An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--I. Basic concepts, description of the model, analysis of a one-link system movement

Different methods of determining mechanical energy expenditure for human movement are used in scientific research. However, the validity of some of these methods is open to question. The concept of 'sources' and 'fractions' of mechanical energy is introduced in this paper. Power phenomena in moving a one-link system are analyzed through the use of 'energy balance equations'. They represent the interrelationships between the powers of the 'sources' and the time rate of change the mechanical energy 'fractions'. Two ways of minimizing mechanical energy expenditure are discussed. They correspond to 'whip-type' and 'pendulum-type' motion.     

An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--IV. Criticism of the concept of 'energy transfers within and between links'

The methods of evaluation of mechanical energy economy during human movement based on the calculation of three different values of work (Wwb, Ww, Wn), corresponding to three hypothetical types of energy exchange, are subject to criticism. Only the value of work, Wwb, calculated under the assumption of energy transfers between links and energy transformations within links, can be useful as the lowest limit of mechanical energy expenditure (MEE) for the control (for the cases when the powers of the external sources are equal to zero). In the particular case when all of the joint powers Mi,i+1 (phi i+1 -phi i) have the same signs and all sources of external energy are absent, Wwb equals the MEE for the control.     

Quantitative analysis of the energy requirements for development of obesity

OBJECTIVE: Obesity is typically developed over long time and reflected in an energy imbalance, which is too small to be measured and controlled. Our objective is to formulate a mathematical model for the relation between the change in body mass and the values of the energy intake and the energy expenditure, controlled by the physical activity factor PAF. DATA AND THEORY: The uncontrolled components of energy expenditure increases as result of body mass increase: expenditure of a larger mass and expenditure to convert matter in intake into tissue. Both contributions depend on the fraction of fat in the added tissue. Based on data from the literature, the fraction of fat in added tissue and the energy required to convert energy into tissue are estimated and included in the model. RESULTS: Application of the theory shows that an increase in body mass of 1 kg/year corresponds to an energy imbalance of 71 kJ/d for men. Of this imbalance, 82% are stored as new tissue, while 18% are used for energy conversion. If a man in steady state changes energy intake by 0.1 MJ/d, keeping the physical activity factor constant, then the corresponding increase in steady-state body mass is 1.77 kg/PAF, and it will take 320/PAF days before half the change of body mass has taken place. A typical value for PAF is 1.8. CONCLUSION: Energy-based theoretical relations between the various factors involved in energy balance help identifying and quantifying the components of the energy balance and understanding their relations during development of obesity. The inclusion of increased energy expenditure to convert food energy to tissue changes previous estimates of the energy imbalance by about 20 percent.     

An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--V. The mechanical energy expenditure reduction during motion of the multi-link system

Mechanical energy economy during motion of the multi-link system is analyzed on the basis of the theory developed in the previous publications (parts I-IV of this series, J. Biomechanics 19, 287-309). The compensation coefficients for the F- and M-sources and also the absolute compensation coefficient reflecting the mechanical energy economy due to four possible resources are introduced. These resources are the antiphase fluctuations of (I) each link's total energy fractions involving energy transformations between (1) rotational and translational fractions by F-sources, (2) kinetic and potential fractions by mg-source; (II) the links' total energies involving energy transfers between (3) links by F-sources, (4) links by M-sources. The conditions of mechanical energy economy, particularly due to M-sources, are analyzed.     

An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--III. Mechanical energy expenditure reduction during one link motion

Mechanical energy economy and transformation during one link motion are analyzed on the basis of the theory developed in the previous publications (parts I and II of this series, J. Biomechanics 19, 287-300). The 'compensation coefficient' characterizing mechanical energy economy is introduced. The attempts to estimate MEE using only energy curves and neglecting the powers of real sources of energy implicitly lead to replacement of real force and moment systems by the systems reduced to the centers of mass. But such an unintentional substitution of imaginary sources for real ones, specifically, the reduction of forces acting on the link to the equivalent system, changes estimates of mechanical energy expenditure (MEE). That is why the methods of calculating MEE economy based on the determination of so-called 'quasi-mechanical' work (the sum of the kinetic and potential energy increases per one cycle of motion) are not correct. There are two mechanisms to reduce the MEE using the antiphase fluctuations (corresponding to energy transformations) of the (a) rotational and translational fractions of the total energy (at the expense of the F-sources); (b) potential and kinetic energies (at the expense of the mg-source).     

A quantitative assessment of the "tendon" action of two-joint muscles]

Two-joint muscles are able to transmit mechanical energy between the links of the body having no common joint ("tendon action" of the muscles). It is proposed to calculate difference between control moment power in a joint and the sum of powers developed by all muscles serving this joint in order to determine the direction and rate of mechanical energy transfer through the two-joint muscles. It was shown that in the shock-absorbing phase of support in running two-joint muscles the energy transfers from distal to proximal links (from foot to thigh, and from shank to pelvis), in take-off phase-from proximal links to distal ones (from pelvis to shank, and from thigh to foot).     

Urinary C-peptide is not an accurate bioindicator of energy balance in humans

The apprehension of the factors that affect long term regulation of energy balance is indispensable to understand the rise in obesity prevalence as well as to delineate levers to prevent it. Accurate measurements of energy balance are however challenging during free‐living conditions. Recent studies proposed urinary C‐peptide, a metabolic byproduct of insulin synthesis, as reliable noninvasive assessment of energy balance. These studies were in fact essentially based on correlations between urinary C‐peptide and energy intake and only focused on nonhuman primates. During a bed‐rest study conducted in 16 healthy women in a controlled environment, we tested the existence of a relationship between 24 h‐urinary C‐peptide and energy balance in humans. Daily energy intake and body mass, body composition (dual‐energy X‐ray absorptiometry (DXA)) and total energy expenditure (doubly labeled water (DLW) method) was measured and energy balance was calculated as the difference between energy intake and expenditure. Urinary C‐peptide was positively correlated with bed‐rest‐induced changes in fat mass (r² = 0.285; P = 0.03) and energy balance assessed at the end of the bed‐rest (r² = 0.302; P = 0.027). However, in this tightly controlled environment, urinary C‐peptide only accounted for 30% of variations in energy balance. No relationship was noted between urinary C‐peptide and body or fat mass both at baseline and at the end of the bed‐rest. These results indicate that urinary C‐peptide cannot be used as an accurate biomarker of energy balance in the general human population in free‐living conditions.     

Implications of nonshivering thermogenesis for energy balance regulation in humans

The incidence of the metabolic syndrome has reached epidemic levels in the Western world. With respect to the energy balance, most attention has been given to reducing energy (food) intake. Increasing energy expenditure is an important alternative strategy. Facultative thermogenesis, which is the increase in energy expenditure in response to cold or diet, may be an effective way to affect the energy balance. The recent identification of functional brown adipose tissue (BAT) in adult humans promoted a renewed interest in nonshivering thermogenesis (NST). The purpose of this review is to highlight the recent insight in NST, general aspects of its regulation, the major tissues involved, and its metabolic consequences. Sustainable NST in adult humans amounts to 15% of the average daily energy expenditure. Calculations based on the limited available literature show that BAT thermogenesis can amount to 5% of the basal metabolic rate. It is likely that at least a substantial part of NST can be attributed to BAT, but it is possible that other tissues contribute to NST. Several studies on mitochondrial uncoupling indicate that skeletal muscle is another potential contributor to facultative thermogenesis in humans. The general and synergistic role of the sympathetic nervous system and the thyroid axis in relation to NST is discussed. Finally, perspectives on BAT and skeletal muscle NST are given.     

An Experimental Study on the Gait Patterns and Kinematics of Chinese Mitten Crabs

Despite the many studies on eight-legged animals and the importance of their mechanics of terrestrial locomotion, the mechanical energy of crabs in voluntary locomotion on uneven, unpredictable terrain surfaces has received little attention thus far. In this paper, motion video images of Chinese mitten crab (Eriocheir sinensis Milne-Edwards) locomotion on five types of terrains were recorded using a high-speed three-dimensional (3D) recording video system. The typical variables of locomotion such as gait patterns, duty factor, mechanical energy of the mass center, mass-specific rate of the total mechanical power of the mass center, and percentage recovery, were analyzed. Results show that the Chinese mitten crab uses random gaits instead of the alternating tetrapod gait with the increasing terrain roughness. The duty factors of the rows of the leading legs are greater for all terrains than those of the rows of the trailing legs. On smooth terrain, the duty factors of the rows of the trailing legs are greater than that on rough terrains. Kinematic measurements and calculations reveal that similar to mammals, birds, and arthropods, the Chinese mitten crab uses two fundamental gaits to save mechanical energy: the inverted pendulum gait and the bouncing gait. The bouncing gait is the main pattern of mechanical energy conservation. The low probability of injury and energy expenditure due to adaptations to various terrains induce the Chinese mitten crab to modify the mass-specific rate of the total mechanical power of the mass center. The statistical results of percentage recovery also reveal that the Chinese mitten crab has lower energy recovery efficiency over rough terrains compared with smooth terrains.     

The role of exercise in thermogenesis and energy balance

The role of exercise training in energy balance has been reviewed. Recent well-conducted studies showed that exercise may increase energy expenditure not only during the period of exercise itself but during the postexercise period as well. This notion of excess postexercise oxygen consumption (EPOC), which has been a controversial issue for many years, is now becoming a generally well-accepted concept, the consensus being that EPOC takes place following prolonged and strenuous exercise bouts. Besides, the role of EPOC in long-term energy balance remains to be determined. Long-term energy balance studies carried out in rats show that exercise affects energy balance by altering food intake and promoting energy expenditure. In male rats exercise causes a marked decrease in energy intake which contributes, in association with the expenditure of exercise itself, to retard lean and fat tissue growth. From the suppressed deposition of lean body mass, decreases in basal metabolic rate can be predicted in males. In female rats, exercise does not affect food intake; the lower energy gain of exercise-trained females results from the elevated expenditure rate associated with exercise itself. In both male and female rats, there is no evidence that exercise training affects energy expenditure other than during exercise itself unless the habitual feeding pattern of the rats is radically modified. The interactive effects of diet and exercise, which have to be further investigated in long-term energy balance, emerge as a promising area of research.     

Cost of living in free-ranging degus (Octodon degus): seasonal dynamics of energy expenditure

Animals process and allocate energy at different seasons at variable rates, depending on their breeding season and changes in environmental conditions and resulting physiological demands. Overall total energy expenditure, in turn, should either increase in some seasons due to special added demands (e.g. reproduction) or it could simply remain at about the same level, in which case the animals must show compensatory rebalancing of other expenditures that can be reduced. To test for the alternative hypotheses of seasonal variability or compensation, we measured total daily energy expenditure (DEE) in free-living degus (Octodon degus) at four seasons and followed this with determinations of basal metabolic rate (BMR) in the laboratory in the same individuals. DEE varied seasonally but was only significantly different (lower) in summer (non-breeding season), with a DEE:BMR ratio of only 1.6, whereas autumn, winter and spring DEE values were statistically indistinguishable from one another and showed DEE:BMR ratios ranging from 1.9 to 2.2. Our values of DEE in the field fall within the broad range of allometric expectation for herbivorous mammals in general, but the ratios of DEE:BMR are lower than expected. This, together with the lack of strong major shifts in total levels of DEE, suggests that degus are showing compensatory shifts among various categories of energy expenditure that allow them to manage their overall energy balance by minimizing total expenditure.     

Role of thermogenesis in the regulation of energy balance in relation to obesity

Obligatory thermogenesis is a necessary accompaniment of all metabolic processes involved in maintenance of the body in the living state, and occurs in all organs. It includes energy expenditure involved in ingesting, digesting, and processing food (thermic effect of food (TEF]. At certain life stages extra energy expenditure for growth, pregnancy, or lactation would also be obligatory. Facultative thermogenesis is superimposed on obligatory thermogenesis and can be rapidly switched on and rapidly suppressed by the nervous system. Facultative thermogenesis is important in both thermal balance, in which control of thermoregulatory thermogenesis (shivering in muscle, nonshivering in brown adipose tissue (BAT] balances neural control of heat loss mechanisms, and in energy balance, in which control of facultative thermogenesis (exercise-induced in muscle, diet-induced thermogenesis (DIT) in BAT) balances control of energy intake. Thermal balance (i.e., body temperature) is much more stringently controlled than energy balance (i.e., body energy stores). Reduced energy expenditure for thermogenesis is important in two types of obesity in laboratory animals. In the first type, deficient DIT in BAT is a prominent feature of altered energy balance. It may or may not be associated with hyperphagia. In a second type, reduced cold-induced thermogenesis in BAT as well as in other organs is a prominent feature of altered thermal balance. This in turn results in altered energy balance and obesity, exacerbated in some examples by hyperphagia. In some of the hyperphagic obese animals it is likely that the exaggerated obligatory thermic effect of food so alters thermal balance that BAT thermogenesis is suppressed. In all obese animals, deficient hypothalamic control of facultative thermogenesis and (or) food intake is implicated.     

Daily energy expenditure across the course of lactation among urban Bangladeshi women

Measures of energy intake of lactating women in developing countries show that intakes are often lower than those recommended by international bodies, while fat-mass losses are often substantially less than the 3-4 kg used in the calculations of recommendations, suggesting that physiological adaptation must be commonplace among such women. The cost of lactation may be met by reduction in energy expenditure, including reduced physical activity, as well as by mobilization of bodily soft tissue. However, daily energy expenditure of lactating women has been shown to increase across the course of lactation among women in a rural population in the Philippines and an urban population in India, with a decline in body weight across the course of lactation in both studies. In the present study, total daily energy expenditure and anthropometric body composition were measured longitudinally in 68 mothers from a poor urban area of Dhaka, Bangladesh, at 0, 1, 2, 4, and 8 months of lactation, to determine whether the increasing energy expenditure across lactation observed elsewhere also occurs in Bangladeshi women. In addition, the extent to which an extended period of lactation was accompanied by weight and body fat change in these women was determined. Energy expenditure by heart-rate monitoring and activity report, and body composition from anthropometry was carried out four times across the 8-month period of lactation. A small decline in body fat mass and a significant increase in total energy expenditure across this period were observed, confirming similar observations elsewhere in the developing world.     

Mechanical energy expenditure on human movement and the anthropomorphic mechanism]

Mechanical energy expenditures of the man and anthropomorphic locomotion machine during movement are compared theoretically. Sources of the mechanical energy affecting movement of human's lower extremity are modelled by 8 muscles, 3 of which are the two-joint muscles. The model of the lower extremity of anthropomorphic locomotion machine is moved by joint moments. It was shown that in the same movement the model of the human lower extremity can spend less mechanical energy than that of the model of the anthropomorphic locomotion machine. It is caused by the presence of two-joint muscles in the first model. Such an economy of mechanical energy expenditures realized by the two-joint muscle is possible at simultaneous execution of three conditions: 1) signs of the muscle powers, which are produced by that muscle at both joints, are opposite; 2) moments produced by that muscle at each of both joints have the same direction with the joint moments at these joints; 3) one-joint antagonistic muscles are not active. An expression which makes it possible to estimate the mechanical energy savings by the two-joint muscles during humans' movement was developed.     

Modeling Body Mass Variation: Incorporating Social Influence into Calculations of Caloric Intake and Energy Expenditure

Variations in individual body mass and composition have long been a key focus in the health sciences, particularly now that overweight and obesity are considered as public health problems. We study a mathematical model that describes body mass variations which are determined by the energy balance between caloric intake and total energy expenditure. To calculate the change in caloric intake and energy expenditure over time, we proposed a relationship for each of these quantities, and we used measured values that are reported in the literature for the initial conditions. To account for small variations in the daily energy balance of an individual, we include social interactions as the multiplication of two terms: social proximity and social influence. We observe that social interactions have a considerable effect when the body mass of an individual is quite constant and social interactions take random values. However, when an individual''s mass value changes (either increases or decreases), social interactions do not have a notable effect. In our simulation, we tested two different models that describe the body mass composition, and it resulted that one fits better the data.     

The budget model of ecosystem of a shallow highly eutrophic lake

A model of energy budget of Lake Bolshoi Okunenok ecosystem was based on the data received during field studies from May through November 1986. The model takes into account 36 components including dissolved organic matter, bacteria, phytoplankton, zooplankton, meiobenthos, macrobenthos, fish, suspended and sediment detritus. The growing season has been divided into 16 intervals according to the number of observations. The balance equation for each live component describes the change in its biomass for a time interval between two successive sampling dates. The change is considered as a balance of energy input with assimilation or feeding, and energy loss due to respiration, excretion, predation, natural mortality, fishery catchment or and emergence of imago insects. For non-live components we estimate an increase and a decrease in their mass due to the activity of living organisms, as well as organic matter exchange between water and sediments. Seasonal value of balance elements for each component are equal to sums of appropriate interval value. Comparison of energy flows through different links of a trophic web has shown that the role of a bacterial-detrial link was extremely important in Lake Bolshoi Okunenok for the growth season of 1986. Detritus constituted 58% of seasonal diet of non-predatory zooplankton, 39% of diet of predatory zooplankton, 50% of diet of planktivorous fish (fry of whitefish) and 92% of diet of benthivorous fish (fry of carp). The contribution of bacteria to the total seasonal decomposition amounted to 46%. Approximately 57% of the forage phytoplankton production, 86% of non-predatory benthos production, and 23-38% of the other trophic groups production were consumed by all grazers. "Coefficient of energy transformation" is proposed. It is calculated as: CET(s, k) = Ps(k)/Pk, where Ps(k) is production of consumers "s", built due to consumption of source "k"; Pk is production of source "k" itself. In Lake Bolshoi Okunenok only 14% of energy built by phytoplankton were accumulated in organic matter of zooplankton due to direct consumption.     

A note on energy expenditure in walking on level ground and uphill

In walking, energy is wasted in the process of up-and-down movement of the center of gravity of the body during each step, as well as in the kinetic energy involved in the swinging forward of each extrèmity. In this paper the frictional loss in muscles is not considered. It is shown that for a prescribed available amount of metabolic power expenditure there exists an optimal size of the step and an optimal (maximal) speed of walking for the size of the step. Calculated values are of the correct order of magnitude. In walking uphill there exists a type of step for which there is no “lost” up-and-down motion of the center of gravity of the body. This step is optimal for walking up a hill of a given incline.     

Use of the doubly labeled water method for measurement of energy expenditure, total body water, water intake, and metabolizable energy intake in humans and small animals

The basis of the doubly labeled water method is measurement of the differential rates of disappearance of two isotopes of water (H2 18O and either 2H2O or 3H2O, administered at the start of the study) from body water. Published studies indicate that, in its current forms, this technique can be used to provide accurate and reasonably precise information on carbon dioxide production, total body water, and water intake in free-living humans and many small animals. Total energy expenditure can be calculated from carbon dioxide production with little loss of precision. Metabolizable energy intake can also be predicted, as the sum of total energy expenditure plus an estimate for the change in body energy stores during the measurement, but this prediction is unlikely to be accurate and precise unless the subject is in approximate energy balance.     

Role of resting metabolic rate and energy expenditure in hunger and appetite control: a new formulation

A long-running issue in appetite research concerns the influence of energy expenditure on energy intake. More than 50 years ago, Otto G. Edholm proposed that “the differences between the intakes of food [of individuals] must originate in differences in the expenditure of energy”. However, a relationship between energy expenditure and energy intake within any one day could not be found, although there was a correlation over 2 weeks. This issue was never resolved before interest in integrative biology was replaced by molecular biochemistry. Using a psychobiological approach, we have studied appetite control in an energy balance framework using a multi-level experimental system on a single cohort of overweight and obese human subjects. This has disclosed relationships between variables in the domains of body composition [fat-free mass (FFM), fat mass (FM)], metabolism, gastrointestinal hormones, hunger and energy intake. In this Commentary, we review our own and other data, and discuss a new formulation whereby appetite control and energy intake are regulated by energy expenditure. Specifically, we propose that FFM (the largest contributor to resting metabolic rate), but not body mass index or FM, is closely associated with self-determined meal size and daily energy intake. This formulation has implications for understanding weight regulation and the management of obesity.