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

Abstract

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.

Figure 1

Protocol for the Minnesota human starvation study. After a 12 wk control period with balanced energy intake and expenditure, energy intake (closed circles) was reduced to about 1600 kcal/d and adjusted so that the 32 subjects would achieve a 24% loss of body mass (open diamonds) during the next 24 wks. Arrows indicate body mass at weeks C12 (end of control period), and after 12 and 24 weeks (S12 and S24) of energy restriction when most data were collected. During the recovery phase, 4 groups were fed different amounts of energy at increasing levels. The bar at the bottom indicates the control period (unfilled), starvation (hashed) and recovery (stippled).

Figure 2

Model behavior compared to predictive equation used by Keys. Upper panel shows observed values for body mass (closed diamonds), values predicted by the Keys equation (open triangles), and results of fitting the data to a monoexponential approach to steady state (open squares). Lower panel shows solutions for fat mass (open triangles), fat free mass (open circles), calculated body mass (open squares) and observed body mass (filled diamonds) over 24 weeks of partial fasting.

Figure 3

Observed and theoretical values for study endpoints. Top panel shows results for fitting data for BMI (squares) and waist girth (circles) to a monoexponential model for approach to steady state. Bottom panel shows results for resting energy expenditure (REE, triangles) and the Harvard work test (diamonds). The filled symbols represent the observed group means for each endpoint.

Figure 4

Change in weight for a relatively lean subject compared to an overweight subject. Comparisons between subjects were made based on best fit of the model to data from weeks C12 through S24 and then projecting through the midpoint of week 72. During the 24 weeks of the study, the model fit the data for subjects 5 and 127 with R² of 0.998 and 0.996, respectively.