Allometric Scaling Laws Research Articles

Taxonomic identity best explains variation in body nutrient stoichiometry in a diverse marine animal community

Animal-mediated nutrient dynamics are critical processes in ecosystems. Previous research has found animal-mediated nutrient supply (excretion) to be highly predictable based on allometric scaling, but similar efforts to find universal predictive relationships for an organism’s body nutrient content have been inconclusive. We use a large dataset from a diverse tropical marine community to test three frameworks for predicting body nutrient content. We show that body nutrient content does not follow allometric scaling laws and that it is not well explained by trophic status. Instead, we find strong support for taxonomic identity (particularly at the family level) as a predictor of body nutrient content, indicating that evolutionary history plays a crucial role in determining an organism’s composition. We further find that nutrients are “stoichiometrically linked” (e.g., %C predicts %N), but that the direction of these relationships does not always conform to expectations, especially for invertebrates. Our findings demonstrate that taxonomic identity, not trophic status or body size, is the best baseline from which to predict organismal body nutrient content.

Universal scaling laws rule explosive growth in human cancers.

Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly-complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings.

Elastohydrodynamic Scaling Law for Heart Rates.

Animal hearts are soft shells that actively pump blood to oxygenate tissues. Here, we propose an allometric scaling law for the heart rate based on the idea of elastohydrodynamic resonance of a fluid-loaded soft active elastic shell that buckles and contracts axially when twisted periodically. We show that this picture is consistent with numerical simulations of soft cylindrical shells that twist-buckle while pumping a viscous fluid, yielding optimum ejection fractions of 35%-40% when driven resonantly. Our scaling law is consistent with experimental measurements of heart rates over 2 orders of magnitude, and provides a mechanistic basis for how metabolism scales with organism size. In addition to providing a physical rationale for the heart rate and metabolism of an organism, our results suggest a simple design principle for soft fluidic pumps.

Dimensionless process development for lattice structure design in laser powder bed fusion

Laser powder bed fusion enables the fabrication of complex components such as thin-walled cellular structures including lattice or honeycomb structures. Numerous manufacturing parameters are involved in the resulting properties of the fabricated component and a material and machine-dependent process window development is necessary to determine a suitable process map. For cellular structures the thickness, which correlates with the process parameters, directly influences the mechanical properties of the component. Thus, dimensionless scaling laws describing the correlation between strut thickness, process parameters, and material properties enable predictive lattice structure design for laser powder bed fusion. This contribution develops material independent dimensionless allometric scaling laws for both single track and contour exposure to enable process-driven design of lattice structures in laser powder bed fusion. The theory derived with dimensional analysis is validated for the powder alloys stainless steel alloy 1.4404, nickel alloy 2.4856, aluminum alloy AlSi10Mg and Scalmalloy AlMgSc. The results can be used for the process-driven design of lattice structures and dense material obtaining high precision in the micrometer range or economic production with high melt pool widths.

Allometric scaling patterns among the human coronary artery tree, myocardial mass, and coronary artery flow.

Human coronary artery tree is a physiological transport system for oxygen and vital materials through a hierarchical vascular network to match the energy demands of myocardium, which has the highest oxygen extraction ratio among body organs and heavily depends on the blood flow for its energy supply. Therefore, it would be reasonable to expect that the key design principle of this arterial network is to minimize energy expenditure, which can be described by allometric scaling law. We enrolled patients who underwent coronary computed tomography angiography without obstructive lesion. The cumulative arterial length (L), volume (V), and diameter (D) in relation to the artery‐specific myocardial mass (M) were assessed. Flow rate (Q) was computed using quantitative flow ratio (QFR) measurement in patients who underwent invasive angiography. A total of 638 arteries from 43 patients (mean age 61 years, male gender 65%) were analyzed. A significant power‐law relationship was found among L–M, V–M, D–M, V–L, D–L, and V–D, and also among Q–M, Q–L, Q–V, and Q–D in 106 arteries interrogated with QFR (p < .001, all). Our results suggest that the fundamental design principle of the human coronary arterial network may follow allometric scaling law.

Allometric scaling law and ergodicity breaking in the vascular system

Allometry or the quantitative study of the relationship of body size to living organism physiology is an important area of biophysical scaling research. The West-Brown-Enquist (WBE) model of fractal branching in a vascular network explains the empirical allometric Kleiber law (the ¾ scaling exponent for metabolic rates as a function of animal’s mass). The WBE model raises a number of new questions, such as how to account for capillary phenomena more accurately and what are more realistic dependencies for blood flow velocity on the size of a capillary. We suggest a generalized formulation of the branching model and investigate the ergodicity in the fractal vascular system. In general, the fluid flow in such a system is not ergodic, and ergodicity breaking is attributed to the fractal structure of the network. Consequently, the fractal branching may be viewed as a source of ergodicity breaking in biophysical systems, in addition to such mechanisms as aging and macromolecular crowding. Accounting for non-ergodicity is important for a wide range of biomedical applications where long observations of time series are impractical. The relevance to microfluidics applications is also discussed.

The genetic control of leaf allometry in the common bean, Phaseolus vulgaris

BackgroundTo maximize photosynthetic efficiency, plants have evolved a capacity by which leaf area scales allometrically with leaf mass through interactions with the environment. However, our understanding of genetic control of this allometric relationship remains limited.ResultsWe integrated allometric scaling laws expressed at static and ontogenetic levels into genetic mapping to identify the quantitative trait loci (QTLs) that mediate how leaf area scales with leaf mass and how such leaf allometry, under the control of these QTLs, varies as a response to environment change. A major QTL detected by the static model constantly affects the allometric growth of leaf area vs. leaf mass for the common bean (Phaseolus vulgaris) in two different environments. The ontogenetic model identified this QTL plus a few other QTLs that determine developmental trajectories of leaf allometry, whose expression is contingent heavily upon the environment.ConclusionsOur results gain new insight into the genetic mechanisms of how plants program their leaf morphogenesis to adapt to environmental perturbations.

Allometric Scaling of Mutual Information in Complex Networks: A Conceptual Framework and Empirical Approach

Complexity and information theory are two very valuable but distinct fields of research, yet sharing the same roots. Here, we develop a complexity framework inspired by the allometric scaling laws of living biological systems in order to evaluate the structural features of networks. This is done by aligning the fundamental building blocks of information theory (entropy and mutual information) with the core concepts in network science such as the preferential attachment and degree correlations. In doing so, we are able to articulate the meaning and significance of mutual information as a comparative analysis tool for network activity. When adapting and applying the framework to the specific context of the business ecosystem of Japanese firms, we are able to highlight the key structural differences and efficiency levels of the economic activities within each prefecture in Japan. Moreover, we propose a method to quantify the distance of an economic system to its efficient free market configuration by distinguishing and quantifying two particular types of mutual information, total and structural.

Abstract WMP64: From Static Imaging to Hemodynamic Modelling: Validation of Intracranial Blood Flow Simulations Against Population-Based PC-MRI Studies

Purpose: Modelling blood flow in cerebral arteries presents an opportunity to go beyond current luminal stenosis. These models could improve stroke prognostication by adding hemodynamic biomarkers such as translesional shear stress and pressure gradient. Such models, however, are rarely validated against real clinical data. We evaluated the accuracy of a computational fluid dynamics (CFD) model which uses allometric scaling laws against population-based Phase Contrast MRI (PC-MRI) measurements of blood flow in the brain. Methods: 3D models of the anterior circulation of 23 healthy subjects were reconstructed based on their MRA Time of Flight (TOF) images and CFD was used for modelling the blood flow. Lumped parameter Windkessel models were used as boundary conditions and allometric scaling laws were used to divide the flow and tune these boundary conditions, i.e. the resistance at each boundary was automatically adjusted based on the dimensions and branching of upstream vasculature. The results were compared against 4 PC-MRI studies from literature, covering a combined number of 417 healthy subjects. Results: The flow rate across 3 major intracranial arteries (ICA, MCA, and ACA) was obtained from the CFD simulations and was in good agreement with population-based PC-MRI studies. The agreement was 82.6% for the ICA, 85.9% for the MCA, and 80.4% for the ACA when comparing the average flow rate. The inter-patient variability of the flow rate (i.e. standard deviation) obtained from CFD simulations matched closely with the variation range measured in the literature. Allometric scaling enabled the model to accurately divide the flow at bifurcations (MCA/ICA flow ratio was 58.6% for the model vs 56.3% in the literature). We observed an average of 8 mmHg in pressure drop along the anterior circulation of healthy subjects (from ICA to MCA-M1 and ACA-A1), which agrees with the physiological range reported in the literature. Conclusion: This study shows the potential of accurately modelling blood flow based only on static images and demonstrates the validity of using allometric scaling in intracranial CFD simulations. The current modelling approach can potentially assist in stroke prognostication by obtaining hemodynamic risk factors from standard MRA TOF or CTA.

From quantum chemistry to quantum biology: a path toward consciousness.

This paper presents a historical overview of quantum physics methodology's development and application to various science fields beyond physics, especially biology and consciousness. Following a successful interpretation of several early 20t⁢h century experiments, quantum physics gradually provided a conceptual framework for molecular bonds via quantum chemistry. In recent years individual biological phenomena such as photosynthesis and bird navigation have been experimentally and theoretically analyzed using quantum methods, building conceptual foundations for quantum physics' entry into biology. Quantum concepts have also been recently employed to explain physiology's allometric scaling laws by introducing quantum metabolism theory. In the second part of this work, we discuss how quantum physics may also be pivotal to our understanding of consciousness, which has been touted by some researchers as the last frontier of modern science. Others believe that consciousness does not belong within the realm of science at all. Several hypotheses, especially the Orch OR theory, have been suggested over the past two decades to introduce a scientific basis to consciousness theory. We discuss the merits and potential extensions of these approaches.

Allometric scaling laws linking biomass and rooting depth vary across ontogeny and functional groups in tropical dry forest lianas and trees

There are two theories about how allocation of metabolic products occurs. The allometric biomass partitioning theory (APT) suggests that all plants follow common allometric scaling rules. The optimal partitioning theory (OPT) predicts that plants allocate more biomass to the organ capturing the most limiting resource. Whole-plant harvests of mature and juvenile tropical deciduous trees, evergreen trees, and lianas and model simulations were used to address the following knowledge gaps: (1) Do mature lianas comply with the APT scaling laws or do they invest less biomass in stems compared to trees? (2) Do juveniles follow the same allocation patterns as mature individuals? (3) Is either leaf phenology or life form a predictor of rooting depth? It was found that: (1) mature lianas followed the same allometric scaling laws as trees; (2) juveniles and mature individuals do not follow the same allocation patterns; and (3) mature lianas had shallowest coarse roots and evergreen trees had the deepest. It was demonstrated that: (1) mature lianas invested proportionally similar biomass to stems as trees and not less, as expected; (2) lianas were not deeper-rooted than trees as had been previously proposed; and (3) evergreen trees had the deepest roots, which is necessary to maintain canopy during simulated dry seasons.

Gestational growth trajectories derived from a dynamic fetal-placental scaling law.

Fetal trajectories characterizing growth rates in utero have relied primarily on goodness of fit rather than mechanistic properties exhibited in utero. Here, we use a validated fetal-placental allometric scaling law and a first principles differential equations model of placental volume growth to generate biologically meaningful fetal-placental growth curves. The growth curves form the foundation for understanding healthy versus at-risk fetal growth and for identifying the timing of key events in utero.

Fractal dimensions derived from spatial allometric scaling of urban form

The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric scaling law, which indicates spatial allometry of cities. This paper is devoted to exploring the fractal dimension proceeding from urban spatial allometry. By theoretical reasoning and empirical analysis of urban traffic network, we can derive a set of fractal dimension from the spatial allometry and reveal the basic property of the new fractal parameters. The findings are as follows. First, the fractal dimension values of traffic lines are higher than those of traffic nodes. Second, the fractal dimension values based on variable boundaries are lower than those based on the concentric circles. Conclusions can be reached that the fractal dimensions coming from spatial allometry are a type of correlation dimension rather than capacity dimension, and the relative growth rate of traffic points is greater than that of traffic nodes. This study provides new way of understanding allometry, fractals, and scaling in urban systems.

Reduced Amount or Integrity of Arterial Elastic Fibers Alters Allometric Scaling Relationships for Aortic Diameter and Heart Weight, But Not Cardiac Function in Maturing Mice.

Allometric scaling laws relate physiologic parameters to body weight. Genetically modified mice allow investigation of allometric scaling laws when fundamental cardiovascular components are altered. Elastin haploinsufficient (Eln+/-) mice have reduced elastin amounts, and fibulin-5 knockout (Fbln5-/-) mice have compromised elastic fiber integrity in the large arteries which may alter cardiovascular scaling laws. Previously published echocardiography data used to investigate aortic and left ventricular function in Eln+/- and Fbln5-/- mice throughout postnatal development and early adulthood were reanalyzed to determine cardiovascular scaling laws. Aortic diameter, heart weight, stroke volume, and cardiac output have scaling exponents within 1-32% of the predicted theoretical range, indicating that the scaling laws apply to maturing mice. For aortic diameter, Eln+/- and Eln+/+ mice have similar scaling exponents, but different scaling constants, suggesting a shift in starting diameter, but no changes in aortic growth with body weight. In contrast, the scaling exponent for aortic diameter in Fbln5-/- mice is lower than Fbln5+/+ mice, but the scaling constant is similar, suggesting that aortic growth with body weight is compromised in Fbln5-/- mice. For both Eln+/- and Fbln5-/- groups, the scaling constant for heart weight is increased compared to the respective control group, suggesting an increase in starting heart weight, but no change in the increase with body weight during maturation. The scaling exponents and constants for stroke volume and cardiac output are not significantly affected by reduced elastin amounts or compromised elastic fiber integrity in the large arteries, highlighting a robust cardiac adaptation despite arterial defects.

Pollinator size and its consequences: Robust estimates of body size in pollinating insects.

Body size is an integral functional trait that underlies pollination‐related ecological processes, yet it is often impractical to measure directly. Allometric scaling laws have been used to overcome this problem. However, most existing models rely upon small sample sizes, geographically restricted sampling and have limited applicability for non‐bee taxa. Allometric models that consider biogeography, phylogenetic relatedness, and intraspecific variation are urgently required to ensure greater accuracy. We measured body size as dry weight and intertegular distance (ITD) of 391 bee species (4,035 specimens) and 103 hoverfly species (399 specimens) across four biogeographic regions: Australia, Europe, North America, and South America. We updated existing models within a Bayesian mixed‐model framework to test the power of ITD to predict interspecific variation in pollinator dry weight in interaction with different co‐variates: phylogeny or taxonomy, sexual dimorphism, and biogeographic region. In addition, we used ordinary least squares regression to assess intraspecific dry weight ~ ITD relationships for ten bees and five hoverfly species. Including co‐variates led to more robust interspecific body size predictions for both bees and hoverflies relative to models with the ITD alone. In contrast, at the intraspecific level, our results demonstrate that the ITD is an inconsistent predictor of body size for bees and hoverflies. The use of allometric scaling laws to estimate body size is more suitable for interspecific comparative analyses than assessing intraspecific variation. Collectively, these models form the basis of the dynamic R package, “pollimetry,” which provides a comprehensive resource for allometric pollination research worldwide.

Predicting species-habitat relationships: does body size matter?

Allometric scaling laws are foundational to structuring processes from cellular to ecosystem levels. The idea that allometric relationships underlie species characteristic selection scales, the spatial scales at which species respond to landscape features, has recently been investigated, however, supporting empirical evidence is scarce. Lack of pattern can be explained by inaccurate estimation, low power, confounding factors, or absence of a relationship. In this paper, we evaluate the relationship between body size and species characteristic selection scales after overcoming limitations of previous study designs. We conducted 1328 avian point counts across the state of Nebraska using the robust sampling design to account for imperfect detection. We used Bayesian latent indicator scale selection with N-mixture models to estimate species’ characteristic selection scales of six habitat features for 86 species. We propagated the uncertainty associated with assigning characteristic scales to a model of the relationship between body size and characteristic spatial scales. Species characteristic scales varied across habitat predictors, and varied in the uncertainty associated with selecting single characteristic scales. After propagating uncertainty our results do not support a relationship between species’ body size and the spatial scales at which they respond to landscape features. As species abundance integrates birth, death, immigration, and emigration processes, each of which are influenced by ecological processes manifesting at various scales, we question whether a general allometric relationship should be expected. Our results suggest that selection may act on responses to specific environmental features, rather than responses to spatial scale per se.

Collision-based energetic comparison of rolling and hopping over obstacles.

Locomotion of machines and robots operating in rough terrain is strongly influenced by the mechanics of the ground-machine interactions. A rolling wheel in terrain with obstacles is subject to collisional energy losses, which is governed by mechanics comparable to hopping or walking locomotion. Here we investigate the energetic cost associated with overcoming an obstacle for rolling and hopping locomotion, using a simple mechanics model. The model considers collision-based interactions with the ground and the obstacle, without frictional losses, and we quantify, analyse, and compare the sources of energetic costs for three locomotion strategies. Our results show that the energetic advantages of the locomotion strategies are uniquely defined given the moment of inertia and the Froude number associated with the system. We find that hopping outperforms rolling at larger Froude numbers and vice versa. The analysis is further extended for a comparative study with animals. By applying size and inertial properties through an allometric scaling law of hopping and trotting animals to our models, we found that the conditions at which hopping becomes energetically advantageous to rolling roughly corresponds to animals’ preferred gait transition speeds. The energetic collision losses as predicted by the model are largely verified experimentally.

Cardiovascular Function of Modern Pigs Does not Comply with Allometric Scaling Laws

Growing concerns have been expressed regarding cardiovascular performance in modern farm pigs, which has been proposed as a critical factor contributing to the reduced adaptability of modern pigs to stress. Here we tested the hypothesis that cardiac dimensions and pump function in modern heavy farm pigs are disproportionally low for their body weight, and investigated potential underlying mechanisms. The results from the present study indeed demonstrate disproportionally low values for stroke volume and cardiac output in pigs with bodyweights over 150 kg. Importantly, these low values were not the result of impaired left ventricular (LV) systolic contractile function, but were due to a disproportionally small LV end-diastolic volume. The latter was associated with changes in determinants of LV passive stiffness, including (i) an increase in LV myocardial collagen, (ii) a shift from the compliant N2BA titin isoform towards the stiff N2B, and (iii) a marked elevation of aortic blood pressure. Taken together, these results demonstrate reduced pumping capacity of the hearts of heavy modern pigs, due to structural abnormalities in the LV myocardium.

Coronary lumen volume to myocardial mass ratio in primary microvascular angina

BackgroundMicrovascular angina (MVA) is an incompletely understood clinical entity. Computational analysis of coronary Computed Tomography Angiography (CTA) has shown an association between low coronary lumen volume to myocardial mass (V/M) ratio and lower Fractional Flow Reserve values, independent of plaque measures. We hypothesized that low V/M ratio may be present in patients with MVA. MethodsA retrospective case-control analysis was performed using patients fulfilling guideline criteria for MVA with controls matched for age, gender, coronary risk factors and atherosclerotic plaque burden. V/M was extracted off site (Heartflow Inc; Redwood City, CA) employing allometric scaling laws that allow the definition of the coronary circulation beyond the epicardium. FFRCT values were calculated in the major epicardial coronary arteries for each group. ResultsA total of 30 patients with MVA and 32 matched controls were included in the study. Mean total coronary lumen volume (2302 mm3 ± 109 vs 2978 mm3 ± 134, p < 0.001) and mean myocardial mass (90.4 g ± 13.7 vs 100.4 g ± 20.1, p = 0.029) were lower in MVA patients compared to controls. Mean V/M ratio was significantly lower in MVA compared to controls (25.6 mm3/g ± 5.9 vs 30.0 mm3/g ± 6.5, p = 0.007; c-statistic 0.69). V/M ratio did not differ significantly between subclasses of angina severity (p = 0.747). No difference in mean nadir FFRCT values was found between MVA and control groups in the LAD (0.86 ± 0.07 vs 0.83 ± 0.07, p = 0.154), LCX (0.90 ± 0.05 vs 0.90 ± 0.06, p = 0.240) and RCA (0.90 ± 0.04 vs 0.90 ± 0.03, p = 0.773) vessels. ConclusionPatients with microvascular angina demonstrate a significantly lower coronary CTA-derived coronary volume/myocardial mass ratio than asymptomatic controls.

Novel Mammalian Similarity Principle Predicted from the Standard Minimal Closed‐loop Cardiovascular Model

Allometric scaling laws are empirical relationships relating particular parameters to body weight. Investigators have identified only a small number of allometric invariants for the mammalian cardiovascular system‐‐combinations of parameters that have constant values independent of species weight. Although many allometric invariants have arisen from applying optimality principles, the physics governing blood pressures and flows impose constraints that strictly limit parameter values. Therefore, the purpose of the present work is to derive a novel mammalian similarity principle, assuming a closed‐loop cardiovascular model. First, we assumed the standard minimal closed‐loop model consisting of two ventricles, four vascular compartments, and two resistances. Because ventricles were characterized by the time‐varying elastance model, cardiac contractility was characterized by end‐systolic elastance (Ees). Second, we linearized model equations. Third, we assumed systemic arterial pressure (Psa) is regulated by renal control of blood volume. We then solved the model equations algebraically for stroke volume (SV). The equation was then rearranged to form a novel non‐dimensional relationship (EesSV/Psa) as a function of sets of cardiovascular parameters, most of which are recognized as allometric invariants. We then verified that EesSV/Psa is itself invariant across mammals by substituting measured values from mammalian species of greatly varying weights. Although values of Ees can vary at least four orders of magnitude, EesSV/Psa varies less than a factor of 2. We thus provide a novel allometric invariant derived from the fundamental principles governing blood flow rather than teleological arguments. Furthermore, this algebraic formulation provides a novel tool to scale results from diverse animal models involving cardiac contractility.