The left and right coronary arteries provide the entire blood supply of the myocardium. Blood flow through these vessels is determined by the interplay of ventricular and aortic pressures (and therefore by heart rate), by local control which matches flow to myocardial work, and by autonomic control.
Left coronary artery
Right coronary artery
Venous drainage is via the great cardiac vein, which begins paired with the LAD and wraps around the course of the LCx until it becomes the coronary sinus, where it drains into the RV. There are also thebesian veins that drain directly into both atria, contributing to anatomical shunt.
$$Q = \frac{\Delta P}{R}$$
The major backpressure to coronary perfusion comes from the compressive forces within the myocardium during systole. To put it another way:
$$Q = \frac{P_{\text{Aorta}} - P_{\text{Ventricle}}}{R}$$
This effectively means that the left ventricle is best perfused during diastole, and in early systole there the flow is abolished or reversed. The right ventricle is supplied during both systole and diastole, because the RV pressures are so much lower (and never overcome the aortic pressure).
Increased myocardial work increases blood flow to maintain the oxygen supply/demand ratio by coronary vasodilation, reducing the resistance to flow. This is achieved by four mechanisms.
Direct action of \(K_{\text{ATP}}\) channels
These channels are the same that are on pancreatic beta cells. They open in response to low intracellular ATP, causing an outwards potassium leak from myocardiocytes (decreasing myocardial work), and hyperpolarization of vascular (coronary) smooth muscle \(\to\) decreased Ca influx \(\to\) vasodilation.
Nitric Oxide
Local hypoxia causes upregulation of eNOS (probably also by \(K_ATP\) channels) \(\to\) NO release and diffusion into SM cells \(\to\) upregulation of guanylate cyclase \(\to\) increase cGMP \(\to\) vasodilation
Sensing byproducts of metabolism (Adenosine, pH, lactate, potassium)
All cause smooth muscle dilation
Myogenic mechanism: Increased intraluminal pressure directly causes smooth muscle vasodilation
Alpha-1 agonism: PLC -> IP3 + DAG -> increase intracellular calcium -> vasoconstriction
Beta-2 agonsism: adenylate cyclase -> cAMP -> PKA -> posphorylation (inactivation) of MLCK
Overall effect of endogenous catecholamines: Coronary vasoconstriction (alpha > beta); catecholamines also increase LV systolic pressure and heart rate, which can impair flow; but they also increase myocardial work which can overcome all those things and increase flow.
M2-agonism: Coronary arteries have M2 (rather than M3) receptors, which cause vasodilation by a guanylate cyclase -> cGMP pathway