The factorial approach derives nutrient requirements as the sum of two (in the case of parenteral requirements) or three components (in the case of enteral requirements). The largest component, and the component that changes most with body size, is the growth component, i.e., nutrient accretion. The other components are inevitable losses and, in the case of enteral nutrient requirements, efficiency of nutrient absorption.
Determination of the growth component requires knowledge of nutrient accretion with 'normal' growth. Because it is generally agreed that postnatal growth should 'approximate the in utero growth of a normal fetus' , the fetus serves as the model from which nutrient accretion is derived. Beginning in the 19th century, the body composition of stillborn infants and infants deceased soon after birth, including premature infants, has been analyzed by a number of investigators. Sparks  and Forbes [7, 8] have provided comprehensive summaries of the chemical analysis of some 160 fetuses. Gestational age was not always available, but because most body constituents change as a function of body size (the notable exception being body fat ), the data can be used to derive accretion rates even when gestational age is not explicitly known [6, 7]. Ziegler et al.  used only data from fetuses with known gesta-tional age for the construction of a 'reference fetus' and derivation of fetal accretion rates. In spite of the differences in approaches (i.e., size vs. age) to the establishment of fetal body composition, nutrient accretion rates derived by the different approaches [6, 7, 9] are actually quite similar . The fetal accretion data presented in table 1 represent a synthesis of the different approaches [6, 7, 9] in combination with contemporary fetal growth data . The data represent our current best estimates of nutrient accretion. In the case of protein, accretion rates shown in table 1 are corrected for presumed inefficiency (90%) of the conversion of dietary protein to body protein. In the case of energy, the accretion value includes the energy cost of growth, estimated by Micheli et al.  at 10kcal/kg/day.
Inevitable losses of protein (nitrogen) occur through desquamation of skin and as urinary nitrogen excretion mostly in the form of urea (desquamation of intestinal cells is accounted for in the correction for efficiency of intestinal absorption). Based on dermal nitrogen losses determined by Snyderman et al. , we have assumed average dermal losses of 27mg/kg/day. Based on published data [14, 15] we have assumed urinary nitrogen losses to be 133mg/kg/ day. Energy losses comprise resting energy expenditure plus an allowance for miscellaneous expenditures, e.g., occasional cold exposure and physical activity. Based on recent studies [16-18] we have assumed resting expenditure to be 45kcal/kg/day in infants weighing <900g and 50kcal/kg/day in larger infants. Miscellaneous energy expenditures have been assumed to be 15kcal/kg/day in infants under 1,200 g and 20kcal/kg/day in larger infants.
Table 1. Estimated nutrient intakes needed to achieve fetal weight gain
Body weight, g
500-700 700-900 900- 1,200- 1,500- 1,8001,200 1,500 1,800 2,200
Fetal weight gaina g/day 13
Protein (Nx6.25), g Inevitable 1.0
(accretion)c Required intake
Energy, kcal Loss Resting expenditure Miscellaneous expenditure Growth
(accretion)f Required intake Parenterald Enteral8
Because nutrient needs are closely related to body weight and weight gain, the nutrient needs apply to all postnatal ages. All values are per kg per day except where noted [modified from 18].
aBased on data of Kramer et al. .
bUrinary nitrogen loss of 133mg/kg/day [14, 15] and dermal loss of 27 mg/kg/day . cIncludes correction for 90% efficiency of conversion from dietary to body protein. dSum of loss and accretion.
eSame as parenteral but assuming 88% absorption of dietary protein. fEnergy accretion plus 10kcal/kg/day cost of growth. gAssuming 85% absorption of dietary energy.
Parenteral requirements for protein and energy (table 1) are calculated as the sum of accretion plus inevitable losses. Enteral requirements are calculated as accretion plus inevitable losses corrected for efficiency of absorption, assumed to be 88% for protein and 85% for energy. Requirements (per kg of
Table 2. Requirements for major minerals and electrolytes determined by the factorial method, listed by body weight
1,500-2,000g accretion requirement accretion requirement accretion requirement
body weight per day) are presented in table 1 in relation to body weight rather than gestational age because requirements are more closely related to body weight than to gestational age.
Although absolute fetal weight gain (g/day) increases with increasing body size, the fractional fetal weight gain (g/kg/day), as shown in table 1, decreases markedly as a function of weight. In spite of this decrease in the fractional growth rate, the rate of protein accretion remains constant up to a weight of 1,200 g. This is so because the protein content of fat-free body mass increases with increasing body size/age, and this increase offsets the effect of the decrease in fractional growth rate on protein accretion. Energy accretion, on the other hand, increases with increasing body weight. This is due to a marked increase in body fat content, which more than counteracts the decrease in fractional weight gain.
Whereas estimates of requirements for protein are quite firm, estimates of energy requirements are more uncertain. This is in part so because there is a paucity of data regarding resting energy expenditure of small premature infants and, especially, nonresting energy expenditure. Uncertainty also derives from the fact that body fat accumulation of the preterm infant may deviate from that of the fetus without apparent ill consequences for the premature infant. Available energy seems to be prioritized to meeting ongoing needs and is deposited as fat only after all other needs have been met.
Requirements for major minerals and electrolytes derived by the factorial method are summarized in table 2. Although the dermal and urinary losses (not shown in table 2) used in deriving these requirements are based on data from the literature , there is considerable uncertainty regarding the minimal urinary losses of electrolytes and of P by premature infants. Also, there is uncertainty concerning the efficiency of intestinal absorption of calcium, which is influenced by multiple dietary and other factors, and there is uncertainty with regard to the amount of bone mineral (Ca, P) that must be deposited in order to maintain bone health. It has become evident that accretion of bone mineral at somewhat less than the fetal rate can be compatible with good bone health, but it is impossible to translate such observations into quantitative estimates of the amounts of dietary calcium and phosphorus needed to maintain bone health.
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