Modeling of vascular networks

Microvascular anatomy suggests varying aerobic activity levels in the adipose tissues of diving tetrapods

Adipose tissue has many important functions including metabolic energy storage, endocrine functions, thermoregulation and structural support. Given these varied functions, the microvascular characteristics within the tissue will have important roles in determining rates/limits of exchange of nutrients, waste, gases and molecular signaling molecules between adipose tissue and blood. Studies on skeletal muscle have suggested that tissues with higher aerobic capacity contain higher microvascular density (MVD) with lower diffusion distances (DD) than less aerobically active tissues. However, little is known about MVD in adipose tissue of most vertebrates; therefore, we measured microvascular characteristics (MVD, DD, diameter and branching) and cell size to explore the comparative aerobic activity in the adipose tissue across diving tetrapods, a group of animals facing additional physiological and metabolic stresses associated with diving. Adipose tissues of 33 animals were examined, including seabirds, sea turtles, pinnipeds, baleen whales and toothed whales. MVD and DD varied significantly (P < 0.001) among the groups, with seabirds generally having high MVD, low DD and small adipocytes. These characteristics suggest that microvessel arrangement in short duration divers (seabirds) reflects rapid lipid turnover, compared to longer duration divers (beaked whales) which have relatively lower MVD and greater DD, perhaps reflecting the requirement for tissue with lower metabolic activity, minimizing energetic costs during diving. Across all groups, predictable scaling patterns in MVD and DD such as those observed in skeletal muscle did not emerge, likely reflecting the fact that unlike skeletal muscle, adipose tissue performs many different functions in marine organisms, often within the same tissue compartment.

Evolution of metabolic scaling among the tetrapod: Effect of phylogeny, the geologic time of class formation and uniformity of species within a class

The metabolic scaling in the animal has been discussed for over 90 years, but no consensus has been reached. Our analysis of 2,126 species of vertebrates reveals a significant allometric exponent heterogeneity. We show that classes of terrestrial vertebrates exhibit the evolution of metabolic scaling. Both the allometric coefficient "a" and the allometric exponent "b" change naturally, but differently depending on the geological time of group formation. The allometric coefficient "a" shows the measure of the evolutionary development of systems that forms resting metabolism in animals. Endothermic classes, such as birds and mammals, have a metabolic rate that is in an order of magnitude higher than that in ectothermic classes, including amphibians and reptiles. In the terrestrial vertebrate phylogeny, we find that the metabolic scaling is characterized by three main allometric exponent values: b = 3/4 (mammals), b > 3/4 (ectotherms, such as amphibians and reptiles), and b < 3/4 (birds). The heterogeneity of the allometric exponent is a natural phenomenon associated with the general evolution of vertebrates. The scaling factor decreases depending on both the external design and the size (birds vs mammals) of the animal. The metabolic rate and uniformity of species within a class increase as the geological start date of formation of the class approaches the present time. The higher the mass-specific standard metabolic rate in the class, the slower metabolic rate grows with increasing body size in this class. Our results lay the groundwork for further exploration of the evolutionary and ecological aspects of the development of metabolic scaling in animals. This article is protected by copyright. All rights reserved.

Properties of the Vascular Networks in Malignant Tumors

This work presents an analysis for real and synthetic angiogenic networks using a tomography image that obtains a portrait of a vascular network. After the image conversion into a binary format it is possible to measure various network properties, which includes the average path length, the clustering coefficient, the degree distribution and the fractal dimension. When comparing the observed properties with that produced by the Invasion Percolation algorithm (IPA), we observe that there exist differences between the properties obtained by the real and the synthetic networks produced by the IPA algorithm. Taking into account the former, a new algorithm which models the expansion of an angiogenic network through randomly heuristic rules is proposed. When comparing this new algorithm with the real networks it is observed that now both share some properties. Once creating synthetic networks, we prove the robustness of the network by subjecting the original angiogenic and the synthetic networks to the removal of the most connected nodes, and see to what extent the properties changed. Using this concept of robustness, in a very naive fashion it is possible to launch a hypothetical proposal for a therapeutic treatment based on the robustness of the network.

Evolution and Functional Differentiation of the Diaphragm Muscle of Mammals

Symmorphosis is a concept of economy of biological design, whereby structural properties are matched to functional demands. According to symmorphosis, biological structures are never over designed to exceed functional demands. Based on this concept, the evolution of the diaphragm muscle (DIAm) in mammals is a tale of two structures, a membrane that separates and partitions the primitive coelomic cavity into separate abdominal and thoracic cavities and a muscle that serves as a pump to generate intra-abdominal (Pab ) and intrathoracic (Pth ) pressures. The DIAm partition evolved in reptiles from folds of the pleural and peritoneal membranes that was driven by the biological advantage of separating organs in the larger coelomic cavity into separate thoracic and abdominal cavities, especially with the evolution of aspiration breathing. The DIAm pump evolved from the advantage afforded by more effective generation of both a negative Pth for ventilation of the lungs and a positive Pab for venous return of blood to the heart and expulsive behaviors such as airway clearance, defecation, micturition, and child birth. © 2019 American Physiological Society. Compr Physiol 9:715-766, 2019.

Concerted evolution of body mass and cell size: similar patterns among species of birds (Galliformes) and mammals (Rodentia)

Cell size plays a role in body size evolution and environmental adaptations. Addressing these roles, we studied body mass and cell size in Galliformes birds and Rodentia mammals, and collected published data on their genome sizes. In birds, we measured erythrocyte nuclei and basal metabolic rates (BMRs). In birds and mammals, larger species consistently evolved larger cells for five cell types (erythrocytes, enterocytes, chondrocytes, skin epithelial cells, and kidney proximal tubule cells) and evolved smaller hepatocytes. We found no evidence that cell size differences originated through genome size changes. We conclude that the organism-wide coordination of cell size changes might be an evolutionarily conservative characteristic, and the convergent evolutionary body size and cell size changes in Galliformes and Rodentia suggest the adaptive significance of cell size. Recent theory predicts that species evolving larger cells waste less energy on tissue maintenance but have reduced capacities to deliver oxygen to mitochondria and metabolize resources. Indeed, birds with larger size of the abovementioned cell types and smaller hepatocytes have evolved lower mass-specific BMRs. We propose that the inconsistent pattern in hepatocytes derives from the efficient delivery system to hepatocytes, combined with their intense involvement in supracellular function and anabolic activity.

Upper limits to body size imposed by respiratory-structural trade-offs in Antarctic pycnogonids

Across metazoa, surfaces for respiratory gas exchange are diverse, and the size of those surfaces scales with body size. In vertebrates with lungs and gills, surface area and thickness of the respiratory barrier set upper limits to rates of metabolism. Conversely, some organisms and life stages rely on cutaneous respiration, where the respiratory surface (skin, cuticle, eggshell) serves two primary functions: gas exchange and structural support. The surface must be thin and porous enough to transport gases but strong enough to withstand external forces. Here, we measured the scaling of surface area and cuticle thickness in Antarctic pycnogonids, a group that relies on cutaneous respiration. Surface area and cuticle thickness scaled isometrically, which may reflect the dual roles of cuticle in gas exchange and structural support. Unlike in vertebrates, the combined scaling of these variables did not match the scaling of metabolism. To resolve this mismatch, larger pycnogonids maintain steeper oxygen gradients and higher effective diffusion coefficients of oxygen in the cuticle. Interactions among scaling components lead to hard upper limits in body size, which pycnogonids could evade only with some other evolutionary innovation in how they exchange gases.

Body mass scaling of passive oxygen diffusion in endotherms and ectotherms

The area and thickness of respiratory surfaces, and the constraints they impose on passive oxygen diffusion, have been linked to differences in oxygen consumption rates and/or aerobic activity levels in vertebrates. However, it remains unclear how respiratory surfaces and associated diffusion rates vary with body mass across vertebrates, particularly in relation to the body mass scaling of oxygen consumption rates. Here we address these issues by first quantifying the body mass dependence of respiratory surface area and respiratory barrier thickness for a diversity of endotherms (birds and mammals) and ectotherms (fishes, amphibians, and reptiles). Based on these findings, we then use Fick's law to predict the body mass scaling of oxygen diffusion for each group. Finally, we compare the predicted body mass dependence of oxygen diffusion to that of oxygen consumption in endotherms and ectotherms. We find that the slopes and intercepts of the relationships describing the body mass dependence of passive oxygen diffusion in these two groups are statistically indistinguishable from those describing the body mass dependence of oxygen consumption. Thus, the area and thickness of respiratory surfaces combine to match oxygen diffusion capacity to oxygen consumption rates in both air- and water-breathing vertebrates. In particular, the substantially lower oxygen consumption rates of ectotherms of a given body mass relative to those of endotherms correspond to differences in oxygen diffusion capacity. These results provide insights into the long-standing effort to understand the structural attributes of organisms that underlie the body mass scaling of oxygen consumption.

Diverse forms of pulmonary hypertension remodel the arterial tree to a high shear phenotype

Pulmonary hypertension (PH) is associated with progressive changes in arterial network complexity. An allometric model is derived that integrates diameter branching complexity between pulmonary arterioles of generation n and the main pulmonary artery (MPA) via a power-law exponent (X) in dn = dMPA2(-n/X) and the arterial area ratio β = 2(1-2/X). Our hypothesis is that diverse forms of PH demonstrate early decrements in X independent of etiology and pathogenesis, which alters the arteriolar shear stress load from a low-shear stress (X > 2, β > 1) to a high-shear stress phenotype (X < 2, β < 1). Model assessment was accomplished by comparing theoretical predictions to retrospective morphometric and hemodynamic measurements made available from a total of 221 PH-free and PH subjects diagnosed with diverse forms (World Health Organization; WHO groups I-IV) of PH: mitral stenosis, congenital heart disease, chronic obstructive pulmonary lung disease, chronic thromboembolism, idiopathic pulmonary arterial hypertension (IPAH), familial (FPAH), collagen vascular disease, and methamphetamine exposure. X was calculated from pulmonary artery pressure (PPA), cardiac output (Q) and body weight (M), utilizing an allometric power-law prediction of X relative to a PH-free state. Comparisons of X between PAH-free and PAH subjects indicates a characteristic reduction in area that elevates arteriolar shear stress, which may contribute to mechanisms of endothelial dysfunction and injury before clinically defined thresholds of pulmonary vascular resistance and PH. We conclude that the evaluation of X may be of use in identifying reversible and irreversible phases of PH in the early course of the disease process.

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.

Detection of growth-restricted fetuses using a patient-specific model

Fetal growth restriction (FGR) is one of the major contributors to adverse perinatal outcome. The purpose of this work was to extend the use of Ultrasound Doppler measurements and allow early and accurate detection of FGR. To this end, a mathematical model was developed to represent the major fetal hemodynamic mechanisms involved. Based on model parameters' values, the forward model predicted flow waveforms at the locations where Doppler measurements are routinely performed. Blood velocity waveforms measured in 20 FGR and 20 normal fetuses were used as inputs to an inverse model solution to obtain the parameters' values of the specific fetus. Model predictions indicated significant changes in the circulation of FGR fetuses compared to normal fetuses. Estimated cardiac output was significantly lower in the FGR group compared to the control group (330 ± 52 ml min(-1) Kg(-1) compared to 396 ± 52 ml min(-1) Kg(-1), P<0.001). Also, estimated cardiac output distribution towards the placenta was lower for the FGR group (145 ± 49 ml min(-1) Kg(-1) compared to 181 ± 31 ml min(-1) Kg(-1), P<0.01). In the FGR group the model indicated also significant increase in estimated cardiac output distribution towards the brain (9.6 ± 0.7%, compared to 8.0 ± 1.6 %, P<0.01) and in the degree of blood shunted by the ductus venosus (60.6 ± 17.7 %, compared to 39.7 ± 14.8 %, P<0.01), indicating severe brain-sparing state in these fetuses. We conclude that patient-specific mathematical modeling is a promising direction for personalizing and optimizing the treatment options in pregnancies complicated by fetal growth-restriction.

Scaling adult doses of antifungal and antibacterial agents to children

My general pharmacokinetic scaling theory is discussed for the important matter of determining pediatric dosing for existing and new therapeutic drugs when optimal, or near-optimal, dosing for adults is known. The basis for the scaling is the requirement of a time-scaled likeness of the free-drug concentration time histories of children and adults. Broad categories of single and periodic dosing are considered. The former involves the scaling of dosage, and the latter involves both the dosage and schedule. The validity of the scaling relations is demonstrated by using measurements from previously reported clinical trials with adults and children (with ages generally 1 year or older) for the relatively new antifungal agent caspofungin and for the relatively new antibacterial agent linezolid. Standard pharmacodynamic effectiveness criteria are shown to be satisfied for the scaled dosage and schedule for children to the same extent that they are for the referenced adult. Consideration of scaling from adults to children is discussed for the case of new agents where no pediatric data are available and needed parameters are determined from in vitro measurements and preclinical animal data. A connection is also made between the allometric representation of clearance data and the dosing formulas. Limitations of the scaling results for infants because of growth and maturational matters are discussed. The general conclusion from this work is that the scaling theory does indeed have application to pediatric dosing for children, for both confirmation and refinement of present practice and guidance in pediatric treatment with new therapeutic agents.

Temporal profiles and 2-dimensional oxy-, deoxy-, and total-hemoglobin somatosensory maps in rat versus mouse cortex

BACKGROUND

Mechanisms of neurovascular coupling-the relationship between neuronal chemoelectrical activity and compensatory metabolic and hemodynamic changes-appear to be preserved across species from rats to humans despite differences in scale. However, previous work suggests that the highly cellular dense mouse somatosensory cortex has different functional hemodynamic changes compared to other species.

METHODS

We developed novel hardware and software for 2-dimensional optical spectroscopy (2DOS). Optical changes at four simultaneously recorded wavelengths were measured in both rat and mouse primary somatosensory cortex (S1) evoked by forepaw stimulation to create four spectral maps. The spectral maps were converted to maps of deoxy-, oxy-, and total-hemoglobin (HbR, HbO, and HbT) concentration changes using the modified Beer-Lambert law and phantom HbR and HbO absorption spectra.

RESULTS

: Functional hemodynamics were different in mouse versus rat neocortex. On average, hemodynamics were as expected in rat primary somatosensory cortex (S1): the fractional change in the log of HbT concentration increased monophasically 2 s after stimulus, whereas HbO changes mirrored HbR changes, with HbO showing a small initial dip at 0.5 s followed by a large increase 3.0 s post stimulus. In contrast, mouse S1 showed a novel type of stimulus-evoked hemodynamic response, with prolonged, concurrent, monophasic increases in HbR and HbT and a parallel decrease in HbO that all peaked 3.5-4.5 s post stimulus onset. For rats, at any given time point, the average size and shape of HbO and HbR forepaw maps were the same, whereas surface veins distorted the shape of the HbT map. For mice, HbO, HbR, and HbT forepaw maps were generally the same size and shape at any post-stimulus time point.

CONCLUSIONS

2DOS using image splitting optics is feasible across species for brain mapping and quantifying the map topography of cortical hemodynamics. These results suggest that during physiologic stimulation, different species and/or cortical architecture may give rise to different hemodynamic changes during neurovascular coupling.

Microcirculation: nexus of comorbidities in diabetes

Generalized capillary dysfunction is a morbid element in the metabolic syndrome, and it is likely involved in its complications. We tested the hypothesis that vast amounts of serum albumin previously observed in kidneys of rats with the metabolic syndrome were caused, in part, by leakage from renal peritubular capillaries. We report herein large scale leaks of plasma fluid in peritubular capillaries of rats with the metabolic syndrome. This finding was directly demonstrated in vivo, and the presence of leftover albumin residue confirmed the leak in postmortem kidney specimens. Moreover, renal interstitial fibrosis and tubular atrophy were found in a distribution similar to the leaked renal albumin in obese rats. We suggest that there is an important link between peritubular capillary damage and interstitial fibrosis, represented as tubulointerstitial disease in the metabolic syndrome. We propose that maintenance of the peritubular microcirculation may improve renal outcomes in diabetes and the metabolic syndrome.

Design of cerebellar and nontegmental rhombencephalic microvascular bed in the sterlet, Acipenser ruthenus: a scanning electron microscope and 3D morphometry study of vascular corrosion casts

The design of the microvasculature of cerebellum and nontegmental rhombencephalic areas was studied in eight adult Acipenser ruthenus L. by scanning electron microscopy of vascular corrosion casts and three-dimensional morphometry. Gross vascularization was described and diameters and total branching angles of parent and daughter vessels of randomly selected arterial and capillary bifurcations (respectively, venous mergings) were measured. With diameters ranging from 15.9 +/- 1.9 microm (cerebellum; mean +/- S.D.) to 15.9 +/- 1.7 mm (nontegmental rhombencephalon; mean +/- S.D.) capillaries in Acipenser were significantly (p > or = .05) smaller than in cyclostomes (18-20 microm) but significantly thicker than in higher vertebrates and men (6-8 microm). With the exception of the area ratio beta (i.e., sum of squared daugther diameters divided by squared diameter of parent vessel) of the venular mergings in the nontegmental rhombencephalon, no significant differences (p > or = .05) existed between the two brain areas. Data showed that arteriolar and capillary bifurcations and venular mergings are optimally designed in respect to diameters of parent vessel to daughter vessels and to branching (merging) angles. Quantitative data are discussed both in respect to methodical pitfalls and the optimality principles possibly underlying the design of vascular bifurcations/mergings in selected brain areas of a nonteleost primitive actinopterygian fish.

Problems of allometric scaling analysis: examples from mammalian reproductive biology

Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2)objective recognition of divergent subsets in the data (allometric grades);(3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution,greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation(rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of `independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.