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The (micro)circulation is a very prominent example for the interplay of physical factors with molecular and cellular processes in generating and maintaining crucial structural and functional features of organs and systems in the body. In this special issue, various aspects of this interaction are explored in an attempt to better understand the ‘‘engineering principles of vascular networks’’. An adequate understanding of these principles and their representation in quantitative models will allow meaningful predictions of clinically relevant parameters, as done in the present issue in the article by Wijngaard et al. [18] on subendocardial perfusion in the presence of epicardial artery stenosis. Since the heart is the first functionally active organ of the embryo, blood flow and to a lesser degree, blood pressure are established very early during prenatal development. Their spatial and temporal (pulsatility) patterns entail relevant information on the functional behaviour of the vascular system. Therefore, it is very logical that these signals are used intensively to control vascular growth and differentiation in order to establish adequate hemodynamic conditions [5, 11]. Direct cellular sensors for both blood flow rate and blood pressure are difficult to envisage and the related physical quantities which elicit responses of vessels and vascular cells (Fig. 1) are most likely shear stress (related to flow rate) and circumferential wall stress (related to blood pressure). The importance of shear stress (flow) for the control of vascular network design is evidenced by the fact that it is addressed in a larger fraction of the articles in this special issue [6, 7, 11, 14]. A key feature is the translation of shear stress into a biological response. Thus, shear stress elicits the release of molecules such as H2O2 and nitric oxide, that cause flow-mediated dilation. In this issue, Liu et al. [6] show that the cytoskeleton of endothelial cells, directly exposed to the flowing blood, are a critical component herein. Shear stress is not always steady, as in organs such as the heart, where blood flow is pulsatile due to the contraction of the myocardium. This pulsatile flow modulates the release of nitric oxide, a labile molecule that can be detected by a catheter-type sensor [2]. Shear stress also relates to the best known engineering concept for vascular design, ‘Murray’s law [10]: If the shear stress is the same in all vessels of a vascular bed, the overall energy requirement for blood flow and maintenance of the blood and the vessels is minimal. Minimizing energy consumption, however, is a goal which is secondary to the fulfillment of the central biological requirements of the circulation, e.g., adequate distribution of oxygen, low capillary pressures and a large regulatory capacity in the distal arterial tree. Therefore, living circulatory systems show substantial deviations from Murray’s predictions as discussed in this special issue by Renemann and Hoeks [14]. One obvious example is the arterio-venous difference of average shear stress levels [13]. Also, it was stated by A. R. Pries (&) Department of Physiology, Charité Berlin, Arnimallee 22, 14195 Berlin, Germany e-mail: axel.pries@charite.de

MBEC special issue on microcirculation “engineering principles of vascular networks”