Mechanical ventilation is the main supportive therapy to re-establish sufficient oxygen supply to peripheral organs in patients with acute respiratory distress syndrome (ARDS). As with any therapy, mechanical ventilation may expose patients to side effects. Alveolar rupture and air leak, the so-called barotraumas, were recognized early as the main side effects of mechanical ventilation . However, in 1974, Webb and Tierney showed that mechanical ventilation could also be responsible for ultra-structural injury, independent of air leaks . The potential clinical implication of these data was not realized until a series of studies showed that, apart from the physical alveolar disruption, mechanical ventilation can induce further injury to the lung by increasing alveolar-capillary permeability through the overdistension of the lung (volutrauma)  and/or worsening lung injury through the tidal recruitment-derecruitment ofthe collapsed alveoli (atelectrauma) [4, 5], and lead to even more subtle injury manifested by the activation of the inflammatory process (biotrauma) [6-8]. All these experimental and clinical data led to the concept that all the patho-physiological mechanisms involved in ARDS (ventilation-perfusion mismatch and reduced compliance, lung edema, atelectasis, pulmonary inflammation) may be worsened by the mechanical stress caused by inappropriate ventilator settings. In the early nineties, an international consensus conference concluded that both tidal overdistension of normal alveoli and opening-closing of collapsed alveoli, contribute to a component of a progressive lung injury that arises not only from the disease process itself, but also from the impact of the ventilator patterns applied during the course ofthe disease . Ventilator-induced lung injury (VILI) was therefore defined as acute lung injury (ALI) directly induced by mechanical ventilation [10, 11].
Although randomized clinical trials [8, 12, 13] have successfully demonstrated that a ventilatory strategy designed to minimize overdistension and opening-closing may reduce mortality in patients with ARDS, information regarding the bio-mechanical characteristics of stress applied to the ventilated lungs is still missing. VILI is, in fact, determined by the dynamic and continuous interaction between: a) the mechanical characteristics of the lung; and b) the ventilator settings. The relationship between these terms is conditioned by the dynamic variations in respiratory mechanics as determined by the status and evolution of the pathological process and by the consequences of ventilator parameters on the mechanical characteristics of the lung. Therefore, clinicians have to choose tidal volume (Vt), positive end-expiratory pressure (PEEP) and recruiting maneuvers assuming that the ventilator settings are not causing VILI but lacking a clinical tool able to identify whether the interaction between the currently used ventilator settings and the actual status of pulmonary mechanics results in mechanical stress or not.
The mechanical characteristics of animal models [4, 6,14] and patients [15,16] with ARDS have been investigated by the analysis of the static pressure-volume (PV) curve of the respiratory system. Bedside analysis of the PV curve provided most of the physiological rationale explaining the pulmonary injury due to VILI. The static PV curve is, in fact, characterized by a lower (LIP) and an upper (UIP) inflection point that are thought to represent the average critical opening pressure above which alveolar units start to re-open and the volume/pressure values above which stretching and overdistension start to occur, respectively . Several studies have demonstrated that tidal inflation starting below the LIP on the PV curve leads to tidal recruitment/de-recruitment of previously collapsed alveoli while tidal ventilation occurring above the UIP results in pulmonary over-stretching both leading to a spectrum of pulmonary and systemic lesions such as air leaks , alterations in lung fluid balance , increases in endothelial and epithelial permeability [19, 20], severe tissue damage , and pulmonary  and systemic [11, 21] production of inflammatory mediators.
Because of this link between VILI and assessment of the PV curve, and in an effort to make the measurement of the PV curve available at the bedside, a growing interest in the development of new technologies and on the clinical interpretation of the PV curve has become evident in the last few years [22-30]. However, although a large number of experimental studies correlated PV curves to histological  and biological [6, 21] manifestations of VILI, only two randomized trials showed that a protective ventilatory strategy individually tailored to the PV curve minimized pulmonary and systemic inflammation  and decreased mortalityin patients with ALI . Furthermore, despite the fact that several studies have proposed new techniques to perform PV curves at the bedside [23, 24, 27], confirming that the LIP and UIP correspond to computed tomography (CT) scan evidence of atelectasis and overdistension [26, 28, 29] and demonstrating the ability of the PV curve to estimate alveolar recruitment with PEEP [15, 16], no large clinical studies have assessed whether such measurements can be performed in all ICUs as a monitoring tool to orient ventilator therapy.
This chapter will:
a) review the basic principles of mechanical stress;
b) discuss how to measure and interpret the static PV curve to minimize VILI;
c) revise the potential advantage of the use of dynamic PV curves to monitor, prevent and minimize VILI.
Respiratory mechanics is classically partitioned into the relationships between pressure and volume (elastic mechanics) and the relationships between pressure and flow (resistive mechanics). Resistive and elastic mechanics is usually described at a "macro-level' using various geometrical bodies (e.g., octahedrons, dodecahedrons and combinations of spheroids, cones and ellipsoids) to describe the tridimensional structure of the alveolar region [31-33]. These models provide useful information on the gross mechanical behavior but cannot take into account the internal distribution of stresses within the alveolar wall. On the other hand, the mechanics of the alveolar tissue lies at the 'micro-level'. The alveolar septum is a tiny structural framework that insures a minimal barrier between air and blood, while a relatively enormous surface of contact is maintained for efficient gas exchange. It consists of a skeleton of fine collagen and elastin fibers that are interlaced with the capillary network . This structural organization comprises a 'composite' made of extensible elastin fibers woven into non-extensible collagen networks, allowing the lung to inflate within the normal range also providing support and a high stiffness at limiting volumes. The study by Gefen et al.  aimed to overcome the limitations inherent to a 'macro' description, by describing the internal stresses in a two-dimensional slice ofan alveolar sac. The authors found that significant stress concentrations arise in lungs with emphysema (up to 6 times the stresses of a normal lung) at a lung volume of 60% of the total capacity. This provides progressive damage to the elastin fibers during breathing cycles. The pioneering study by Mead et al.  developed a two-dimensional static model at the alveolar scale to investigate the mechanics of deformation of a non-homogeneous lung. However, this model does not take into in account that: a) alveolar deformation takes place at a three-dimensional level; b) the inter-dependence among the various scales of the anatomic and functional pulmonary structures (more than 20 scales are involved in the respiratory mechanics); c) the multi-physics of the process due to the coupling the air flow process with the mechanical deformations and the surface tension.
The Mechanics of Stress, Strain, and Elasticity in Solid Media
Basic principles of stress and deformation within solid bodies were originally described by Timoshenko . Central to Timoshenko theory is the description of infinitesimal deformations within the solid body that can be described by continuum mechanics. This theory has been proved to be effective in many fields of engineering, includingbio-engineering, e.g., for the design ofhip prostheses, dental implants and tubular stents. In the presence of soft tissues, however, the theory must be enriched by removing the hypothesis of small deformations and considering explicitly large strains and finite displacements of the body points. This provides cumbersome analytical models, of less immediate physical explanation than the infinitesimal theory. In the following, the elementary concepts of the infinitesimal theory will be outlined, in order to get the physical insight into continuum mechanics and create the basis for a correct nomenclature of the mechanical quantities.
The basic concepts of the so-called continuum mechanics are the concepts of strain and stress. In order to measure the deformation field within a solid body, the so-called strain tensor (e) needs to be introduced. Such a quantity is defined at any
Fig. 1. Normal stresses and normal strains (a); shear stresses and distortions (b) in the XY plane.
point of the medium and, in a cartesian space, is a function of the three axes X,Y ,Z and of the normal (n) to a generic plane which the deformation is referred to. It is formally a symmetric 3x3 matrix, with three normal strain £ corresponding to elongation in the X, Y, Z directions (which provide volume changes in the body) and three tangential strains y corresponding to shape distortions of the infinitesimal volume around the considered point (Fig. 1). The strains are non-dimensional quantities, i.e., normal strains represent the deformation of the oriented fibers divided by the initial length of the fiber, whereas tangential strains represent angular variations with respect to n/2. Without going into the details, it can be shown that, at any point of the body, there exist three orthogonal principal directions that do not alter their orientation during deformation and are subjected only to the (normal) principal strains. In order to calculate the (elastic) energy that is stored in the body in correspondence to a certain strain field, the static counterpart of strain is introduced and is named the stress tensor [o]. The stress field is tensorial because the stress vector, defined at any point P of the medium, depends also on the plane considered to which the components are referred (Fig. 2). In perfect correspondence to the strain tensor, [o] is a symmetric matrix made of three normal stresses o acting in the X, Y, Z directions (e.g., acting orthogonal to the planes defined by the normal vectors parallel to X, Y, Z) and of three tangential or shear stresses t. These quantities have the physical dimension of pressures, i.e., forces per unit area. When the stress vector is orthogonal to the plane, we speak of a principal plane, and the stress coincides with its normal component. In the general case, there will also be the tangential components in the plane. As can be deduced from Figure 1, normal stresses o (which can be positive, or tensile, and negative or compressive) work for the corresponding normal strains £ (respectively, fiber elongation or contraction), whereas shear stresses t are coupled to the angular distortions y. It should be noted that the stress is an abstract entity, i.e., it is a quantity that cannot be measured directly. On the contrary, strains are measurable, and therefore experimental measures of stresses rely on the direct evaluation of the strains. Accurate measurements of strains on soft (biologic) tissues, like the lung tissue, are currently a major challenge from the technological point of
view, both due to relatively large deformation of tissues and to their irregular shapes.
The relation between stresses and strains is called the constitutive law of the material. All solid materials possess to a certain extent the property of elasticity, i.e., if external forces producing deformation of a structure do not exceed a certain limit, the deformation disappears with the removal of the forces. This implies that the strain energy is totally recovered, i.e., the material does not dissipate energy in any form. Elastic materials are modeled by means of a constitutive relation between stress and strain, i.e., by a functional form [o] = [o(e)].
The determination of the stress and strain fields within the lung represents an awkward task in mechanics. This is due to the large deformations (compared to traditional structural materials) and to the hierarchical structure of the lung, with more than 20 levels of scales characterized by specific meso- and micro-structures, each with well-defined geometrical characteristics . The first 16 levels, starting from the trachea down to the terminal bronchioles, constitute the conductive zone, where flow occurs to and from the lungs. From level 17 to level 24 (corresponding to the almost 300,000,000 alveoli with capillaries lying in their septae), the so-called respiratory zone, gas exchange occurs and the effects of air velocity are negligible. At the scale of alveoli, the surface tension of the surfactant is comparable to the mechanical actions, thereby complicating even further the scenario. The mechanical interdependence of airways and alveoli within the lung has probably been designed with the aim to support uniform expansion of air spaces. In non-uni-formly expanded lungs, the effective pressure differs from trans-pulmonary pres sure, giving rise to shear stresses and consequent synergetic enhancement of the pathologies.
It is well known that solid materials suffer mostly due to shear stresses rather than to normal stresses. Shear stresses or the elastic energy due to distortions are responsible for material crisis according to the widely used criteria of material's strength (e.g., Tresca or von Mises criteria, ). Stresses in the pulmonary tissue, however, cannot be described by a continuous field, as is commonly done in continuous homogeneous media and has been briefly described in the previous section. A more precise description of lung mechanics, from the point of view of the alveolar tissue, must be pursued by means of more complicated theories such as the theory of cellular materials, which can account for the multiscale character of the stress/strain fields . As is schematically shown in Figure 3, the mechanics of cellular materials explicitly considers the constituent geometry of the structures,
at a certain level of observation. From a mathematical point of view, such a discretization can be considered as an approximation of the continuum theory although, in reality, there are profound differences. Shear stresses, for instance, arise in the alveolar walls not only under the action of shear forces (Fig. 3), but also in the presence of normal forces, due to the microstructural characteristics. From the pictures, it appears evident how, in the absence of adequate surface tension and consequent homogeneous distension of the alveoli, the forces exerted by the surrounding sacs tend to induce distortion ofthe septae of the sick alveoli, enhancing their tendency to collapse.
Patients with ARDS are characterized by a reduction in the range of volume excursion, because of the reduction in the ventilating units, and a smaller change in volume for unit of change in pressure. The initial part of the PV curve, at very low lung volume, is therefore considerably flatter than the rest ofthe curve, showing the amount of pressure required to open collapsed peripheral alveoli. This 'lower inflection point' separates a tract of the curve with bad elastic properties from the tract characterized by optimal elastic properties. After this initial tract, the curve presents a linear section in which the open alveoli are ventilated. Then the PV curve flattens again at values of Vt lower than those observed in normal subjects. This 'upper inflection point' indicates that stretching and overdistension of at least some alveolar structures is occurring.
Inflation of an excised lung requires a critical opening pressure to be applied in order to re-expand the collapsed alveoli . This critical pressure appears on the PV curve as the pressure corresponding to the sudden change in slope of the curve after the initial inflation. In normal subjects, this critical opening pressure amounts to ~20 cmH2O. Similarly, in patients with ARDS, the inspiratory PV curve shows a LIP, that is the sudden change in slope occurring at the onset oftidal inflation,when the applied pressure varies between 10-20 cmH2O. This shows that in ARDS the vast majority of the lung is collapsed at the beginning of inspiration. The pressure corresponding to the LIP should therefore represent the minimal level of PEEP that should be applied in order to have tidal inflation within an open lung. Considering that ARDS and ALI are conditions of in-homogeneous lung parenchyma, CT densities are more concentrated in dependent lung regions, where there is a more positive pleural pressure if compared with nondependent regions (0 cmH2O and -3, -5 cmH2O, respectively). The influence of this vertical gradient in pleural pressure in the supine position, maybe enhanced by the gravitational distribution ofedema.
The decrease of the PV curve slope indicates the end of alveolar recruitment, the beginning of alveolar overdistension and so the maximal alveolar pressure that shouldbe applied to obtain the maximal amount of alveolar recruitment. In normal subjects, the UIP is reached at a lung volume that is 85-90% of TLC (total lung capacity); in patients with ARDS, UIP occurs at a much lower volume. An increase in pressure above the UIP only gives overdistension without any other increase in volume, with a maximal stretch of lung aerated areas.
Techniques to Assess Static PV Curve Super-syringe technique
This is the first technique used to assess the status of elastic properties of the respiratory system in mechanically ventilated ALI/ARDS patients in supine position sedated and paralyzed, to permit the slow inflation of the lung with a predetermined gas volume of oxygen. The inflated volume is 100-200 ml. The syringe stops for 2-3 sec, then the respiratory system is inflated with intermittent pause until a volume of 25 ml/kg or an airway pressure of 40 cmH2O is reached. With this technique it is easy to detect the lower and upper inflection points but, on the other hand, paralysis, sedation and disconnection of the patient from the ventilator are required.
This technique is based on a single-breath occlusion at different inflations during mechanical ventilation. With inspiratory flow constant, different volumes are achieved. Each occlusion is maintained until a plateau in the open airways pressure is obtained thus representing the static pressure of the total respiratory system. Using different volumes the static PV curve can be constructed. Advantages of this technique include no need for patient disconnection and the ability to identify the elastic properties of the respiratory system as determined by the actual volume. In addition, the measurement does not require special devices. However, patients must be paralyzed and sedated and curves are not immediately available since single data points need to be first collected and recorded and than plotted; identification of LIP and UIP is not easy.
This method is based on the assumption that when inspiratory flow is constant during passive inflation the rate of change in the airway opening pressure is related to the elastance of the respiratory system and the resistive components are nil. There is no need to disconnect the patient from the ventilator, special devices are not required and results are available at the bedside; lower and upper inflection points are usually easily identified. Yet, this method requires paralysis, sedation and only few ventilators are equipped with such a monitoring tool.
In patients with ARDS, the rapid airway occlusion technique (static PV curve) provides the same information as the constant flow technique (with a flow of 3 l/min) regarding the elastic properties of the respiratory system, whereas the PV curve obtained by the 9 l/min constant flow is slightly shifted to the right . The slopes ofthe PV curves and the LIP are not differentbetween all methods, indicating that the resistive component induced by administering a constant flow equal to or less than 9 l/min is not of clinical relevance. However, all methods have an intrinsic risk of adverse effects, including hypoxemia at low lung volumes and de-recruitment at low levels of PEEP [26-28]. Other problems include hemodynamic changes (decrease of venous return) or complications related to sedation or paralysis required to obtain the characteristics of passive mechanic of respiratory system. For all these reasons, PV curves are not usually obtained in the routine clinical assessment .
A non-linear model of respiratory mechanics in ARDS has recently been used to verify the physiological interpretation of the LIP and UIP and to examine their potential use in the clinical setting to set mechanical ventilation [30, 40]. This analysis showed that: i) the initial increase in slope of the PV curve indicates the minimal pressure at which alveolar recruitment starts to occur rather than the maximum level of PEEP able to provide maximum recruitment. Under these circumstances, a PEEP level equal to the LIP underestimates the optimal level of PEEP able to minimize end-expiratory alveolar collapse; ii) the decrease in the slope of the PV curve does not indicate the beginning of alveolar overdistension but the end of alveolar recruitment. According to this mathematical model, the UIP is therefore unrelated to alveolar overdistension being caused by the decrease in the rate of alveolar recruitment during lung inflation. Under these circumstances, the LIP will indicate the maximal alveolar pressure that should be applied to obtain the maximal amount of alveolar recruitment. Animal and clinical experiments are consistent with these data and have shown that recruitment occurs throughout the entire lung inflation from end-expiratory lung volume to TLC rather than being an 'all or none' phenomenon [41, 42].
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