Comparison of various approaches to calculating the optimal hematocrit in vertebrates

The role of the heart in the evolution of aerobic performance

Aerobic metabolism underlies vital traits such as locomotion and thermogenesis, and aerobic capacity influences fitness in many animals. The heart is a key determinant of aerobic capacity, but the relative influence of cardiac output versus other steps in the O2 transport pathway remains contentious. In this Commentary, we consider this issue by examining the mechanistic basis for adaptive increases in aerobic capacity (thermogenic V̇O2,max; also called summit metabolism) in deer mice (Peromyscus maniculatus) native to high altitude. Thermogenic V̇O2,max is increased by acclimation to cold hypoxia (simulating high-altitude conditions), and high-altitude populations generally have greater V̇O2,max than their low-altitude counterparts. This plastic and evolved variation in V̇O2,max is associated with corresponding variation in maximal cardiac output, along with variation in other traits across the O2 pathway (e.g. arterial O2 saturation, blood haemoglobin content and O2 affinity, tissue O2 extraction, tissue oxidative capacity). By applying fundamental principles of gas exchange, we show that the relative influence of cardiac output on V̇O2,max depends on the O2 diffusing capacity of thermogenic tissues (skeletal muscles and brown adipose tissues). Functional interactions between cardiac output and blood haemoglobin content determine circulatory O2 delivery and thus affect V̇O2,max, particularly in high-altitude environments where erythropoiesis can increase haematocrit and blood viscosity. There may also be functional linkages between cardiac output and tissue O2 diffusion due to the role of blood flow in determining capillary haematocrit and red blood cell flux. Therefore, the functional interactions between cardiac output and other traits in the O2 pathway underlie the adaptive evolution of aerobic capacities.

Optimal hematocrit theory: a review

In humans and many animals, a trade-off between a sufficiently high concentration of erythrocytes (hematocrit) to bind oxygen and sufficiently low blood viscosity to allow rapid blood flow has been achieved during evolution. The optimal value lies between the extreme cases of pure blood plasma, which cannot practically transport any oxygen, and 100% hematocrit, which would imply very slow blood flow or none at all. As oxygen delivery to tissues is the main task of the cardiovascular system, it is reasonable to expect that maximum oxygen delivery has been achieved during evolution. Optimal hematocrit theory, based on this optimality principle, has been successful in predicting hematocrit values of about 0.3-0.5, which are indeed observed in the systemic circulation of humans and many animal species. Similarly, the theory can explain why a hematocrit higher than normal, ranging from 0.5 to 0.7, can promote better exertional performance. Here, we present a review of theoretical approaches to the calculation of the optimal hematocrit value under different conditions and discuss them in a broad physiological context. Several physiological and medical implications are outlined, for example, in view of blood doping, temperature adaptation, dehydration, and life at high altitudes.

The value of hematocrit for predicting bronchopulmonary dysplasia in very low birth weight preterm infants

To determine hematocrit (HCT) and to identify independent risk factors for predicting bronchopulmonary dysplasia (BPD) in preterm infants with very low birth weight (VLBW) infants. This retrospective study included 296 premature infants with VLBW in the neonatal intensive care unit of the First Affiliated Hospital of the University of Science and Technology of China between January 2015 and December 2019. Maternal pregnant information and clinical information as well as hematological parameters of preterm babies were collected and compared. Then the maximum area under the curve of receiver operating characteristic curve was developed to estimate the predictive indicator in the blood. Finally, differential variables together with the predictive index were screened for multiple logistic regression analysis to determine independent prognostic factors for BPD. Infants were divided into a BPD group (134 cases) and a non-BPD group (162 cases). The area under the curve of HCT at postnatal 1 week was 0.737 with the sensitivity of 52.30 % and the specificity of 86.00%. Birth weight (BW) <1.12 kg, gestational age <28.4 weeks, newborn respiratory distress syndrome, mechanical ventilation ≥ 7 days, ventilation associated pneumonia, patent arterial duct, PaO2/FiO2 <300 mm Hg and HCT <0.455 at postnatal 1 week were risk factors for BPD of VLBW infants. HCT levels below 0.455 at 1 week after birth serve as a valuable indicator for the potential development of BPD.

Comparisons of Hematological and Biochemical Profiles in Brahman and Yunling Cattle

Brahman cattle are tolerant to parasite challenges and heat stress. Yunling cattle are three-way hybrids that are half Brahman cattle, a fourth Murray Grey cattle and a fourth Yunnan Yellow cattle, with good beef performance. The hematological and biochemical parameters can reflect the physiology and metabolic conditions of cattle, and there are valuable indicators of production performance and adaptability that can be found by studying the cattle. To assess the health status and differences, we compared 55 hematological and biochemical parameters of 28 Brahman cattle and 65 Yunling cattle using an automatic biochemical analyzer. Our results showed that 27 hematological and biochemical indices of Brahman cattle were lower than those of Yunling cattle, whereas the other parameters were higher. There are 20 indices with significant differences that were detected between Brahman and Yunling cattle (with p ≤ 0.01 or 0.01 ≤ p ≤ 0.05, respectively), and no significant differences were found for other indices (p > 0.05). Based on these results, Yunling cattle may have a better physical condition than Brahman cattle, may be better at adapting to local environments, and can maintain a good production and reproduction performance. As a new breed that is half Brahman, the abilities of Yunling cattle, including adaptability, stress resistance and tolerance to crude feed, were better than Brahman cattle under the same management conditions.

Trade-Offs (and Constraints) in Organismal Biology

AbstractTrade-offs and constraints are inherent to life, and studies of these phenomena play a central role in both organismal and evolutionary biology. Trade-offs can be defined, categorized, and studied in at least six, not mutually exclusive, ways. (1) Allocation constraints are caused by a limited resource (e.g., energy, time, space, essential nutrients), such that increasing allocation to one component necessarily requires a decrease in another (if only two components are involved, this is referred to as the Y-model, e.g., energy devoted to size versus number of offspring). (2) Functional conflicts occur when features that enhance performance of one task decrease performance of another (e.g., relative lengths of in-levers and out-levers, force-velocity trade-offs related to muscle fiber type composition). (3) Shared biochemical pathways, often involving integrator molecules (e.g., hormones, neurotransmitters, transcription factors), can simultaneously affect multiple traits, with some effects being beneficial for one or more components of Darwinian fitness (e.g., survival, age at first reproduction, fecundity) and others detrimental. (4) Antagonistic pleiotropy describes genetic variants that increase one component of fitness (or a lower-level trait) while simultaneously decreasing another. (5) Ecological circumstances (or selective regime) may impose trade-offs, such as when foraging behavior increases energy availability yet also decreases survival. (6) Sexual selection may lead to the elaboration of (usually male) secondary sexual characters that improve mating success but handicap survival and/or impose energetic costs that reduce other fitness components. Empirical studies of trade-offs often search for negative correlations between two traits that are the expected outcomes of the trade-offs, but this will generally be inadequate if more than two traits are involved and especially for complex physiological networks of interacting traits. Moreover, trade-offs often occur only in populations that are experiencing harsh environmental conditions or energetic challenges at the extremes of phenotypic distributions, such as among individuals or species that have exceptional athletic abilities. Trade-offs may be (partially) circumvented through various compensatory mechanisms, depending on the timescale involved, ranging from acute to evolutionary. Going forward, a pluralistic view of trade-offs and constraints, combined with integrative analyses that cross levels of biological organization and traditional boundaries among disciplines, will enhance the study of evolutionary organismal biology.

Polymorphisms in the ovine GP5 gene associated with blood physiological indices

This study aimed to analyze the effects of polymorphisms in GP5 on blood physiological indices of 1065 sheep. The coefficients of variation of the red blood cell count (RBC), hemoglobin concentration (HGB), mean platelet volume (MPV), mean erythrocyte hemoglobin content (MCH), and red blood cell distribution-coefficient of variation (RDW-CV) were greater than 10%, and there was a very significant correlation between the main indices such as RBC, white blood cell, and platelet count (PLT) and most other indices (p < 0.01). qRT-PCR showed that GP5 was expressed in the heart, liver, spleen, lung, kidney, rumen, duodenum, muscle, tail fat, and lymph tissue, with significantly higher expression in the lymph. Subsequently, we detected single nucleotide polymorphisms (SNPs) in GP5 from group, which identified synonymous mutation g.657 T > C in the first exon of GP5. Association analysis showed significant correlations between the SNP and the physiological traits (p < 0.05), in which the RBC, neutrophilic granulocyte (NEUT) and RDW-CV values in sheep with the TC genotype and TT genotype were markedly lower than those in the CC genotype (p < 0.05). Thus, GP5 polymorphisms could be candidate biomarkers to screen blood physiological indices.

Calculating the optimal hematocrit under the constraint of constant cardiac power

In humans and higher animals, a trade-off between sufficiently high erythrocyte concentrations to bind oxygen and sufficiently low blood viscosity to allow rapid blood flow has been achieved during evolution. Optimal hematocrit theory has been successful in predicting hematocrit (HCT) values of about 0.3-0.5, in very good agreement with the normal values observed for humans and many animal species. However, according to those calculations, the optimal value should be independent of the mechanical load of the body. This is in contradiction to the exertional increase in HCT observed in some animals called natural blood dopers and to the illegal practice of blood boosting in high-performance sports. Here, we present a novel calculation to predict the optimal HCT value under the constraint of constant cardiac power and compare it to the optimal value obtained for constant driving pressure. We show that the optimal HCT under constant power ranges from 0.5 to 0.7, in agreement with observed values in natural blood dopers at exertion. We use this result to explain the tendency to better exertional performance at an increased HCT.

Hematocrit, age, and survival in a wild vertebrate population

Understanding trade-offs in wild populations is difficult, but important if we are to understand the evolution of life histories and the impact of ecological variables upon them. Markers that reflect physiological state and predict future survival would be of considerable benefit to unraveling such trade-offs and could provide insight into individual variation in senescence. However, currently used markers often yield inconsistent results. One underutilized measure is hematocrit, the proportion of blood comprising erythrocytes, which relates to the blood's oxygen-carrying capacity and viscosity, and to individual endurance. Hematocrit has been shown to decline with age in cross-sectional studies (which may be confounded by selective appearance/disappearance). However, few studies have tested whether hematocrit declines within individuals or whether low hematocrit impacts survival in wild taxa. Using longitudinal data from the Seychelles warbler (Acrocephalus sechellensis), we demonstrated that hematocrit increases with age in young individuals (<1.5 years) but decreases with age in older individuals (1.5-13 years). In breeders, hematocrit was higher in males than females and varied relative to breeding stage. High hematocrit was associated with lower survival in young individuals, but not older individuals. Thus, while we did not find support for hematocrit as a marker of senescence, high hematocrit is indicative of poor condition in younger individuals. Possible explanations are that these individuals were experiencing dehydration and/or high endurance demands prior to capture, which warrants further investigation. Our study demonstrates that hematocrit can be an informative metric for life-history studies investigating trade-offs between survival, longevity, and reproduction.

Hypercapnia increases brain viscoelasticity

Brain function, the brain's metabolic activity, cerebral blood flow (CBF), and intracranial pressure are intimately linked within the tightly autoregulated regime of intracranial physiology in which the role of tissue viscoelasticity remains elusive. We applied multifrequency magnetic resonance elastography (MRE) paired with CBF measurements in 14 healthy subjects exposed to 5-min carbon dioxide-enriched breathing air to induce cerebral vasodilatation by hypercapnia. Stiffness and viscosity as quantified by the magnitude and phase angle of the complex shear modulus, |G*| and ϕ, as well as CBF of the whole brain and 25 gray matter sub-regions were analyzed prior to, during, and after hypercapnia. In all subjects, whole-brain stiffness and viscosity increased due to hypercapnia by 3.3 ± 1.9% and 2.0 ± 1.1% which was accompanied by a CBF increase of 36 ± 15%. Post-hypercapnia, |G*| and ϕ reduced to normal values while CBF decreased by 13 ± 15% below baseline. Hypercapnia-induced viscosity changes correlated with CBF changes, whereas stiffness changes did not. The MRE-measured viscosity changes correlated with blood viscosity changes predicted by the Fåhræus-Lindqvist model and microvessel diameter changes from the literature. Our results suggest that brain viscoelastic properties are influenced by microvessel blood flow and blood viscosity: vasodilatation and increased blood viscosity due to hypercapnia result in an increase in MRE values related to viscosity.

Optimal hematocrit in an artificial microvascular network

BACKGROUND

Higher hematocrit increases the oxygen-carrying capacity of blood but also increases blood viscosity, thus decreasing blood flow through the microvasculature and reducing the oxygen delivery to tissues. Therefore, an optimal value of hematocrit that maximizes tissue oxygenation must exist.

STUDY DESIGN AND METHODS

We used viscometry and an artificial microvascular network device to determine the optimal hematocrit in vitro. Suspensions of fresh red blood cells (RBCs) in plasma, normal saline, or a protein-containing buffer and suspensions of stored red blood cells (at Week 6 of standard hypothermic storage) in plasma with hematocrits ranging from 10 to 80% were evaluated.

RESULTS

For viscometry, optimal hematocrits were 10, 25.2, 31.9, 37.1, and 37.5% for fresh RBCs in plasma at shear rates of 3.2 or less, 11.0, 27.7, 69.5, and 128.5 inverse seconds. For the artificial microvascular network, optimal hematocrits were 51.1, 55.6, 59.2, 60.9, 62.3, and 64.6% for fresh RBCs in plasma and 46.4, 48.1, 54.8, 61.4, 65.7, and 66.5% for stored RBCs in plasma at pressures of 2.5, 5, 10, 20, 40, and 60 cm H₂ O.

CONCLUSION

Although exact optimal hematocrit values may depend on specific microvascular architecture, our results suggest that the optimal hematocrit for oxygen delivery in the microvasculature depends on perfusion pressure. Therefore, anemia in chronic disorders may represent a beneficial physiological response to reduced perfusion pressure resulting from decreased heart function and/or vascular stenosis. Our results may help explain why a therapeutically increasing hematocrit in such conditions with RBC transfusion frequently leads to worse clinical outcomes.

Hematocrit and hematocrit viscosity ratio during exercise in athletes: Even closer to predicted optimal values?

The hemorheological theory of optimal hematocrit suggests that the best value of hematocrit (hct) should be that which results in the highest value of the hematocrit/viscosity (h/η) ratio. Trained athletes compared to sedentary subjects have a lower hct, but a higher h/η, and endurance training reduces the discrepancy between the actual hct and the ⪡ideal⪢ hct that can be predicted with a theoretical curve of h/η vs hct constructed with Quemada's model. In this study we investigated what becomes this homeostasis of h/η and hct during acute exercise in 19 athletes performing a 25 min exercise test. VO2max is negatively correlated to resting hct and positively correlated to discrepancy between actual and ideal resting hct which is correlated to the maximal rise in hct during exercise. Predicted and actual values of the h/η were fairly correlated (r = 0.970 p < 0.001) but the actual value was lower at rest and this discrepancy vanished at 25 min exercise. Exercise-induced decrease in discrepancy between actual and theoretical h/η was negatively correlated with the score of overtraining. All these findings suggest that h/η is a regulated parameter and that its model-predicted ⪡optimal⪢ values yield a ⪡theoretical optimal⪢ hct which is close to the actual value and even closer when athletes are well trained. In addition, acute exercise sets h/η closer from its predicted ideal value and this adaptation is impaired when athletes quote elevated scores on the overtraining questionnaire.

The optimum hematocrit

The hematocrit (Hct) determines the oxygen carrying capacity of blood, but also increases blood viscosity and thus flow resistance. From this dual role the concept of an optimum Hct for tissue oxygenation has been derived. Viscometric studies using the ratio Hct/blood viscosity at high shear rate showed an optimum Hct of 50-60% for red blood cell (RBC) suspensions in plasma. For the perfusion of an artificial microvascular network with 5-70μm channels the optimum Hct was 60-70% for high driving pressures. With lower shear rates or driving pressures the optimum Hct shifted towards lower values. In healthy, well trained athletes an increase of the Hct to supra-normal levels can increase exercise performance. These data with healthy individuals suggest that the optimum Hct for oxygen transport may be higher than the physiological range (35-40% in women, 39-50% in men). This is in contrast to clinical observations. Large clinical studies have repeatedly shown that a correction of anemia in a variety of disorders such as chronic kidney disease, heart failure, coronary syndrome, oncology, acute gastrointestinal bleeding, critical care, or surgery have better clinical outcomes when restrictive transfusion strategies are applied. Actual guidelines, therefore, recommend a transfusion threshold of 7-8 g/dL hemoglobin (Hct 20-24%) in stable, hospitalized patients. The discrepancy between the optimum Hct in health and disease may be due to factors such as decreased perfusion pressures (low cardiac output, vascular stenoses, change in vascular tone), endothelial cell dysfunction, leukocyte adhesion and others.

Actual vs optimal fetal hematocrit measured with punctures of cord blood in utero: Relationship with umbilical artery resistance

Physiological studies on fetal blood in narrow glass tubes have suggested that fetal optimal hematocrit (hct) might be as high as 60%. A theoretical 'ideal' hct can also be predicted with a theoretical curve of hematocrit/viscosity (h/η) ratio vs hct constructed with Quemada's model. We used the database of one of our previous papers on fetal hemorheology to reinterpret its results with this concept. A series of 28 intrauterine cord punctures (between 19 and 33 weeks gestation) with doppler measurements of resistance in umbilical arteries was studied. The theoretical 'optimal hematocrit' was well correlated to actual (r = 0.857, p < 0.01) but systematically lower (Bland-Altman plot +12.1[8.52-15.7]) than the actual one. Umbilical artery resistance index is correlated with actual hematocrit (r = 0.407, p < 0.05), the discrepancy between ideal and actual (r = - 0.542, p < 0.05) but not predicted ideal hematocrit, suggesting that the discrepancy between ideal and actual may reflect an adaptative decrease aiming at reducing vascular resistance. These findings indicate that prediction of ideal hematocrit with Quemada's equation makes sense in fetal blood, and suggest that a 'viscoregulatory mechanism' maintains hematocrit below this theoretical value in order to avoid excess vascular resistance.

Intracerebral Cell Implantation: Preparation and Characterization of Cell Suspensions

Intracerebral cell transplantation is increasingly finding a clinical translation. However, the number of cells surviving after implantation is low (5-10%) compared to the number of cells injected. Although significant efforts have been made with regard to the investigation of apoptosis of cells after implantation, very little optimization of cell preparation and administration has been undertaken. Moreover, there is a general neglect of the biophysical aspects of cell injection. Cell transplantation can only be an efficient therapeutic approach if an optimal transfer of cells from the dish to the brain can be ensured. We therefore focused on the in vitro aspects of cell preparation of a clinical-grade human neural stem cell (NSC) line for intracerebral cell implantation. NSCs were suspended in five different vehicles: phosphate-buffered saline (PBS), Dulbecco's modified Eagle medium (DMEM), artificial cerebral spinal fluid (aCSF), HypoThermosol, and Pluronic. Suspension accuracy, consistency, and cell settling were determined for different cell volume fractions in addition to cell viability, cell membrane damage, and clumping. Maintenance of cells in suspension was evaluated while being stored for 8 h on ice, at room temperature, or physiological normothermia. Significant differences between suspension vehicles and cellular volume fractions were evident. HypoThermosol and Pluronic performed best, with PBS, aCSF, and DMEM exhibiting less consistency, especially in maintaining a suspension and preserving viability under different storage conditions. These results provide the basis to further investigate these preparation parameters during the intracerebral delivery of NSCs to provide an optimized delivery process that can ensure an efficient clinical translation.

Association of Hematological Variables with Team-Sport Specific Fitness Performance

Purpose

We investigated association of hematological variables with specific fitness performance in elite team-sport players.

Methods

Hemoglobin mass (Hb_mass) was measured in 25 elite field hockey players using the optimized (2 min) CO-rebreathing method. Hemoglobin concentration ([Hb]), hematocrit and mean corpuscular hemoglobin concentration (MCHC) were analyzed in venous blood. Fitness performance evaluation included a repeated-sprint ability (RSA) test (8 x 20 m sprints, 20 s of rest) and the Yo-Yo intermittent recovery level 2 (YYIR2).

Results

Hb_mass was largely correlated (r = 0.62, P<0.01) with YYIR2 total distance covered (YYIR2_TD) but not with any RSA-derived parameters (r ranging from -0.06 to -0.32; all P>0.05). [Hb] and MCHC displayed moderate correlations with both YYIR2_TD (r = 0.44 and 0.41; both P<0.01) and RSA sprint decrement score (r = -0.41 and -0.44; both P<0.05). YYIR2_TD correlated with RSA best and total sprint times (r = -0.46, P<0.05 and -0.60, P<0.01; respectively), but not with RSA sprint decrement score (r = -0.19, P>0.05).

Conclusion

Hb_mass is positively correlated with specific aerobic fitness, but not with RSA, in elite team-sport players. Additionally, the negative relationships between YYIR2 and RSA tests performance imply that different hematological mechanisms may be at play. Overall, these results indicate that these two fitness tests should not be used interchangeably as they reflect different hematological mechanisms.

Quantitative aspects of drug permeation across in vitro and in vivo barriers

The kinetics of permeation across epithelial and endothelial cell sheets and across cell membranes is determinant for the pharmacokinetics of a drug. In vitro transport experiments with cultured cells or artificial barriers have tremendously improved the predictability of the in vivo behaviour of tested compounds. This article focuses on the parameters and calculation methods that are used to describe permeation quantitatively, with a focus on in vitro experiments and the prediction of intestinal absorption and blood-brain barrier passage. It shows under which in vitro experimental conditions standard calculations are adequate and under which conditions equations should be adapted to the experimental details. The impact of volume differences between donor and receiver compartments, pH gradients, addition of albumin, accumulation in the barrier and unidirectional transport by an efflux transporter on the results is shown in simulations. The article should make researchers aware of experimental factors that affect the outcome of a permeation experiment and how to account for this during data analysis. Finally, strategies to predict the in vivo behaviour of a compound based on the in vitro data are discussed. The goal of the article is to support researchers in choosing experimental conditions and calculation methods that deliver appropriate and reproducible results in permeation studies in vitro.

Causes of upregulation of glycolysis in lymphocytes upon stimulation. A comparison with other cell types

In this review, we revisit the metabolic shift from respiration to glycolysis in lymphocytes upon activation, which is known as the Warburg effect in tumour cells. We compare the situation in lymphocytes with those in several other cell types, such as muscle cells, Kupffer cells, microglia cells, astrocytes, stem cells, tumour cells and various unicellular organisms (e.g. yeasts). We critically discuss and compare several explanations put forward in the literature for the observation that proliferating cells adopt this apparently less efficient pathway: hypoxia, poisoning of competitors by end products, higher ATP production rate, higher precursor supply, regulatory effects, and avoiding harmful effects (e.g. by reactive oxygen species). We conclude that in the case of lymphocytes, increased ATP production rate and precursor supply are the main advantages of upregulating glycolysis.

Dynamics of blood viscosity regulation during hypoxic challenges in the chicken embryo (Gallus gallus domesticus)

Hypoxia in chicken embryos increases hematocrit (Hct), blood O2 content, and blood viscosity. The latter may limit O2 transport capacity (OTC) via increased peripheral resistance. Hct increase may result from increased nucleated red blood cell concentration ([RBC]) and mean corpuscular volume (MCV) or reduced plasma volume. We hypothesized changes in Hct, hemoglobin concentration ([Hb]), [RBC] and MCV and their effects on viscosity would reduce OTC. Five experimental treatments that increase Hct were conducted on day 15 embryos: 60min water submergence with 60min recovery in air; exposure to 15% O2 with or without 5% CO2 for 24 h with 6 h recovery; or exposure to 10% O2 with or without 5% CO2 for 120 min with 120 min recovery. Control Hct, [Hb], [RBC], MCV, and viscosity were approximately 26%, 9g%, 2.0 10(6)μL(-1), 130μm(3), and 1.6mPas, respectively. All manipulations increased Hct and blood viscosity without changing blood osmolality (276mmolkg(-1)). Increased viscosity was attributed to increased [RBC] and MCV in submerged embryos, but solely MCV in embryos experiencing 10% O2 regardless of CO2. Blood viscosity in embryos exposed to 15% O2 increased via increased MCV alone, and viscosity was constant during recovery despite increased [RBC]. Consequently, blood viscosity was governed by MCV and [RBC] during submergence, while MCV was the strongest determinant of blood viscosity in extrinsic hypoxia with or without hypercapnia. Increased Hct and blood O2 content did not compensate for the effect of increased viscosity on OTC during these challenges.

Hematocrit dispersion in asymmetrically bifurcating vascular networks

Quantitative modeling of physiological processes in vasculatures requires an accurate representation of network topology, including vessel branching. We propose a new approach for reconstruction of vascular network, which determines how vessel bifurcations distribute red blood cells (RBC) in the microcirculation. Our method follows the foundational premise of Murray's law in postulating the existence of functional optimality of such networks. It accounts for the non-Newtonian behavior of blood by allowing the apparent blood viscosity to vary with discharge hematocrit and vessel radius. The optimality criterion adopted in our approach is the physiological cost of supplying oxygen to the tissue surrounding a blood vessel. Bifurcation asymmetry is expressed in terms of the amount of oxygen consumption associated with the respective tissue volumes being supplied by each daughter vessel. The vascular networks constructed with our approach capture a number of physiological characteristics observed in in vivo studies. These include the nonuniformity of wall shear stress in the microcirculation, the significant increase in pressure gradients in the terminal sections of the network, the nonuniformity of both the hematocrit partitioning at vessel bifurcations and hematocrit across the capillary bed, and the linear relationship between the RBC flux fraction and the blood flow fraction at bifurcations.

Vertebrate blood cell volume increases with temperature: implications for aerobic activity

Aerobic activity levels increase with body temperature across vertebrates. Differences in these levels, from highly active to sedentary, are reflected in their ecology and behavior. Yet, the changes in the cardiovascular system that allow for greater oxygen supply at higher temperatures, and thus greater aerobic activity, remain unclear. Here we show that the total volume of red blood cells in the body increases exponentially with temperature across vertebrates, after controlling for effects of body size and taxonomy. These changes are accompanied by increases in relative heart mass, an indicator of aerobic activity. The results point to one way vertebrates may increase oxygen supply to meet the demands of greater activity at higher temperatures.

A theoretical study of lipid accumulation in the liver-implications for nonalcoholic fatty liver disease

A hallmark of the nonalcoholic fatty liver disease is the accumulation of lipids. We developed a mathematical model of the hepatic lipid dynamics to simulate the fate of fatty acids in hepatocytes. Our model involves fatty acid uptake, lipid oxidation, and lipid export. It takes into account that storage of triacylglycerol within hepatocytes leads to cell enlargement reducing the sinusoids radius and impairing hepatic microcirculation. Thus oxygen supply is reduced, which impairs lipid oxidation. The analysis of our model revealed a bistable behavior (two stable steady states) of the system, in agreement with histological observations showing distinct areas of lipid accumulation in lobules. The first (healthy) state is characterized by intact lipid oxidation and a low amount of stored lipids. The second state in our model may correspond to the steatotic cell; it is marked by a high amount of stored lipids and a reduced lipid oxidation caused by impaired oxygen supply. Our model stresses the role of insufficient oxygen supply for the development of steatosis. We discuss implications of our results in regard to the experimental design aimed at exploring lipid metabolism reactions under steatotic conditions. Moreover, the model helps to understand the reversibility of lipid accumulation and predicts the reversible switch to show hysteresis. The system can switch from the steatotic state back to the healthy state by reduction of fatty acid uptake below the threshold at which steatosis started. The reversibility corresponds to the observation that caloric restriction can reduce the lipid content in the liver.

Optimal concentration for sugar transport in plants

Vascular plants transport energy in the form of sugars from the leaves where they are produced to sites of active growth. The mass flow of sugars through the phloem vascular system is determined by the sap flow rate and the sugar concentration. If the concentration is low, little energy is transferred from source to sink. If it is too high, sap viscosity impedes flow. An interesting question is therefore at which concentration is the sugar flow optimal. Optimization of sugar flow and transport efficiency predicts optimal concentrations of 23.5 per cent (if the pressure differential driving the flow is independent of concentration) and 34.5 per cent (if the pressure is proportional to concentration). Data from more than 50 experiments (41 species) collected from the literature show an average concentration in the range from 18.2 per cent (all species) to 21.1 per cent (active loaders), suggesting that the phloem vasculature is optimized for efficient transport at constant pressure and that active phloem loading may have developed to increase transport efficiency.

Optimal concentrations in transport systems

Many biological and man-made systems rely on transport systems for the distribution of material, for example matter and energy. Material transfer in these systems is determined by the flow rate and the concentration of material. While the most concentrated solutions offer the greatest potential in terms of material transfer, impedance typically increases with concentration, thus making them the most difficult to transport. We develop a general framework for describing systems for which impedance increases with concentration, and consider material flow in four different natural systems: blood flow in vertebrates, sugar transport in vascular plants and two modes of nectar drinking in birds and insects. The model provides a simple method for determining the optimum concentration copt in these systems. The model further suggests that the impedance at the optimum concentration μopt may be expressed in terms of the impedance of the pure (c = 0) carrier medium μ0 as μopt 2(α)μ0, where the power α is prescribed by the specific flow constraints, for example constant pressure for blood flow (α = 1) or constant work rate for certain nectar-drinking insects (α = 6). Comparing the model predictions with experimental data from more than 100 animal and plant species, we find that the simple model rationalizes the observed concentrations and impedances. The model provides a universal framework for studying flows impeded by concentration, and yields insight into optimization in engineered systems, such as traffic flow.