Biomechanical consequences of scaling

Abstract

SUMMARY To function over a lifetime of use, materials and structures must be designed to have sufficient factors of safety to avoid failure. Vertebrates are generally built from materials having similar properties. Safety factors are most commonly calculated based on the ratio of a structure's failure stress to its peak operating stress. However, yield stress is a more likely limit, and work of fracture relative to energy absorption is likely the most relevant measure of a structure's safety factor, particularly under impact loading conditions characteristic of locomotion. Yet, it is also the most difficult to obtain. For repeated loading, fatigue damage and eventual failure may be critical to the design of biological structures and will result in lower safety factors. Although area:volume scaling predicts that stresses will increase with size, interspecific comparisons of mammals and birds show that skeletal allometry is modest, with most groups scaling(l∝d0.89) closer to geometric similarity(isometry: l ∝d1.0) than to elastic similarity (l ∝d0.67) or stress similarity(l ∝d0.5). To maintain similar peak bone and muscle stresses, terrestrial mammals change posture when running, with larger mammals becoming more erect. More erect limbs increases their limb muscle mechanical advantage (EMA) or ratio of ground impulse to muscle impulse(r/R=∫G/∫Fm). The increase in limb EMA with body weight (∝W0.25) allows larger mammals to match changes in bone and muscle area (∝W0.72-0.80) to changes in muscle force generating requirements (∝W0.75), keeping bone and muscle stresses fairly constant across a size range 0.04-300 kg. Above this size, extremely large mammals exhibit more pronounced skeletal allometry and reduced locomotor ability. Patterns of ontogenetic scaling during skeletal growth need not follow broader interspecific scaling patterns. Instead,negative allometric growth (becoming more slender) is often observed and may relate to maturation of the skeleton's properties or the need for younger animals to move at faster speeds compared with adults. In contrast to bone and muscle stress patterns, selection for uniform safety factors in tendons does not appear to occur. In addition to providing elastic energy savings, tendons transmit force for control of motion of more distal limb segments. Their role in elastic savings requires that some tendons operate at high stresses (and strains), which compromises their safety factor. Other `low stress' tendons have larger safety factors, indicating that their primary design is for stiffness to reduce the amount of stretch that their muscles must overcome when contracting to control movement.

Longitudinal gait development and variability of growing pigs reared on three different floor types

“…Yet the ranges of motion in both stance and swing phases decreased over time. Increased flexion during walking may be correlated to factors such as leg length and walking speed (Back et al, 1994;Biewener, 2005), but this was generally not the case for the pigs in this study. However, BW showed a consistent trend for a negative correlation with the elbow swing range of motion within captures among all pigs.…”

The effect of body size on the wing movements of pteropodid bats, with insights into thrust and lift production

“…These, and many other important aspects of an organism's life, scale predictably with body mass, according to fundamental form-function relationships (Brown and West, 2000;Dial et al, 2008). The influence of body size on locomotion is no less striking, and biomechanical investigations have revealed that just as body shape changes with size, so too do locomotor kinematics (Biewener, 1983;Biewener, 2005;Heglund and Taylor, 1988).…”

The architectural and functional specifications of intrinsic muscles of the fore limb of the Egyptian Baladi goats (Capra hircus)

“…The PCSA was estimated using the following equation. PCSA = Volume (mass/density) / fiber length While the maximal isometric force was estimated using this equation Force = PCSA * maximal isometric stress According to Biewener (2005), to overcome the difficulties associated with comparing anatomical measurements between muscles that have been removed from geometrically similar animals but vary in size, mass should be scaled directly to body mass, length should be scaled directly to (body mass) 1/3 and PCSA should scaled to (body mass) 2/3 . The raw data were normalized by dividing muscle mass by body mass, mean fiber length by (body mass) 1/3 and PCSA by (body mass) 2/3 (Payne et al, 2006).…”