Applications of Laplace's law in clinical medicine: a radiological pictorial review

Stress & strain in mechanically nonuniform alveoli using clinical input variables: a simple conceptual model

Clinicians currently monitor pressure and volume at the airway opening, assuming that these observations relate closely to stresses and strains at the micro level. Indeed, this assumption forms the basis of current approaches to lung protective ventilation. Nonetheless, although the airway pressure applied under static conditions may be the same everywhere in healthy lungs, the stresses within a mechanically non-uniform ARDS lung are not. Estimating actual tissue stresses and strains that occur in a mechanically non-uniform environment must account for factors beyond the measurements from the ventilator circuit of airway pressures, tidal volume, and total mechanical power. A first conceptual step for the clinician to better define the VILI hazard requires consideration of lung unit tension, stress focusing, and intracycle power concentration. With reasonable approximations, better understanding of the value and limitations of presently used general guidelines for lung protection may eventually be developed from clinical inputs measured by the caregiver. The primary purpose of the present thought exercise is to extend our published model of a uniform, spherical lung unit to characterize the amplifications of stress (tension) and strain (area change) that occur under static conditions at interface boundaries between a sphere's surface segments having differing compliances. Together with measurable ventilating power, these are incorporated into our perspective of VILI risk. This conceptual exercise brings to light how variables that are seldom considered by the clinician but are both recognizable and measurable might help gauge the hazard for VILI of applied pressure and power.

From pressure to tension: a model of damaging inflation stress

Although the stretch that generates ventilator-induced lung injury (VILI) occurs within the peripheral tissue that encloses the alveolar space, airway pressures and volumes monitor the gas within the interior core of the lung unit, not its cellular enclosure. Measured pressures (plateau pressure, positive end-expiratory pressure, and driving pressure) and tidal volumes paint a highly relevant but incomplete picture of forces that act on the lung tissues themselves. Convenient and clinically useful measures of the airspace, such as pressure and volume, neglect the partitioning of tidal elastic energy into the increments of tension and surface area that constitute actual stress and strain at the alveolar margins. More sharply focused determinants of VILI require estimates of absolute alveolar dimension and morphology and the lung's unstressed volume at rest. We present a highly simplified but informative mathematical model that translates the radial energy of pressure and volume of the airspace into its surface energy components. In doing so it elaborates conceptual relationships that highlight the forces tending to cause end-tidal hyperinflation of aerated units within the 'baby lung' of acute respiratory distress syndrome (ARDS).

Non-destructive vacuum-assisted measurement of lung elastic modulus

In living tissues, mechanical stiffness and biological function are intrinsically linked. Alterations in the stiffness of tissues can induce pathological interactions that affect cellular activity and tissue function. Underlying connections between tissue stiffness and disease highlights the importance of accurate quantitative characterizations of soft tissue mechanics, which can improve our understanding of disease and inform therapeutic development. In particular, accurate measurement of lung mechanical properties has been especially challenging due to the anatomical and mechanobiological complexities of the lung. Discrepancies between measured mechanical properties of dissected lung tissue samples and intact lung tissues in vivo has limited the ability to accurately characterize integral lung mechanics. Here, we report a non-destructive vacuum-assisted method to evaluate mechanical properties of soft biomaterials, including intact tissues and hydrogels. Using this approach, we measured elastic moduli of rat lung tissue that varied depending on stress-strain distribution throughout the lung. We also observed that the elastic moduli of enzymatically disrupted lung parenchyma increased by at least 64%. The reported methodology enables assessment of the nonlinear viscoelastic characteristics of intact lungs under normal and abnormal (i.e., injured, diseased) conditions and allows measurement of mechanical properties of tissue-mimetic biomaterials for use in therapeutics or in vitro models. STATEMENT OF SIGNIFICANCE: Accurate quantification of tissue stiffness is critical for understanding mechanisms of disease and developing effective therapeutics. Current modalities to measure tissue stiffness are destructive and preclude accurate assessment of lung mechanical properties, as lung mechanics are determined by complex features of the intact lung. To address the need for alternative methods to assess lung mechanics, we report a non-destructive vacuum-based approach to quantify tissue stiffness. We applied this method to correlate lung tissue mechanics with tissue disruption, and to assess the stiffness of biomaterials. This method can be used to inform the development of tissue-mimetic materials for use in therapeutics and disease models, and could potentially be applied for in-situ evaluation of tissue stiffness as a diagnostic or prognostic tool.

Decision Tree Based Classification of Abdominal Aortic Aneurysms Using Geometry Quantification Measures

Abdominal aortic aneurysm (AAA) is an asymptomatic aortic disease with a survival rate of 20% after rupture. It is a vascular degenerative condition different from occlusive arterial diseases. The size of the aneurysm is the most important determining factor in its clinical management. However, other measures of the AAA geometry that are currently not used clinically may also influence its rupture risk. With this in mind, the objectives of this work are to develop an algorithm to calculate the AAA wall thickness and abdominal aortic diameter at planes orthogonal to the vessel centerline, and to quantify the effect of geometric indices derived from this algorithm on the overall classification accuracy of AAA based on whether they were electively or emergently repaired. Such quantification was performed based on a retrospective review of existing medical records of 150 AAA patients (75 electively repaired and 75 emergently repaired). Using an algorithm implemented within the MATLAB computing environment, 10 diameter- and wall thickness-related indices had a significant difference in their means when calculated relative to the AAA centerline compared to calculating them relative to the medial axis. Of these 10 indices, nine were wall thickness-related while the remaining one was the maximum diameter (D_max). D_max calculated with respect to the medial axis is over-estimated for both electively and emergently repaired AAA compared to its counterpart with respect to the centerline. C5.0 decision trees, a machine learning classification algorithm implemented in the R environment, were used to construct a statistical classifier. The decision trees were built by splitting the data into 70% for training and 30% for testing, and the properties of the classifier were estimated based on 1000 random combinations of the 70/30 data split. The ensuing model had average and maximum classification accuracies of 81.0 and 95.6%, respectively, and revealed that the three most significant indices in classifying AAA are, in order of importance: AAA centerline length, L2-norm of the Gaussian curvature, and AAA wall surface area. Therefore, we infer that the aforementioned three geometric indices could be used in a clinical setting to assess the risk of AAA rupture by means of a decision tree classifier. This work provides support for calculating cross-sectional diameters and wall thicknesses relative to the AAA centerline and using size and surface curvature based indices in classification studies of AAA.

The - Not So - Solid 5.5 cm Threshold for Abdominal Aortic Aneurysm Repair: Facts, Misinterpretations, and Future Directions

Abdominal aortic aneurysms (AAAs) represent a focal dilation of the aorta exceeding 1.5 times its normal diameter. It is reported that 4-8% of men and 0.5-1% of women above 50 years of age bear an AAA. Rupture represents the most disastrous complication of aneurysmal disease that is accompanied by an overall mortality of 80%. Autopsy data have shown that nearly 13% of AAAs with a maximum diameter ≤5 cm were ruptured and 60% of the AAAs >5 cm in diameter never ruptured. It is therefore obvious that the "maximum diameter criterion," as a single parameter that fits all patients, is obsolete. Investigators have begun a search for more reliable rupture risk markers for AAA expansion, such as the level and change of peak wall stress or AAA geometry. Furthermore, it is becoming more and more evident that intraluminal thrombus (ILT), which is present in 75% of all AAAs, affects AAA features and promotes their expansion. Though these hemodynamic properties of AAAs are significant and seem to better describe rupture risk, they are in need of specialized equipment and software and demand time for processing making them difficult in use and unattractive to clinicians in everyday practice. In the search for the addition of other risk factors or user-friendly tools, which may predict AAA expansion and rupture, the use of the asymmetrical ILT deposition index seems appealing since it has been reported to identify AAAs that may have an increased or decreased growth rate.