Allometric Scaling Laws Research Articles

New Allometric Scaling Laws Revealed for Microorganisms

Allometric scaling relationships based on microbial data sets are revealing novel biological principles; for example, the abundance and diversity of animal-associated microbes scale with individual animal mass. The global abundance of animal-associated microbes and biosphere species richness have also been estimated. The potential for further microbe-inclusive macroecological insights is high.

Allometric scaling in scientific fields

Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific fields. By performing an analysis of the outputs/inputs of various scientific fields, including the numbers of publications, citations, and references, with respect to the number of authors, we find that in all fields that we have studied thus far, including physics, mathematics and economics, there are allometric scaling laws relating the outputs/inputs and the sizes of scientific fields. Furthermore, the exponents of the scaling relations have remained quite stable over the years. We also find that the deviations of individual subfields from the overall scaling laws are good indicators for ranking subfields independently of their sizes.

A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014

The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf’s law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.

Noninvasive CT-Derived FFR Based on Structural and Fluid Analysis: A Comparison With Invasive FFR for Detection of Functionally Significant Stenosis

ObjectivesThis study describes the feasibility and accuracy of a novel computed tomography (CT) fractional flow reserve (FFR) technique based on alternative boundary conditions. BackgroundTechniques used to compute FFR based on images acquired from coronary computed tomography angiography (CTA) are described. Boundary conditions were typically determined by allometric scaling laws and assumptions regarding microvascular resistance. Alternatively, boundary conditions can be derived from the structural deformation of coronary lumen and aorta, although its accuracy remains unknown. MethodsForty-two patients (78 vessels) in a single institution prospectively underwent 320-detector coronary CTA and FFR. Deformation of coronary cross-sectional lumen and aorta, computed from coronary CTA images acquired over diastole, was used to determine the boundary conditions based on hierarchical Bayes modeling. CT-FFR was derived using a reduced order model performed using a standard desktop computer and dedicated software. First, 12 patients (20 vessels) formed the derivation cohort to determine optimal CT-FFR threshold with which to detect functional stenosis, defined as FFR of ≤0.8, which was validated in the subsequent 30 patients (58 vessels). ResultsDerivation cohort results demonstrated optimal threshold for CT-FFR was 0.8 with 67% sensitivity and 91% specificity. In the validation cohort, CT-FFR was successfully computed in 56 of 58 vessels (97%). Compared with coronary CTA, CT-FFR at ≤0.8 demonstrated a higher specificity (87% vs. 74%, respectively) and positive predictive value (74% vs. 60%, respectively), with comparable sensitivity (78% vs. 79%, respectively), negative predictive value (89% vs. 88%, respectively), and accuracy (area under the curve: 0.88 vs. 0.77, respectively; p = 0.22). Based on Bland-Altman analysis, mean intraobserver and interobserver variability values for CT-FFR were, respectively, −0.02 ± 0.05 (95% limits of agreement: −0.12 to 0.08) and 0.03 ± 0.06 (95% limits: 0.07 to 0.19). Mean time per patient for CT-FFR analysis was 27.07 ± 7.54 min. ConclusionsCT-FFR based on alternative boundary conditions and reduced-order fluid model is feasible, highly reproducible, and may be accurate in detecting FFR ≤ 0.8. It requires a short processing time and can be completed at point-of-care. Further validation is required in large prospective multicenter settings.

1095 Cardiovascular performance of modern swine does not comply with allometric scaling laws

1095 Cardiovascular performance of modern swine does not comply with allometric scaling laws

Hierarchical Size Scaling during Multicellular Growth and Development

Multicellular organisms must regulate their growth across the diverse length scales of biological organization, but how this growth is controlled from organelle to body, while coordinating interdependent functions at each scale, remains poorly understood. We utilized the C.elegans worm intestine as a model system to identify distinct allometric scaling laws, revealing that the growth of individual structures is differentially regulated during development. We show that the volume of the nucleolus, a subcellular organelle, is directly proportional (isometric) to cell size during larval development. In contrast to findings in a variety of other systems, the size of the nucleus grows more slowly and is hypoallometric to the cell. We further demonstrate that the relative size of the nucleolus, the site of ribosome biogenesis, is predictive of the growth rate of the entire worm. These results highlight the importance of subcellular size for organism-level function in multicellular organisms.

Variation in Elevation and Sward Height Facilitate Coexistence of Goose Species through Allometric Responses in Wetlands

Allometric scaling law predicts that herbivores respond differently to the availability of resources, mediated by body size. However, studies of allometric responses have often focused on animals with a relatively large difference in body size. Here, using a correlative field study, habitat use by two herbivorous species, the Bean Goose (Anser fabalis) and the Greater White-fronted Goose (A. albifrons), with a relatively small difference in body size was investigated during the wintering period. Both a generalized linear mixed model and a mixed logistic regression model showed that both species selected lower lying areas that were recently exposed, and, as expected, the smaller Greater White-fronted Goose showed a stronger selection of foraging habitat than the larger Bean Goose. Sward height also influenced habitat selection by both species, and the smaller species selected shorter swards than the larger species. In terms of forage quality, both models failed to detect a significant effect of nitrogen content on goose habitat selection. A logistic regression model showed that structural heterogeneity of the sward negatively correlated with the patch selection of the smaller species, but for the larger species such a correlation was not found. In agreement with our hypotheses, our results provide some preliminary indication that coexistence of the two goose species studied here might be mediated by an allometric response even if the difference in body size is relatively small.

Scaling laws of coronary circulation in health and disease

The heterogeneity and complexity of coronary vasculature (structure) and myocardial flow (function) have fractal-like characteristics and can be described by scaling laws with remarkable simplicity. In contrast with allometric (interspecific) scaling law, intraspecific scaling laws describe the design rules of vascular trees within a species. This paper provides an overview of intraspecific scaling laws of vascular trees and the physiological and clinical implications thereof. The significance and shortcomings of these scaling laws are discussed in relation to diffuse coronary artery disease, Glagov’s positive remodeling in early stages of coronary atherosclerosis, treatment guidelines of complex bifurcation lesions, and for estimation of outlet resistance values for computation of blood flow in epicardial coronary arteries. Finally, we summarize the highlights of scaling relations and suggest some future directions.

A model for allometric scaling of mammalian metabolism with ambient heat loss

BackgroundAllometric scaling, which represents the dependence of biological traits or processes on body size, is a long-standing subject in biological science. However, there has been no study to consider heat loss to the ambient and an insulation layer representing mammalian skin and fur for the derivation of the scaling law of metabolism. MethodsA simple heat transfer model is proposed to analyze the allometry of mammalian metabolism. The present model extends existing studies by incorporating various external heat transfer parameters and additional insulation layers. The model equations were solved numerically and by an analytic heat balance approach. ResultsA general observation is that the present heat transfer model predicted the 2/3 surface scaling law, which is primarily attributed to the dependence of the surface area on the body mass. External heat transfer effects introduced deviations in the scaling law, mainly due to natural convection heat transfer, which becomes more prominent at smaller mass. These deviations resulted in a slight modification of the scaling exponent to a value < 2/3. ConclusionThe finding that additional radiative heat loss and the consideration of an outer insulation fur layer attenuate these deviation effects and render the scaling law closer to 2/3 provides in silico evidence for a functional impact of heat transfer mode on the allometric scaling law in mammalian metabolism.

Influence of segmented vessel size due to limited imaging resolution on coronary hyperemic flow prediction from arterial crown volume.

Computational predictions of the functional stenosis severity from coronary imaging data use an allometric scaling law to derive hyperemic blood flow (Q) from coronary arterial volume (V), Q = αV(β) Reliable estimates of α and β are essential for meaningful flow estimations. We hypothesize that the relation between Q and V depends on imaging resolution. In five canine hearts, fluorescent microspheres were injected into the left anterior descending coronary artery during maximal hyperemia. The coronary arteries of the excised heart were filled with fluorescent cast material, frozen, and processed with an imaging cryomicrotome to yield a three-dimensional representation of the coronary arterial network. The effect of limited image resolution was simulated by assessing scaling law parameters from the virtual arterial network at 11 truncation levels ranging from 50 to 1,000 μm segment radius. Mapped microsphere locations were used to derive the corresponding relative Q using a reference truncation level of 200 μm. The scaling law factor α did not change with truncation level, despite considerable intersubject variability. In contrast, the scaling law exponent β decreased from 0.79 to 0.55 with increasing truncation radius and was significantly lower for truncation radii above 500 μm vs. 50 μm (P< 0.05). Hyperemic Q was underestimated for vessel truncation above the reference level. In conclusion, flow-crown volume relations confirmed overall power law behavior; however, this relation depends on the terminal vessel radius that can be visualized. The scaling law exponent β should therefore be adapted to the resolution of the imaging modality.

Non-dimensional physics of pulsatile cardiovascular networks and energy efficiency.

In Nature, there exist a variety of cardiovascular circulation networks in which the energetic ventricular load has both steady and pulsatile components. Steady load is related to the mean cardiac output (CO) and the haemodynamic resistance of the peripheral vascular system. On the other hand, the pulsatile load is determined by the simultaneous pressure and flow waveforms at the ventricular outlet, which in turn are governed through arterial wave dynamics (transmission) and pulse decay characteristics (windkessel effect). Both the steady and pulsatile contributions of the haemodynamic power load are critical for characterizing/comparing disease states and for predicting the performance of cardiovascular devices. However, haemodynamic performance parameters vary significantly from subject to subject because of body size, heart rate and subject-specific CO. Therefore, a 'normalized' energy dissipation index, as a function of the 'non-dimensional' physical parameters that govern the circulation networks, is needed for comparative/integrative biological studies and clinical decision-making. In this paper, a complete network-independent non-dimensional formulation that incorporates pulsatile flow regimes is developed. Mechanical design variables of cardiovascular flow systems are identified and the Buckingham Pi theorem is formally applied to obtain the corresponding non-dimensional scaling parameter sets. Two scaling approaches are considered to address both the lumped parameter networks and the distributed circulation components. The validity of these non-dimensional number sets is tested extensively through the existing empirical allometric scaling laws of circulation systems. Additional validation studies are performed using a parametric numerical arterial model that represents the transmission and windkessel characteristics, which are adjusted to represent different body sizes and non-dimensional haemodynamic states. Simulations demonstrate that the proposed non-dimensional indices are independent of body size for healthy conditions, but are sensitive to deviations caused by off-design disease states that alter the energetic load. Sensitivity simulations are used to identify the relationship between pulsatile power loss and non-dimensional characteristics, and optimal operational states are computed.

CFD study of constructal microchannel networks for liquid-cooling of electronic devices

The heat transfer performance of liquid-cooled heat sinks with a constructal design of the flow field configurations is assessed in the present investigation. Y- and Ψ-shaped microfluidic networks embedded on a silicon substrate are numerically analyzed and compared in order to propose an alternative cooling layer for integrated circuits (ICs). The shape, path and geometric dimensions of the flow channels are designed with the Phi number and Allometric scaling laws based on constructal networks, resulting in tree-shaped flow paths with variable hydraulic diameter. The thermal and hydraulic performances of eight different configurations are discussed in terms of the average surface temperature and pressure drop, respectively. Results indicate that the Ψ-shaped heat sink designs offer a higher degree of temperature uniformity than Y-shaped designs, with the penalty of a slightly higher flow restriction. It was observed that the Phi number ratio has a strong effect on thermal performance, with enhanced results for higher ratios. Discussions about heat transfer area, temperature uniformity and pressure drop are given for the different cases, proposing an enhanced design for electronics cooling applications.

High-Throughput Tissue Bioenergetics Analysis Reveals Identical Metabolic Allometric Scaling for Teleost Hearts and Whole Organisms.

Organismal metabolic rate, a fundamental metric in biology, demonstrates an allometric scaling relationship with body size. Fractal-like vascular distribution networks of biological systems are proposed to underlie metabolic rate allometric scaling laws from individual organisms to cells, mitochondria, and enzymes. Tissue-specific metabolic scaling is notably absent from this paradigm. In the current study, metabolic scaling relationships of hearts and brains with body size were examined by improving on a high-throughput whole-organ oxygen consumption rate (OCR) analysis method in five biomedically and environmentally relevant teleost model species. Tissue-specific metabolic scaling was compared with organismal routine metabolism (RMO2), which was measured using whole organismal respirometry. Basal heart OCR and organismal RMO2 scaled identically with body mass in a species-specific fashion across all five species tested. However, organismal maximum metabolic rates (MMO2) and pharmacologically-induced maximum cardiac metabolic rates in zebrafish Danio rerio did not show a similar relationship with body mass. Brain metabolic rates did not scale with body size. The identical allometric scaling of heart and organismal metabolic rates with body size suggests that hearts, the power generator of an organism’s vascular distribution network, might be crucial in determining teleost metabolic rate scaling under routine conditions. Furthermore, these findings indicate the possibility of measuring heart OCR utilizing the high-throughput approach presented here as a proxy for organismal metabolic rate—a useful metric in characterizing organismal fitness. In addition to heart and brain OCR, the current approach was also used to measure whole liver OCR, partition cardiac mitochondrial bioenergetic parameters using pharmacological agents, and estimate heart and brain glycolytic rates. This high-throughput whole-organ bioenergetic analysis method has important applications in toxicology, evolutionary physiology, and biomedical sciences, particularly in the context of investigating pathogenesis of mitochondrial diseases.

Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities.

More than a half of world population is now living in cities and this number is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific characterization of cities and for the availability of an unprecedented amount of data, academics have recently immersed in this topic and one of the most striking and universal finding was the discovery of robust allometric scaling laws between several urban indicators and the population size. Despite that, most governmental reports and several academic works still ignore these nonlinearities by often analyzing the raw or the per capita value of urban indicators, a practice that actually makes the urban metrics biased towards small or large cities depending on whether we have super or sublinear allometries. By following the ideas of Bettencourt et al. [PLoS ONE 5 (2010) e13541], we account for this bias by evaluating the difference between the actual value of an urban indicator and the value expected by the allometry with the population size. We show that this scale-adjusted metric provides a more appropriate/informative summary of the evolution of urban indicators and reveals patterns that do not appear in the evolution of per capita values of indicators obtained from Brazilian cities. We also show that these scale-adjusted metrics are strongly correlated with their past values by a linear correspondence and that they also display crosscorrelations among themselves. Simple linear models account for 31%–97% of the observed variance in data and correctly reproduce the average of the scale-adjusted metric when grouping the cities in above and below the allometric laws. We further employ these models to forecast future values of urban indicators and, by visualizing the predicted changes, we verify the emergence of spatial clusters characterized by regions of the Brazilian territory where we expect an increase or a decrease in the values of urban indicators.

Food restriction alters energy allocation strategy during growth in tobacco hornworms (Manduca sexta larvae).

Growing animals must alter their energy budget in the face of environmental changes and prioritize the energy allocation to metabolism for life-sustaining requirements and energy deposition in new biomass growth. We hypothesize that when food availability is low, larvae of holometabolic insects with a short development stage (relative to the low food availability period) prioritize biomass growth at the expense of metabolism. Driven by this hypothesis, we develop a simple theoretical model, based on conservation of energy and allometric scaling laws, for understanding the dynamic energy budget of growing larvae under food restriction. We test the hypothesis by manipulative experiments on fifth instar hornworms at three temperatures. At each temperature, food restriction increases the scaling power of growth rate but decreases that of metabolic rate, as predicted by the hypothesis. During the fifth instar, the energy budgets of larvae change dynamically. The free-feeding larvae slightly decrease the energy allocated to growth as body mass increases and increase the energy allocated to life sustaining. The opposite trends were observed in food restricted larvae, indicating the predicted prioritization in the energy budget under food restriction. We compare the energy budgets of a few endothermic and ectothermic species and discuss how different life histories lead to the differences in the energy budgets under food restriction.

On the complex relationship between energy expenditure and longevity: Reconciling the contradictory empirical results with a simple theoretical model

The relationship between energy expenditure and longevity has been a central theme in aging studies. Empirical studies have yielded controversial results, which cannot be reconciled by existing theories. In this paper, we present a simple theoretical model based on first principles of energy conservation and allometric scaling laws. The model takes into considerations the energy tradeoffs between life history traits and the efficiency of the energy utilization, and offers quantitative and qualitative explanations for a set of seemingly contradictory empirical results. We show that oxidative metabolism can affect cellular damage and longevity in different ways in animals with different life histories and under different experimental conditions. Qualitative data and the linearity between energy expenditure, cellular damage, and lifespan assumed in previous studies are not sufficient to understand the complexity of the relationships. Our model provides a theoretical framework for quantitative analyses and predictions. The model is supported by a variety of empirical studies, including studies on the cellular damage profile during ontogeny; the intra- and inter-specific correlations between body mass, metabolic rate, and lifespan; and the effects on lifespan of (1) diet restriction and genetic modification of growth hormone, (2) the cold and exercise stresses, and (3) manipulations of antioxidant.

TCTAP A-084 Lesion-Specific Myocardial Mass: A New Index for Diagnosis and Treatment of Coronary Artery Disease

Accurate quantification of the myocardial mass by coronary computed tomography angiography (CCTA) has become available. And lesion-specific myocardial mass (LMM) could be estimated with clinical applications of allometric scaling law. The aim of this study was to estimate the influence of the amount

Temporal patterns of energy equivalence in temperate soil invertebrates.

The question whether total population energy use is invariant to species body size (the energy equivalence hypothesis) is central to metabolic ecology and continues to be controversial. While recent comparative field work and meta-analyses pointed to systematic deviations of the underlying allometric scaling laws from predictions of metabolic theory none of these studies included the variability of metabolic scaling in ecological time. Here we used extensive data on the invertebrate soil fauna of Kampinos National Park (Poland) obtained from six consecutive quantitative sampling seasons to show that phylogenetically corrected species density—body weight and population energy use—body weight relationships across all soil fauna species and within trophic groups and body weight classes were highly variable in time. On average, population energy use tended to increase with species body weight in decomposers and phytophages, but not in predators. Despite these trends, our data do not exclude the possibility that energy equivalence marks the central tendency of energy use in the edaphon. Our results highlight the need for long-term studies on energy use to unequivocally assess predictions of metabolic theory.Electronic supplementary materialThe online version of this article (doi:10.1007/s00442-015-3317-3) contains supplementary material, which is available to authorized users.

Heterogeneity of cells may explain allometric scaling of metabolic rate

The origin of allometric scaling of metabolic rate is a long-standing question in biology. Several models have been proposed for explaining the origin; however, they have advantages and disadvantages. In particular, previous models only demonstrate either two important observations for the allometric scaling: the variability of scaling exponents and predominance of 3/4-power law. Thus, these models have a dispute over their validity. In this study, we propose a simple geometry model, and show that a hypothesis that total surface area of cells determines metabolic rate can reproduce these two observations by combining two concepts: the impact of cell sizes on metabolic rate and fractal-like (hierarchical) organization. The proposed model both theoretically and numerically demonstrates the approximately 3/4-power law although several different biological strategies are considered. The model validity is confirmed using empirical data. Furthermore, the model suggests the importance of heterogeneity of cell size for the emergence of the allometric scaling. The proposed model provides intuitive and unique insights into the origin of allometric scaling laws in biology, despite several limitations of the model.

Fractals and Fractal Dimension of Systems of Blood Vessels: An Analogy between Artery Trees, River Networks, and Urban Hierarchies

An analogy between the fractal nature of networks of arteries and that of systems of rivers has been drawn in the previous works. However, the deep structure of the hierarchy of blood vessels has not yet been revealed. This paper is devoted to researching the fractals, allometric scaling, and hierarchy of blood vessels. By analogy with Horton-Strahler's laws of river composition, three exponential laws have been put forward. These exponential laws can be reconstructed and transformed into three linear scaling laws, which can be named composition laws of blood vessels network. From these linear scaling laws it follows a set of power laws, including the three-parameter Zipf's law on the rank-size distribution of blood vessel length and the allometric scaling law on the length-diameter relationship of blood vessels in different orders. The models are applied to the observed data on human beings and animals early given by other researchers, and an interesting finding is that human bodies more conform to natural rules than dog's bodies. An analogy between the hierarchy of blood vessels, river networks, and urban systems are further drawn, and interdisciplinary studies of hierarchies will probably provide new revealing examples for the science of complexity.