Structural Control of Microvessel Diameters: Origins of Metabolic Signals

Mathematical models of developmental vascular remodelling: A review

Over the past 40 years, there has been a strong focus on the development of mathematical models of angiogenesis, while developmental remodelling has received little such attention from the mathematical community. Sprouting angiogenesis can be seen as a very crude way of laying out a primitive vessel network (the raw material), while remodelling (understood as pruning of redundant vessels, diameter control, and the establishment of vessel identity and hierarchy) is the key to turning that primitive network into a functional network. This multiscale problem is of prime importance in the development of a functional vasculature. In addition, defective remodelling (either during developmental remodelling or due to a reactivation of the remodelling programme caused by an injury) is associated with a significant number of diseases. In this review, we discuss existing mathematical models of developmental remodelling and explore the important contributions that these models have made to the field of vascular development. These mathematical models are effectively used to investigate and predict vascular development and are able to reproduce experimentally observable results. Moreover, these models provide a useful means of hypothesis generation and can explain the underlying mechanisms driving the observed structural and functional network development. However, developmental vascular remodelling is still a relatively new area in mathematical biology, and many biological questions remain unanswered. In this review, we present the existing modelling paradigms and define the key challenges for the field.

Modeling Reactive Hyperemia to Better Understand and Assess Microvascular Function: A Review of Techniques

Reactive hyperemia is a well-established technique for the non-invasive evaluation of the peripheral microcirculatory function, measured as the magnitude of limb re-perfusion after a brief period of ischemia. Despite widespread adoption by researchers and clinicians alike, many uncertainties remain surrounding interpretation, compounded by patient-specific confounding factors (such as blood pressure or the metabolic rate of the ischemic limb). Mathematical modeling can accelerate our understanding of the physiology underlying the reactive hyperemia response and guide in the estimation of quantities which are difficult to measure experimentally. In this work, we aim to provide a comprehensive guide for mathematical modeling techniques that can be used for describing the key phenomena involved in the reactive hyperemia response, alongside their limitations and advantages. The reported methodologies can be used for investigating specific reactive hyperemia aspects alone, or can be combined into a computational framework to be used in (pre-)clinical settings.

Development of Novel Fractal Method for Characterizing the Distribution of Blood Flow in Multi-Scale Vascular Tree

Blood perfusion is an important index for the function of the cardiovascular system and it can be indicated by the blood flow distribution in the vascular tree. As the blood flow in a vascular tree varies in a large range of scales and fractal analysis owns the ability to describe multi-scale properties, it is reasonable to apply fractal analysis to depict the blood flow distribution. The objective of this study is to establish fractal methods for analyzing the blood flow distribution which can be applied to real vascular trees. For this purpose, the modified methods in fractal geometry were applied and a special strategy was raised to make sure that these methods are applicable to an arbitrary vascular tree. The validation of the proposed methods on real arterial trees verified the ability of the produced parameters (fractal dimension and multifractal spectrum) in distinguishing the blood flow distribution under different physiological states. Furthermore, the physiological significance of the fractal parameters was investigated in two situations. For the first situation, the vascular tree was set as a perfect binary tree and the blood flow distribution was adjusted by the split ratio. As the split ratio of the vascular tree decreases, the fractal dimension decreases and the multifractal spectrum expands. The results indicate that both fractal parameters can quantify the degree of blood flow heterogeneity. While for the second situation, artificial vascular trees with different structures were constructed and the hemodynamics in these vascular trees was simulated. The results suggest that both the vascular structure and the blood flow distribution affect the fractal parameters for blood flow. The fractal dimension declares the integrated information about the heterogeneity of vascular structure and blood flow distribution. In contrast, the multifractal spectrum identifies the heterogeneity features in blood flow distribution or vascular structure by its width and height. The results verified that the proposed methods are capable of depicting the multi-scale features of the blood flow distribution in the vascular tree and further are potential for investigating vascular physiology.

Evaluation of Microcirculation, Cytokine Profile, and Local Antioxidant Protection Indices in Periodontal Health, and Stage II, Stage III Periodontitis

Periodontitis, initiated by the subgingival biofilm and modified by the individual’s inflammatory/immune response, has been associated with vascular dysfunction. To analyze microcirculation indices in periodontal tissues and determine the activity of the enzymatic component of antioxidant defense and humoral immunity factors, a single-blind non-invasive clinical trial was realized. Forty subjects, aged from 30 to 65 years, with moderate to severe chronic periodontitis (chronic generalized periodontitis, CGP) vs. 40 subjects as periodontally healthy were recruited. Information such as capillary diameter, capillary blood flow velocity, concentration of pro- and anti-inflammatory cytokines in serum, vascular endothelial growth factor, and enzymatic component of antioxidant protection were taken. The revealed microcirculatory dysfunctions in patients with CGP clearly demonstrate the progressive disorder of periodontal tissue perfusion and oxygenation, the presence of increased vascular permeability and functional failure of the microvascular system in the lesion. Cytokine profile of CGP patients’ blood serum demonstrated a significant increase of interleukin (IL)-1β, IL-6, tumor necrosis factor α (TNF-α), IL-4 levels as well as statistically significant decrease of IL-1ra, IL-10 concentration. Participants with CGP demonstrated a dominant superiority of IgM and IgG levels. In conclusion, these results contribute to a better understanding of potential correlation between microvascular changes and local and systemic markers of inflammation.

Distinct roles of red-blood-cell-derived and wall-derived mechanisms in metabolic regulation of blood flow

OBJECTIVE

A theoretical model is used to analyze combinations of RBC-derived and wall-derived (RBC-independent) mechanisms for metabolic blood flow regulation, with regard to their oxygen transport properties.

METHODS

Heterogeneous microvascular network structures are derived from observations in rat mesentery and hamster cremaster. The effectiveness of metabolic blood flow regulation using combinations of RBC-dependent and RBC-independent mechanisms is simulated in these networks under conditions of reduced oxygen delivery and increased oxygen demand.

RESULTS

Metabolic regulation by a wall-derived mechanism results in higher predicted total blood flow rate and number of flowing vessels, and lower tissue hypoxic fraction, than regulation by combinations of RBC-derived and wall-derived signals. However, a combination of RBC-derived and wall-derived signals results in a higher predicted median tissue P_O2 than either mechanism acting alone.

CONCLUSIONS

Model results suggest complementary roles for RBC-derived and wall-derived mechanisms of metabolic flow regulation, with the wall-derived mechanism responsible for avoiding hypoxia, and the RBC-derived mechanism responsible for maintaining P_O2 levels high enough for optimal tissue function.

More homogeneous capillary flow and oxygenation in deeper cortical layers correlate with increased oxygen extraction

Our understanding of how capillary blood flow and oxygen distribute across cortical layers to meet the local metabolic demand is incomplete. We addressed this question by using two-photon imaging of resting-state microvascular oxygen partial pressure (PO₂) and flow in the whisker barrel cortex in awake mice. Our measurements in layers I-V show that the capillary red-blood-cell flux and oxygenation heterogeneity, and the intracapillary resistance to oxygen delivery, all decrease with depth, reaching a minimum around layer IV, while the depth-dependent oxygen extraction fraction is increased in layer IV, where oxygen demand is presumably the highest. Our findings suggest that more homogeneous distribution of the physiological observables relevant to oxygen transport to tissue is an important part of the microvascular network adaptation to local brain metabolism. These results will inform the biophysical models of layer-specific cerebral oxygen delivery and consumption and improve our understanding of the diseases that affect cerebral microcirculation.

Bifurcation Asymmetry of Small Coronary Arteries in Juvenile and Adult Mice

Background: Microvascular bifurcation asymmetry is of significance for regulation of coronary flow heterogeneity during juvenile and adult growth. The aim of the study is to investigate the morphometric and hemodynamic variation of coronary arterial bifurcations in mice of different ages.

Methods: Pulsatile blood flows were computed from a Womersley-type model in the reconstructed left coronary arterial (LCA) trees from Micro-CT images in normal mice at ages of 3 weeks, 6 weeks, 12 weeks, 5-6 months, and >8 months. Diameter and flow ratios and bifurcation angles were determined in each bifurcation of the LCA trees.

Results: The blood volume and inlet flow rate of LCA trees increase and decrease during juvenile and adult growth, respectively. As vessel diameters decrease, the increased ratios of small to large daughter vessel diameters (D_s/D_l) result in more uniform flows and lower velocities. There are significant structure-functional changes of LCA trees in mice of >8 months compared with mice of < 8 months. As D_s/D_l increases, the variation trend of bifurcation angle during juvenile growth is different from that during adult growth.

Conclusions: Although inlet flows are different in adult vs. juvenile mice, the adult still have uniform flow and low velocity. This is accomplished through a decrease in diameter. The design ensures ordered dispersion of red cells through asymmetric branching patterns into the capillaries.