Mechanics of blood flow in capillaries

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Blood is a concentrated suspension of red blood cells (RBCs). Motion and deformation of RBCs can be analyzed based on knowledge of their mechanical characteristics. Models for single-file motion of RBCs in capillaries yield predictions of apparent viscosity in good agreement with experimental results for diameters up to about 8 μm. In living microvessels, flow resistance is also strongly influenced by the presence of a ~ 1-micron layer of macromolecules bound to the inner lining of vessel walls, the endothelial surface layer. Two-dimensional simulations, in which each RBC is represented as a set of interconnected viscoelastic elements, predict that off-center RBCs take asymmetric shapes and drift toward the center-line. Predicted trajectories agree closely with observations in microvessels of the rat mesentery. Realistic simulation of multiple interacting RBCs in microvessels remains as a major challenge for future work.This work was supported by NIH Grant HL034555

Microcirculatory blood flow: Functional implications of a complex fluid

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute

A hybrid discrete–continuum approach for modelling microcirculatory blood flow

In recent years, biological imaging techniques have advanced significantly and it is now possible to digitally reconstruct microvascular network structures in detail, identifying the smallest capillaries at sub-micron resolution and generating large 3D structural data sets of size >106 vessel segments. However, this relies on ex vivo imaging; corresponding in vivo measures of microvascular structure and flow are limited to larger branching vessels and are not achievable in three dimensions for the smallest vessels. This suggests the use of computational modelling to combine in vivo measures of branching vessel architecture and flows with ex vivo data on complete microvascular structures to predict effective flow and pressures distributions. In this paper, a hybrid discrete–continuum model to predict microcirculatory blood flow based on structural information is developed and compared with existing models for flow and pressure in individual vessels. A continuum-based Darcy model for transport in the capillary bed is coupled via point sources of flux to flows in individual arteriolar vessels, which are described explicitly using Poiseuille’s law. The venular drainage is represented as a spatially uniform flow sink. The resulting discrete–continuum framework is parameterized using structural data from the capillary network and compared with a fully discrete flow and pressure solution in three networks derived from observations of the rat mesentery. The discrete–continuum approach is feasible and effective, providing a promising tool for extracting functional transport properties in situations where vascular branching structures are well defined

Uptake Rate of Cationic Mitochondrial Inhibitor MKT-077 Determines Cellular Oxygen Consumption Change in Carcinoma Cells

<div><h3>Objective</h3><p>Since tumor radiation response is oxygen-dependent, radiosensitivity can be enhanced by increasing tumor oxygenation. Theoretically, inhibiting cellular oxygen consumption is the most efficient way to increase oxygen levels. The cationic, rhodacyanine dye-analog MKT-077 inhibits mitochondrial respiration and could be an effective metabolic inhibitor. However, the relationship between cellular MKT-077 uptake and metabolic inhibition is unknown. We hypothesized that rat and human mammary carcinoma cells would take up MKT-077, causing a decrease in oxygen metabolism related to drug uptake.</p> <h3>Methods</h3><p>R3230Ac rat breast adenocarcinoma cells were exposed to MKT-077. Cellular MKT-077 concentration was quantified using spectroscopy, and oxygen consumption was measured using polarographic electrodes. MKT-077 uptake kinetics were modeled by accounting for uptake due to both the concentration and potential gradients across the plasma and mitochondrial membranes. These kinetic parameters were used to model the relationship between MKT-077 uptake and metabolic inhibition. MKT-077-induced changes in oxygen consumption were also characterized in MDA-MB231 human breast carcinoma cells.</p> <h3>Results</h3><p>Cells took up MKT-077 with a time constant of ∼1 hr, and modeling showed that over 90% of intracellular MKT-077 was bound or sequestered, likely by the mitochondria. The uptake resulted in a rapid decrease in oxygen consumption, with a time constant of ∼30 minutes. Surprisingly the change in oxygen consumption was proportional to uptake rate, not cellular concentration. MKT-077 proved a potent metabolic inhibitor, with dose-dependent decreases of 45–73% (p = 0.003).</p> <h3>Conclusions</h3><p>MKT-077 caused an uptake rate-dependent decrease in cellular metabolism, suggesting potential efficacy for increasing tumor oxygen levels and radiosensitivity <em>in vivo</em>.</p> </div

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour

Quantification of longitudinal tissue pO2 gradients in window chamber tumours: impact on tumour hypoxia

We previously reported that the arteriolar input in window chamber tumours is limited in number and is constrained to enter the tumour from one surface, and that the pO2 of tumour arterioles is lower than in comparable arterioles of normal tissues. On average, the vascular pO2 in vessels of the upper surface of these tumours is lower than the pO2 of vessels on the fascial side, suggesting that there may be steep vascular longitudinal gradients (defined as the decline in vascular pO2 along the afferent path of blood flow) that contribute to vascular hypoxia on the upper surface of the tumours. However, we have not previously measured tissue pO2 on both surfaces of these chambers in the same tumour. In this report, we investigated the hypothesis that the anatomical constraint of arteriolar supply from one side of the tumour results in longitudinal gradients in pO2 sufficient in magnitude to create vascular hypoxia in tumours grown in dorsal flap window chambers. Fischer-344 rats had dorsal flap window chambers implanted in the skin fold with simultaneous transplantation of the R3230AC tumour. Tumours were studied at 9–11 days after transplantation, at a diameter of 3–4 mm; the tissue thickness was 200 μm. For magnetic resonance microscopic imaging, gadolinium DTPA bovine serum albumin (BSA-DTPA-Gd) complex was injected i.v., followed by fixation in 10% formalin and removal from the animal. The sample was imaged at 9.4 T, yielding voxel sizes of 40 μm. Intravital microscopy was used to visualize the position and number of arterioles entering window chamber tumour preparations. Phosphorescence life time imaging (PLI) was used to measure vascular pO2. Blue and green light excitations of the upper and lower surfaces of window chambers were made (penetration depth of light ~50 vs >200 μm respectively). Arteriolar input into window chamber tumours was limited to 1 or 2 vessels, and appeared to be constrained to the fascial surface upon which the tumour grows. PLI of the tumour surface indicated greater hypoxia with blue compared with green light excitation (P < 0.03 for 10th and 25th percentiles and for per cent pixels < 10 mmHg). In contrast, illumination of the fascial surface with blue light indicated less hypoxia compared with illumination of the tumour surface (P < 0.05 for 10th and 25th percentiles and for per cent pixels < 10 mmHg). There was no significant difference in pO2 distributions for blue and green light excitation from the fascial surface nor for green light excitation when viewed from either surface. The PLI data demonstrates that the upper surface of the tumour is more hypoxic because blue light excitation yields lower pO2 values than green light excitation. This is further verified in the subset of chambers in which blue light excitation of the fascial surface showed higher pO2 distributions compared with the tumour surface. These results suggest that there are steep longitudinal gradients in vascular pO2 in this tumour model that are created by the limited number and orientation of the arterioles. This contributes to tumour hypoxia. Arteriolar supply is often limited in other tumours as well, suggesting that this may represent another cause for tumour hypoxia. This report is the first direct demonstration that longitudinal oxygen gradients actually lead to hypoxia in tumours. © 1999 Cancer Research Campaig

Oxygen Consumption Can Regulate the Growth of Tumors, a New Perspective on the Warburg Effect

The unique metabolism of tumors was described many years ago by Otto Warburg, who identified tumor cells with increased glycolysis and decreased mitochondrial activity. However, "aerobic glycolysis" generates fewer ATP per glucose molecule than mitochondrial oxidative phosphorylation, so in terms of energy production, it is unclear how increasing a less efficient process provides tumors with a growth advantage.We carried out a screen for loss of genetic elements in pancreatic tumor cells that accelerated their growth as tumors, and identified mitochondrial ribosomal protein L28 (MRPL28). Knockdown of MRPL28 in these cells decreased mitochondrial activity, and increased glycolysis, but paradoxically, decreased cellular growth in vitro. Following Warburg's observations, this mutation causes decreased mitochondrial function, compensatory increase in glycolysis and accelerated growth in vivo. Likewise, knockdown of either mitochondrial ribosomal protein L12 (MRPL12) or cytochrome oxidase had a similar effect. Conversely, expression of the mitochondrial uncoupling protein 1 (UCP1) increased oxygen consumption and decreased tumor growth. Finally, treatment of tumor bearing animals with dichloroacetate (DCA) increased pyruvate consumption in the mitochondria, increased total oxygen consumption, increased tumor hypoxia and slowed tumor growth.We interpret these findings to show that non-oncogenic genetic changes that alter mitochondrial metabolism can regulate tumor growth through modulation of the consumption of oxygen, which appears to be a rate limiting substrate for tumor proliferation

Cerebral small vessel disease: capillary pathways to stroke and cognitive decline

Cerebral small vessel disease (SVD) gives rise to one in five strokes worldwide and constitutes a major source of cognitive decline in the elderly. SVD is known to occur in relation to hypertension, diabetes, smoking, radiation therapy and in a range of inherited and genetic disorders, autoimmune disorders, connective tissue disorders, and infections. Until recently, changes in capillary patency and blood viscosity have received little attention in the aetiopathogenesis of SVD and the high risk of subsequent stroke and cognitive decline. Capillary flow patterns were, however, recently shown to limit the extraction efficacy of oxygen in tissue and capillary dysfunction therefore proposed as a source of stroke-like symptoms and neurodegeneration, even in the absence of physical flow-limiting vascular pathology. In this review, we examine whether capillary flow disturbances may be a shared feature of conditions that represent risk factors for SVD. We then discuss aspects of capillary dysfunction that could be prevented or alleviated and therefore might be of general benefit to patients at risk of SVD, stroke or cognitive decline

FEM-based oxygen consumption and cell viability models for avascular pancreatic islets

<p>Abstract</p> <p>Background</p> <p>The function and viability of cultured, transplanted, or encapsulated pancreatic islets is often limited by hypoxia because these islets have lost their vasculature during the isolation process and have to rely on gradient-driven passive diffusion, which cannot provide adequate oxygen transport. Pancreatic islets (islets of Langerhans) are particularly susceptible due to their relatively large size, large metabolic demand, and increased sensitivity to hypoxia. Here, finite element method (FEM) based multiphysics models are explored to describe oxygen transport and cell viability in avascular islets both in static and in moving culture media.</p> <p>Methods</p> <p>Two- and three-dimensional models were built in COMSOL Multiphysics using the convection and diffusion as well as the incompressible Navier-Stokes fluid dynamics application modes. Oxygen consumption was assumed to follow Michaelis-Menten-type kinetics and to cease when local concentrations fell below a critical threshold; in a dynamic model, it was also allowed to increase with increasing glucose concentration.</p> <p>Results</p> <p>Partial differential equation (PDE) based exploratory cellular-level oxygen consumption and cell viability models incorporating physiologically realistic assumptions have been implemented for fully scaled cell culture geometries with 100, 150, and 200 <it>μ</it>m diameter islets as representative. Calculated oxygen concentrations and intra-islet regions likely to suffer from hypoxia-related necrosis obtained for traditional flask-type cultures, oxygen-permeable silicone-rubber membrane bottom cultures, and perifusion chambers with flowing media and varying incoming glucose levels are presented in detail illustrated with corresponding colour-coded figures and animations.</p> <p>Conclusion</p> <p>Results of the computational models are, as a first estimate, in good quantitative agreement with existing experimental evidence, and they confirm that during culture, hypoxia is often a problem for non-vascularised islet and can lead to considerable cell death (necrosis), especially in the core region of larger islets. Such models are of considerable interest to improve the function and viability of cultured, transplanted, or encapsulated islets. The present implementation allows convenient extension to true multiphysics applications that solve coupled physics phenomena such as diffusion and consumption with convection due to flowing or moving media.</p

A Systems Approach for Tumor Pharmacokinetics

Recent advances in genome inspired target discovery, small molecule screens, development of biological and nanotechnology have led to the introduction of a myriad of new differently sized agents into the clinic. The differences in small and large molecule delivery are becoming increasingly important in combination therapies as well as the use of drugs that modify the physiology of tumors such as anti-angiogenic treatment. The complexity of targeting has led to the development of mathematical models to facilitate understanding, but unfortunately, these studies are often only applicable to a particular molecule, making pharmacokinetic comparisons difficult. Here we develop and describe a framework for categorizing primary pharmacokinetics of drugs in tumors. For modeling purposes, we define drugs not by their mechanism of action but rather their rate-limiting step of delivery. Our simulations account for variations in perfusion, vascularization, interstitial transport, and non-linear local binding and metabolism. Based on a comparison of the fundamental rates determining uptake, drugs were classified into four categories depending on whether uptake is limited by blood flow, extravasation, interstitial diffusion, or local binding and metabolism. Simulations comparing small molecule versus macromolecular drugs show a sharp difference in distribution, which has implications for multi-drug therapies. The tissue-level distribution differs widely in tumors for small molecules versus macromolecular biologic drugs, and this should be considered in the design of agents and treatments. An example using antibodies in mouse xenografts illustrates the different in vivo behavior. This type of transport analysis can be used to aid in model development, experimental data analysis, and imaging and therapeutic agent design.National Institutes of Health (U.S.) (grant T32 CA079443