A progressive rupture model of soft tissue stress relaxation

Prediction of diabetic foot ulcer progression: a computational study

The development of foot ulcers is a common consequence of severe diabetes. Due to vascular disorders and impeded healing caused by the disease, most foot ulcers have been reported to be affected by body weight and progress with time. Also, abnormal distribution of plantar pressures has been observed to cause the formation of additional ulcers, which may collectively lead to traumatic amputations. While a study of such pathophysiology is not possible through experiments, a few computational modelling works have investigated diabetic foot ulcers. To date, ulcers with a few sizes and locations have been studied, and their effect on the plantar stresses has been quantified. In this work, we have attempted to study the effect of all possible ulcer locations on the generated plantar peak stresses and peak stress locations where additional ulcers may form. Also, the effect of ulcer location on the possible ulcer growth was investigated. A full-scale foot model was developed and a total of 52 ulcer locations were simulated separately, with standing and walking loads. The generated stresses were normalised with the foot size and statistically analysed to develop novel formulations for predicting peak plantar stresses and their locations for any known ulcer location. The results from this study are anticipated to provide important guidelines to doctors and medical practitioners for predicting foot ulcer progression in diabetic patients with existing ulcers and allow the administration of timely preventive interventions.

Percolation of collagen stress in a random network model of the alveolar wall

Fibrotic diseases are characterized by progressive and often irreversible scarring of connective tissue in various organs, leading to substantial changes in tissue mechanics largely as a result of alterations in collagen structure. This is particularly important in the lung because its bulk modulus is so critical to the volume changes that take place during breathing. Nevertheless, it remains unclear how fibrotic abnormalities in the mechanical properties of pulmonary connective tissue can be linked to the stiffening of its individual collagen fibers. To address this question, we developed a network model of randomly oriented collagen and elastin fibers to represent pulmonary alveolar wall tissue. We show that the stress-strain behavior of this model arises via the interactions of collagen and elastin fiber networks and is critically dependent on the relative fiber stiffnesses of the individual collagen and elastin fibers themselves. We also show that the progression from linear to nonlinear stress-strain behavior of the model is associated with the percolation of stress across the collagen fiber network, but that the location of the percolation threshold is influenced by the waviness of collagen fibers.

Regional lung viscoelastic properties in supine and prone position in a porcine model of acute respiratory distress syndrome

Regional viscoelastic properties of thoracic tissues in acute respiratory distress syndrome (ARDS) and their change with position and positive end-expiratory pressure (PEEP) are unknown. In an experimental porcine ARDS, dorsal and ventral lung (R₂,L and E₂,L) and chest wall (R₂,cw and E₂,cw) viscoelastic resistive (R) and elastic (E) parameters were measured at 20, 15, 10, and 5 cmH₂O PEEP in supine and prone position. E₂ and R₂ were obtained by fitting the decay of pressure after end-inspiratory occlusion to the equation: P_viscmax (t) =R₂ e^-t/τ₂, where t is the length of occlusion and τ₂ time constant. E₂ was equal to R₂/τ₂. R₂,cw and E₂,cw were measured from esophageal, dorsal, and ventral pleural pressures. Global R₂,L and E₂,L were obtained from the global transpulmonary pressure (airway pressure-esophageal pressure), and regional R₂,L and E₂,L from the dorsal and ventral airway pressure-pleural pressure difference. Lung ventilation was measured by electrical impedance tomography (EIT). Global R₂,cw and E₂,cw did not change with PEEP or position. Global R₂,L [median(Q1-Q3)] was 37.1 (11.0-65.1), 5.1 (4.3-5.5), 12.1 (8.4-19.5), and 41.0 (26.6-53.5) cmH₂O/L/s in supine, and 15.3 (9.1-41.9), 7.9 (5.7-11.0), 8.0 (5.1-12.1), and 12.9 (6.4-19.4) cmH₂O/L in prone from 20 to 5 cmH₂O PEEP (P = 0.06 for PEEP and P = 0.06 for position). Dorsal R₂,L significantly and positively correlated with the amount of collapse measured with EIT. Global and regional lung and chest wall viscoelastic parameters can be described by a simple rheological model. Regional E₂ and R₂ were uninfluenced by PEEP and position except for PEEP on dorsal E₂,L and position on dorsal E₂,cw.NEW & NOTEWORTHY In a porcine model of acute respiratory distress syndrome, data were successfully fitted to a rheological model of the nonlinear behavior of viscoelastic properties of lung and chest wall at different positive end-expiratory pressure (PEEP) in the supine and prone position. Prone position tended to decrease lung viscoelastic resistive component. PEEP had a significant effect on dorsal lung viscoelastic elastance. Finally, lung viscoelastic resistance correlated with the amount of lung collapse assessed by electrical impedance tomography.

The Functionally Grading Elastic and Viscoelastic Properties of the Body Region of the Knee Meniscus

The knee meniscus is a highly porous structure which exhibits a grading architecture through the depth of the tissue. The superficial layers on both femoral and tibial sides are constituted by a fine mesh of randomly distributed collagen fibers while the internal layer is constituted by a network of collagen channels of a mean size of 22.14 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}μm aligned at a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$30^{\circ }$$\end{document}30∘ inclination with respect to the vertical. Horizontal dog-bone samples extracted from different depths of the tissue were mechanically tested in uniaxial tension to examine the variation of elastic and viscoelastic properties across the meniscus. The tests show that a random alignment of the collagen fibers in the superficial layers leads to stiffer mechanical responses (E = 105 and 189 MPa) in comparison to the internal regions (E = 34 MPa). All regions exhibit two modes of relaxation at a constant strain (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _1 = 6.4$$\end{document}τ1=6.4 to 7.7 s, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _2$$\end{document}τ2 = 49.9 to 59.7 s).

Time dependent stress relaxation and recovery in mechanically strained 3D microtissues

Characterizing the time-dependent mechanical properties of cells is not only necessary to determine how they deform but also to understand how external forces trigger biochemical-signaling cascades to govern their behavior. At present, mechanical properties are largely assessed by applying local shear or compressive forces on single cells grown in isolation on non-physiological 2D surfaces. In comparison, we developed the microfabricated vacuum actuated stretcher to measure tensile loading of 3D multicellular "microtissue" cultures. Using this approach, we here assessed the time-dependent stress relaxation and recovery responses of microtissues and quantified the spatial viscoelastic deformation following step length changes. Unlike previous results, stress relaxation and recovery in microtissues measured over a range of step amplitudes and pharmacological treatments followed an augmented stretched exponential behavior describing a broad distribution of inter-related timescales. Furthermore, despite the variety of experimental conditions, all responses led to a single linear relationship between the residual elastic stress and the degree of stress relaxation, suggesting that these mechanical properties are coupled through interactions between structural elements and the association of cells with their matrix. Finally, although stress relaxation could be quantitatively and spatially linked to recovery, they differed greatly in their dynamics; while stress recovery acted as a linear process, relaxation time constants changed with an inverse power law with the step size. This assessment of microtissues offers insights into how the collective behavior of cells in a 3D collagen matrix generates the dynamic mechanical properties of tissues, which is necessary to understand how cells deform and sense mechanical forces in vivo.

Quantification of Age-Related Lung Tissue Mechanics under Mechanical Ventilation

Elderly patients with obstructive lung diseases often receive mechanical ventilation to support their breathing and restore respiratory function. However, mechanical ventilation is known to increase the severity of ventilator-induced lung injury (VILI) in the elderly. Therefore, it is important to investigate the effects of aging to better understand the lung tissue mechanics to estimate the severity of ventilator-induced lung injuries. Two age-related geometric models involving human bronchioles from generation G10 to G23 and alveolar sacs were developed. The first is for a 50-year-old (normal) and second is for an 80-year old (aged) model. Lung tissue mechanics of normal and aged models were investigated under mechanical ventilation through computational simulations. Results obtained indicated that lung tissue strains during inhalation (t = 0.2 s) decreased by about 40% in the alveolar sac (G23) and 27% in the bronchiole (G20), respectively, for the 80-year-old as compared to the 50-year-old. The respiratory mechanics parameters (work of breathing per unit volume and maximum tissue strain) over G20 and G23 for the 80-year-old decreased by about 64% (three-fold) and 80% (four-fold), respectively, during the mechanical ventilation breathing cycle. However, there was a significant increase (by about threefold) in lung compliance for the 80-year-old in comparison to the 50-year-old. These findings from the computational simulations demonstrated that lung mechanical characteristics are significantly compromised in aging tissues, and these effects were quantified in this study.

Systems-level airway models of bronchoconstriction

Understanding lung and airway behavior presents a number of challenges, both experimental and theoretical, but the potential rewards are great in terms of both potential treatments for disease and interesting biophysical phenomena. This presents an opportunity for modeling to contribute to greater understanding, and here, we focus on modeling efforts that work toward understanding the behavior of airways in vivo, with an emphasis on asthma. We look particularly at those models that address not just isolated airways but many of the important ways in which airways are coupled both with each other and with other structures. This includes both interesting phenomena involving the airways and the layer of airway smooth muscle that surrounds them, and also the emergence of spatial ventilation patterns via dynamic airway interaction. WIREs Syst Biol Med 2016, 8:459-467. doi: 10.1002/wsbm.1349 For further resources related to this article, please visit the WIREs website.