Allometric Analysis of Physical Performance Measures in Older Adults

Background and Purpose. Body mass is a confounding variable in human performance, and adjusting physical performance measures for body mass differences would allow meaningful individual and group comparisons. The purpose of this study was to allometrically determine the relationship between body mass and handgrip and ankle dorsiflexor performance on the Timed “Up & Go” Test (TUGT). Subjects. One hundred thirty-one subjects (33 male and 98 female) participated. Methods. All physical performance measures were adjusted for the influence of body mass, sex, and age using an allometric scaling procedure. Results. For handgrip force, the body mass exponent from allometric analysis was 0.63. For the TUGT, the body mass exponent was 0.073. For ankle dorsiflexor force and torque, the body mass exponents were 0.82 and 0.91, respectively. Discussion and Conclusion. The body mass exponents for handgrip force and the TUGT agree with previous clinical data and theoretical expectations. Studies investigating normalized handgrip force in older adults should consider an allometric scaling approach. [Pua YH. Allometric analysis of physical performance measures in older adults. Phys Ther. 2006;86:1263–1270.]

CHAOS AND STOCHASTICITY IN DETERMINISTICALLY GENERATED MULTIFRACTAL MEASURES

Successful usage of a large family of deterministically generated measures to model complex nonlinear phenomena (e.g. rainfall, turbulence and groundwater contaminant transport) has been reported recently.1–7 As these measures, generated as derived distributions of multifractal measures via fractal interpolating functions (FIF), i.e. the fractal-multifractal (FM) approach, have been found to share the inherent character of natural sets, the present study further investigates their dynamical (chaotic or stochastic) properties. It is shown, through a variety of examples and via the use of power spectrum, mass exponents and false nearest neighbors in the state-space, that the FM approach indeed generates deterministic measures whose behavior (depending on their parameters) may be classified as low-dimensional and chaotic or as high-dimensional and stochastic. These results suggest the general suitability of the FM approach for understanding and modeling nonlinear natural phenomena.

Allometric scaling relationships of jumping performance in the striped marsh frog Limnodynastes peronii

We constructed a force platform to investigate the scaling relationships of the detailed dynamics of jumping performance in striped marsh frogs (Limnodynastes peronii). Data were used to test between two alternative models that describe the scaling of anuran jumping performance; Hill's model, which predicts mass- independence of jump distance, and Marsh's model, which predicts that jump distance increases as M(0.2), where M is body mass. From the force platform, scaling relationships were calculated for maximum jumping force (F(max)), acceleration, take-off velocity (U(max)), mass-specific jumping power (P(max)), total jumping distance (D(J)) and total contact time for 75 L. peronii weighing between 2.9 and 38. 4 g. F(max) was positively correlated with body mass and was described by the equation F(max)=0.16M(0.61), while P(max) decreased significantly with body mass and was described by the equation P(max)=347M(−)(0.46). Both D(J) and U(max) were mass-independent over the post-metamorph size range, and thus more closely resembled Hill's model for the scaling of locomotion. We also examined the scaling relationships of jumping performance in metamorph L. peronii by recording the maximum jump distance of 39 animals weighing between 0.19 and 0.58 g. In contrast to the post-metamorphic L. peronii, D(J) and U(max) were highly dependent on body mass in metamorphs and were described by the equations D(J)=38M(0.53) and U(max)=1.82M(0.23), respectively. Neither model for the scaling of anuran jumping performance resembled data from metamorph L. peronii. Although the hindlimbs of post-metamorphic L. peronii scaled geometrically (body mass exponent approximately 0.33), the hindlimbs of metamorphs showed greater proportional increases with body mass (mass exponents of 0.41-0.42).

Multifractal behaviour of river networks

A numerical multifractal analysis was performed for five river networks extracted from Calabrian natural basins represented on 1:25000 topographic sheets. The spectrum of generalised fractal dimensions, D(q), and the sequence of mass exponents, τ(q), were obtained using an efficient generalised box-counting algorithm. The multi-fractal spectrum, f(α), was deduced with a Legendre transform. Results show that the nature of the river networks analysed is multifractal, with support dimensions, D(0), ranging between 1.76 and 1.89. The importance of the specific number of digitised points is underlined, in order to accurately define, the geometry of river networks through a direct generalised box-counting measure that is not influenced by their topology. The algorithm was also applied to a square portion of the Trionto river network to investigate border effects. Results confirm the multifractal behaviour, but with D(0) = 2. Finally, some open mathematical problems related to the assessment of the box-counting dimension are discussed. Keywords: River networks; measures; multifractal spectrum

Cardiorespiratory Responses of Trained Boys to Treadmill and Arm Ergometry: Effect of Training Specificity

The purpose of this study was to examine the maximal cardiorespiratory responses of trained adolescent male swimmers (SWM, N = 18), soccer players (SOC, N = 18), and moderately active reference subjects (CON, N = 16) to treadmill running (TRD) and arm ergometry (ARM). Mean values (±SD)for skeletal age were similar among the three groups (12.5± 1.9, 12.7 ± 1.1, and 12.5 ± 1.6 years, for the SWM, SOC, and CON, respectively). Allometric scaling procedures, relating VO2max and body mass, were used and mass exponents of .80 and .74 were identified for TRD and ARM data, respectively. During TRD testing SOC attained significantly higher VO2max values when expressed in ml · kg−1 · min−1, or ml · kg−0.80 · min−1 than the other two groups. However, during ARM testing, the SWM achieved significantly higher VO2peak values (ml · kg−0.74 · min−1 and scaled to arm-CSA) than SOC. The ratio of ARM-VAT to TRD-VAT was significantly higher in SWM (50.1± 9%) compared to SOC (41.2±5%), or CON (41.9 ± 6%).

U(1) Lattice Gauge Theory and N=2 Supersymmetric Yang–Mills Theory

We discuss the physics of four-dimensional compact U(1) lattice gauge theory from the point of view of softly broken N=2 supersymmetric SU(2) Yang–Mills theory. We provide arguments in favor of (pseudo-)critical mass exponents 1/3, 5/11 and 1/2, in agreement with the values observed in the computer simulations. We also show that the J CP assignment of some of the lowest lying states can be naturally explained.

Allometry of muscle, tendon, and elastic energy storage capacity in mammals

This paper considers the structural properties of muscle-tendon units in the hindlimbs of mammals as a function of body mass. Morphometric analysis of the ankle extensors, digital flexors, and digital extensors from 35 quadrupedal species, ranging in body mass from 0.04 to 545 kg, was carried out. Tendon dimensions scale nearly isometrically, as does muscle mass. The negative allometry of muscle fiber length results in positive allometric scaling of muscle cross-sectional areas in all but digital extensors. Maximum muscle forces are predicted to increase allometrically, with mass exponents as high as 0.91 in the plantaris, but nearly isometrically (0.69) in the digital extensors. Thus the maximum amount of stress a tendon may experience in vivo, as indicated by the ratio of muscle and tendon cross-sectional areas, increases with body mass in digital flexors and ankle extensors. Consequently, the capacity for elastic energy storage scales with positive allometry in these tendons but is isometric in the digital extensors, which probably do not function as springs in normal locomotion. These results suggest that the springlike tendons of large mammals can potentially store more elastic strain energy than those of smaller mammals because their disproportionately stronger muscles can impose higher tendon stresses.

MULTIFRACTAL ELECTRONIC WAVE FUNCTIONS IN THE ANDERSON MODEL OF LOCALIZATION

Investigations of the multifractal properties of electronic wave functions in disordered samples are reviewed. The characteristic mass exponents of the multifractal measure, the generalized dimensions and the singularity spectra are discussed for typical cases. New results for large 3D systems are reported, suggesting that the multifractal properties at the mobility edge which separates localized and extended states are independent of the microscopic details of the model.