Tri-axial dynamic acceleration as a proxy for animal energy expenditure; should we be summing values or calculating the vector?

Abstract

Dynamic body acceleration (DBA) has been used as a proxy for energy expenditure in logger-equipped animals, with researchers summing the acceleration (overall dynamic body acceleration--ODBA) from the three orthogonal axes of devices. The vector of the dynamic body acceleration (VeDBA) may be a better proxy so this study compared ODBA and VeDBA as proxies for rate of oxygen consumption using humans and 6 other species. Twenty-one humans on a treadmill ran at different speeds while equipped with two loggers, one in a straight orientation and the other skewed, while rate of oxygen consumption (VO2) was recorded. Similar data were obtained from animals but using only one (straight) logger. In humans, both ODBA and VeDBA were good proxies for VO2 with all r(2) values exceeding 0.88, although ODBA accounted for slightly but significantly more of the variation in VO2 than did VeDBA (P<0.03). There were no significant differences between ODBA and VeDBA in terms of the change in VO2 estimated by the acceleration data in a simulated situation of the logger being mounted straight but then becoming skewed (P = 0.744). In the animal study, ODBA and VeDBA were again good proxies for VO2 with all r(2) values exceeding 0.70 although, again, ODBA accounted for slightly, but significantly, more of the variation in VO2 than did VeDBA (P<0.03). The simultaneous contraction of muscles, inserted variously for limb stability, may produce muscle oxygen use that at least partially equates with summing components to derive DBA. Thus, a vectorial summation to derive DBA cannot be assumed to be the more 'correct' calculation. However, although within the limitations of our simple study, ODBA appears a marginally better proxy for VO2. In the unusual situation where researchers are unable to guarantee at least reasonably consistent device orientation, they should use VeDBA as a proxy for VO2.

Figure 1. Heave (continuous line), sway (dotted line) and surge (dashed line) acceleration axes displayed graphically over one stride (from each leg) during walking (i) and running (ii).

Figure 2. Instantaneous ODBA plotted against VeDBA using all data from a participant recorded during a full max test.

In this example, as with all other participants, the relationship between ODBA and VeDBA was highly significant (VeDBA = 0.014+0.6418 ODBA, r² = 0.987, P<0.001).

Figure 3. Relationship between mean ODBA and mean VeDBA (means taken for each running speed) for a test participant during a max test.

Only data during the period when the participant did not exceed the ventilatory threshold (for definition see text) are included. as with all other participants, the relationship between ODBA and VeDBA was highly significant (VeDBA = 0.014+0.6418 ODBA, r² = 0.987, P<0.001).

Figure 4. Dynamic body accelerations (ODBA – circles, and VeDBA –crosses) from straight- versus skew-mounted accelerometers (for details see text).

Each point denotes a mean value derived from a three-minute trial of a participant moving at one particular speed below the lactate threshold. Data from all participants are included.

Figure 5. An example plot of uptake against ODBA (black circles) and VeDBA (grey triangles) over the duration of the trial following removal of the points above the participant's anaerobic threshold.

Figure 6. Schematic representation of a movement arc (curved arrow) elicited by one bone (light grey) with respect to another and brought about by contraction of multiple muscles (dark grey) with varying forces (F) with differing angles of insertion (θ).

Figure 7. Predicted difference between straight- and skew-mounted ODBA derived from recordings on a tri-axial accelerometer subjected to equal acceleration in the heave, surge and sway axes as a function of pitch, roll and yaw differences between straight and skew.

Contour lines show 2.5% intervals.