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We describe a mathematical model of digestion in the small intestine. The main interest of our work is to consider simultaneously the different aspects of digestion i.e. transport of the bolus all along the intestine, feedstuffs degradation according to the enzymes and local physical conditions, and nutrients absorption. A system of coupled ordinary differential equations is used to model these phenomena. The major unknowns of this system are the position of the bolus and its composition. This system of equations is solved numerically. We present several numerical computations for the degradation, absorption and transport of the bolus with acceptable accuracy regarding the overall behavior of the model and also when challenged versus experimental data. The main feature and interest of this model are its genericity. Even if we are at an early stage of development, our approach can be adapted to deal with contrasted feedstuffs in nonruminant animal to predict the composition and velocity of bolus in the small intestine.

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The experiment was conducted to evaluate the sparing effect of microbial phytase on the need for dietary zinc supplementation in chicks. A maize-soya-bean meal basal diet, containing 33 mg of zinc and 16 mg of copper per kg, supplemented with 0, 6, 12, 18, 24, 30 or 60 mg of zinc as sulphate per kg or with 250, 500, 750 or 1000 units (FTU) of microbial phytase (3-phytase from Aspergillus niger, Natuphos R ) per kg was given to 1-day-old chicks for 20 days. Sixteen chicks placed in individual cages were assigned to each diet except the unsupplemented basal diet which was assigned to 32 cages. Actual range of phytase supplementation was 280 to 850 FTU per kg diet. Growth performance was not affected by microbial phytase. Chicks given the unsupplemented basal diet and the basal diet supplemented with 60 mg of zinc per kg displayed similar performance. Bone weight, bone ash, liver weight and liver dry matter were independent (P . 0.1) of zinc and phytase supplementations. Plasma, bone and liver zinc concentrations increased linearly (P , 0.001) and quadratically (P , 0.001; P , 0.001 and P , 0.05, respectively) with zinc added. Plasma zinc tended to increase linearly (P 5 0.07) and bone zinc increased linearly (P , 0.01) with phytase added but no quadratic response was detected (P . 0.1). Liver zinc was unresponsive to phytase added (P . 0.1). Liver copper decreased linearly (P , 0.001) and quadratically (P , 0.01) with zinc supplementation. Mathematical functions were fitted to the responses of plasma and bone zinc to zinc and phytase added and used to calculate zinc equivalency values of phytase. The models included a linear plateau response to zinc added and a linear response to phytase added. In diets without phytase, plasma and bone zinc concentrations were maximised for a dietary zinc concentration of 55 and 51 mg/kg, respectively. Over the range of 280 to 850 FTU, 100 FTU was equivalent to 1 mg of zinc as sulphate. Consequently, in a maize-soya-bean meal chicken diet formulated to contain 60 mg zinc per kg, zinc ingested, and in turn, zinc excreted may be reduced by around 10% if the diet contains 500 FTU as Natuphos R per kg.

Pollution relative to phosphorus excretion in poultry manure as well as the soaring prices of phosphate, a non-renewable resource, remain of major importance. Thus, a good understanding of bird response regarding dietary phosphorus (P) is a prerequisite to optimise the utilisation of this essential element in broiler diets. A database built from 15 experiments with 203 treatments was used to predict the response of 21-day-old broilers to dietary non-phytate P (NPP), taking into account the main factors of variation, calcium (Ca) and microbial phytase derived from Aspergillus niger, in terms of average daily feed intake (ADFI), average daily gain (ADG), gain to feed (G:F) and tibia ash concentration. All criteria evolve linearly ( P , 0.001) and quadratically ( P , 0.001) with dietary NPP concentration. Dietary Ca affected the intercept and linear component for ADG ( P , 0.01), G:F ( P , 0.05) and tibia ash concentration ( P , 0.001), whereas for ADFI, it affected only the intercept ( P , 0.01). Microbial phytase addition impacted on the intercept, the linear and the quadratic coefficient for ADFI ( P , 0.01), ADG ( P , 0.001) and G:F ( P , 0.05), and on the intercept and the linear component ( P , 0.001) for tibia ash concentration. An evaluation of these models was then performed on a database built from 28 experiments and 255 treatments that were not used to perform the models. Results showed that ADFI, ADG and Tibia ash concentration were predicted fairly well (slope and intercept did not deviate from 0 to 1, respectively), whereas this was not the case for G:F. The increase in dietary Ca concentration aggravated P deficiency for all criteria while phytase addition had a positive effect. The more P deficiency was marked, the more the bird response to ADFI, ADG, G:F and tibia ash concentration was exacerbated. It must also be considered that even if the decrease in dietary Ca may improve P utilisation, it could in turn become limiting for bone mineralisation. In conclusion, this meta-analysis provides ways to reduce dietary P in broiler diets without impairing performance, taking into account dietary Ca and microbial phytase.