Interaction of biomechanics with extracellular matrix components in abdominal aortic aneurysm wall.

OBJECTIVE: Little is known about the interactions between extracellular matrix (ECM) proteins and locally acting mechanical conditions and material macroscopic properties in abdominal aortic aneurysm (AAA). In this study, ECM components were investigated with correlation to corresponding biomechanical properties and loads in aneurysmal arterial wall tissue. METHODS: Fifty-four tissue samples from 31 AAA patients (30♂; max. diameter Dmax 5.98 ± 1.42 cm) were excised from the aneurysm sac. Samples were divided for corresponding immunohistological and mechanical analysis. Collagen I and III, total collagen, elastin, and proteoglycans were quantified by computational image analysis of histological staining. Pre-surgical CT data were used for 3D segmentation of the AAA and calculation of mechanical conditions by advanced finite element analysis. AAA wall stiffness and strength were assessed by repeated cyclical, sinusoidal and destructive tensile testing. RESULTS: Amounts of collagen I, III, and total collagen were increased with higher local wall stress (p = .002, .017, .030, respectively) and strain (p = .002, .012, .020, respectively). AAA wall failure tension exhibited a positive correlation with collagen I, total collagen, and proteoglycans (p = .037, .038, .022, respectively). α-Stiffness correlated with collagen I, III, and total collagen (p = .011, .038, and .008), while ß-stiffness correlated only with proteoglycans (p = .028). In contrast, increased thrombus thickness was associated with decreased collagen I, III, and total collagen (p = .003, .020, .015, respectively), and AAA diameter was negatively associated with elastin (p = .006). CONCLUSIONS: The present results indicate that in AAA, increased locally acting biomechanical conditions (stress and strain) involve increased synthesis of collagen and proteoglycans with increased failure tension. These findings confirm the presence of adaptive biological processes to maintain the mechanical stability of AAA wall.

A single charge in the actin binding domain of fascin can independently tune the linear and non-linear response of an actin bundle network.

Actin binding proteins (ABPs) not only set the structure of actin filament assemblies but also mediate the frequency-dependent viscoelastic moduli of cross-linked and bundled actin networks. Point mutations in the actin binding domain of those ABPs can tune the association and dissociation dynamics of the actin/ABP bond and thus modulate the network mechanics both in the linear and non-linear response regime. We here demonstrate how the exchange of a single charged amino acid in the actin binding domain of the ABP fascin triggers such a modulation of the network rheology. Whereas the overall structure of the bundle networks is conserved, the transition point from strain-hardening to strain-weakening sensitively depends on the cross-linker off-rate and the applied shear rate. Our experimental results are consistent both with numerical simulations of a cross-linked bundle network and a theoretical description of the bundle network mechanics which is based on non-affine bending deformations and force-dependent cross-link dynamics.

Using parametric model order reduction for inverse analysis of large nonlinear cardiac simulations.

Predictive high-fidelity finite element simulations of human cardiac mechanics commonly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90% of the computation time is spent solving linear systems of equations. We propose to reduce the structural dimension of a monolithically coupled structure-Windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom, while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. Following a brief comparison of subspace interpolation methods, we demonstrate how projection-based model order reduction can be easily integrated into a gradient-based optimization. We demonstrate the performance of our method in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting.

The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms.

If computational models are ever to be used in high-stakes decision making in clinical practice, the use of personalized models and predictive simulation techniques is a must. This entails rigorous quantification of uncertainties as well as harnessing available patient-specific data to the greatest extent possible. Although researchers are beginning to realize that taking uncertainty in model input parameters into account is a necessity, the predominantly used probabilistic description for these uncertain parameters is based on elementary random variable models. In this work, we set out for a comparison of different probabilistic models for uncertain input parameters using the example of an uncertain wall thickness in finite element models of abdominal aortic aneurysms. We provide the first comparison between a random variable and a random field model for the aortic wall and investigate the impact on the probability distribution of the computed peak wall stress. Moreover, we show that the uncertainty about the prevailing peak wall stress can be reduced if noninvasively available, patient-specific data are harnessed for the construction of the probabilistic wall thickness model.

A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics.

We present a computational model for the interaction of surface- and volume-bound scalar transport and reaction processes with a deformable porous medium. The application in mind is pericellular proteolysis, i.e. the dissolution of the solid phase of the extracellular matrix (ECM) as a response to the activation of certain chemical species at the cell membrane and in the vicinity of the cell. A poroelastic medium model represents the extra cellular scaffold and the interstitial fluid flow, while a surface-bound transport model accounts for the diffusion and reaction of membrane-bound chemical species. By further modelling the volume-bound transport, we consider the advection, diffusion and reaction of sequestered chemical species within the extracellular scaffold. The chemo-mechanical coupling is established by introducing a continuum formulation for the interplay of reaction rates and the mechanical state of the ECM. It is based on known experimental insights and theoretical work on the thermodynamics of porous media and degradation kinetics of collagen fibres on the one hand and a damage-like effect of the fibre dissolution on the mechanical integrity of the ECM on the other hand. The resulting system of partial differential equations is solved via the finite-element method. To the best of our knowledge, it is the first computational model including contemporaneously the coupling between (i) advection-diffusion-reaction processes, (ii) interstitial flow and deformation of a porous medium, and (iii) the chemo-mechanical interaction impelled by the dissolution of the ECM. Our numerical examples show good agreement with experimental data. Furthermore, we outline the capability of the methodology to extend existing numerical approaches towards a more comprehensive model for cellular biochemo-mechanics.

Computational evaluation of aortic occlusion and the proposal of a novel, improved occluder: Constrained endo-aortic balloon occlusion.

Because aortic occlusion is arguably one of the most dangerous aortic manipulation maneuvers during cardiac surgery in terms of perioperative ischemic neurological injury, the purpose of this investigation is to assess the structural mechanical impact resulting from the use of existing and newly proposed occluders. Existing (clinically used) occluders considered include different cross-clamps (CCs) and endo-aortic balloon occlusion (EABO). A novel occluder is also introduced, namely, constrained EABO (CEABO), which consists of applying a constrainer externally around the aorta when performing EABO. Computational solid mechanics are employed to investigate each occluder according to a comprehensive list of functional requirements. The potential of a state of occlusion is also considered for the first time. Three different constrainer designs are evaluated for CEABO. Although the CCs were responsible for the highest strains, largest deformation, and most inefficient increase of the occlusion potential, it remains the most stable, simplest, and cheapest occluder. The different CC hinge geometries resulted in poorer performance of CC used for minimally invasive procedures than conventional ones. CEABO with a profiled constrainer successfully addresses the EABO shortcomings of safety, stability, and positioning accuracy, while maintaining its complexities of operation (disadvantage) and yielding additional functionalities (advantage). Moreover, CEABO is able to achieve the previously unattainable potential to provide a clinically determinable state of occlusion. CEABO offers an attractive alternative to the shortcomings of existing occluders, with its design rooted in achieving the highest patient safety. Copyright © 2016 John Wiley & Sons, Ltd.

A stable approach for coupling multidimensional cardiovascular and pulmonary networks based on a novel pressure-flow rate or pressure-only Neumann boundary condition formulation.

In many biomedical flow problems, reversed flows along with standard treatment of Neumann boundary conditions can cause instabilities. We have developed a method that resolves these instabilities in a consistent way while maintaining correct pressure and flow rate values. We also are able to remove the necessary prescription of both pressure and velocities/flow rates to problems where only pressure is known. In addition, the method is extended to coupled 3D/reduced-D fluid and fluid-structure interaction models. Numerical examples mainly focus on using Neumann boundary condition in cardiovascular and pulmonary systems, particularly, coupled with 3D-1D and 3D-0D models. Inflow pressure, traction, and impedance boundary conditions are first tested on idealized tubes for various Womersley numbers. Both pressure and flow rate are shown to match the analytical solutions for these examples. Our method is then tested on a coupled 1D-3D-1D artery example, demonstrating the power and simplicity of extending this method toward fluid-structure interaction. Finally, the proposed method is investigated for a coupled 3D-0D patient-specific full lung model during spontaneous breathing. All coupled 3D/reduced-D results show a perfect matching of pressure and flow rate between 3D and corresponding reduced-D boundaries. The methods are straight-forward to implement in contrast to using Lagrange multipliers as previously proposed in other studies.

Numerical identification method for the non-linear viscoelastic compressible behavior of soft tissue using uniaxial tensile tests and image registration - application to rat lung parenchyma.

This paper presents an improved identification method of the constitutive properties of lung parenchyma. We aim to determine the non-linear viscoelastic behavior of lung parenchyma with a particular focus on the compressible properties - i.e. the ability to change volume. Uniaxial tensile tests are performed on living precision-cut rat lung slices. Image registration is used to compute the displacement field at the surface of the sample. The constitutive model consists of a hyperelastic potential split into volumetric and isochoric contributions and a viscous contribution. This allows for the description of the experimentally observed hysteresis loop. The identification is performed numerically: each test is simulated using the realistic geometry of the sample; the difference between the measured and computed displacements is minimized with an optimization algorithm. We compare several hyperelastic potentials and we can determine the most suitable law for rat lung parenchyma. An exponential potential or a polynomial potential with a first order term and a third or higher order term give similarly satisfactory results. The identified parameters are: for the volumetric contribution: κ=7.25e4Pa, for the exponential form: k1=4.34e3Pa, k2=5.92, for the polynomial form: C1=2.87e3Pa, C3=3.83e4Pa. The identification of the time parameter for the viscous contribution shows that it depends on the loading frequency (0.2Hz: τ=0.257s, 0.4Hz: τ=0.123s, 0.8Hz: τ=0.050s). Adding a viscous contribution significantly increases the accuracy of the identification.

Coupled and reduced dimensional modeling of respiratory mechanics during spontaneous breathing.

In this paper, we develop a total lung model based on a tree of 0D airway and acinar models for studying respiratory mechanics during spontaneous breathing. This model utilizes both computer tomography-based geometries and artificially generated lobe-filling airway trees to model the entire conducting region of the lung. Beyond the conducting airways, we develop an acinar model, which takes into account the alveolar tissue resistance, compliance, and the intrapleural pressure. With this methodology, we compare four different 0D models of airway mechanics and determine the best model based on a comparison with a 3D-0D coupled model of the conducting airways; this methodology is possible because the majority of airway resistance is confined to the lower generations, that is, the trachea and the first few bronchial generations. As an example application of the model, we simulate the flow and pressure dynamics under spontaneous breathing conditions, that is, at flow conditions driven purely by pleural space pressure. The results show good agreement, both qualitatively and quantitatively, with reported physiological values. One of the key advantages of this model is the ability to provide insight into lung ventilation in the peripheral regions. This is often crucial because this is where information, specifically for studying diseases and gas exchange, is needed. Thus, the model can be used as a tool for better understanding local peripheral lung mechanics without excluding the upper portions of the lung. This tool will be also useful for in vitro investigations of lung mechanics in both health and disease.

Measuring and modeling patient-specific distributions of material properties in abdominal aortic aneurysm wall.

Both the clinically established diameter criterion and novel approaches of computational finite element (FE) analyses for rupture risk stratification of abdominal aortic aneurysms (AAA) are based on assumptions of population-averaged, uniform material properties for the AAA wall. The presence of inter-patient and intra-patient variations in material properties is known, but has so far not been addressed sufficiently. In order to enable the preoperative estimation of patient-specific AAA wall properties in the future, we investigated the relationship between non-invasively assessable clinical parameters and experimentally measured AAA wall properties. We harvested n = 163 AAA wall specimens (n = 50 patients) during open surgery and recorded the exact excision sites. Specimens were tested for their thickness, elastic properties, and failure loads using uniaxial tensile tests. In addition, 43 non-invasively assessable patient-specific or specimen-specific parameters were obtained from recordings made during surgery and patient charts. Experimental results were correlated with the non-invasively assessable parameters and simple regression models were created to mathematically describe the relationships. Wall thickness was most significantly correlated with the metabolic activity at the excision site assessed by PET/CT (ρ = 0.499, P = 4 × 10(-7)) and to thrombocyte counts from laboratory blood analyses (ρ = 0.445, P = 3 × 10(-9)). Wall thickness was increased in patients suffering from diabetes mellitus, while it was significantly thinner in patients suffering from chronic kidney disease (CKD). Elastic AAA wall properties had significant correlations with the metabolic activity at the excision site (PET/CT), with existent calcifications, and with the diameter of the non-dilated aorta proximal to the AAA. Failure properties (wall strength and failure tension) had correlations with the patient's medical history and with results from laboratory blood analyses. Interestingly, AAA wall failure tension was significantly reduced for patients with CKD and elevated blood levels of potassium and urea, respectively, both of which are associated with kidney disease. This study is a first step to a future preoperative estimation of AAA wall properties. Results can be conveyed to both the diameter criterion and FE analyses to refine rupture risk prediction. The fact that AAA wall from patients suffering from CKD featured reduced failure tension implies an increased AAA rupture risk for this patient group at comparably smaller AAA diameters.

Local strain distribution in real three-dimensional alveolar geometries.

Mechanical ventilation is not only a life saving treatment but can also cause negative side effects. One of the main complications is inflammation caused by overstretching of the alveolar tissue. Previously, studies investigated either global strains or looked into which states lead to inflammatory reactions in cell cultures. However, the connection between the global deformation, of a tissue strip or the whole organ, and the strains reaching the single cells lining the alveolar walls is unknown and respective studies are still missing. The main reason for this is most likely the complex, sponge-like alveolar geometry, whose three-dimensional details have been unknown until recently. Utilizing synchrotron-based X-ray tomographic microscopy, we were able to generate real and detailed three-dimensional alveolar geometries on which we have performed finite-element simulations. This allowed us to determine, for the first time, a three-dimensional strain state within the alveolar wall. Briefly, precision-cut lung slices, prepared from isolated rat lungs, were scanned and segmented to provide a three-dimensional geometry. This was then discretized using newly developed tetrahedral elements. The main conclusions of this study are that the local strain in the alveolar wall can reach a multiple of the value of the global strain, for our simulations up to four times as high and that thin structures obviously cause hotspots that are especially at risk of overstretching.

Material model of lung parenchyma based on living precision-cut lung slice testing.

We describe a novel constitutive model of lung parenchyma, which can be used for continuum mechanics based predictive simulations. To develop this model, we experimentally determined the nonlinear material behavior of rat lung parenchyma. This was achieved via uni-axial tension tests on living precision-cut rat lung slices. The resulting force-displacement curves were then used as inputs for an inverse analysis. The Levenberg-Marquardt algorithm was utilized to optimize the material parameters of combinations and recombinations of established strain-energy density functions (SEFs). Comparing the best-fits of the tested SEFs we found Wpar = 4.1 kPa(I1-3)2 + 20.7 kPa(I1 - 3)3 + 4.1 kPa(-2 ln J + J2 - 1) to be the optimal constitutive model. This SEF consists of three summands: the first can be interpreted as the contribution of the elastin fibers and the ground substance, the second as the contribution of the collagen fibers while the third controls the volumetric change. The presented approach will help to model the behavior of the pulmonary parenchyma and to quantify the strains and stresses during ventilation.

Neutron computed tomography of rat lungs.

Using conventional methods, three-dimensional imaging of the lung is challenging because of the low contrast between air and tissue and the large differences in dimensions between various pulmonary structures. The small distal airway structures and the high air-to-tissue ratio of lung tissue require an imaging technique which reliably discriminates between air and water. The objective of this study was to assess whether neutron computed tomography would satisfy such a requirement. This method utilizes the unique characteristic of neutrons of directly interacting with the atomic nucleus rather than being scattered by the atomic shell. Neutron computed tomography was tested in rats and allowed differentiation of larger lung structures (e.g., lobes) and distal airways. Airways could be identified reliably down to the sixth bronchial generation, in some cases even down to the tenth generation. The lung could be stabilized for sufficiently long exposure times to achieve an image resolution of 50-60 µm, which is the current physical resolution limit of the neutron computed tomography facility. Neutron computed tomography allowed excellent lung imaging without the need for additional tissue preparation or contrast media. The enhanced structural resolution obtained by applying this new research technique may improve understanding of lung physiology and respiratory therapy.

A comparison of diameter, wall stress, and rupture potential index for abdominal aortic aneurysm rupture risk prediction.

An abdominal aortic aneurysm (AAA) is a balloon-like dilation of the aorta, which is potentially fatal in case of rupture. Computational finite element (FE) analysis is a promising approach to a more accurate and patient-specific rupture risk prediction. AAA wall strength and rupture potential index (RPI) calculation are implemented in our FE software. Static structural FE simulations are performed on n = 30 non-ruptured asymptomatic, n = 9 non-ruptured symptomatic, and n = 14 ruptured AAAs. We calculate maximum values for diameter, wall displacement, strain, stress, and RPI as well as minimum wall strength for every AAA. All investigated quantities, except minimum strength, show statistically significant differences between non-ruptured asymptomatic and symptomatic/ruptured AAAs. Maximum wall stress and especially the RPI are notably increased for symptomatic and ruptured AAAs. The biggest difference is found to be the RPI (Δ = 44.9%, p = 8.0e-5). Lowest RPI obtained for symptomatic or ruptured AAAs is 0.3. The RPI of more than 55% of the investigated asymptomatic AAAs falls below this value. Maximum wall stress and maximum RPI criteria enable a reliable rupture risk evaluation for AAAs. Especially in the diameter range where surgical indication is not obvious, the RPI holds great potential for improvement of clinical decisions.

Biaxial distension of precision-cut lung slices.

The mechanical forces acting on lung parenchyma during (mechanical) ventilation and its (patho)physiological consequences are currently under intense scrutiny. Several in vivo and cell culture models have been developed to study the pulmonary responses to mechanical stretch. While providing extremely useful information, these models do also suffer from limitations in being either too complex for detailed mechanical or mechanistic studies, or in being devoid of the full complexity present in vivo (e.g., different cell types and interstitial matrix). Therefore in the present study it was our aim to develop a new model, based on the biaxial stretching of precision-cut lung slices (PCLS). Single PCLS were mounted on a thin and flexible carrier membrane of polydimethylsiloxane (PDMS) in a bioreactor, and the membrane was stretched by applying varying pressures under static conditions. Distension of the membrane-PCLS construct was modeled via finite element simulation. According to this analysis, lung tissue was stretched by up to 38% in the latitudinal and by up to 44% in the longitudinal direction, resulting in alveolar distension similar to what has been described in intact lungs. Stretch for 5 min led to increased cellular calcium levels. Lung slices were stretched dynamically with a frequency of 15/min for 4 h without causing cell injury {3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide (MTT) test; live/dead straining}. These findings suggest that stretching of PCLS on PDMS-membranes may represent a useful model to investigate lung stretch in intact lung tissue in vitro for several hours.

Impact of calcifications on patient-specific wall stress analysis of abdominal aortic aneurysms.

As a degenerative and inflammatory desease of elderly patients, about 80% of abdominal aortic aneurysms (AAA) show considerable wall calcification. Effect of calcifications on computational wall stress analyses of AAAs has been rarely treated in literature so far. Calcifications are heterogeneously distributed, non-fibrous, stiff plaques which are most commonly found near the luminal surface in between the intima and the media layer of the vessel wall. In this study, we therefore investigate the influence of calcifications as separate AAA constituents on finite element simulation results. Thus, three AAAs are reconstructed with regard to intraluminal thrombus (ILT), calcifications and vessel wall. Each patient-specific AAA is simulated twice, once including all three AAA constituents and once neglecting calcifications as it is still common in literature. Parameters for constitutive modeling of calcifications are thereby taken from experiments performed by the authors, showing that calcifications exhibit an almost linear stress-strain behavior with a Young's modulus E ≥ 40 MPa. Simulation results show that calcifications exhibit significant load-bearing effects and reduce stress in adjacent vessel wall. Average stress within the vessel wall is reduced by 9.7 to 59.2%. For two out of three AAAs, peak wall stress decreases when taking calcifications into consideration (8.9 and 28.9%). For one AAA, simulated peak wall stress increases by 5.5% due to stress peaks near calcification borders. However, such stress singularities due to sudden stiffness jumps are physiologically doubtful. It can further be observed that large calcifications are mostly situated in concavely shaped regions of the AAA wall. We deduce that AAA shape is influenced by existent calcifications, thus crucial errors occur if they are neglected in computational wall stress analyses. A general increase in rupture risk for calcified AAAs is doubted.

Prestressing in finite deformation abdominal aortic aneurysm simulation.

In abdominal aortic aneurysm (AAA) simulation the patient-specific geometry of the object of interest is very often reconstructed from in vivo medical imaging such as CT scans. Such geometries represent a deformed configuration stressed by typical in vivo conditions. However, commonly, such structures are considered stress-free in simulation. In this contribution we sketch and compare two methods to introduce a physically meaningful stress/strain state to the obtained geometry for simulations in the finite strain regime and demonstrate the necessity of such prestressing techniques. One method is based on an inverse design analysis to calculate a stress-free reference configuration. The other method developed here is based on a modified updated Lagrangian formulation. Formulation of both methods is provided. Applicability and accurateness of both approaches are compared and evaluated utilizing fully three-dimensional patient-specific AAA structures in the finite strain regime.