Scaling laws for capillary vessels of mammals at rest and in exercise

In vivo label-free tissue histology through a microstructured imaging window

Tissue histopathology, based on hematoxylin and eosin (H&E) staining of thin tissue slices, is the gold standard for the evaluation of the immune reaction to the implant of a biomaterial. It is based on lengthy and costly procedures that do not allow longitudinal studies. The use of non-linear excitation microscopy in vivo, largely label-free, has the potential to overcome these limitations. With this purpose, we develop and validate an implantable microstructured device for the non-linear excitation microscopy assessment of the immune reaction to an implanted biomaterial label-free. The microstructured device, shaped as a matrix of regular 3D lattices, is obtained by two-photon laser polymerization. It is subsequently implanted in the chorioallantoic membrane (CAM) of embryonated chicken eggs for 7 days to act as an intrinsic 3D reference frame for cell counting and identification. The histological analysis based on H&E images of the tissue sections sampled around the implanted microstructures is compared to non-linear excitation and confocal images to build a cell atlas that correlates the histological observations to the label-free images. In this way, we can quantify the number of cells recruited in the tissue reconstituted in the microstructures and identify granulocytes on label-free images within and outside the microstructures. Collagen and microvessels are also identified by means of second-harmonic generation and autofluorescence imaging. The analysis indicates that the tissue reaction to implanted microstructures is like the one typical of CAM healing after injury, without a massive foreign body reaction. This opens the path to the use of similar microstructures coupled to a biomaterial, to image in vivo the regenerating interface between a tissue and a biomaterial with label-free non-linear excitation microscopy. This promises to be a transformative approach, alternative to conventional histopathology, for the bioengineering and the validation of biomaterials in in vivo longitudinal studies.

Vessel Metrics: A software tool for automated analysis of vascular structure in confocal imaging

Images contain a wealth of information that is often under analyzed in biological studies. Developmental models of vascular disease are a powerful way to quantify developmentally regulated vessel phenotypes to identify the roots of the disease process. We present vessel Metrics, a software tool specifically designed to analyze developmental vascular microscopy images that will expedite the analysis of vascular images and provide consistency between research groups. We developed a segmentation algorithm that robustly quantifies different image types, developmental stages, organisms, and disease models at a similar accuracy level to a human observer. We validate the algorithm on confocal, lightsheet, and two photon microscopy data in a zebrafish model expressing fluorescent protein in the endothelial nuclei. The tool accurately segments data taken by multiple scientists on varying microscopes. We validate vascular parameters such as vessel density, network length, and diameter, across developmental stages, genetic mutations, and drug treatments, and show a favorable comparison to other freely available software tools. Additionally, we validate the tool in a mouse model. Vessel Metrics reduces the time to analyze experimental results, improves repeatability within and between institutions, and expands the percentage of a given vascular network analyzable in experiments.

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.

Inflation instability in the lung: an analytical model of a thick-walled alveolus with wavy fibres under large deformations

Inflation of hollow elastic structures can become unstable and exhibit a runaway phenomenon if the tension in their walls does not rise rapidly enough with increasing volume. Biological systems avoid such inflation instability for reasons that remain poorly understood. This is best exemplified by the lung, which inflates over its functional volume range without instability. The goal of this study was to determine how the constituents of lung parenchyma determine tissue stresses that protect alveoli from instability-related overdistension during inflation. We present an analytical model of a thick-walled alveolus composed of wavy elastic fibres, and investigate its pressure-volume behaviour under large deformations. Using second-harmonic generation imaging, we found that collagen waviness follows a beta distribution. Using this distribution to fit human pressure-volume curves, we estimated collagen and elastin effective stiffnesses to be 1247 kPa and 18.3 kPa, respectively. Furthermore, we demonstrate that linearly elastic but wavy collagen fibres are sufficient to achieve inflation stability within the physiological pressure range if the alveolar thickness-to-radius ratio is greater than 0.05. Our model thus identifies the constraints on alveolar geometry and collagen waviness required for inflation stability and provides a multiscale link between alveolar pressure and stresses on fibres in healthy and diseased lungs.

Oxygen Deficient (OD) Combustion and Metabolism: Allometric Laws of Organs and Kleiber’s Law from OD Metabolism?

The biology literature presents allometric relations for the specific metabolic rate (SMRk) of an organ k of mass mk within the body of mass mB: SMRk ∝ mBfk (body mass allometry, BMA). Wang et al. used BMA, summed-up energy from all organs and validated Kleiber’s law of the whole body: SMRM ∝ mBb’, b’ = −0.25. The issues raised in biology are: (i) why fk and b’ < 0, (ii) how do the organs adjust fk to yield b’? The current paper presents a “system” approach involving the field of oxygen deficient combustion (ODC) of a cloud of carbon particles and oxygen deficient metabolism (ODM), and provides partial answers by treating each vital organ as a cell cloud. The methodology yields the following: (i) a dimensionless “group” number GOD to indicate extent of ODM, (ii) SMRk of an organ in terms of the effectiveness factor; (iii) curve fitting of the effectiveness factor to yield the allometric exponents for the organ mass-based allometric laws (OMA); (iv) validation of the results with data from 111 biological species (BS) with mB ranging from 0.0075 to 6500 kg. The “hypoxic” condition at organ level, particularly for COVID-19 patients, and the onset of cancer and virus multiplication are interpreted in terms of ODM and glycolysis.

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.

Image-guided, Laser-based Fabrication of Vascular-derived Microfluidic Networks

This detailed protocol outlines the implementation of image-guided, laser-based hydrogel degradation for the fabrication of vascular-derived microfluidic networks embedded in PEGDA hydrogels. Here, we describe the creation of virtual masks that allow for image-guided laser control; the photopolymerization of a micromolded PEGDA hydrogel, suitable for microfluidic network fabrication and pressure head-driven flow; the setup and use of a commercially available laser scanning confocal microscope paired with a femtosecond pulsed Ti:S laser to induce hydrogel degradation; and the imaging of fabricated microfluidic networks using fluorescent species and confocal microscopy. Much of the protocol is focused on the proper setup and implementation of the microscope software and microscope macro, as these are crucial steps in using a commercial microscope for microfluidic fabrication purposes that contain a number of intricacies. The image-guided component of this technique allows for the implementation of 3D image stacks or user-generated 3D models, thereby allowing for creative microfluidic design and for the fabrication of complex microfluidic systems of virtually any configuration. With an expected impact in tissue engineering, the methods outlined in this protocol could aid in the fabrication of advanced biomimetic microtissue constructs for organ- and human-on-a-chip devices. By mimicking the complex architecture, tortuosity, size, and density of in vivo vasculature, essential biological transport processes can be replicated in these constructs, leading to more accurate in vitro modeling of drug pharmacokinetics and disease.

Allometric Scaling and Cell Ratios in Multi-Organ in vitro Models of Human Metabolism

Intelligent in vitro models able to recapitulate the physiological interactions between tissues in the body have enormous potential as they enable detailed studies on specific two-way or higher order tissue communication. These models are the first step toward building an integrated picture of systemic metabolism and signaling in physiological or pathological conditions. However, the rational design of in vitro models of cell–cell or cell–tissue interaction is difficult as quite often cell culture experiments are driven by the device used, rather than by design considerations. Indeed, very little research has been carried out on in vitro models of metabolism connecting different cell or tissue types in a physiologically and metabolically relevant manner. Here, we analyze the physiological relationship between cells, cell metabolism, and exchange in the human body using allometric rules, downscaling them to an organ-on-a-plate device. In particular, in order to establish appropriate cell ratios in the system in a rational manner, two different allometric scaling models (cell number scaling model and metabolic and surface scaling model) are proposed and applied to a two compartment model of hepatic-vascular metabolic cross-talk. The theoretical scaling studies illustrate that the design and hence relevance of multi-organ models is principally determined by experimental constraints. Two experimentally feasible model configurations are then implemented in a multi-compartment organ-on-a-plate device. An analysis of the metabolic response of the two configurations demonstrates that their glucose and lipid balance is quite different, with only one of the two models recapitulating physiological-like homeostasis. In conclusion, not only do cross-talk and physical stimuli play an important role in in vitro models, but the numeric relationship between cells is also crucial to recreate in vitro interactions, which can be extrapolated to the in vivo reality.

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.

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.

Scaling of brain metabolism and blood flow in relation to capillary and neural scaling

Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales with brain volume raised to a power of around 5/6. This value is significantly higher than the more common exponent 3/4 relating whole body resting metabolism with body mass and several other physiological variables in animals and plants. This article investigates the reasons for brain allometric distinction on a level of its microvessels. Based on collected empirical data it is found that regional cerebral blood flow CBF across gray matter scales with cortical volume as , brain capillary diameter increases as , and density of capillary length decreases as . It is predicted that velocity of capillary blood is almost invariant (), capillary transit time scales as , capillary length increases as , and capillary number as , where is typically a small correction for medium and large brains, due to blood viscosity dependence on capillary radius. It is shown that the amount of capillary length and blood flow per cortical neuron are essentially conserved across mammals. These results indicate that geometry and dynamics of global neuro-vascular coupling have a proportionate character. Moreover, cerebral metabolic, hemodynamic, and microvascular variables scale with allometric exponents that are simple multiples of 1/6, rather than 1/4, which suggests that brain metabolism is more similar to the metabolism of aerobic than resting body. Relation of these findings to brain functional imaging studies involving the link between cerebral metabolism and blood flow is also discussed.

Analytic theories of allometric scaling

During the 13 years since it was first advanced, the fractal network theory (FNT), an analytic theory of allometric scaling, has been subjected to a wide range of methodological, mathematical and empirical criticisms, not all of which have been answered satisfactorily. FNT presumes a two-variable power-law relationship between metabolic rate and body mass. This assumption has been widely accepted in the past, but a growing body of evidence during the past quarter century has raised questions about its general validity. There is now a need for alternative theories of metabolic scaling that are consistent with empirical observations over a broad range of biological applications. In this article, we briefly review the limitations of FNT, examine the evidence that the two-variable power-law assumption is invalid, and outline alternative perspectives. In particular, we discuss quantum metabolism (QM), an analytic theory based on molecular-cellular processes. QM predicts the large variations in scaling exponent that are found empirically and also predicts the temperature dependence of the proportionality constant, issues that have eluded models such as FNT that are based on macroscopic and network properties of organisms.

Scaling theory for information networks

Networks distribute energy, materials and information to the components of a variety of natural and human-engineered systems, including organisms, brains, the Internet and microprocessors. Distribution networks enable the integrated and coordinated functioning of these systems, and they also constrain their design. The similar hierarchical branching networks observed in organisms and microprocessors are striking, given that the structure of organisms has evolved via natural selection, while microprocessors are designed by engineers. Metabolic scaling theory (MST) shows that the rate at which networks deliver energy to an organism is proportional to its mass raised to the 3/4 power. We show that computational systems are also characterized by nonlinear network scaling and use MST principles to characterize how information networks scale, focusing on how MST predicts properties of clock distribution networks in microprocessors. The MST equations are modified to account for variation in the size and density of transistors and terminal wires in microprocessors. Based on the scaling of the clock distribution network, we predict a set of trade-offs and performance properties that scale with chip size and the number of transistors. However, there are systematic deviations between power requirements on microprocessors and predictions derived directly from MST. These deviations are addressed by augmenting the model to account for decentralized flow in some microprocessor networks (e.g. in logic networks). More generally, we hypothesize a set of constraints between the size, power and performance of networked information systems including transistors on chips, hosts on the Internet and neurons in the brain.

Growth hormone receptor deficiency in mice results in reduced systolic blood pressure and plasma renin, increased aortic eNOS expression, and altered cardiovascular structure and function

To study the role of the growth hormone receptor (GHR) in the development of cardiovascular structure and function, female GHR gene-disrupted or knockout (KO) and wild-type (WT) mice at age 18 wk were used. GHR KO mice had lower plasma renin levels (12 +/- 2 vs. 20 +/- 4 mGU/ml, P < 0.05) and increased aortic endothelial NO synthase (eNOS) expression (146%, P < 0.05) accompanied by a 25% reduction in systolic blood pressure (BP, 110 +/- 4 vs. 147 +/- 3 mmHg, P < 0.001) compared with WT mice. Aldosterone levels were unchanged, whereas the plasma potassium concentration was elevated by 14% (P < 0.05) in GHR KO. Relative left ventricular weight was 14% lower in GHR KO mice (P < 0.05), and cardiac dimensions as analyzed by echocardiography were similarly reduced. Myograph studies revealed a reduced maximum contractile response in the aorta to norepinephrine (NE) and K(+) (P < 0.05), and aorta media thickness was decreased in GHR KO (P < 0.05). However, contractile force was normal in mesenteric arteries, whereas sensitivity to NE was increased (P < 0.05). Maximal acetylcholine-mediated dilatation was similar in WT and GHR KO mice, whereas the aorta of GHR KO mice showed an increased sensitivity to acetylcholine (P < 0.05). In conclusion, loss of GHR leads to low BP and decreased levels of renin in plasma as well as increase in aortic eNOS expression. Furthermore, GHR deficiency causes functional and morphological changes in both heart and vasculature that are beyond the observed alterations in body size. These data suggest an important role for an intact GH/IGF-I axis in the maintenance of a normal cardiovascular system.

Beyond the '3/4-power law': variation in the intra- and interspecific scaling of metabolic rate in animals

In this review I show that the '3/4-power scaling law' of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described mainly for animals, but also for unicells and plants. Much of this variation, which can be related to taxonomic, physiological, and/or environmental differences, is not adequately explained by existing theoretical models, which are also reviewed. As a result, synthetic explanatory schemes based on multiple boundary constraints and on the scaling of multiple energy-using processes are advocated. It is also stressed that a complete understanding of metabolic scaling will require the identification of both proximate (functional) and ultimate (evolutionary) causes. Four major types of intraspecific metabolic scaling with body mass are recognized [based on the power function R=aMb, where R is respiration (metabolic) rate, a is a constant, M is body mass, and b is the scaling exponent]: Type I: linear, negatively allometric (b<1); Type II: linear, isometric (b=1); Type III: nonlinear, ontogenetic shift from isometric (b=1), or nearly isometric, to negatively allometric (b<1); and Type IV: nonlinear, ontogenetic shift from positively allometric (b>1) to one or two later phases of negative allometry (b<1). Ontogenetic changes in the metabolic intensity of four component processes (i.e. growth, reproduction, locomotion, and heat production) appear to be important in these different patterns of metabolic scaling. These changes may, in turn, be shaped by age (size)-specific patterns of mortality. In addition, major differences in interspecific metabolic scaling are described, especially with respect to mode of temperature regulation, body-size range, and activity level. A 'metabolic-level boundaries hypothesis' focusing on two major constraints (surface-area limits on resource/waste exchange processes and mass/volume limits on power production) can explain much, but not all of this variation. My analysis indicates that further empirical and theoretical work is needed to understand fully the physiological and ecological bases for the considerable variation in metabolic scaling that is observed both within and among species. Recommended approaches for doing this are discussed. I conclude that the scaling of metabolism is not the simple result of a physical law, but rather appears to be the more complex result of diverse adaptations evolved in the context of both physico-chemical and ecological constraints.

Dermal capillary clearance: physiology and modeling

Substances applied to the skin surface may permeate deeper tissue layers and pass into the body's systemic circulation by entering blood or lymphatic vessels in the dermis. The purpose of this review is an in-depth analysis of the dermal clearance/exchange process and its constituents: transport through the interstitium, permeability of the microvascular barrier and removal via the circulation. We adapt an 'engineering' viewpoint with emphasis on quantifying the dermal microcirculatory physiology, providing the theoretical framework for the physics of key transport processes and reviewing the available computational clearance models in a comparative manner. Selected experimental data which may serve as valuable input to modeling attempts are also reported.

Modeling of vascular networks

Vascular networks refer here mainly to the microscale capillary networks of the vascular system of mammals, although they may also be considered to include the small arteries that feed the capillaries and the small veins that drain them. The modeling of these networks for resting mammals is reviewed within the context of describing related scaling laws for mammals of vastly different size. Basic processes are considered and alternative approaches mentioned. All lead to the same scaling laws for the radius, length and number of the vessels. The applicability of the relations is illustrated using existing measurements. Discussion is also included on the effect of strenuous exercise on the scaling law for number of capillary vessels and matters related to it.