Modeling transitions in body composition: the approach to steady state for anthropometric measures and physiological functions in the Minnesota human starvation study

Background

This study evaluated whether the changes in several anthropometric and functional measures during caloric restriction combined with walking and treadmill exercise would fit a simple model of approach to steady state (a plateau) that can be solved using spreadsheet software (Microsoft Excel^®). We hypothesized that transitions in waist girth and several body compartments would fit a simple exponential model that approaches a stable steady-state.

Methods

The model (an equation) was applied to outcomes reported in the Minnesota starvation experiment using Microsoft Excel's Solver^® function to derive rate parameters (k) and projected steady state values. However, data for most end-points were available only at t = 0, 12 and 24 weeks of caloric restriction. Therefore, we derived 2 new equations that enable model solutions to be calculated from 3 equally spaced data points.

Results

For the group of male subjects in the Minnesota study, body mass declined with a first order rate constant of about 0.079 wk^-1. The fractional rate of loss of fat free mass, which includes components that remained almost constant during starvation, was 0.064 wk^-1, compared to a rate of loss of fat mass of 0.103 wk^-1. The rate of loss of abdominal fat, as exemplified by the change in the waist girth, was 0.213 wk^-1.On average, 0.77 kg was lost per cm of waist girth. Other girths showed rates of loss between 0.085 and 0.131 wk^-1. Resting energy expenditure (REE) declined at 0.131 wk^-1. Changes in heart volume, hand strength, work capacity and N excretion showed rates of loss in the same range. The group of 32 subjects was close to steady state or had already reached steady state for the variables under consideration at the end of semi-starvation.

Conclusion

When energy intake is changed to new, relatively constant levels, while physical activity is maintained, changes in several anthropometric and physiological measures can be modeled as an exponential approach to steady state using software that is widely available. The 3 point method for parameter estimation provides a criterion for testing whether change in a variable can be usefully modelled with exponential kinetics within the time range for which data are available.