With progressive occlusion of a coronary main artery, some anastomotic vessels are recruited in order to supply blood to the ischemic region. This collateral circulation is an important factor in the preservation of the myocardium until reperfusion of the area at risk. An accurate estimation of collateral flow is crucial in surgical bypass planning as it alters the blood flow distribution in the coronary network and can influence the outcome of a given treatment for a given patient. The evaluation of collateral flow is frequently achieved using an index based on pressure measurements. It is named collateral flow index (CFI) and defined as: (P_w−P_v)/(P_ao−P_v), where P_w is the pressure distal to the thrombosis, P_ao the aortic pressure and P_v the central venous pressure. In the present work, we study patients with severe coronary disease (stenoses on the left branches and total occlusion of the right coronary artery). Using a mathematical model that describes the coronary hemodynamics in that situation, we demonstrate that the dependence of the collateral circulation to the pressure values is not as simple as it is commonly believed: using pressures alone as an index of collateral flow is likely to result in misinterpretation of the collateral flow contribution, because collateral flow depends on many other factors related to the status of the native stenosed arteries and to the microvascular resistances (capillary and collateral resistances, and the proportion between them).