Estimating food sets in view of NASA's nutrition requirements for long-duration missions

Prior to making a space menu, it is necessary to estimate the suitability of food candidates (FCs) intended for Bioregenerative Life Support Systems. In our computer model FCs were represented as column vectors. Each column vector member represented the mass of nutrients in 100 g of FCs. A set of column vectors formed the "nutrient-FCs" matrix with the size 30x46, where "30" is the number of monitored nutrients and "46" is the number of FCs. FCs masses were considered as independent continuous variables with lower and upper bounds. FCs were programmatically selected from "nutrient-FCs" matrix according to the nutritional requirements stated in the NASA Constellation Program (C_P), document 70024 "Human-Systems Integration Requirements", section 3.5.1.3.1 (Cooper et al., 2011). Calculations were carried out in Matlab using the knitromatlab function. The best fit to the NASA's nutrition requirements was obtained after selecting nineteen FCs, i.e.: sodium chloride, water, rice, white potato, beet, cabbage, squash, sufflower oil, soybeans, chickpeas, cowpea, strawberries, onion, garlic, poultry, snail, tilapia, goat milk, and sugar. The total calculated masses of magnesium, potassium, thiamin, riboflavin, niacin, vitamin B12, vitamin E, vitamin K and omega 6 fatty acids in the set of selected FCs exceeded the corresponding normative daily intakes. However, we could not approve these results because the upper bounds for these nutrients are not established. The calculated masses of iron and phosphorus also exceeded the upper bounds designated for these nutrients. Conversely, we revealed the deficiency of pantothenic acid and vitamin D. Changing the number of selected FCs within 10-46 did not eliminate the nutrient misbalances. Implementation of NASA's nutrition requirement "2/3 of total protein should be in the form of animal protein" was a sufficient condition to support the scores above 100 for all indispensable amino acids.