Total, average and marginal rates of basal heat production during human growth

Michael R. Murphy, Bruce M. Hannon

Research output: Contribution to journalArticlepeer-review


Our goal was to examine how total, average (heat production rate per unit mass) and marginal (the increase in the heat production rate per unit increase in mass) rates of basal heat production changed as mass increased in growing humans. Specifically, our hypotheses were that the marginal basal heat production rate did not decrease monotonically as humans grew; and that an energetically optimal mass, one at which the average basal heat production rate of a growing human was minimal, existed. Marginal rates of heat production were estimated and six potential models to describe the effect of mass during human growth on basal heat production rate were evaluated using a large, meticulously curated, dataset from the literature. Marginal rates of heat production were quadratically related to body mass during growth; they declined initially, reached a minimum, and then increased. This suggested that the relationship between basal heat production rate and mass was cubic. Of the six potential models evaluated, a three-parameter cubic polynomial best described the data. Marginal rates of heat production were minimal for 56-kg females and 62-kg males. Basal heat production rates per unit mass of a growing human were minimal (i.e., energetically optimal) for 83- kg females and 93-kg males; the average masses of U.S. adults have been increasing and approaching these optima over the last 60 yr.

Original languageEnglish (US)
Pages (from-to)6806-6818
Number of pages13
JournalMathematical Biosciences and Engineering
Issue number5
StatePublished - 2021


  • basal metabolism
  • body mass
  • energy metabolism
  • heat production rate
  • optimal size

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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