Constructal law of vascular trees for facilitation of flow

Mechanical regulation of the early stages of angiogenesis

Favouring or thwarting the development of a vascular network is essential in fields as diverse as oncology, cardiovascular disease or tissue engineering. As a result, understanding and controlling angiogenesis has become a major scientific challenge. Mechanical factors play a fundamental role in angiogenesis and can potentially be exploited for optimizing the architecture of the resulting vascular network. Largely focusing on in vitro systems but also supported by some in vivo evidence, the aim of this Highlight Review is dual. First, we describe the current knowledge with particular focus on the effects of fluid and solid mechanical stimuli on the early stages of the angiogenic process, most notably the destabilization of existing vessels and the initiation and elongation of new vessels. Second, we explore inherent difficulties in the field and propose future perspectives on the use of in vitro and physics-based modelling to overcome these difficulties.

An Overview of Self-Healable Polymers and Recent Advances in the Field

The search for materials with better performance, longer service life, lower environmental impact, and lower overall cost is at the forefront of polymer science and material engineering. This has led to the development of self-healing polymers with a range of healing mechanisms including capsular-based, vascular, and intrinsic self-healing polymers. The development of self-healable systems has been inspired by the healing of biological systems such as skin wound healing and broken bone reconstruction. The goal of using self-healing polymers in various applications is to extend the service life of polymers without the need for replacement or human intervention especially in restricted access areas such as underwater/underground piping where inspection, intervention, and maintenance are very difficult. Through an industrial and scholarly lens, this paper provides (a) an overview of self-healing polymers, (b) classification of different self-healing polymers and polymer-based composites, (c) mechanical, thermal, and electrical analysis characterization, (d) applications in coating, composites, and electronics, (e) modeling and simulation, and (f) recent development in the past 20 years . This review highlights the importance of healable polymers for an economically and environmentally sustainable future, the most recent advances in the field, and current limitations in fabrication, manufacturing, and performance. This article is protected by copyright. All rights reserved.

Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung

Fractal geometry (FG) is a branch of mathematics that instructively characterizes structural complexity. Branched structures are ubiquitous in both the physical and the biological realms. Fractility has therefore been termed nature's design. The fractal properties of the bronchial (airway) system, the pulmonary artery and the pulmonary vein of the human lung generates large respiratory surface area that is crammed in the lung. Also, it permits the inhaled air to intimately approximate the pulmonary capillary blood across a very thin blood-gas barrier through which gas exchange to occur by diffusion. Here, the bronchial (airway) and vascular systems were simultaneously cast with latex rubber. After corrosion, the bronchial and vascular system casts were physically separated and cleared to expose the branches. The morphogenetic (Weibel's) ordering method was used to categorize the branches on which the diameters and the lengths, as well as the angles of bifurcation, were measured. The fractal dimensions (DF) were determined by plotting the total branch measurements against the mean branch diameters on double logarithmic coordinates (axes). The diameter-determined DF values were 2.714 for the bronchial system, 2.882 for the pulmonary artery and 2.334 for the pulmonary vein while the respective values from lengths were 3.098, 3.916 and 4.041. The diameters yielded DF values that were consistent with the properties of fractal structures (i.e. self-similarity and space-filling). The data obtained here compellingly suggest that the design of the bronchial system, the pulmonary artery and the pulmonary vein of the human lung functionally comply with the Hess-Murray law or 'the principle of minimum work'.

Topologic and Hemodynamic Characteristics of the Human Coronary Arterial Circulation

Background

Many processes contributing to the functional and structural regulation of the coronary circulation have been identified. A proper understanding of the complex interplay of these processes requires a quantitative systems approach that includes the complexity of the coronary network. The purpose of this study was to provide a detailed quantification of the branching characteristics and local hemodynamics of the human coronary circulation.

Methods

The coronary arteries of a human heart were filled post-mortem with fluorescent replica material. The frozen heart was alternately cut and block-face imaged using a high-resolution imaging cryomicrotome. From the resulting 3D reconstruction of the left coronary circulation, topological (node and loop characteristics), topographic (diameters and length of segments), and geometric (position) properties were analyzed, along with predictions of local hemodynamics (pressure and flow).

Results

The reconstructed left coronary tree consisted of 202,184 segments with diameters ranging from 30 μm to 4 mm. Most segments were between 100 μm and 1 mm long. The median segment length was similar for diameters ranging between 75 and 200 μm. 91% of the nodes were bifurcations. These bifurcations were more symmetric and less variable in smaller vessels. Most of the pressure drop occurred in vessels between 200 μm and 1 mm in diameter. Downstream conductance variability affected neither local pressure nor median local flow and added limited extra variation of local flow. The left coronary circulation perfused 358 cm³ of myocardium. Median perfused volume at a truncation level of 100 to 200 μm was 20 mm³ with a median perfusion of 5.6 ml/min/g and a high local heterogeneity.

Conclusion

This study provides the branching characteristics and hemodynamic analysis of the left coronary arterial circulation of a human heart. The resulting model can be deployed for further hemodynamic studies at the whole organ and local level.

Toward an optimal design principle in symmetric and asymmetric tree flow networks

Fluid flow in tree-shaped networks plays an important role in both natural and engineered systems. This paper focuses on laminar flows of Newtonian and non-Newtonian power law fluids in symmetric and asymmetric bifurcating trees. Based on the constructal law, we predict the tree-shaped architecture that provides greater access to the flow subjected to the total network volume constraint. The relationships between the sizes of parent and daughter tubes are presented both for symmetric and asymmetric branching tubes. We also approach the wall-shear stresses and the flow resistance in terms of first tube size, degree of asymmetry between daughter branches, and rheological behavior of the fluid. The influence of tubes obstructing the fluid flow is also accounted for. The predictions obtained by our theory-driven approach find clear support in the findings of previous experimental studies.