A mathematical model for the vessel recruitment in coronary microcirculation in the absence of active autoregulation Alice Saracco a , Matteo Bauckneht b , Edoardo Verna c , Sergio Ghiringhelli c , Rodolfo Repetto d , Gianmario Sambuceti b , Stefano Provasoli c , Marco Storace a, ⁎ a Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture — DITEN, University of Genoa, Italy b Nuclear Medicine, Dept. of Health Science, IRCCS-AOU San Martino-IST, Genoa, Italy c Department of Cardiology, Cardiac Catheterization Lab., Ospedale di Circolo e Fondazione Macchi, University Hospital, Varese, Italy d Department of Civil, Chemical and Environmental Engineering — DICCA, University of Genoa, Italy abstract article info Article history: Received 1 October 2015 Revised 10 November 2015 Accepted 25 November 2015 Available online 30 November 2015 This paper proposes a mathematical model for vessel recruitment in the microvascular coronary network. The model is based on microvascular network units (MVNUs), where we define a MVNU as a portion of the microvas- cular network comprising seven generations of identical, parallel-arranged vessels (upstream arteries, large and small arterioles, capillaries, small and large venules, and downstream veins). The model implements a new mechanism to describe the variation in the number of MVNU in response to sudden variations of the local input pressure. In particular, it describes a recruitment mechanism dependent on distal pressure which operates in the coronary microcirculatory network even in maximally dilated conditions. We apply the model to interpret data from 29 patients who underwent revascularization by percutaneous coronary intervention (PCI). Treated vessels were the left anterior descending coronary artery, the left circumflex and the right coronary artery in 26, 2 and 1 patients, respectively. Following intracoronary adenosine administration, distal coronary pressure and blood flow were 48 ± 18 mm Hg and 45 ± 30 ml/min before PCI, respectively, and significantly increased afterwards to 80 ± 17 mm Hg and 68 ± 32 ml/min (p b 0.001). The model predicts an increase in MVNU number in patients with preserved wall motion in the myocardial region which underwent PCI. On the contrary, a de- crease in MVNU number is predicted by the model in patients with regional dysfunction and implies a relatively lower response of maximal flow to revascularization. © 2015 Elsevier Inc. All rights reserved. Keywords: Mathematical model of microcirculation Vessels recruitment Coronary microcirculation Capillary pressure Introduction The hallmark of coronary artery disease (CAD) is the presence of ath- erosclerotic plaques on major epicardial coronary arteries. Classical models of coronary physiology assume a microvascular adaptation to upstream flow resistance, which preserves baseline coronary blood flow (CBF), while ischemia occurs whenever myocardial oxygen demand exceeds the impaired maximal flow capacity (Chilian et al., 1986). These models, however, represent an over-simplification of the hydraulic consequences of arterial obstructions. A variation in a section of a vessel lumen causes a pressure drop whose functional conse- quences have to be counteracted by an adaptation of the downstream vascular bed. This adaptation preserves stable values of capillary pressure, despite the inevitable variability in flow. Several signaling pathways contribute to this process and provide an integrated control of flow and pressure throughout the coronary microcirculation. From a theoretical point of view, these mechanisms can be divided into intrinsic vascular reactions, for control of pressure distribution in the whole tree, and extrinsic, tissue-produced, signals which reg- ulate flow demand to a specific local vascular network (Sambuceti et al., 2013). Among the intrinsic vascular reactions, the myogenic reflex (Chilian, 1997) accounts for autoregulation (Dole, 1987), which maintains CBF stability despite variations in input pressure. It implies the existence of a pressure sensor, located in parallel with the contractile elements and capable of modulating the vessel diameter (Welsh et al., 2000). This va- soconstrictor response, secondary to sudden increases in arterial pres- sure, has been extensively studied as a mechanism able to preserve physiologic exchange rates between capillary and interstitial fluids (Spaan, 1991). On the contrary, vasodilator response, following pres- sure drop caused by severe stenosis, has been studied in relatively less detail in the coronary circulation, because ischemic left ventricular dys- function alters the influence of extravascular pressure. Moreover, the control mechanisms of vasomotor tone are profoundly hampered by atherosclerotic endothelial dysfunction (Durand and Gutterman, 2013). Microvascular Research 104 (2016) 38–45 ⁎ Corresponding author at: Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture — DITEN, University of Genoa, Via Opera Pia 11a, 16145 Genoa, Italy. E-mail address: marco.storace@unige.it (M. Storace). http://dx.doi.org/10.1016/j.mvr.2015.11.006 0026-2862/© 2015 Elsevier Inc. All rights reserved. Contents lists available at ScienceDirect Microvascular Research journal homepage: www.elsevier.com/locate/ymvre