Linear model of nitrogen balance and examination of the nature of true metabolisable energy and its nitrogen corrected form

1. The nature of nitrogen (N) corrected true metabolisable energy (TMEN) was derived using a linear model of N balance, constructed from the relationship between excreted and ingested N. 2. TME was described in terms of a regression line, formed from 'fed' points relating energy voided to energy ingested (GE), as GE- (afed + bGE)+afast. On assignment of theoretical excreta and ingested energy components, a deviation from conceptual metabolisable energy (MEc), equal to the difference between afed and afast, was established and attributed to metabolic urinary energy (UmE). 3. The N balance model is based on the form of relationship between N excreted and N ingested (Nl) that exhibits a linear deviation at 'initial' rates of N ingestion. The model postulates the following: The deviation is the result of a sparing effect of ingested N on the N component of UmE, viz. metabolic urinary N (UmN); The magnitude of UmN, through 'initial' values of fed N, is described by an intercept component, a a slope quantity, -(bnr-bna) Nl, where bNna and bnr are respectively the slopes of N excretion through 'initial' and 'subsequent' rates of ingested food N; The magnitude of the deviation from zero nitrogen balance (ZNB) through 'initial' and 'subsequent' rates of ingested N is the sum of the previous terms and aNm -(1-bNr) Nl, where aNm is the intercept component representing maintenance losses of N at fasting and (1- bNr) NI is the quantity of fed N retained to replace maintenance N loss. 4. Application of the appropriate energetic forms of UmN and aNm, viz. Et aNp -Et (bNr-bNna) NI and EuaNm, to the expression for obtaining TME, demonstrated that TME exceeded MEc by the quantities Et (bNr-bNna) NI and EtaNp, for test food intakes resulting in 'initial' and 'subsequent' rates of food N, respectively. 5. Application of appropriate energetic components of the model to simulate correction of TME to ZNB, demonstrated TMEZNB to be a biased quantity, deviating from MEc by the amount -Eu (1-bnr) NI or expressed as an excreta energy slope component, bEu(1-bNrNI/GE)GE where Eu is an appropriate energy coefficient. An alternative perspective is that ZNB correction removes the energetic form of UmN as a source of bias, but introduces one related to EuaNm. Its nature may be perceived by regarding TME as a function of a regression line relating energy excreted (EE) to energy ingested that has been corrected for UmN energetic bias and is pivoting on a fulcrum vertically aligned with the position of ZNB on the GE (x) axis. The regression line rotates anti-clockwise in response to ZNB correction by an amount equal to the magnitude of EuaNm measured on the EE (y) axis from the point of interception. 6. The study identified processes that may be employed to remove bias and improve precision of TME.