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Whey protein isolate (WPI) was donated by Davisco Food International, Inc. (USA). Maltodextrin (DE 15) was kindly donated by Productos de Maíz SA (Argentina). Low density sodium alginate (SA) was provided by Cargill (Argentina) (MW 135 kDa). Flaxseed oil was purchased from Sigma Aldrich (USA) and it was used without further purification. According to literature, -linolenic acid content of flaxseed oil is within the range of 48-57% of total fatty acids 14,15,16. 2.2. Microcapsule formation from oil-in-water multilayer emulsions Preparation of multilayer emulsion was done by the procedure described in previous work 12. Briefly, a primary emulsion was obtained by blending 20% (w/w) oil phase with 80% (w/w) aqueous phase having WPI-MD dispersions using a high-speed blender (Waring Blender, USA) for 2 min at the highest speed (24000 rpm), followed by a sonication step (75% Amplitude, 150 s) performed by a 20 KHz ultrasonic probe with 13 mm diameter tip (Sonics & Materials, USA). Samples were placed in an ice bath to avoid overheating during sonication, and the final temperature of primary emulsions was 25°C. These fixed conditions for ultrasonic processing were previously chosen on the basis of preliminary experiments where different combinations of wave amplitudes (AMP) and times of sonication were assessed, with the aim to produce droplet sizes in the range of 1 m to enhance emulsion stability against creaming and coalescence mechanisms. Primary emulsion was then diluted by adding sodium alginate (SA) dispersion and adjusting pH to 5 with HCl 2N to form secondary emulsion, with final composition presented in Table 1. These %EE = TO (g/100g powder)-FO (g/100g powder) / TO (g/100g powder) x 100 Eq. 1 2.3.2. Water activity Water activity of powdered microcapsules was determined at ambient temperature (25°C) by an Aqualab system (Washington, USA). Samples were measured in triplicate. 2.3.3. Morpholigical analysis The microstructure of powdered samples was investigated by scanning electron microscopy (JSM-35C, JEOL, Japan). Samples were placed on the SEM stubs using a two-sided adhesive tape, and were then coated with gold using a magnetron sputter coater. Coated samples were analyzed at an accelerating voltage of 20 kV. 2.4. Oxidative stability of flaxseed oil 2.4.1. Primary oxidation compounds Lipid hydroperoxides were determined weekly using a method adapted from Shanta and Decker 19 (IDF method) which comprised an additional extraction step in which 0.3 mL of reconstituted emulsion was added to a mixture of 1.5 mL isooctane/isopropanol (3:2 v/v) followed by vortexing three times for 10 s each and centrifugation (3400 g, 5 min). Next, 0.2 mL of the upper

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The mathematical model developed can help to find proper particle features to reach specific delivery rates in the animals. This not only save time, money and effort but also minimized experimentation with animals which is desired from an ethical point of view.