A mathematical model for the vessel recruitment in coronary microcirculation in the absence of active autoregulation

• New mathematical model for vessel recruitment in the microvascular coronary network
• Physiological values of the capillary pressure preserved by the model
• Model used to classify data from 29 patients underwent percutaneous coronary intervention.
• Patients subdivided into two categories clinically different in statistically significant terms

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 microvascular 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 < 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 decrease in MVNU number is predicted by the model in patients with regional dysfunction and implies a relatively lower response of maximal flow to revascularization.