**1. Introduction**

Pulmonary hypertension (PH) is a complex and multifactorial syndrome, partly unknown, characterized by a profound alteration of pulmonary vasculature and, consequentially, a rise in the pulmonary vascular load, leading to hypertrophy and remodeling of the right heart chambers.

#### **1.1 Basic principles of pulmonary circulation**

Pulmonary circulation, includes a vast network of arteries, veins, and lymphatic vessels and is unique, both in function and volume: it is a low-pressure, low-resistance, highly distensible system, and it is capable of accommodating large increases in blood flow with none or minimal elevations of its pressure. During embryonic life, the pulmonary circulation is a low-flow and high-resistance circuit. After birth, once the baby takes his first breath, the high resistance in the lungs drops dramatically: from now on, blood can enter lungs for oxygenation. Oxygen relaxes the pulmonary vessels and causes closure of the fetal shunts: at this precise moment, the baby's blood flow is identical to that of an adult [1]. Therefore, this vasculature dilates, in order to take in the entire cardiac output (CO), with high blood flow at low intravascular pulmonary arterial pressure (PAP). Anatomically, pulmonary arteries have thinner walls with less

smooth muscle and lack of basal tone: this happens because of the elevated production of endogenous vasodilators and low production of vasoconstrictors from the endothelium of the pulmonary vessel walls. These mechanisms result in the maintenance of a normal pulmonary vascular resistance (PVR) [2]. Pulmonary circulation differs functionally from the systemic one because it carries mixed venous blood. Deoxygenated blood is channeled through the pulmonary artery directly in the alveolar/capillary units where gas exchange occurs and blood releases carbon dioxide and is replenished with oxygen. Then, oxygenated blood is carried back to the left atrium by the pulmonary veins, in order to be distributed to the systemic circulation.

#### **1.2 Physiological bases of hemodynamic classification**

In order to better understand the hemodynamic classification of PH, we should recall Poiseuille's law, one of the most important laws of fluid dynamics (1):

$$Q = (P\_1 - P\_2) \times \pi r^4 / 8\mu l \tag{1}$$

Where Q is flow (l/min) and then Cardiac Output (CO), if we apply the equation to the pulmonary circulation; P1 is mean pulmonary arterial pressure (mPAP), the pressure at the beginning of the pulmonary circulation, P2 is the pulmonary artery wedge pressure (PAWP) equivalent to the left atrial pressure, the pressure at the end point of the pulmonary circulation, when measured at right heart catheterization in the absence of pulmonary vein stenosis. 8μl/πr <sup>4</sup> is a measure of the pulmonary vasculature resistance (PVR).

According to Poiseuille's law, pulmonary vasculature resistance (PVR) is inversely related to the fourth power of arterial radius: in this equation, l represents the length of the vessel, r its radius, and *μ* the viscosity of the fluid, in our case, blood. PVR is used to characterize PH because this parameter allows us to quantify abnormalities of the pulmonary vasculature, as it is mainly related to the anatomical geometry of small distal arterioles of the lung. PVR can also be expressed as (2):

$$\text{PVR} = (\text{mPAP-PAWP})/\text{CO} \tag{2}$$

Therefore, PVR reflects the functional status of pulmonary vascular endothelium/ smooth muscle cell coupled system, and it is also positively related to blood viscosity. Additionally, PVR may be influenced by changes in perivascular alveolar and pleural pressure. According to Poiseuille's law mPAP depends on cardiac output, left atrial pressure, and PVR (3)

$$\text{mPAP} = (\text{CO} \times \text{PVR}) + \text{PAWP} \tag{3}$$

whereas pressure does not depend on the size of the body, and PAP from different patients can be evaluated without considerable differences in their body size [3, 4]. PAWP is an acceptable estimate of left atrial pressure (LAP) or left ventricular enddiastolic pressure (LVEDP) in the absence of mitral stenosis or pulmonary vein stenosis. Furthermore, PAWP and LVEDP are usually considered to be interchangeable, even if some pathological scenarios, such as atrial fibrillation, rheumatic disease, or large diameter of the left atrium are associated with a PAWP higher than LVEDP. PAWP and LVEDP measurements should be obtained at the end of the expiratory phase and the end of the diastolic phase, QRS gated [4].
