In vivo porcine left atrial wall stress: Computational model

Most computational models of the heart have so far concentrated on the study of the left ventricle, mainly using simplified geometries. The same approach cannot be adopted to model the left atrium, whose irregular shape does not allow morphological simplifications. In addition, the deformation of the left atrium during the cardiac cycle strongly depends on the interaction with its surrounding structures. We present a procedure to generate a comprehensive computational model of the left atrium, including physiological loads (blood pressure), boundary conditions (pericardium, pulmonary veins and mitral valve annulus movement) and mechanical properties based on planar biaxial experiments. The model was able to accurately reproduce the in vivo dynamics of the left atrium during the passive portion of the cardiac cycle. A shift in time between the peak pressure and the maximum displacement of the mitral valve annulus allows the appendage to inflate and bend towards the ventricle before the pulling effect associated with the ventricle contraction takes place. The ventricular systole creates room for further expansion of the appendage, which gets in close contact with the pericardium. The temporal evolution of the volume in the atrial cavity as predicted by the finite element simulation matches the volume changes obtained from CT scans. The stress field computed at each time point shows remarkable spatial heterogeneity. In particular, high stress concentration occurs along the appendage rim and in the region surrounding the pulmonary veins.     

It's all relative: allometry and variation in the baculum (os penis) of the harp seal, Pagophilus groenlandicus (Carnivora: Phocidae)

We compared allometry and variation in the baculum (os penis), mandible, and humerus of the harp seal, Pagophilus groenlandicus. This species is presumed to have a promiscuous mating system in which choice of mate by females during intromission with different males is likely. The baculum is large and grows throughout life so may be an honest indicator of males' quality (size) or viability (age). We predicted that bacular size would exhibit stronger allometry relative to body size than mandibles or humeri. The baculum is less functionally (mechanically) constrained than mandibles or humeri so we also predicted it would be more variable, though less variable than sexually selected traits which do not function as honest indicators. Our sample (N=67 seals) represented broad ranges of size and age (0–35 yr) so we compared variation using residuals from allometric regressions of skeletal measurements on body length. Bacular size was isometric to body length until ∼ 137 cm (when some seals enter puberty) in body length then was highly positively allometric; mandibular and humeral size were negatively allometric to body length throughout growth. Bacula were more variable than mandibles or humeri. Bacular size in large specimens (>137 cm in body length) was related strongly to body length and weakly to age. We interpret bacular size to be an uncheatable honest indicator of male quality and viability. High bacular variation conforms with theoretical predictions of females' asymmetrical choice of mate and choice of extremes, and may reflect corresponding anatomical variation among females. Some bacular variation may also result incidentally from positive allometry coupled with lifelong bacular growth, which can amplify early differences between reproductive and somatic growth, enabled by weak selection on bacular form in relation to function.     

Growth and energy allocation in the deep-sea urchin Echinus affinis

Growth of regular echinoids, expressed as test diameter through time, generally shows a sigmoidal pattern. However, when urchin size is considered in terms of test volume we show that growth of the deep-sea echinoid Echinus affinis is ultimately linear, rather than saturating. We construct a simple allometric model of energy allocation that produces linear growth in volume in mature urchins by allocating an increasing proportion of net assimilate to reproduction. This model provides an excellent fit to the observed growth curve data. Data on gonad weight as a function of test diameter allow us to test the relationship between allocation to reproduction and urchin size predicted from the growth curve fit. Simultaneous fitting of the growth curve and gonad weight data allow us to consider a model where the allometry of net assimilation is allowed to vary. We investigate possible explanations for the fact that net assimilation appears to rise faster than linearly with weight in E. affinis. We conclude that strategic models of individual energetics provide a useful tool for the analysis of the limited data available on deep-sea populations.     

Size and shape: the developmental regulation of static allometry in insects

Among all organisms, the size of each body part or organ scales with overall body size, a phenomenon called allometry. The study of shape and form has attracted enormous interest from biologists, but the genetic, developmental and physiological mechanisms that control allometry and the proportional growth of parts have remained elusive. Recent progress in our understanding of body-size regulation provides a new synthetic framework for thinking about the mechanisms and the evolution of allometric scaling. In particular, insulin/IGF signaling, which plays major roles in longevity, diabetes and the regulation of cell, organ and body size, might also be centrally involved in regulating organismal shape. Here we review recent advances in the fields of growth regulation and endocrinology and use them to construct a developmental model of static allometry expression in insects. This model serves as the foundation for a research program that will result in a deeper understanding of the relationship between growth and form, a question that has fascinated biologists for centuries.     

Respective impacts of aortic stenosis and systemic hypertension on left ventricular hypertrophy

It has been reported that 30-40% of patients with aortic stenosis are hypertensive. In such patients, the left ventricle faces a double (i.e. valvular and vascular) pressure overload, which results in subsequent wall volume hypertrophy. From a clinical standpoint, it is difficult to separate the respective contributions of aortic stenosis and systemic hypertension to left ventricular burden and patient's symptoms and thus to predict whether valve replacement would be beneficial. The objective of this theoretical study was therefore to investigate the relative effects of valvular and vascular afterloads on left ventricular hypertrophy. We used a ventricular-valvular-vascular mathematical model in combination with the Arts' model describing the myofiber stress. Left ventricular wall volume was computed for different aortic blood pressure levels and different degrees of aortic stenosis severity. Our simulations show that the presence of concomitant systemic hypertension has a major influence on the development of left ventricular hypertrophy in patients with aortic stenosis. These results also suggest that mild-to-moderate aortic stenosis has a minor impact on left ventricular wall volume when compared with hypertension. On the other hand, when aortic stenosis is severe, wall volume increases exponentially with increasing aortic stenosis severity and the impact of aortic stenosis on left ventricular hypertrophy becomes highly significant.     

Statistical model of variable allometric growth: otolith growth in Micropogonias furnieri(Actinopterygii, Sciaenidae)

The main objective of this study was to develop a statistical model for accurate estimates of relative growth. The method was based on identifying patterns of the residuals obtained from the Huxley's allometric equation. Three different approaches were applied: (1) growth with variable proportionality and constant allometry coefficient, (2) growth with constant proportionality and variable allometry coefficient and (3) distinct growth phases in which proportionality and allometry coefficients remained constant. The proposed statistical models were applied to the relationship of the otolith size and fish size of whitemouth croaker Micropogonias furnieri . The best fit was obtained when using approach (3). A change in the growth parameters was associated with the attainment of sexual maturity.     

The developmental basis for allometry in insects

Within all species of animals, the size of each organ bears a specific relationship to overall body size. These patterns of organ size relative to total body size are called static allometry and have enchanted biologists for centuries, yet the mechanisms generating these patterns have attracted little experimental study. We review recent and older work on holometabolous insect development that sheds light on these mechanisms. In insects, static allometry can be divided into at least two processes: (1) the autonomous specification of organ identity, perhaps including the approximate size of the organ, and (2) the determination of the final size of organs based on total body size. We present three models to explain the second process: (1) all organs autonomously absorb nutrients and grow at organ-specific rates, (2) a centralized system measures a close correlate of total body size and distributes this information to all organs, and (3) autonomous organ growth is combined with feedback between growing organs to modulate final sizes. We provide evidence supporting models 2 and 3 and also suggest that hormones are the messengers of size information. Advances in our understanding of the mechanisms of allometry will come through the integrated study of whole tissues using techniques from development, genetics, endocrinology and population biology.     

Variation in the ontogenetic allometry of horn length in bovids along a body mass continuum

Allometric relationships describe the proportional covariation between morphological, physiological, or life‐history traits and the size of the organisms. Evolutionary allometries estimated among species are expected to result from species differences in ontogenetic allometry, but it remains uncertain whether ontogenetic allometric parameters and particularly the ontogenetic slope can evolve. In bovids, the nonlinear evolutionary allometry between horn length and body mass in males suggests systematic changes in ontogenetic allometry with increasing species body mass. To test this hypothesis, we estimated ontogenetic allometry between horn length and body mass in males and females of 19 bovid species ranging from ca. 5 to 700 kg. Ontogenetic allometry changed systematically with species body mass from steep ontogenetic allometries over a short period of horn growth in small species to shallow allometry with the growth period of horns matching the period of body mass increase in the largest species. Intermediate species displayed steep allometry over long period of horn growth. Females tended to display shallower ontogenetic allometry with longer horn growth compared to males, but these differences were weak and highly variable. These findings show that ontogenetic allometric slope evolved across species possibly as a response to size‐related changes in the selection pressures acting on horn length and body mass.     

Thermodynamics Constrains Allometric Scaling of Optimal Development Time in Insects

Development time is a critical life-history trait that has profound effects on organism fitness and on population growth rates. For ectotherms, development time is strongly influenced by temperature and is predicted to scale with body mass to the quarter power based on 1) the ontogenetic growth model of the metabolic theory of ecology which describes a bioenergetic balance between tissue maintenance and growth given the scaling relationship between metabolism and body size, and 2) numerous studies, primarily of vertebrate endotherms, that largely support this prediction. However, few studies have investigated the allometry of development time among invertebrates, including insects. Abundant data on development of diverse insects provides an ideal opportunity to better understand the scaling of development time in this ecologically and economically important group. Insects develop more quickly at warmer temperatures until reaching a minimum development time at some optimal temperature, after which development slows. We evaluated the allometry of insect development time by compiling estimates of minimum development time and optimal developmental temperature for 361 insect species from 16 orders with body mass varying over nearly 6 orders of magnitude. Allometric scaling exponents varied with the statistical approach: standardized major axis regression supported the predicted quarter-power scaling relationship, but ordinary and phylogenetic generalized least squares did not. Regardless of the statistical approach, body size alone explained less than 28% of the variation in development time. Models that also included optimal temperature explained over 50% of the variation in development time. Warm-adapted insects developed more quickly, regardless of body size, supporting the “hotter is better” hypothesis that posits that ectotherms have a limited ability to evolutionarily compensate for the depressing effects of low temperatures on rates of biological processes. The remaining unexplained variation in development time likely reflects additional ecological and evolutionary differences among insect species.     

Hemodynamic Response to Exercise After Beta-Adrenergic Blockade with Propranolol in Patients with Mitral Valve Obstruction

Propranolol (P) .13 mg./kg. was given to seven patients with mitral valve obstruction the changes in resting and exercise hemodynamics were followed by means of combined right and left heart catheterization. Changes were variable. At rest there was a decrease in heart rate of 10 beats/min. with no consistent change in stroke volume, cardiac output, left ventricular systolic (LVS) or left atrial (LA) pressure after P. Mean left ventricular end-diastolic (LVED) pressure was increased 3 mm., mean pulmonary artery (PA) pressure was increased 4 mm., and mean mitral valve gradient was reduced 3 mm. Hg by P. During exercise, mean LVS pressure was decreased 31 mm., mean LVED pressure increased 3 mm., mean LA pressure decreased 3 mm., and mean mitral valve gradient was reduced 5 mm. Hg after P. Mean exercise PA pressure was unchanged, cardiac output was reduced 0.9 1./min., and mean heart rate was reduced 37 beats/min., while stroke volume increased 3 ml./beat after P. Exercise pulmonary vascular resistance was increased from 6.1 to 8.2 units by P. Despite a slower heart rate, the diastolic filling period was not increased. P has no place in the treatment of the majority of patients with mitral stenosis because it further reduces cardiac performance below normal.     

Taylor's law and body size in exploited marine ecosystems

Taylor's law (TL), which states that variance in population density is related to mean density via a power law, and density‐mass allometry, which states that mean density is related to body mass via a power law, are two of the most widely observed patterns in ecology. Combining these two laws predicts that the variance in density is related to body mass via a power law (variance‐mass allometry). Marine size spectra are known to exhibit density‐mass allometry, but variance‐mass allometry has not been investigated. We show that variance and body mass in unexploited size spectrum models are related by a power law, and that this leads to TL with an exponent slightly <2. These simulated relationships are disrupted less by balanced harvesting, in which fishing effort is spread across a wide range of body sizes, than by size‐at‐entry fishing, in which only fish above a certain size may legally be caught.     

Hearing dimorphism, trait variation and conflicts over space in the thorax of the bushcricket Requena verticalis (Listroscelidinae: Tettigoniidae: Orthoptera)

The hearing system of Requena verticalis is sexually dimorphic. Previous work has shown size of the auditory spiracle determines absolute threshold and as female spiracles are, on average, larger than males, females are more sensitive to the main energy of the male call. In all measured traits in morphology and physiology, females showed lower coefficient of variation than males. This difference was significant for bulla volume and hearing threshold. In addition, female ear size covaries with thorax dimensions but this is not so in males. Such a finding suggests stabilising selection on ear size in females, perhaps explained by the requirement of females to recognise and locate the male. As the auditory bulla is larger in females than males, so occupying thoracic space, we suggest a possible trade-off in this brachypterous species between hearing sensitivity and sound production. Finally, we examine relative growth of body structures not associated with hearing and those that influence hearing sensitivity. Scaling, where traits are under strong selection, may result in allometry. Female hearing traits show positive allometry with absolute size and while the relationship between bulla volume and spiracle area was positively allometric in females this was not the case for males.     

Crown allometries are less responsive than stem allometry to tree size and habitat variations in an Indian monsoon forest

While theoretical allometric models postulate universal scaling exponents, empirical relationships between tree dimensions show marked variability that reflects changes in the biomass allocation pattern. As growth of the various tree compartments may be controlled by different functions, it is hypothesized that they may respond differently to factors of variation, resulting in variable tree morphologies and potentially in trade-offs between allometric relationships. We explore the variability of tree stem and crown allometries using a dataset of 1,729 trees located in an undisturbed wet evergreen forest of the Western Ghats, India. We specifically test whether species adult stature, terrain slope, tree size and crown light exposure affect the relationships between stem diameter and stem height (stem allometry), and between stem diameter and crown width, crown area and crown volume (crown allometries). Results show that both stem and crown allometries are subject to variations in relation to both endogenous (tree size, species adult stature) and exogenous (terrain slope, crown light exposure) factors. Stem allometry appears to be more affected by these factors than are crown allometries, including the stem diameter–crown volume relationship, which proved to be particularly stable. Our results support the idea that height is a prevailing adjustment factor for a tree facing variable growth (notably light) conditions, while stem diameter–crown volume allometry responds more to internal metabolic constraints. We ultimately discuss the various sources of variability in the stem and crown allometries of tropical trees that likely play an important role in forest community dynamics.     

Vascular growth and remodeling in compensatory lung growth following right lobectomy.

Studies in animal models have shown that, following lobectomy (LBX), there is compensatory growth in the remaining lung. The vascular growth response following right LBX (R-LBX) is poorly understood. To test the hypothesis that arterial growth and remodeling occur in response to LBX, in proportion to the amount of right lung tissue removed, two (24% of lung mass; R-LBX2 group) or three right lobes (52% of lung mass; R-LBX3 group) were removed via thoracotomy from adult rats. Sham control animals underwent thoracotomy only. Arteriograms were generated 3 wk after surgery. The areas of the left lung arteriogram, arterial branching, length of arterial branches, arterial density, and arterial-to-alveolar ratios were measured. To determine whether R-LBX causes vascular remodeling and pulmonary hypertension, muscularization of arterioles and right ventricular hypertrophy were assessed. Lung weight and volume indexes were greater in R-LBX3. Arterial area of the left lung increased 26% in R-LBX2 and 47% in R-LBX3. The length of large arteries increased in R-LBX3 and to a lesser extent in R-LBX2. The ratio of distal pulmonary arteries to alveoli was similar after R-LBX2 compared with sham but was 30% lower in R-LBX3. Muscularization of arterioles increased after R-LBX3, but not in R-LBX2. Right ventricular hypertrophy increased 50-70% in R-LBX3, but not in R-LBX2. Whereas removal of three right lung lobes induced arterial growth in the left lungs of adult rats, which was proportionate to the number of lobes removed, the ratio of distal pulmonary arteries to alveoli was not normal, and vascular remodeling and pulmonary hypertension developed.     

Tooth scaling and evolutionary dwarfism: an investigation of allometry in human pygmies

Gould has predicted that in rapidly dwarfed lineages the postcanine teeth exhibit a different scaling pattern than is the normal interspecific trend. His prediction of strong negative allometry has not been frequently tested in quantitative detail. Here we present results of scaling analyses of the molar teeth in African pygmies compared with other Africans of larger size and in Philippine pygmies compared with Filipinos of larger size. We find a pattern of strong negative allometry of tooth size to skull and body size in both these comparisons. This scaling pattern is explained by recourse to the developmental bases (known or inferred) of dwarfing in these populations. Body size decrease is related to low levels of the growth control substance insulin-like growth factor I (IGF-I), which does not appear to affect the size of the dentition. The implications of such developmental information for our understanding of allometric patterns in general, and dwarfing events in particular, are discussed.     

Mechanisms of hypotension produced by platelet-activating factor

Platelet-activating factor (PAF) is a phospholipid mediator that induces cardiovascular collapse and release of the secondary mediator thromboxane A2 (TxA2). To clarify mechanisms involved in this collapse and, specifically, the relative contribution of left ventricular and right ventricular dysfunction, we studied 12 open-chest pigs. PAF infusion (0.04-0.28 nmol.kg-1.min-1) induced a 5- to 120-fold increase in pulmonary vascular resistance, a 75-98% fall in cardiac output, and systemic arterial hypotension. Right ventricular failure was indicated by chamber enlargement, decreased shortening, and increased right atrial pressures. In contrast, left ventricular dysfunction was accompanied by decreases in chamber dimensions and filling pressures that were unresponsive to volume expansion. U 46619 (a stable TxA2 analogue) and mechanical pulmonary artery constriction induced changes similar to PAF. In 11 additional closed-chest pigs, TxA2 blockade with indomethacin attenuated the PAF-induced rise in pulmonary vascular resistance, right ventricular dysfunction, and systemic hypotension. A specific TxA2 synthase inhibitor, OKY-046, also diminished hemodynamic effects of PAF in six other pigs. Tachyphylaxis was not observed in five pigs repeatedly given PAF. We conclude that acute right ventricular failure as the result of severe increase in pulmonary vascular resistance is the primary mechanism early in the course of PAF-induced shock in the pig. PAF-induced release of TxA2 may contribute significantly to these events.     

ARTIFICIAL SELECTION ON HORN LENGTH-BODY SIZE ALLOMETRY IN THE HORNED BEETLE ONTHOPHAGUS ACUMINATUS (COLEOPTERA: SCARABAEIDAE)

Males of the horned beetle Onthophagus acuminatus Har. (Coleoptera: Scarabaeidae) exhibit horn length dimorphism due to a sigmoidal allometric relationship between horn length and body size: the steep slope of the allometry around the inflection of the sigmoid curve separates males into two groups; those larger than this inflection possess long horns, and those smaller than this inflection have short horns or lack horns. I examined the genetic basis of the allometric relationship between horn length and body size by selecting males that produced unusually long horns, and males that produced unusually short horns, for their respective body sizes. After seven generations of selection, lines selected for relatively long horns had significantly longer horn lengths for a given body size than lines selected for relatively short horns, indicating a heritable component to variation in the allometry. The sigmoidal shape of the allometry was not affected by this selection regime. Rather, selected lines differed in the position of the allometry along the body size axis. One consequence of lateral shifts in this allometric relationship was that the body size separating horned from hornless males (the point of inflection of the sigmoid curve) differed between selection lines: lines in which males were selected for relatively long horns began horn production at smaller body sizes than lines selected for relatively short horns. These results suggest that populations can evolve in response to selection on male horn length through modification of the growth relationship between horn length and body size.     

A quantitative morphometric comparative analysis of the primate temporal lobe

Given their importance in language comprehension, the human temporal lobes and/or some of their component structures might be expected to be larger than allometric predictions for a nonhuman anthropoid brain of human size. Whole brain, T1-weighted MRI scans were collected from 44 living anthropoid primates spanning 11 species. Easyvision software (Philips Medical Systems, The Netherlands) was used to measure the volume of the entire brain, the temporal lobes, the superior temporal gyri, and the temporal lobe white matter. The surface areas of both the entire temporal lobe and the superior temporal gyrus were also measured, as was temporal cortical gyrification.Allometric regressions of temporal lobe structures on brain volume consistently showed apes and monkeys to scale along different trajectories, with the monkeys typically lying at a higher elevation than the apes. Within the temporal lobe, overall volume, surface area, and white matter volume were significantly larger in humans than predicted by the ape regression lines. The largest departure from allometry in humans was for the temporal lobe white matter volume which, in addition to being significantly larger than predicted for brain size, was also significantly larger than predicted for temporal lobe volume. Among the nonhuman primate sample, Cebus have small temporal lobes for their brain size, and Macaca and Papio have large superior temporal gyri for their brain size. The observed departures from allometry might reflect neurobiological adaptations supporting species-specific communication in both humans and old world monkeys.     

Frank-Starling mechanism,fluid responsiveness,and length-dependent activation: Unravelling the multiscale behaviors with an in silico analysis

The Frank-Starling mechanism is a fundamental regulatory property which underlies the cardiac output adaptation to venous filling. Length-dependent activation is generally assumed to be the cellular origin of this mechanism. At the heart scale, it is commonly admitted that an increase in preload (ventricular filling) leads to an increased cellular force and an increased volume of ejected blood. This explanation also forms the basis for vascular filling therapy. It is actually difficult to unravel the exact nature of the relationship between length-dependent activation and the Frank-Starling mechanism, as three different scales (cellular, ventricular and cardiovascular) are involved. Mathematical models are powerful tools to overcome these limitations. In this study, we use a multiscale model of the cardiovascular system to untangle the three concepts (length-dependent activation, Frank-Starling, and vascular filling). We first show that length-dependent activation is required to observe both the Frank-Starling mechanism and a positive response to high vascular fillings. Our results reveal a dynamical length dependent activation-driven response to changes in preload, which involves interactions between the cellular, ventricular and cardiovascular levels and thus highlights fundamentally multiscale behaviors. We show however that the cellular force increase is not enough to explain the cardiac response to rapid changes in preload. We also show that the absence of fluid responsiveness is not related to a saturating Frank-Starling effect. As it is challenging to study those multiscale phenomena experimentally, this computational approach contributes to a more comprehensive knowledge of the sophisticated length-dependent properties of cardiac muscle.