Humans, geometric similarity and the Froude number: is ‘‘reasonably close’’ really close enough?

ObjectiveThe aim of this study was to evaluate age-related changes in metabolic walking energy expenditure in ambulant boys affected by Duchenne muscular dystrophy over a follow-up period of 12 months.MethodsAt baseline (T1) and 12 months later (T2), metabolic walking energy expenditure was assessed during a 6-minute walk test at comfortable speed in 14 ambulant boys with Duchenne (age range: 6.0-12.5 years, mean 8.2). Outcome measures derived from the assessment included the 6-minute comfortable walking distance (m) and net-nondimensional energy cost relative to speed-matched control cost (SMC-EC, %). Statistical comparisons were made using a two-way repeated measures ANOVA (factors: time (T1 versus T2) and age (<8 years of age (yoa) versus ≥8 yoa)).ResultsOver the course of the study, a significant decrease of -28m (−8.2%, p = 0.043) was noted in the walked distance at comfortable speed. Besides, SMC-EC increased with 4.4%, although this change was not significant (p = 0.452). Regarding age groups, boys below 8 yoa showed a smaller annual decrease in the walked distance (−15 m) compared to boys above 8 yoa (−37 m). SMC-EC increased with 10% in the older boys, while in the younger boys it decreased (−2.1%). The main effect of age group on walking distance and SMC-EC however was not significant (p>0.158), and also there were no interaction effects (p>0.248).ConclusionsThe results of our small study suggest that the natural course of walking performance in ambulant boys with Duchenne is characterized by a decrease in comfortable walking distance and an increase in walking energy cost. The rate of energy cost seems to increase with age, while walking distance decreases, which is opposite from the trend in typically developing children.

The energetics of human walking: Is Froude number ( Fr) useful for metabolic comparisons?

The time course of metabolic power during 100–400 m top running performances in world class athletes was estimated assuming that accelerated running on flat terrain is biomechanically equivalent to uphill running at constant speed, the slope being dictated by the forward acceleration. Hence, since the energy cost of running uphill is known, energy cost and metabolic power of accelerated running can be obtained, provided that the time course of the speed is determined. Peak metabolic power during the 100 and 200 m current world records (9.58 and 19.19 s) and during a 400 m top performance (44.06 s) amounted to 163, 99 and 75 W kg−1, respectively. Average metabolic power and overall energy expenditure during 100–5000 m current world records in running were also estimated as follows. The energy spent in the acceleration phase, as calculated from mechanical kinetic energy (obtained from average speed) and assuming 25% efficiency for the transformation of metabolic into mechanical energy, was added to the energy spent for constant speed running (air resistance included). In turn, this was estimated as: (3.8 + k′ v2) · d, where 3.8 J kg−1 m−1 is the energy cost of treadmill running, k′ = 0.01 J s2 kg−1 m−3, v is the average speed (m s−1) and d (m) the overall distance. Average metabolic power decreased from 73.8 to 28.1 W kg−1 with increasing distance from 100 to 5000 m. For the three shorter distances (100, 200 and 400 m), this approach yielded results rather close to mean metabolic power values obtained from the more refined analysis described above. For distances between 1000 and 5000 m the overall energy expenditure increases linearly with the corresponding world record time. The slope and intercept of the regression are assumed to yield maximal aerobic power and maximal amount of energy derived from anaerobic stores in current world records holders; they amount to 27 W kg−1 (corresponding to a maximal O2 consumption of 77.5 ml O2 kg−1 min−1 above resting) and 1.6 kJ kg−1 (76.5 ml O2 kg−1). This last value is on the same order of the maximal amount of energy that can be derived from complete utilisation of phosphocreatine in the active muscle mass and from maximal tolerable blood lactate accumulation. The anaerobic energy yield has also been estimated, throughout the overall set of distances (100–5000 m), assuming that, at work onset, the rate of O2 consumption increases with a time constant of 20 s tending to the appropriate metabolic power, but stops increasing once the maximal O2 consumption is attained. Hence the overall energy expenditure can be partitioned into its aerobic and anaerobic components. This last increases from about 0.6 kJ kg−1 for the shortest distance (100 m) to a maximum close to that estimated above (1.6 kJ kg−1) for distances of 1500 m or longer.

It has been predicted that geometrically similar animals would swim at the same speed with stroke frequency scaling with mass(-1/3). In the present study, morphological and behavioural data obtained from free-ranging penguins (seven species) were compared. Morphological measurements support the geometrical similarity. However, cruising speeds of 1.8-2.3 m s(-1) were significantly related to mass(0.08) and stroke frequencies were proportional to mass(-0.29). These scaling relationships do not agree with the previous predictions for geometrically similar animals. We propose a theoretical model, considering metabolic cost, work against mechanical forces (drag and buoyancy), pitch angle and dive depth. This new model predicts that: (i) the optimal swim speed, which minimizes the energy cost of transport, is proportional to (basal metabolic rate/drag)(1/3) independent of buoyancy, pitch angle and dive depth; (ii) the optimal speed is related to mass(0.05); and (iii) stroke frequency is proportional to mass(-0.28). The observed scaling relationships of penguins support these predictions, which suggest that breath-hold divers swam optimally to minimize the cost of transport, including mechanical and metabolic energy during dive.

BackgroundThe energy that animals devote to locomotion has been of intense interest to biologists for decades and two basic methodologies have emerged to predict locomotor energy expenditure: those based on metabolic and those based on mechanical energy. Metabolic energy approaches share the perspective that prediction of locomotor energy expenditure should be based on statistically significant proxies of metabolic function, while mechanical energy approaches, which derive from many different perspectives, focus on quantifying the energy of movement. Some controversy exists as to which mechanical perspective is “best”, but from first principles all mechanical methods should be equivalent if the inputs to the simulation are of similar quality. Our goals in this paper are 1) to establish the degree to which the various methods of calculating mechanical energy are correlated, and 2) to investigate to what degree the prediction methods explain the variation in energy expenditure.Methodology/Principal FindingsWe use modern humans as the model organism in this experiment because their data are readily attainable, but the methodology is appropriate for use in other species. Volumetric oxygen consumption and kinematic and kinetic data were collected on 8 adults while walking at their self-selected slow, normal and fast velocities. Using hierarchical statistical modeling via ordinary least squares and maximum likelihood techniques, the predictive ability of several metabolic and mechanical approaches were assessed. We found that all approaches are correlated and that the mechanical approaches explain similar amounts of the variation in metabolic energy expenditure. Most methods predict the variation within an individual well, but are poor at accounting for variation between individuals.ConclusionOur results indicate that the choice of predictive method is dependent on the question(s) of interest and the data available for use as inputs. Although we used modern humans as our model organism, these results can be extended to other species.

Mechanical energy estimation during walking: Validity and sensitivity in typical gait and in children with cerebral palsy

Human physique classification by somatotype assumes that adult humans are geometric similar to each other. However, this assumption has yet to be adequately tested in athletic and nonexercising human populations. In this study, we assessed this assumption by comparing the mass exponents associated with girth measurements taken at 13 different sites throughout the body in 478 subjects (279 athletic subjects, and 199 nonexercising controls). Corrected girths which account for subcutaneous adipose tissue at the upper arm, thigh, and calf sites, and which simulate muscle circumference, were also calculated. If subjects are geometrically similar to each other, girth exponents should be approximately proportional to M(1/3), where M is the subjects' body mass. This study confirms that human adult physiques are not geometrically similar to each other. In both athletic subjects and nonexercising controls, body circumferences/limb girths develop at a greater rate than that anticipated by geometric similarity in fleshy sites containing both muscle and fat (upper arms and legs), and less than anticipated in bony sites (head, wrists, and ankles). Interestingly, head girths appear to remain almost constant, irrespective of subjects' body size/mass. The results also suggest that thigh muscle girths of athletes and controls increase at a greater rate than that predicted by geometric similarity, proportional to body mass (M(0.439) and M(0.377), respectively). These systematic deviations from geometric similarity have serious implications for the allometric scaling of variables such as energy expenditure, oxygen uptake, anaerobic power, and thermodynamic or anthropometric studies involving individuals of differing size.

Daily energy expenditure is influenced by several factors and physical activity (PA) is the most variable (Foureaux et al., 2006). However, depending on activity’s intensity, different substrates can be metabolized to consume energy. PURPOSE: This study aimed to analyse differences in metabolic indicators and energy expenditure in two different types of fitness classes: Aerobic Dance (AD) and Localized Fitness (LF). METHODS: Participants were 15 adult women aged 33,3±8,3 years with a minimum of six months experience in AD and LF. Maximum oxygen uptake (VO2max) and maximum heart rate (HRmax) were measured directly during a maximal treadmill test. During exercise sessions (AD and LF), heart rate (HR), oxygen uptake (VO2), respiratory exchange ratio (RER) metabolic equivalents (MET), percentage of fat oxidation (%FAT), percentage of carbohydrates oxidation (%CHO) and energy expenditure (EE), were assessed using a portable gas analyser (K4b2, Cosmed, Italy). Paired samples Student’s T-test was used to analyse differences between AD and LF. Significance level as set at 5%. RESULTS: Results indicated greater values during the AD session in comparison to the LF session on the following variables: VO2 (35.7±4.7 vs. 20.2±3.4 ml.kg-1.min-1; P<0.001), HR (160.9±13.2 vs. 133.9±19.4 bpm; P<0.001); MET (10.2±1.3 vs. 5.8±1.0 MET; P<0.001), EE (608.9±73.7 vs. 350.3±64.5 kcal.h-1; P<0.001), total fat oxidation (5.6±4.6 vs. 2.7±2.0 g.h-1; P<0.001) and total CHO oxidation (139.9±14.1 vs. 81.6±16.5 g.h-1; P<0.001). No differences were found for RER, %FAT and %CHO. During AD sessions, %CHO was higher than %FAT (92.3±6.2 vs. 7.9±6.4%; P<0.001). During LF sessions, %CHO was higher than %FAT (92.9±5.43 vs. 7.2±5.4%; P<0.001). CONCLUSION: These results suggest that AD induces greater metabolic demands and energy expenditure than LF. However, engaging AD or LF 3 to 5 times a week seems enough to achieve PA recommendations of 150 minutes of moderate-to-vigorous intensity activities per week (WHO, 2010), promoting several health benefits (ACSM, 2011). Although, AD and LF are equivalents on the percentage of fat and carbohydrate oxidation, carbohydrate is the main energy supply for both fitness classes.

During locomotion, force-producing limb muscles are predominantly responsible for an animal's whole body metabolic energy expenditure. Animals can change the length of their force-producing muscle fascicles by altering body posture (e.g., joint angles), the structural properties of their biological tissues over time (e.g., tendon stiffness), or the body's kinetics (e.g., body weight). Currently, it is uncertain whether relative muscle fascicle operating lengths have a measurable effect on the metabolic energy expended during cyclic locomotion-like contractions. To address this uncertainty, we quantified the metabolic energy expenditure of human participants, as they cyclically produced two distinct ankle moments at three ankle angles (90°, 105°, and 120°) on a fixed-position dynamometer using their soleus. Overall, increasing participant ankle angle from 90° to 120° (more plantar flexion) reduced minimum soleus fascicle length by 17% (both moment levels, P < 0.001) and increased metabolic energy expenditure by an average of 208% across both moment levels (both P < 0.001). For both moment levels, the increased metabolic energy expenditure was not related to greater fascicle positive mechanical work (higher moment level, P = 0.591), fascicle force rate (both P ≥ 0.235), or model-estimated active muscle volume (both P ≥ 0.122). Alternatively, metabolic energy expenditure correlated with average relative soleus fascicle length (r = -0.72, P = 0.002) and activation (r = 0.51, P < 0.001). Therefore, increasing active muscle fascicle operating lengths may reduce metabolic energy expended during locomotion.NEW & NOTEWORTHY During locomotion, active muscles undergo cyclic length-changing contractions. In this study, we isolated confounding variables and revealed that cyclically producing force at relatively shorter fascicle lengths increases metabolic energy expenditure. Therefore, muscle fascicle operating lengths likely have a measurable effect on the metabolic energy expenditure during locomotion.

Nicotinamide Riboside Supplementation Attenuates Obesity-Induced Adipose Tissue Fibrosis and Inflammation in Female Mouse Model

ABSTRACTThe aim of this study was to advance muscle models that unify mechanical behaviour and metabolic energy expenditure. To that end, we compared predictions of force and metabolic energy expenditure of a Huxley-type muscle–tendon complex (MTC) model with previously obtained experimental data. In our published model, we extended the classic Huxley formulation by incorporating force–length dependency, series elasticity and activation dynamics. Metabolic energy expenditure was modelled as the weighted sum of cross-bridge cycling and calcium pumping costs. In the associated experiment, fibre bundles from nine mouse soleus muscles underwent sinusoidal contractions, while oxygen consumption and tendon force were measured. The bundles were stimulated during both shortening and lengthening, and measurements were taken before and after adding blebbistatin, which blocks cross-bridge cycling but leaves calcium handling unaffected. This enabled separate estimation of metabolic energy costs for each process. In the present study, we modelled these previously published data. Parameters governing model mechanical behaviour were calibrated using trials without oxygen measurements. We used these parameters in simulations of the oxygen measurement trials, and metabolic parameters were optimized to best match average metabolic power. We found that simulated and measured forces corresponded well (root-mean-square error, RMSE <10% of maximum force). Metabolic energy predictions showed higher error (mean RMSE 20.3%, s.d. 12.6% of measured value), with large inter-animal variability. In four animals, where repeated measures were consistent and data followed expected trends, predictions of metabolic energy expenditure were accurate (RMSE <15%). In the remaining five, greater variability or inconsistent data patterns led to poorer fits. Despite this, given the within-animal variability in oxygen measurements, the metabolic predictions are promising. Combined with previous findings, these results support the potential of Huxley-type models in predictive simulations of human metabolic energy expenditure.

* Member, AIAA. † Senior member, AIAA. Introduction Theoretical models for chemical lasers depend on a variety of assumptions and empirical data to provide closure and simplify the computationally expensive solution of the governing equations. Among the various assumptions and empirical data built into models for chemical lasers are two assumptions that have direct bearing upon the predicted flow structure: steadiness in the time domain and geometric similarity of the physical domain. Steadiness in the time domain implies that no fluctuations in the flow structure occur due to the amplification of finite disturbances by flow instabilities, and correspondingly that temporal variations of laser gain and power are not large. Geometric similarity of the physical domain, or laser hardware, means that the domain may be reduced to geometrically similar units, or ‘unit-cells’ that contain the essential physics of the large domain and that these physics are identical and symmetric about boundaries separating these units. The two assumptions are related in the sense that geometric similarity may be removed by the presence of flow unsteadiness. An example is a cylinder in crossflow at Reynolds numbers below 280, for which the flow is two-dimensional. An infinite circular cylinder placed in a uniform, steady flow normal to the axis of the cylinder is symmetric about a plane parallel to the flow splitting the circular cross section of the cylinder. However, instabilities in the flow within the wake of the cylinder cause the development of a Karman vortex street, producing spatial and temporal fluctuations in the flow properties about the axis of symmetry. Whereas a time average of the flow at a time scale much greater than those of the fluctuations will be symmetric, samples taken at the time scale of the fluctuations are decidedly nonsymmetric, breaking down the geometric similarity argument. Steady-state 3-D reacting flow Navier-Stokes simulations of chemical oxygen-iodine laser (COIL) flowfields employing unit-cell approximations have been successfully employed by a number of researchers to predict laser gain and laser power and guide the development of laser hardware. COIL simulation provides a good example of the use of these approximations, since COIL flowfields combine complex physics potentially sensitive to the assumptions with geometrically complex hardware. COIL reactant mixing nozzles commonly use transverse jet injection of one of the reactants as a mixing mechanism, with geometric similarity existing in the array of injector orifices. The computational cost of the complex physical models dictates that some reduction in the modeled physical domain be made. Madden and Miller utilized a 3-D, steady-state, unit-cell Navier-Stokes model to predict laser gains at a variety of flow conditions to an accuracy within the error bars of the experiment data. Buggeln et al and Masuda et al have used a steady-state, unit-cell 3-D Navier-Stokes model coupled to a power extraction model to predict laser power and laser gain in efforts to validate and guide hardware development. Thus, it can be safely stated that the steady-state, unit-cell approach is not without merit. Fluid dynamics experiments for jets issuing transverse to a primary flow, known in the literature as the ‘jet in crossflow,’ provide sufficient reason to suspect that the steady-state assumption used in COIL models is not valid. Investigations by Moussa et al, Coelho and Hunt, Fric and Roshko, Blanchard et al, Rivero et al, and Camussi et al in composite provide a picture of the jet in crossflow that is anything but steady. Throughout the Reynolds number range, the jet in crossflow is characterized by a variety of structures that are sources or potential sources for unsteadiness including horseshoe vortices associated with the primary flow boundary layer wrapping around the base of the jet; the counter rotating pair of vortices entrained in the sides of the jet flow that result from the action of shear forces in the primary flow/jet flow interface; jet shear layer type instabilities that occur in 34th AIAA Plasmadynamics and Lasers Conference 23-26 June 2003, Orlando, Florida AIAA 2003-4309

Effect of Different Larval Rearing Temperatures on the Productivity (R_o) and Morphology of the Malaria Vector<i>Anopheles superpictus</i>Grassi (Diptera: Culicidae) Using Geometric Morphometrics

This study analyzed force plate, kinematic, and metabolic energy data of 14 able-bodied subjects standing statically with upright and trunk-flexed postures. To explore the effect of trunk-flexed postures on balance and metabolic energy expenditure during standing. Abnormal trunk posture often occurs in the presence of spinal deformities, such as lumbar flatback. It is unclear whether alterations in trunk posture affect energy expenditure and the location of the body's center of mass in the transverse plane (BCOMtrans) during standing. Kinematic, kinetic, and energy expenditure data were collected with upright trunk alignment and with 25 degrees +/- 7 degrees and 50 degrees +/- 7 degrees of trunk flexion from the vertical. The mean location of the BCOMtrans was estimated from the net center of pressure (COP), which is a weighted average of the COP beneath both feet. The fore-aft position of the net COP under the base of support was not significantly different between postures (P < 0.08). At each posture, the net COP was located 16% of the foot length anterior to the ankle joint centers. However, with increasing trunk flexion, there was a significant increase in oxygen consumption rate (P < 0.001 for all postures). Compensatory actions, such as ankle plantarflexion and hip flexion, allowed the mean position of the net COP to remain within a narrowly defined region irrespective of trunk posture. Changes in muscle activity associated with a trunk-flexed posture and the associated compensations likely contributed to the increased energy expenditure.

Introduction In this chapter, a turbomachinery-related nondimensional groupings of geometrical dimensions and thermodynamic properties will be derived. These will aid us in many tasks, such as: Investigating the full-size version of a turbomachine by testing (instead) a much smaller version of it (in terms of the total-to-total pressure ratio), an alternative that would require a much smaller torque and shaft speed, particularly in compressors; Alleviating the need for blade cooling in the component test rig of a high-pressure turbine section by reducing (in light of specific rules) the inlet total temperature; Predicting the consequences of the off-design operation by a turbomachine using the so-called turbine and compressor maps; Making a decision, at an early design phase, in regard to the flow path type (axial or radial) of a turbomachine for optimum performance. A good starting point is to outline the so-called similitude principle, beginning with the definition of geometric and dynamic similarities as they pertain to turbomachines. Geometrical Similarity Two turbomachines are said to be geometrically similar if the corresponding dimensions are proportional to one another. In this case, one turbomachine is referred to as a scaled-up (or scaled-down) version of the other. An obvious (but not silly) case here is the turbomachine and itself. Dynamic Similarity Two geometrically similar turbomachines are said to be dynamically similar if the velocity vectors at all pairs of corresponding locations are parallel to one another and with proportional magnitudes. In this case, the fluid-exerted forces, at corresponding locations, will be proportional to each other.