the compatibility of ingredients and the taste of the dishes. The prognosis of the antioxidant activity of the daily menu will be of practical significance when the corresponding dietary standard for cosmonauts is deter- mined. We see the prospects for further investigation of the problem in the development of recipes and the expansion of the variety of dishes intended for the use by cosmonauts in BLSS, taking into account individual preferences. In addition, the results of the work provide a basis for expanding the diversity of plants species included in the phototrophic link of closed ecosystems and planning stud- ies to assess the tolerance of the cenosis of these plants to environmental factors in such ecosystems.

About the authors

V. S. Kovalev

Institute of Biophysics SB RAS

Email: kovalev49@mail.ru
50/50, Akademgorodok, Krasnoyarsk, 660036, Russian Federation

N. S. Manukovsky

Reshetnev Siberian State University of Science and Technologies; Institute of Biophysics SB RAS

31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation; 50/50, Akademgorodok, Krasnoyarsk, 660036, Russian Federation

A. A. Tikhomirov

Reshetnev Siberian State University of Science and Technologies; Institute of Biophysics SB RAS

31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation; 50/50, Akademgorodok, Krasnoyarsk, 660036, Russian Federation

References

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